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rahuldandekar
2005-Nov-17, 04:58 PM
Well, I have seen many times, with my friends, with some hoaxers on this board, and with people in general: They do not understand the scientific method, where it applies, why it is important. I do not pretend to either.

But having used the scientific method in a presentation on Astrology in my class, I have realised how true and important it is. Many psuedo-sciences, hoax theories can be proved unscientific by the scientific method. But the question is always raised: So what if something is not science. Literature is not science.

So, I would like to initiate a discussion on this topic.

My own thoughts, paraphrased, are that the scientific method should be applicable to anything that claims to apply to reality. That's it. If something claims to make predictions, give an alternate explanation, it should have supporting evidence/ experiments.

And of course, Occam's Razor should be applied.

:)

rahuldandekar
2005-Nov-22, 04:05 PM
Well, someone please reply with your thoughts. :)

George
2005-Nov-22, 04:58 PM
My own thoughts, paraphrased, are that the scientific method should be applicable to anything that claims to apply to reality. That's it. If something claims to make predictions, give an alternate explanation, it should have supporting evidence/ experiments...

[I am surprised you haven't seen responses so far to this.]

I suppose you mean physical reality. There are a lot of real things not associated with physical attributes: thought, beauty, etc.

I was watching Charlie Rose the other night, a week or so ago, and heard part of his interview with an Assoc. Chief Justice of the Supreme Court. He was outlining six steps necessary to meet their criteria for court action. They seem to have qualities which would be helpful in qualifying the scientific method. Unfortunately, I did not write them down, but I did write down, somewhere, the name of the book being plugged. The Supreme Court handles about 80 cases per year and must reject thousands. Their rejection method might be worth comparing to the rejection process of bad scientific conjectures claiming to be "theory".

Grey
2005-Nov-22, 05:21 PM
My own thoughts, paraphrased, are that the scientific method should be applicable to anything that claims to apply to reality. That's it. If something claims to make predictions, give an alternate explanation, it should have supporting evidence/ experiments.

...

Well, someone please reply with your thoughts. :)I think you haven't received much in the way of replies because this seems like an eminently reasonable statement, and most people here on the board are likely to agree.


And of course, Occam's Razor should be applied.As for this, I'd say it's a good general guideline, but it's not necessarily always correct. Sometimes a more complex theory turns out to describe things better. I think Einstein said it best: "Everything should be made as simple as possible. But not simpler."

Wolverine
2005-Nov-22, 05:27 PM
Thread moved to a more suitable location. ;)

aurora
2005-Nov-22, 07:08 PM
I think that the power of the scientific method (and statistics in inference) is reinforced in Carl Sagan’s book “The Demon-Haunted World : Science As a Candle in the Dark”.

Sagan explains that in science we start with experimental results, data, observations, measurements and other facts. We invent, if we can, an array of possible explanations and systematically confront each explanation with the facts. If a new idea survives examination by the tools we use (Sagan calls this a “baloney detection kit”), then we accept the idea, although tentatively.

In Sagan’s “baloney detection kit” are the tools for skeptical thinking. It also overlaps with a lot of statistical techniques, including DOE (Design of Experiments).

Sagan lists the following tools:
• Wherever possible there must be independent confirmation of the facts.
• Arguments from authorities carry little weight. Authorities have made mistakes in the past.
• Think about alternative hypotheses. Then think of tests that could disprove each one.
• Try not to get overly attached to a hypothesis just because it is yours.
• Quantify. What is vague and qualitative is open to many explanations.
• If there is a chain of argument, every link in the chain must work, not just most of them.
• Occam’s razor: When faced with two hypotheses that explain the data equally well, choose the simpler.
• Always ask if the hypothesis can be falsified. Propositions that are untestable are not worth much.
• Carefully designed and controlled experiments are key.

There was an episode of Bill Nye the Science Guy (science show for younger viewers) which did a very nice job of describing what science is through comparisons to pseudoscience. Among the points made in the episode were:

• Extraordinary claims require extraordinary proof
• Theories must be testable (claims and ideas can be tested)
• Experiments can be repeated
• If something is unexplained, it doesn’t mean that it is mystical or magic, it just means that it can’t be explained.

Candy
2005-Nov-22, 07:24 PM
I did write down, somewhere, the name of the book being plugged. The Supreme Court handles about 80 cases per year and must reject thousands. Their rejection method might be worth comparing to the rejection process of bad scientific conjectures claiming to be "theory".
I'd be interested in knowing the title when you find it, George.

Ken G
2005-Nov-22, 08:17 PM
As for this, I'd say it's a good general guideline, but it's not necessarily always correct. Sometimes a more complex theory turns out to describe things better.
Perhaps it would be helpful to better define Occam's razor, since I feel that it is one of the cornerstones of the scientific method. In the movie "Contact", the usual incorrect definition is given (I don't know if Sagan made this mistake in the book, I would rather doubt it). IIRC, they defined Occam's razor as the idea that "given two theories that fit the data, the simpler one is more likely to be right". But of course science has no business accepting axioms about what is "more likely to be right". In actuality, Occam's razor is far less grandiose-- it merely states that of all the theories that fit the data, the simplest one is the most useful, because the whole point of science is to make the understanding of nature as simple as possible. Thus the simplest theory is always accepted as the working hypothesis. Grey's point is only that just because you have a very simple theory that works great, you should not be surprised if future data from better experiments reveals that a more complicated theory is actually the more successful one. When that happens, you simply apply Occam's razor again. Science is iterative, and so is that bloody razor! And it has cut deeply into the greatest thinkers in human history.

George
2005-Nov-22, 08:44 PM
I'd be interested in knowing the title when you find it, George.
Ok. I'll check this evening. I went to Charlie Rose's site, but no quick luck.

grant hutchison
2005-Nov-22, 08:53 PM
-- it merely states that of all the theories that fit the data, the simplest one is the most useful, because the whole point of science is to make the understanding of nature as simple as possible.Pluralitas non est ponenda sine necessitate, said old William, which freely translates as "Don't make things more complicated than they need to be".
So I think perhaps your idea of usefulness adds an extra interpretive layer to Occam: he just wanted to make things simple, and you've added the idea that simplicity is useful.
The idea of rightness is a different interpretive layer: if you've dragged in more stuff to the explanation than is required by the problem, then part of your explanation is not currently supported by the evidence, and so is less likely to be right (or, indeed, useful :)).
But the simplistic equation of simple=right is, as you say, misleading.

Grant Hutchison

Ken G
2005-Nov-22, 09:17 PM
So I think perhaps your idea of [i]usefulness adds an extra interpretive layer to Occam: he just wanted to make things simple, and you've added the idea that simplicity is useful.

Yes, but we must avoid the tautology of "science chooses the simpler successful approach because it's simpler". There has to be an inferred advantage to simplicity, and I argue it is "simply" that this is the purpose of science, to bring as much of what is 'out there' [expansive gesture] in here [points to head]. Or in some cases, in there [points, reluctantly, to computer].



The idea of rightness is a different interpretive layer: if you've dragged in more stuff to the explanation than is required by the problem, then part of your explanation is not currently supported by the evidence, and so is less likely to be right (or, indeed, useful :)).

That's not quite what I mean by simplest-- more than is required, yes, but not more than is supported by evidence. The most complicated but completely supportable possible theory of science would be what I might call "Google science": simply write down every single experiment that has ever been done, and what the result was, as quantitatively as possible. Then if you wish to "predict" a new result, just 'google' for similar ones in the past, and do the necessary extrapolation. If the experimental data is rich enough, you would have a perfectly good theory there, indeed probably the most accurate one you could imagine. But it would surely not be simple, as it would require a spectacular amount of data and you would not 'understand' anything. Still, you could build a great bridge, as every aspect of your theory is well supported by data.



But the simplistic equation of simple=right is, as you say, misleading.

Agreed, we're just splitting some hairs here. We'd have made good barbers!

neilzero
2005-Nov-22, 09:20 PM
I think Occum's razor applies more often than not, but it is bad logic to make decissions based on Occum's razor since it is false almost as often as it is is true.
Simplified versions of the scientific method can squelch brainstorming, innovation, free speech, and foster a type of eletism which does not serve humanity well. Open minded is an important element of the scientific method done usefully. Neil

Ken G
2005-Nov-22, 09:32 PM
Occam's razor is never "false". See the above posts. But I see your point about not beguiling onesself about the true range of possibilities of the world.

George
2005-Nov-23, 05:54 AM
I'd be interested in knowing the title when you find it, George.

Ok. Active Liberty (http://www.amazon.com/gp/product/0307263134/102-2526670-6097749?v=glance&n=283155&v=glance) by Stephen Breyer. Dang, I was watching Larry King and Seinfeld when his name was mentioned as a guest after Martha Stewart. I missed him again.

I only caught three elements, of 6 I think, in the brief glance at he and Charlie Rose: presidence, purpose and consequence.

If a theory has presidence, it will relate to what we understand. If it has purpose and consequence, it should be useful with other theories and produce predictable results.

Over 80k to 100K cases are submitted to them. They select about 80. The briefs have the most impact on them. The joke there is...one brief is right, the opposing brief also looks right, yet "they can't both be right" - right. :)

Their framework, of course, is the constitution which he sees evolving in application only, not in principle.

I suppose I sense a useful analogy here. The constitution - the sceintific method; the judicial case study - the study of a proposed theory.

I'll bet an anolgous ID case would not get on the short list. It would not qualify.

Any astronomer/attorneys out there? :)

wayneee
2005-Nov-23, 06:09 AM
think that the power of the scientific method (and statistics in inference) is reinforced in Carl Sagan’s book “The Demon-Haunted World : Science As a Candle in the Dark”.

Great Book, I hope all here have read it.
Also Extraordinary claims demand extraordinary proof is Sagans Quote I believe from Cosmos
Pale Blue Dot is also great

George
2005-Nov-23, 06:15 AM
We'd have made good barbers! I think my skin is a little thin for you two. :)

Let's put someone in your barber chair - Copernicus. He reduced the Ptolemy system from 80+ circles (if you will) to around 27, I think. [it's late, I'm pooped.] Yet, he was a little less accurate than Ptolmey with his heliocentric approach.

Would not Occum's razor play an important role in this case?

George
2005-Nov-23, 06:19 AM
Great Book, I hope all here have read it.
Also Extraordinary claims demand extraordinary proof is Sagans Quote I believe from Cosmos
Pale Blue Dot is also great
I have not. Thanks. It sounds like the hammer for this thread's nail. :)

Ken G
2005-Nov-23, 06:49 AM
Let's put someone in your barber chair - Copernicus. He reduced the Ptolemy system from 80+ circles (if you will) to around 27, I think. [it's late, I'm pooped.] Yet, he was a little less accurate than Ptolmey with his heliocentric approach.

Would not Occum's razor play an important role in this case?
I think it's a very interesting issue as to when Occam's razor cut in Copernicus' favor. Probably not until Kepler discovered the ellipses. Sure it was nice to pare down the epicycles, but it did come at a loss of accuracy as you say, and the worst part is, it challenged a whole lot of other ideas that had already applied Occam's razor! For example, you had to have stars so far away that you couldn't see parallax, so that meant lots of wasted space. Not simple to have such scales. Then again, it means that stars can be like the Sun-- seems simpler there (indeed, I always wondered why that was not the lynchpin right there, even for the Greeks). Also, you have the Greek concepts of motion and gravity-- very simple. So on balance, which theory really was simpler at the time? It's obvious today, Ptolemy's approach would really require some significant modifications and an enormous amount of baggage to keep alive, although it would all be observationally supported baggage. Copernicus needed only a little modification, but stayed fairly intact.

grant hutchison
2005-Nov-23, 12:41 PM
Copernicus very much argued from Occam's Razor (in the simple form articulated by William himself), stating that the elimination of so many epicycles (by collapsing them into the movement of the Earth) was "more pleasing to the mind" than the Earth-centred view.
As far as I know, this was the first argument advanced to support a scientific theory on the grounds of mathematical elegance.

Grant Hutchison

Ken G
2005-Nov-23, 04:38 PM
That's quite interesting that he used that argument (at some level the Greeks liked to argue that way, but it was more of a given for them I think). Note my point was that Occam's razor arguments are not necessarily uniquely determined, I'll bet the Ptolemy people could easily counter that their approach was simpler for the reasons I mentioned. But it sounds like what Grant is saying is they did not use that argument, because they perhaps did not see the relevance of simplicity when it's Truth you are after.

It occurs to me you could follow at least 3 versions of Occam as you try to understand our universe:
1) the truth should be elegant, so look for elegance and simplicity
2) every theory is an idealization of reality, so try to find the heart of the matter and bring in complexity only as needed to zero in on the Full Truth
3) the whole purpose is to find the simplest description, we need not trouble ourselves if we can't tell how things Really Are.

I might guess (1) was sort of what was motivating Einstein's theory of gravity, (2) was motivating Galileo's theory that all things fall at the same rate, and (3) is what we are currently forced into with issues like dark matter and dark energy, and might be stuck with for the foreseeable future (oxymoron?).
I wonder which was Copernicus's approach? I would guess the first.

George
2005-Nov-23, 05:39 PM
Its logic is inescapable. Today's variant to Occam's Razor is KISS (keep it simple, stupid). [Notice which one of the two is the simpler to state. :) Too bad he didn't offer it originally, as a corollary.]

Da Vinci, supposedly, offered his own variant to the razor: "Simplicity is the ultimate sophistication".

The use of the razor for Copernicus is quite interesting. I wonder if he had other related phrasing in his main publication?

George
2005-Nov-23, 08:48 PM
Note my point was that Occam's razor arguments are not necessarily uniquely determined
Yes, and maybe that is a key point; a lack of uniqueness to either choice. Consider this version of the razor: "Given two equally predictive theories, choose the simpler." Neither offer a unique result. However, I can't say that is true of the arguments, I suppose.


I'll bet the Ptolemy people could easily counter that their approach was simpler for the reasons I mentioned. I am not seeing this, sorry. Do you mean, simpler in terms of an equally accurate result? If so, that's a good question as it would be interesting to know how much more complexity Copernicus would have needed. He eliminated the sticky equant, though he may have considered one for his theory: one of his axioms in his Little Commentary was, "The centre of the universe is near the sun". I would assume an equant (near the barycenter :) ) would have given him superiority on all counts due to minimal planetary eccentricities.


It occurs to me you could follow at least 3 versions of Occam as you try to understand our universe:
1) the truth should be elegant, so look for elegance and simplicity
2) every theory is an idealization of reality, so try to find the heart of the matter and bring in complexity only as needed to zero in on the Full Truth
3) the whole purpose is to find the simplest description, we need not trouble ourselves if we can't tell how things Really Are.
Yes. Gravity comes to mind from your points, as an example.


(2) was motivating Galileo's theory that all things fall at the same rate, Would he only hope for simplicity and let the "chips (or balls) fall where they may"? [pun unintended]


(3) is what we are currently forced into with issues like dark matter and dark energy, and might be stuck with for the foreseeable future (oxymoron?).
I would guess you are right on the dark issues, wrong on the lighter issue (i.e. not an oxymoron, I think). [ok, pun intended, obviously] :razz: .


I wonder which was Copernicus's approach? I would guess the first. All three, possibly. I would lean more to your third. Reportedly, it was a pain working through the Ptolemy model each time. I do not know how often he had to apply it. It was used for calculating holy days and astrological/medical applications (maybe more?). The medical use might not need Ptolemey's accuracy - espcecially since they didn't work for the patient's health except as a placebo, I suppose.

dgruss23
2005-Nov-23, 09:05 PM
IMO occam's razor is a useless principle for reasons I discussed here (http://www.bautforum.com/showpost.php?p=83268&postcount=12) and here (http://www.bautforum.com/showpost.php?p=89465&postcount=64) and here (http://www.bautforum.com/showpost.php?p=89635&postcount=70) and here (http://www.bautforum.com/showpost.php?p=110959&postcount=15).

Those posts are repetitive, but hopefully the reasons I say Occam is useless is clearly explained in one of them.

Disinfo Agent
2005-Nov-23, 10:31 PM
I suppose you mean physical reality. There are a lot of real things not associated with physical attributes: thought, beauty, etc.Politics.

Disinfo Agent
2005-Nov-23, 10:40 PM
IMO occam's razor is a useless principle for reasons I discussed here (http://www.bautforum.com/showpost.php?p=83268&postcount=12) and here (http://www.bautforum.com/showpost.php?p=89465&postcount=64) and here (http://www.bautforum.com/showpost.php?p=89635&postcount=70) and here (http://www.bautforum.com/showpost.php?p=110959&postcount=15).

Those posts are repetitive, but hopefully the reasons I say Occam is useless is clearly explained in one of them.As ATP often says (can't recall his new screen name), "Occam's Razor is in the eye of the beholder". It's not really a principle of science; more like a rule of thumb (no wonder engineers are particularly fond of it). Although I may have entered some of those debates on the side of OR, I must admit that I haven't been able to find an instance in theoretical science where letting the evidence decide doesn't do the same job, or even a better job, than Occam's Razor.

Ian Goddard
2005-Nov-24, 03:14 AM
My own thoughts, paraphrased, are that the scientific method should be applicable to anything that claims to apply to reality. That's it. If something claims to make predictions, give an alternate explanation, it should have supporting evidence/ experiments.

Right. In my view scientific claims are claims that purport a mapping between elements of a modeling language and detectable entities in the external universe. The necessity that a scientific claim be falsifiable reflects such a semantic language-to-entity mapping since to falsify a claim is to show that elements in the claim do not map to corresponding entities in the external universe.

The semantics of predicate logic provides a useful model of such a structure of scientific/empirical claims in the definition of the existential quantifier (denoted here as just 'E' rather than the proper inverted E):

V(Ex@) = 1 iff there is a d in D such that Vg[x/d](@) = 1.

Which is to say: the truth Value of the statement "There Exists some x such that @" (where @ denotes a statement about x) is true if and only if there is an entity d in the Domain of the world we're talking about such that the assignment (g) of the variable x to d (ie, g[x/d]) makes the statement @ true. For example, the statement "There exists some x such that x is the sixth planet from the Sun" is true iff there is some planet d orbiting the Sun such that the assignment of the variable x to d makes that statement true, which is the case if x is assigned to Saturn.

It seems to me that such semantic structure serves as a useful model of science where scientific claims are claims purporting that there exist assignments, or mappings, between elements in said claim and entities in some external domain of discourse. The process of hypothesis testing is a process of establishing the reliability of such purported mappings. Mappings that appear reliable are qualified as establishing scientific/empirical knowledge.

Ken G
2005-Nov-24, 04:07 AM
Those posts are repetitive, but hopefully the reasons I say Occam is useless is clearly explained in one of them.
I'd like to differ on this point. I think Occam's razor is actually the defining principle of science. We just take it so for granted that it actually works, we don't even realize we're using it.
Example: Geocentric vs. Heliocentric? Of course a geocentric model would work just fine, it's how we see the universe. It would be a bit more complicated, we'd have to explain why the high-mass Sun can orbit a low-mass Earth, but it's no fundamental problem. And there's that pesky asymmetry in the CMB, but who's really married to the cosmological principle anyway? It's just a simplifying principle, no biggie.

Fram
2005-Nov-24, 11:36 AM
I'd like to differ on this point. I think Occam's razor is actually the defining principle of science. We just take it so for granted that it actually works, we don't even realize we're using it.
Example: Geocentric vs. Heliocentric? Of course a geocentric model would work just fine, it's how we see the universe. It would be a bit more complicated, we'd have to explain why the high-mass Sun can orbit a low-mass Earth, but it's no fundamental problem. And there's that pesky asymmetry in the CMB, but who's really married to the cosmological principle anyway? It's just a simplifying principle, no biggie.

As long as you are talking solar system only, I can follow slightly. Including the universe makes it a moot discussion, as there is no "centre".
But in the solar system, there are more problems than an explanation of why the sun would orbit the earth. You also have to explain why every other planet would orbit the sun, but the whole system would then orbit the earth. No scientific, logic reason can be given how that would work, you need religion or something similar for that. So the theory fails on scientific grounds, and you don't need Occam.

Ken G
2005-Nov-24, 11:50 AM
As long as you are talking solar system only, I can follow slightly. Including the universe makes it a moot discussion, as there is no "centre".

Why not? Are you quoting the cosmological principle? A classic application of Occam's razor. We have no evidence that we are in a special place, other than it looks that way, so the simplest assumption is that we are not. Other assumptions are completely in accordance with observations: we are at the center!



But in the solar system, there are more problems than an explanation of why the sun would orbit the earth. You also have to explain why every other planet would orbit the sun, but the whole system would then orbit the earth.

That's no problem at all, the Sun generates gravity. The Earth does not orbit the Sun however, because there is a special force that the Earth feels which counters the gravity of the Sun. As for the other objects, they feel the Sun's gravity, and a special force I'll call centrifugal and coriolis forces emanating from the Earth. And a few more to handle the minor perturbations. Why not? Oh yeah... Occam.



No scientific, logic reason can be given how that would work, you need religion or something similar for that.
On the contrary, it's not hard at all. Amuse yourself by doing it with every observable, it's all purely scientific, it's just not Occam. You see, you apply Occam so automatically you don't even realize you are doing it!

dgruss23
2005-Nov-24, 02:34 PM
I'd like to differ on this point. I think Occam's razor is actually the defining principle of science. We just take it so for granted that it actually works, we don't even realize we're using it.
Example: Geocentric vs. Heliocentric? Of course a geocentric model would work just fine, it's how we see the universe. It would be a bit more complicated, we'd have to explain why the high-mass Sun can orbit a low-mass Earth, but it's no fundamental problem. And there's that pesky asymmetry in the CMB, but who's really married to the cosmological principle anyway? It's just a simplifying principle, no biggie.

The heliocentric and geocentric models may be the one case that can be presented where occams razor as defined by you (and I agree that that is the definition):


In actuality, Occam's razor is far less grandiose-- it merely states that of all the theories that fit the data, the simplest one is the most useful, because the whole point of science is to make the understanding of nature as simple as possible.

can be applied. But when did Occam come into play in that case? The circular orbits of Copernicus were little better than the geocentric model at predicting the planetary postions. When Kepler provided a solution with elliptical orbits, then perhaps simplicity could be argued as the principle reason for adopting the heliocentric model.

But can you identify a modern example of a situation in which we say theory X is better than theory Y for the sole reason that all other things are equal and so theory X is the "simpler" theory? I'd be surprised if you can. Modern scientific debate is focused upon empirical evidence and the predictive nature of individual theories. Simplicity is not a defining concept. Since the early 80's the Big Bang has added inflation, dark matter, and more recently dark energy. These additions do not simplify the model - but help improve its fit to new observations.

The focus of debate when there is disagreement is the differences predicted by two competing theories and the tests that can distinguish them. When a theory is dropped its not because it is more complex, it is because the new theory provides a better fit to the new observations that tested the theories.

Take Dark Matter vs. MOND. On galaxy scales MOND performs better. CDM suffers from the observed "coupling" between dark and luminous matter. Now perhaps someone would say: "See simplicity is a factor - MOND doesn't require the fine tuning." But the reality is that the observed coupling of dark and luminous matter contradicts the proposed properties of collisionless CDM. However, on the larger scales of clusters and superclusters CDM may perform better than MOND.

So is it MOND, CDM, or something else? The match of the predictions of theories to new observations and the predictive ability of the various theories will determine what becomes the preferred theory rather than simplicity.

I guess I'd hate to be in the position of defending a theory in which the only reason I can say that my preferred theory is more useful than the others is that it is "simpler".

Perhaps my issue here is that in some ATM debates I've seen support of mainstream positions be based upon Occam's razor rather than the evidence. There is not an ATM theory out there that fits the observations just as well as the Big Bang. Rather the ATM ideas are in the more basic stages and their potential merits come from their ability to perhaps explain something that the Big Bang or some aspect of mainstream cosmology cannot explain. These ATM ideas may not replace the Big Bang but rather may eventually be incorporated into the Big Bang much the same way that Punctuated equilibrium became incorporated into Darwinian theory. So in those cases it is completely fallacious to fall back on Occam's razor as a reason for dismissing the ATM idea.

But I also think that another problem that inhibits the usefulness of Occam's razor is the subjectivity of "simplest". If asked, a MOND researchers could probably provide you with reasons for thinking MOND is simpler than CDM, but the CDM researcher would do the same. And why does the MOND researcher think their model is simpler? Most likely because of the observations that he believes are explained better by MOND than CDM. And what about the observations that CDM may explain better? Well, the MOND researcher will seek ways of tweaking (complicate) MOND so that it can also explain those observations. So again, how does a subjective concept like simplicity provide a deciding factor?

grant hutchison
2005-Nov-24, 03:21 PM
But can you identify a modern example of a situation in which we say theory X is better than theory Y for the sole reason that all other things are equal and so theory X is the "simpler" theory?Although this is the usual context in which Occam is explained, I agree it's vanishingly rare in practice. But Occam very frequently guides scientific thinking when look for explanations for new phenomena.
I'd suggest, for instance, that Occam was the main driving force behind Gell-Mann's attempt to rationalize the "particle zoo" by "inventing" quarks.

Grant Hutchison

dgruss23
2005-Nov-24, 03:24 PM
Ken G, In thinking more about this I think the problem is that the modern version of Occam's razor you defined is different from the original version of Ockham's razor which is defined as:


The philosophical rule that entitities should not be multiplied unnecessarily.

This would be one of the principles that is applied in developing scientific hypotheses. Carlo Lastrucci referred to this in his book "The Scientific Approach". In his section on the Principles of science Lastrucci discussed the "Principle of Parsimony." The book is at my office, so I can't recall exactly how he described it, but a typical definition of parsimony is "economy of assumption in reasoning". I agree that this is an important principle in scientific reasoning.

But the principle of parsimony is not the defining factor in which theory a scientist might choose to test or find useful. The ability of a model to provide predictions that future experimentation could test is an even more important factor in the "usefulness" of a hypothesis, model, or theory. And IMO the modern version of Occam's razor has little practical value.

dgruss23
2005-Nov-24, 03:26 PM
Although this is the usual context in which Occam is explained, I agree it's vanishingly rare in practice. But Occam very frequently guides scientific thinking when look for explanations for new phenomena.
I'd suggest, for instance, that Occam was the main driving force behind Gell-Mann's attempt to rationalize the "particle zoo" by "inventing" quarks.

Grant Hutchison

Good example, and I think that would certainly be a case of the Principle of Parsimony in action.

Fram
2005-Nov-24, 03:31 PM
Why not? Are you quoting the cosmological principle? A classic application of Occam's razor. We have no evidence that we are in a special place, other than it looks that way, so the simplest assumption is that we are not. Other assumptions are completely in accordance with observations: we are at the center!


That's no problem at all, the Sun generates gravity. The Earth does not orbit the Sun however, because there is a special force that the Earth feels which counters the gravity of the Sun. As for the other objects, they feel the Sun's gravity, and a special force I'll call centrifugal and coriolis forces emanating from the Earth. And a few more to handle the minor perturbations. Why not? Oh yeah... Occam.


On the contrary, it's not hard at all. Amuse yourself by doing it with every observable, it's all purely scientific, it's just not Occam. You see, you apply Occam so automatically you don't even realize you are doing it!

I see what you mean, and as long as you make your theory complex enough, I guess you can counter me. But then your theory has long ceased to be scientific, as it is hardly testable and based on observations. It gives no reason at all why the Earth would have those special forces. As soon as it gives a reason for this, it becomes testable again, and then it can be considered a scientific theory. But you would need many, many special forces with special capacities to make your theory work. Just to continue yours: why is that force that counters the gravity of the sun not working on the oceans (tides)?

But I repeat, in the end you can always add forces, assumptions, and so on, just to make a competing theory that is not immediately falsifiable (all those undetectable particles!) but that indeed appears to be wrong because it is way way way too complicated. Occam's razor, indeed.

Ken G
2005-Nov-24, 05:16 PM
I see what you mean, and as long as you make your theory complex enough, I guess you can counter me. But then your theory has long ceased to be scientific, as it is hardly testable and based on observations.

Sure it is, the theory I described will be testable, will make all the same predictions of the standard theory, and will be perfectly scientific as a result.



It gives no reason at all why the Earth would have those special forces.

And that's part of science? We have a reason why gravity exists do we?



. Just to continue yours: why is that force that counters the gravity of the sun not working on the oceans (tides)?

No problem at all, that's the Sun's gravity. We still only need one special force on the Earth, the one at its center that pervades the universe. But yes, this is silly for one reason and one alone: Occam's razor. Until some new observation shows my theory is actually necessary... :shhh:

Ken G
2005-Nov-24, 05:22 PM
The book is at my office, so I can't recall exactly how he described it, but a typical definition of parsimony is "economy of assumption in reasoning". I agree that this is an important principle in scientific reasoning.

I'm sorry, how is that the least bit different from my usage of Occam's razor?



But the principle of parsimony is not the defining factor in which theory a scientist might choose to test or find useful. The ability of a model to provide predictions that future experimentation could test is an even more important factor in the "usefulness" of a hypothesis, model, or theory.

We certainly agree there.


And IMO the modern version of Occam's razor has little practical value.
On the contrary, it has enormous practical value. It allows our theories to fit in textbooks, to be taught to students. If you doubt it, imagine the opposite principle:"All simplification is a reflection of mental laziness, we must describe the universe in terms no less than what is actually happening to every molecule, for anything else is an oversimplification". Think that's ridiculous? On the contrary, I would argue that this is exactly the "attitude" of the universe itself! But we already have the universe, the goal of science is to achieve conceptual simplification. This is the heart of Occam (or are we calling it the "Principle of Parsimony" now?), and why it is the defining principle of all science, along with the need to actually work as you point out. Your claim that it has no practical value is merely the proof of how readily we take it for granted.

Ken G
2005-Nov-24, 06:05 PM
But can you identify a modern example of a situation in which we say theory X is better than theory Y for the sole reason that all other things are equal and so theory X is the "simpler" theory? I'd be surprised if you can.

WIthout even breaking a sweat, I just did it for Fram. You are also taking the principle so for granted you don't realize theories that don't obey it never even get to the point of consideration.


Since the early 80's the Big Bang has added inflation, dark matter, and more recently dark energy. These additions do not simplify the model - but help improve its fit to new observations.

This point does not add anything to your argument, as it is has nothing to do with Occam's razor.


When a theory is dropped its not because it is more complex, it is because the new theory provides a better fit to the new observations that tested the theories.

I believe I see what you're saying, you're saying that historically we rarely replace more complex theories with simpler ones that also work. But this is simply because Occam is so fundamental to what we do that the simpler theory is always being attempted right from the outset. For an even simpler one to come along using the same data would require an oversight by the original theorist.



Take Dark Matter vs. MOND.

Please. :lol: (couldn't resist)
Seriously, all you are saying is both theories currently have problems. These are not Occam's problems.


I guess I'd hate to be in the position of defending a theory in which the only reason I can say that my preferred theory is more useful than the others is that it is "simpler".

Are you joking? Then I'll accept your nobel prize on your behalf when you come up with a theory of cosmology that requires neither dark matter nor dark energy, yet merely predicts everything we currently see.



But I also think that another problem that inhibits the usefulness of Occam's razor is the subjectivity of "simplest".

No disagreement there, which is why I made this same point a few posts ago. Or was it a different thread? They all run together after awhile! But note this objection is in relation to the difficulty in applying the razor. Science has no guide for that, we do the best we can, and in many cases alternate pedagogies are not only acceptable, they are useful.

grant hutchison
2005-Nov-24, 07:07 PM
The book is at my office, so I can't recall exactly how he described it, but a typical definition of parsimony is "economy of assumption in reasoning". I agree that this is an important principle in scientific reasoning.I'm sorry, how is that the least bit different from my usage of Occam's razor?I think dgruss23 is perhaps making the same contrast I tried to make in my first post here: that there is nowaday a sort of explanatory overlay (involving utility and choosing between theories) which you've used in your posts but which is lacking in William of Occam's original formulation. Occam's simple formulation is part of the scientific mental toolkit, but the modern pedagogic expression of it based on formally choosing between otherwise equipotent rival explanations is something that hardly ever crops up in real scientific life.

Grant Hutchison

Ken G
2005-Nov-24, 07:50 PM
Occam's simple formulation is part of the scientific mental toolkit, but the modern pedagogic expression of it based on formally choosing between otherwise equipotent rival explanations is something that hardly ever crops up in real scientific life.


I have no other definition of utility other than the fact that something that is simpler is easier to use. Is this in dispute? When we replace "utility" with "parsimony", I completely fail to see the essential distinction that either supports or invalidates Occam as a crucial scientific principle. I will grant you that parsimony is a subset of utility, but it is the only aspect of utility that is applicable to the conversation.

As for the choice between theories, I continue to hold that Occam is so hardwired into our approach that we automatically seek the simplest theory right from the outset, so it rarely needs to be reintroduced later. This is testament not to its irrelevance as a principle, but rather to its indispensability. But yes, it doesn't get cited in papers.

grant hutchison
2005-Nov-24, 09:33 PM
I have no other definition of utility other than the fact that something that is simpler is easier to use. Is this in dispute?Well, yes. I have a simple corkscrew that rips corks to pieces, and a complicated corkscrew that extracts them smoothly. "Simple" may be easier to use, but does not necessarily have utility.

When we replace "utility" with "parsimony", I completely fail to see the essential distinction that either supports or invalidates Occam as a crucial scientific principle.There's no overlap between the meaning of the two words, so that's a problem. Something parsimonious may or may not have utility; something with utility may or may not be parsimonious. Hence my point that you've added an interpretive level to Occam's Razor which Occam did not articulate. I don't see this as necessarily bad, but I think it's contributing to your apparent disagreement with dgruss23.

Grant Hutchison

dgruss23
2005-Nov-25, 02:48 AM
I think dgruss23 is perhaps making the same contrast I tried to make in my first post here: that there is nowaday a sort of explanatory overlay (involving utility and choosing between theories) which you've used in your posts but which is lacking in William of Occam's original formulation. Occam's simple formulation is part of the scientific mental toolkit, but the modern pedagogic expression of it based on formally choosing between otherwise equipotent rival explanations is something that hardly ever crops up in real scientific life.

Grant Hutchison

Yes, this is exactly what I was trying to say. The original version of Occam's razor is really not different than the Principle of Parsimony. I think most scientists would agree that it is an important part of the scientific reasoning process. But the modern description of Occam's razor as choosing between two otherwise equal theories is not a practical description of how scientific theory progresses.

However the more important part of the scientific reasoning process is the comparison of a model with new observations that test its predictions. Those tests result in revision, or refutation of the model as needed. The deciding factor in whether or not a model is refuted is not how simple it is. The formulation of a hypothesis in the first place will of course incorporate the reasoning of the principle of parsimony, but the ultimate fate of that hypothesis after that point has very little to do with its simplicity.

Models proposed to explain the flat rotation curves of spiral galaxies provide a good example of this. You have the prevailing DM hypothesis. DM itself has many candidates. And they have all been evaluated with the limitations that current observational technology allows at this time. Then you have MOND. You also have Plasma Cosmology. The discussion about each of these options is not about simplicity - it is about how well they fit the observations. When a candidate runs into a problem, its proponent might attempt to propose a modification of that candidate. Again, simplicity is not part of the reasoning.

dgruss23
2005-Nov-25, 02:59 AM
I have no other definition of utility other than the fact that something that is simpler is easier to use. Is this in dispute? When we replace "utility" with "parsimony", I completely fail to see the essential distinction that either supports or invalidates Occam as a crucial scientific principle. I will grant you that parsimony is a subset of utility, but it is the only aspect of utility that is applicable to the conversation.

Like Grant, I disagree with this. Simplicity is not the only aspect of utility that is applicable. The ability of a theory to make testable predictions is the more important part of its utility. That's been my point - perhaps not well explained on my part. In practice scientists are focusing on the testable predictions of a model/theory and the observationals results that put the hypothesis to the test rather than the beauty of its simplicity. Simplicity would seem to be more important in the formulation of a hypothesis rather than in the ultimate decision making as to whether a hypothesis should be kept or discarded in favor of another.


As for the choice between theories, I continue to hold that Occam is so hardwired into our approach that we automatically seek the simplest theory right from the outset, so it rarely needs to be reintroduced later. This is testament not to its irrelevance as a principle, but rather to its indispensability. But yes, it doesn't get cited in papers.

But that is the Principle of Parsimony, not the modern Occam's razor at work. Utilizing the principle of parsimony, the scientist attempts to start with a simple model and then adds complication as necessary to keep the model consistent with new observations.

dgruss23
2005-Nov-25, 03:14 AM
WIthout even breaking a sweat, I just did it for Fram. You are also taking the principle so for granted you don't realize theories that don't obey it never even get to the point of consideration.

Principle of Parsimony covers this.



I believe I see what you're saying, you're saying that historically we rarely replace more complex theories with simpler ones that also work. But this is simply because Occam is so fundamental to what we do that the simpler theory is always being attempted right from the outset. For an even simpler one to come along using the same data would require an oversight by the original theorist.

But you agree that simplicity is a subjective concept. So perhaps the theorist thought of the idea, but felt another option had more predictive utility.



Seriously, all you are saying is both theories currently have problems. These are not Occam's problems.

Exactly my point. A preference for MOND or CDM by a theorist has nothing to do with simplicity.


Are you joking? Then I'll accept your nobel prize on your behalf when you come up with a theory of cosmology that requires neither dark matter nor dark energy, yet merely predicts everything we currently see.

You have to be an egomaniac on some level to pursue scientific research for the purpose of getting a Nobel prize. But your response is hardly an answer to my point. Are you actually suggesting that you're in a good position if the only distinction between your theory and another is it is simpler (automatically a subjective criteria). Would you not prefer that your theory offer different observational tests that can distinguish it from the other - and that those tests would ultimately provide the decision over whether to accept or drop the theory?

Ken G
2005-Nov-25, 05:36 AM
Well, yes. I have a simple corkscrew that rips corks to pieces, and a complicated corkscrew that extracts them smoothly. "Simple" may be easier to use, but does not necessarily have utility.

I say you are splitting hairs. Just answer me two questions:
1) Old William says don't be more complicated than necessary. How does that not rule out your simple corkscrew?
2) Old William says don't be more complicated than necessary. Why not?



Hence my point that you've added an interpretive level to Occam's Razor which Occam did not articulate.

The issue is what he intended, obviously. Are you seriously going to claim that Old William had no insinuation of utility in his statement? Perhaps your answer to question (2) will clarify your meaning here.


I don't see this as necessarily bad, but I think it's contributing to your apparent disagreement with dgruss23.

Yes, we must keep the debate to what is actually useful and not banter whose semantics are less technically correct, I agree. I will address dgruss23's comments from the perspective that maybe what he has to say will actually benefit our appreciation for science somehow.

Ken G
2005-Nov-25, 06:52 AM
But the modern description of Occam's razor as choosing between two otherwise equal theories is not a practical description of how scientific theory progresses.

You have redefined it in terms of a binary choice problem, which you are right, does not happen in practice for the reasons I mentioned. Occam's razor is a principle of parsimony, this is what I'm saying. What you have done is take a fundamental pillar of science, state that its meaning has gotten a little confused over time, and then used that to argue it is "useless". Poor William, to suffer such a fate.

To me, the idea that you can choose between two theories with Occam's razor is merely a device to articulate the principle. It was never intended to be taken that literally. I agree that this is often how it is stated, but I always took the meaning to be that you should just shoot for simplicity and elegance from the start. The whole point is, it takes an enormous gaul to even imagine that this is possible. Why it is possible may be the deepest mystery of the universe.



The formulation of a hypothesis in the first place will of course incorporate the reasoning of the principle of parsimony, but the ultimate fate of that hypothesis after that point has very little to do with its simplicity.

We are actually in agreement on this matter. What I took issue with was the idea that the idea that we should shoot for as much simplicity as possible was superfluous, but I now see that you only intended to apply this ignominous fate to your own narrow interpretation of what Occam's razor was all about.



Models proposed to explain the flat rotation curves of spiral galaxies provide a good example of this. You have the prevailing DM hypothesis. DM itself has many candidates. And they have all been evaluated with the limitations that current observational technology allows at this time. Then you have MOND. You also have Plasma Cosmology. The discussion about each of these options is not about simplicity - it is about how well they fit the observations.

But what you fail to recognize is that each of these theories has already applied Occam's razor to its initial creation. As you yourself stated. So the point is, we don't really disagree, because you are arguing that a pointlessly narrow interpretation of the principle is superfluous. So much so that you have to define a whole new principle that you call parsimony. But Occam was there first, and it is a crucial defining principle of science. It is a big part of what science is all about. That's what I had to take issue with. Without Occam, and the fact that it is so not superfluous, is basically the reason I am a scientist in the first place.

Ken G
2005-Nov-25, 07:20 AM
The ability of a theory to make testable predictions is the more important part of its utility.

Utility to whom? Of all the physics you have learned, how much of it have you really used to make a testable prediction? Also, note the importance of the word "more" in your statement, which is in effect conceding the point that simplicity does hold a place in utility. Physics, in particular, is more than a way to make testable predictions, it is a way of approaching problems that involves finding its simple core. It's about Occam's razor, in large part.


Simplicity would seem to be more important in the formulation of a hypothesis rather than in the ultimate decision making as to whether a hypothesis should be kept or discarded in favor of another.

I am fine with this statement, I just think it's Occam's razor! So in the end, we are arguing semantics. Hey, I grew up with a twin brother, I can argue about anything. But my point here is, you can see how we would not like the resolution of this to be "yes, simplicity is useless", when in fact, the resolution is "simplicity is the heart and soul of science, even if accuracy is the arms and hands. One of the most amazing things in the universe is that simple thinking works at all, and as long as this continues to hold, let us hold this as one of our highest principles."

Fram
2005-Nov-25, 09:58 AM
I see what you mean, and as long as you make your theory complex enough, I guess you can counter me. But then your theory has long ceased to be scientific, as it is hardly testable and based on observations.
Sure it is, the theory I described will be testable, will make all the same predictions of the standard theory, and will be perfectly scientific as a result.
I don't think it would be that easy to make it thus, but as long as you make enough assumptions, you can make any theory you like.


It gives no reason at all why the Earth would have those special forces.
And that's part of science? We have a reason why gravity exists do we?
Poorly expressed by me. I meant that it gives no explanation why the Earth has forces, particles, whatever, that other planets don't. We can't detect them (but we can't detect gravitons or so either for now), but we can't give no reason either, from the way the earth is composed, formed, ... that it would have different characteristics.
What I mean is: we have a pretty good explanation why a rocky planet is not a gas giant, and we have a pretty good explanation why a gas giant is not a star. Similarly, we have explanations why some stars become white dwarfs and other ones become black holes.
We would have no explanation (of the scientific kind) why the earth behaves differently from the other planets.
I hope I made myself clearer now.


. Just to continue yours: why is that force that counters the gravity of the sun not working on the oceans (tides)?
No problem at all, that's the Sun's gravity. We still only need one special force on the Earth, the one at its center that pervades the universe. But yes, this is silly for one reason and one alone: Occam's razor. Until some new observation shows my theory is actually necessary...
No, you have a force on earth that counters the sun's gravity (hence we don't orbit the sun, but the sun orbits us), but even though the sun's gravity is countered, it still works on the oceans. This is a contradiction and makes your theory invalid (but you can probably improve it again). So for now, I don't need Occam to throw out your theory, I can do it on the predictions made by it, the observations we have that contradict your theory. And I expect that unless you get very very creative (and much more untestable than most current theories are), this will remain so.
Of course, Occam is a much simpler way to throw out your theory, but I'm not convinced that we need it per se.

Ken G
2005-Nov-25, 10:36 AM
I meant that it gives no explanation why the Earth has forces, particles, whatever, that other planets don't. We can't detect them (but we can't detect gravitons or so either for now), but we can't give no reason either, from the way the earth is composed, formed, ... that it would have different characteristics.

Granted, I agree with you. It would be foolish to give the Earth special characteristics just because we are here. But I would argue this is also basically an application of Occam-- if a planet shows no reason to be special, the simplest assumption is that it isn't. All I'm saying is that science is more than the creation of successful theories. That's relatively easy to do (witness my "google" theory, which states that for every behavior that can occur, there will be something reasonably analogous that has already been observed, if we spend a lot of time quantifying and categorizing everything we can possibly observe. After enough time, we will be able to predict virtually any measurement by extrapolating from previous ones. This is the opposite of Occam, but would likely be more accurate. But it would belie the entire purpose of understanding the universe.). What's hard is to come up with a theory that encapsulates some inner truth about how the universe works. And how do you know when you have such a theory? It has some simple core to it, it is a small number of axioms that generate a huge richness of behavior. That's the goal of science, it's the simplicity that lives at the heart. Without such a principle, science is engineering (no offense to engineers).



No, you have a force on earth that counters the sun's gravity (hence we don't orbit the sun, but the sun orbits us), but even though the sun's gravity is countered, it still works on the oceans. This is a contradiction and makes your theory invalid (but you can probably improve it again).

Well, this was a minor point, but in fact tides are still just going to be a manifestation of the Sun's gravity. I don't have to modify my theory at all for them, they are a perfectly natural consequence.


So for now, I don't need Occam to throw out your theory, I can do it on the predictions made by it, the observations we have that contradict your theory.
There are no such observations. Think it through. I say the universe is pervaded by a force which happens to oppose the force of gravity of the Sun at the Earth's center. Also, it is pervaded by centrifugal and coriolis forces centered on the barycenter of our solar system. Further, I include the forces on the Sun, and it's orbit around the galaxy. Finally, the forces on our galaxy are mysteriously countered. That's all you need, it's a few layers of complexity, but you're done. There is no contradictions anywhere, it's a perfectly successful theory. But I've no plans of writing a book on this trivial extension of a much simpler theory, even though it makes all the same predictions. But it does let us be the center of the universe, so it has that going for it!

grant hutchison
2005-Nov-25, 12:00 PM
I say you are splitting hairsOK. They seemed like moderately important hairs since they were at the root of your apparent disagreement with dgruss23. But since I seem to be causing annoyance I'll bow out.

Grant Hutchison

Edit:To bow out when I said I was going to, rather than drizzling on with final ifs and buts ... :)

Disinfo Agent
2005-Nov-25, 01:50 PM
Did anyone say scientific method (http://www.besse.at/sms/smsintro.html)?

Ken G
2005-Nov-25, 05:31 PM
OK. They seemed like moderately important hairs since they were at the root of your apparent disagreement with dgruss23.
You are certainly not an annoyance Grant, you were trying to elucidate the differences in perspectives on Occam's razor. The reality is, all three of us know perfectly well the importance of simplicity in science, so what are we really arguing about? I agree with dgruss23 that the way Occam is often explained as a binary choice mechanism, if taken literally, is quite a weak element of science. Whereas he would likely agree with the idea that one of the central pillars of science is seeking simple explanations.

George
2005-Nov-26, 07:14 AM
It's looking like Occam's razor is best used for giving a theory a cleaner face. :) It is too rare when two theories are so close to each other that simplicity becomes a deciding factor. Yet, is it not natural to desire elegance in favor of prosaic complexity?

Sometimes we have both qualities in some theory. For instance, Planck's radiation equation is not simple, yet comes Wein's nice little formula (peak wavelength = 2.898/T).

Here is another scientific method (http://phyun5.ucr.edu/~wudka/Physics7/Notes_www/node5.html) site.

rahuldandekar
2005-Nov-27, 05:07 AM
Possibly, another interpretation of Occam's Razor is that a complex theory will have many unproved components while a simpler theory will have less of these. Like, Copernicus heliocentric model could explain the observations just like Ptolemy's epicycles could, but the complex things in Ptolemy's model, like epicycles, did not have direct proof. Copernicus' Model had fewer unproved components.

dgruss23
2005-Nov-27, 03:50 PM
Possibly, another interpretation of Occam's Razor is that a complex theory will have many unproved components while a simpler theory will have less of these. Like, Copernicus heliocentric model could explain the observations just like Ptolemy's epicycles could, but the complex things in Ptolemy's model, like epicycles, did not have direct proof. Copernicus' Model had fewer unproved components.

Yes, that is the essence of the original version of Occam's razor. Scientists try to minimize the number of assumptions needed in creating a model. In this way, the fewer needed assumptions the "simpler" the theory.

dgruss23
2005-Nov-27, 04:43 PM
You have redefined it in terms of a binary choice problem, which you are right, does not happen in practice for the reasons I mentioned.

I think it is more appropriate to say that modern usage has redefined it in those terms - which you re-stated in post #8 of this thread:


In actuality, Occam's razor is far less grandiose-- it merely states that of all the theories that fit the data, the simplest one is the most useful, because the whole point of science is to make the understanding of nature as simple as possible.

This modern version of Occam's razor I find to be worthless. IMO since this modern version of Occam has become the standard usage, it would be better to use the principle of parsimony when discussing the relevance of this concept to the process of science. The modern statement of Occam's razor is not the principle of parsimony. Rather it is an attempt to describe the principle of parsimony in overly simplified, unrealistic terms that rarely - if ever - pop up in the practice of science. As such its not even that useful as a pedagogical tool because it creates an unrealistic sense of this aspect of science.


Occam's razor is a principle of parsimony, this is what I'm saying. What you have done is take a fundamental pillar of science, state that its meaning has gotten a little confused over time, and then used that to argue it is "useless". Poor William, to suffer such a fate.

That's not what I have done. The original meaning is no longer in popular usage - even if it still exists in professional usage. Your first definition of Occam's razor on this thread is the useless version I strongly object to.

I think you're right in your later post that we essentially agree. However, from my perspective, I think of the importance of the utility of simplicity in science in terms of the principle of parsimony. When I see the modern occam's razor, I see a popular distortion of an important concept.


To me, the idea that you can choose between two theories with Occam's razor is merely a device to articulate the principle. It was never intended to be taken that literally. I agree that this is often how it is stated, but I always took the meaning to be that you should just shoot for simplicity and elegance from the start.

But scientists don't use occam's razor to choose between two theories. In fact its worth discussio nas to whether or not the use of the word "simplicity" is misplaced here. The key concept is to attempt to minimize the number of needed assumptions when developing a model. Since a minimum of assumptions may be considered "simpler" than a greater number of assumptions, this is another level of popularization of the concept that has created the misleading description of Occam's razor.



But what you fail to recognize is that each of these theories has already applied Occam's razor to its initial creation. As you yourself stated. So the point is, we don't really disagree, because you are arguing that a pointlessly narrow interpretation of the principle is superfluous. So much so that you have to define a whole new principle that you call parsimony. But Occam was there first, and it is a crucial defining principle of science.

I haven't failed to recognize anything and I haven't re-defined anything. Read Carlo Lastrucci's book "The Scientific Approach" (and let me add that I'm frustrated as heck that I cannot find my copy - it wasn't at work and I can't find it in my office.). He discusses the principle of parsimony - which is defined in terms of the original meaning of occam's razor. Given that the meaning of Occam's razor has been corrupted in a futile attempt to create a popular description of the concept that still retains the original of the concept, I think it is far more appropriate to use the principle of parsimony.

What is wrong with just defining Occam's razor this way?:

"In the practice of science, scientists attempt to develop models that require the minimum number of assumptions needed to explain the observations."

That after all, is the principle of parsimony stated in a way that the average high school science student should be able to grasp. This choosing between two theories garbage is nonsense that somebody at one time must have come up with as a pedagogical tool. Its more than worthless. Its misleading - and its taken over the original meaning of occam's razor.

I think what happened is that at some point instructors realized that the original definition of occam's razor as "the principle that entities should not be multiplied needlessly" is not a very good pedagogical definition - because it needs to be explained. So somebody started using this "choosing between two theories" nonsense in an attempt to explain it and thought that at least their students could understand that definition. And now we have thousands of high school and college students that think scientists are out there grappling with two equally matched theories and just pick the simpler one to work with. A better definition is needed in science instruction. Personally, I like mine in bold above. But I'm open to it being tweaked.

IsaacKuo
2005-Nov-27, 05:39 PM
The "modern" definition of Occam is the impetus for much of modern physics. Without this principle, why bother uniting the electric and magnetic forces? What's the point in uniting energy and matter? Why bother attempting to reconcile Quantum Physics and General Relativity? Why bother with banging together particles at near-c velocities? What exactly is the point of the search for a TOE?

Quintessentially, it's based on the assumption that the CURRENT best theories have "too many entities", and that some alternate theory unites those entities. The whole point of the quest is to FIND the simpler theory.

Occam's Razor isn't just a guiding principle in modern physics. It is THE guiding principle.

dgruss23
2005-Nov-27, 05:52 PM
Note: This is a second attempt at this one because this software keeps telling me I need to log in when I hit submit!!!!! Very annoying!!!!! And I know the message would have submitted if I had simply typed the log in again, but I accidentally hit "back" and lost it all. :mad: :wall:


Utility to whom? Of all the physics you have learned, how much of it have you really used to make a testable prediction?

Testable predictions are useful when scientists are comparing two competing theories. Which one fits the data better? I don't understand the relevance of your question. The modern occam is stated in terms of choosing between competing theories. Scientists don't make this decision based upon simplicity. They make that decision based upon observational results and testable predictions.


Also, note the importance of the word "more" in your statement, which is in effect conceding the point that simplicity does hold a place in utility.

Yes, that's why I put the word "more" in there. I choose my words carefully (most of the time) and you should always expect that I know exactly what I meant - the words I use are not a mystery to me.

To summarize my thoughts on this whole discussion:

~ Simplicity is an important factor in developing hypotheses/ models/theories via minimizing the assumptions used.

~ In the arena of deciding between theories "simplicity" takes a back seat. The match of the theories to observation/analysis/experimental results becomes the most important factor. Scientists do not as a matter of practice choose simplicity as a factor in whether to accept or reject one theory over another.

~ Since the modern version of Occam's razor is stated in terms of simplicity being used to decide between two theories, it is a false description of the practice of science.

~ The Principle of Parsimony, is equivalent to the original version of Occam's razor and is important in the stage of developing models.


I am fine with this statement, I just think it's Occam's razor! So in the end, we are arguing semantics. Hey, I grew up with a twin brother, I can argue about anything. But my point here is, you can see how we would not like the resolution of this to be "yes, simplicity is useless", when in fact, the resolution is "simplicity is the heart and soul of science, even if accuracy is the arms and hands. One of the most amazing things in the universe is that simple thinking works at all, and as long as this continues to hold, let us hold this as one of our highest principles."

But we should always keep in mind the Sun Principle as discussed by John Horgan in the End of Science (page 111):

"More detailed observations of our cosmos will not necessarily resolve questions about the Hubble constant or other issues. Consider: the most mysterious of all stars is our own sun. No one really knows, for example, what causes sunspots or why their numbers wax and wane over periods of roughly a decade. Our ability to describe the universe with simple, elegant models stems in large part from our lack of data, our ignorance. The more clearly we can see the universe in all its glorious detail, the more difficult it will be for us to explain with a simple theory how it came to be that way."

dgruss23
2005-Nov-27, 06:06 PM
The "modern" definition of Occam is the impetus for much of modern physics. Without this principle, why bother uniting the electric and magnetic forces? What's the point in uniting energy and matter? Why bother attempting to reconcile Quantum Physics and General Relativity? Why bother with banging together particles at near-c velocities? What exactly is the point of the search for a TOE?

In some cases because observations suggest such searches are necessary and in others because currently accepted theory suggests such revisions are needed.


Quintessentially, it's based on the assumption that the CURRENT best theories have "too many entities", and that some alternate theory unites those entities. The whole point of the quest is to FIND the simpler theory.

But you're confirming what I'm saying: In the stage of developing theory, simplicity is a factor (principle of parsimony). But if somebody comes up with a new theory that unites Quantum theory and GR, what is the next thing that will happen? Researchers will test the theories predictions against observations. Researchers will not "choose" or accept the new theory just because it is "simpler" in some way. It must be consistent with observational results.


Occam's Razor isn't just a guiding principle in modern physics. It is THE guiding principle.

The "modern" definition is not a useful principle. Its misleading. We're really discussing two parts of science here: (1)Theory development and (2) experimental verification. The problem with the modern Occam is that it is phrased in terms of "choosing" between two rival theories and it states that "simplicity" is the key factor in the decision. That is wrong. Confirmation of the predictions of a theory by experimentation are how scientists choose (if there is ever a clearly defined moment of choice).

hhEb09'1
2005-Nov-28, 02:53 PM
As ATP often says (can't recall his new screen name), "Occam's Razor is in the eye of the beholder". It's not really a principle of science; more like a rule of thumb (no wonder engineers are particularly fond of it).Let me help: it's me! :)

And I am fond of saying that (the imagery reminds me of Dali (http://www.straightdope.com/mailbag/munchienandalou.html)), but I have to give credit to Zathras (http://www.bautforum.com/showthread.php?p=77232&highlight=razor+beholder#post77232). I disagree that Occam's Razor is a scientific principle, it is more like a human tendency--it is the reason that people prefer astrology, for instance, they want things to be ordered and simple. Nevermind that the simple things develop complexities.

It's the reason that some people obstinately prefer a Newtonian explanation of mechanics, deeming it simpler than general relativity, because the solutions of general relativity equations are so complicated. But the final decision is based upon the fact that general relativity works in all known cases (even "Newtonian" ones), whereas Newton's laws are limited.
That's no problem at all, the Sun generates gravity. The Earth does not orbit the Sun however, because there is a special force that the Earth feels which counters the gravity of the Sun. As for the other objects, they feel the Sun's gravity, and a special force I'll call centrifugal and coriolis forces emanating from the Earth. And a few more to handle the minor perturbations. Why not? Oh yeah... Occam.We've discussed this example before--general relativity, in the extreme case, allows it, without the addition of any additional fictitious forces or changes to the physics. So, I don't think it's a valid objection.

George
2005-Nov-28, 03:51 PM
Note: This is a second attempt at this one because this software keeps telling me I need to log in when I hit submit!!!!! Very annoying!!!!! And I know the message would have submitted if I had simply typed the log in again, but I accidentally hit "back" and lost it all. :mad: :wall:
Be sure to click on the "remember me" box when logging in. [Fraser had to point that out to me when I complained. ]


To summarize my thoughts on this whole discussion:

~ Simplicity is an important factor in developing hypotheses/ models/theories via minimizing the assumptions used.
Yes. This seems to be the proper time to make use of Occam. Otherwise, coudln't a huge number of theories be generated with any given observational data set?



~ In the arena of deciding between theories "simplicity" takes a back seat. The match of the theories to observation/analysis/experimental results becomes the most important factor. Scientists do not as a matter of practice choose simplicity as a factor in whether to accept or reject one theory over another.

~ Since the modern version of Occam's razor is stated in terms of simplicity being used to decide between two theories, it is a false description of the practice of science.
Yes. No doubt you are right unless we are comparing two theories which are "equal". But how often does that happen (which is probably implied in your point)?


~ The Principle of Parsimony, is equivalent to the original version of Occam's razor and is important in the stage of developing models.
Yes. I took this for your first point, too. I also looked up the term parsimony (http://www.tk421.net/essays/simple.html). Of course, it's not simple. :razz:


But we should always keep in mind the Sun Principle as discussed by John Horgan in the End of Science (page 111):

"More detailed observations of our cosmos will not necessarily resolve questions about the Hubble constant or other issues. Consider: the most mysterious of all stars is our own sun. No one really knows, for example, what causes sunspots or why their numbers wax and wane over periods of roughly a decade. Our ability to describe the universe with simple, elegant models stems in large part from our lack of data, our ignorance. The more clearly we can see the universe in all its glorious detail, the more difficult it will be for us to explain with a simple theory how it came to be that way."
I don't understand the logic. It has been the more detailed observations of our cosmos which has refined Hubble's constant. The distinction in Cepheids greatly changed it, and the more accurate distance to Andromeda are just two examples. Sunspots are being more understood thanks to helioseismology. These may, or may not, produce a more complex universe. [Of course, the sun's color is another thing. ;)]

dgruss23
2005-Nov-28, 08:49 PM
I don't understand the logic. It has been the more detailed observations of our cosmos which has refined Hubble's constant. The distinction in Cepheids greatly changed it, and the more accurate distance to Andromeda are just two examples.

But I think the Cepheids have provided a good example of the Sun Principle. More recent studies have shown that the P-L relation has a metallicity dependence. So better data has provided a more complicated model for the P-L relation. The simpler models with no metallicity correction are suspect.


Sunspots are being more understood thanks to helioseismology. These may, or may not, produce a more complex universe.

The complexity of the universe will not change - only the complexity of our models that are needed to explain it. Consider the CMB. When it was discovered it was taken as support for the BBT. Since that time there has been COBE ~1990 and more recent CMB results such as WMAP. These new results have indicated some unexpected alignments that may need to be filtered out. But we also see that the new data not only allow more complex modeling, but may in fact require more complex modeling.

I think his point is valid - the more accurate and detailed the available data, the more complex models must become to fit all aspects of the data. So when we talk about how successful simple models are, that must be tempered by understanding that it is likely that the next generation of advancement in data will likely result in more complexity.

rahuldandekar
2005-Nov-29, 04:16 AM
Although a simpler theory is "better" than a complex one, if the complex one has more evidence supporting it, Occam's razor cannot be applied, and the scientific method says that the more complex theory is better.

dgruss23
2005-Nov-29, 02:42 PM
Although a simpler theory is "better" than a complex one, if the complex one has more evidence supporting it, Occam's razor cannot be applied, and the scientific method says that the more complex theory is better.

I agree. This was my point from the start.

George
2005-Nov-29, 03:56 PM
Although a simpler theory is "better" than a complex one, if the complex one has more evidence supporting it, Occam's razor cannot be applied, and the scientific method says that the more complex theory is better.
Which is more likely? Sounds like the simple ones may be all used up? :( Is there a name for this principle favoring the better, though more complex? May I propose Macco's Hammer? If a theory is tough and malleable enough to handle the shaping from the hammering, it is superior to all those that crack and fall apart. [The hammering would be the addition of new terms.] :)

dgruss23
2005-Nov-29, 04:39 PM
Which is more likely? Sounds like the simple ones may be all used up? :( Is there a name for this principle favoring the better, though more complex?

I think this illustrates the whole problem with too much emphasis on simplicity and Occam's razor. What it boils down to is that theories/models/whatever in science must be consistent with the data regardless of the complexity of the model. Their predictions must hold up to new observations. Simplicity is not a deciding factor. Consistency with observations is. Too much emphasis on Occam's razor distracts from a correct understanding the scientific process.

Maddad
2005-Nov-29, 09:24 PM
Ken G
Thank you very much for your discussions on Occam's Razor. I was shocked to see that indeed, I had misunderstood it as you first explained. I've saved this page so that I can reflect on it again several times until I know what's been provided here automatically, without having to figure it out each time like I usually do.

George
2005-Nov-29, 10:47 PM
I think this illustrates the whole problem with too much emphasis on simplicity and Occam's razor. What it boils down to is that theories/models/whatever in science must be consistent with the data regardless of the complexity of the model. Their predictions must hold up to new observations. Simplicity is not a deciding factor. Consistency with observations is. Too much emphasis on Occam's razor distracts from a correct understanding the scientific process.
A nice summary, especially since you've dove-tailed it into the scientific method. :clap:

I believe the majority here hold this view. I also like Grant's cork screw. :)

rahuldandekar
2005-Nov-30, 04:44 AM
Yeah, DrGruss's summary is nice. :)

Instead of applying Occam's razor or somesuch thing, I'd say a theory which has more unobserved components is less likely to be true than a theory with fewer unobserved components but explaining the same evidence. But if the more "complex" theory gets some evidence in it's favour, and if the simpler theory cannot explain that evidence, the complex theory is more plausible.

This is all on basis of the scientific method. Occam's razor fails when one of the two theories explains more observations, but the scientific method still applies. I don't think the scientific method requires anything like "Occam's razor". If two theories explain the same evidence, itis common sense that we take theory with less unproven components.

Ken G
2005-Nov-30, 01:39 PM
The original meaning is no longer in popular usage - even if it still exists in professional usage.

Again, the "popular usage" is merely a device to explain the razor, not a description of an actual process of theories in confrontation. It is a guiding principle that is usually applied from the start, but not always, as was pointed out in regard of the search for the TOE, etc.

Your first definition of Occam's razor on this thread is the useless version I strongly object to.

You obviously see it as an ineffective device. But "useless" is not the right criticism of it, for it is far from useless. Indeed, it is one of the most widely known scientific principles-- obviously it has had some positive effect. The real criticism of the "normal" way of stating Occam is the one I raised originally-- it is so often confused for a principle about what is more likely to be correct. That is the meaning to avoid. The image of theories in confrontation, like contrast, is a highly effective education tool, as evidenced by its widespread appeal.


I think you're right in your later post that we essentially agree. However, from my perspective, I think of the importance of the utility of simplicity in science in terms of the principle of parsimony. When I see the modern occam's razor, I see a popular distortion of an important concept.

Yes, it's ironic that our prose is so focused on argumentation when in fact there is a great deal of agreement. You are simply overstating your distaste for the modern way that Occam gets stated, since you think it makes people believe that scientists are constantly facing off theories based on simplicity when in fact the battle is fought on the evidence. I don't think that people have that impression, I think they understand the way the device is applied, except the business about likelihood to be correct. So that's our only disagreement, even though neither of us have focused our arguments there and so we have both been talking past each other.


What is wrong with just defining Occam's razor this way?:

"In the practice of science, scientists attempt to develop models that require the minimum number of assumptions needed to explain the observations."

Well, that is a perfectly fine formulation, I agree with it completely, but it is pretty dull. If I were to tweak it, I'd reduce the redundancy, and I'd try to breathe a little more life into it, but it certainly demonstates a good understanding of the principle. It is not necessary for me to argue against any particular valid formulation, that is your chosen position. All I have argued, throughout this thread, is that embedded in science is a love for simplicity, a love for making things comprehensible. This means that even when a complete theory is complicated, like the motion of an airplane, it is piggybacked on layers of simpler and simpler ideas. This is what Galileo meant when he claimed that all objects fell at the same rate, even when everyone knew this is not the case. It was the core of the scientific method then, and it still is now, and is the reason many of us do science in the first place.

George
2005-Nov-30, 03:56 PM
Very cool discussion. :clap:

I really don't see much disagreement, but nice articulation.

Apparently, the "Macco's Hammer" idea lacks the elegance and utility necessary to unify with Occam's Razor to produce a complete conceptual picture of the fabrication techniques essential to the scientific method. ;) [Shucks, I had already started on QM and GR unity. Not now, though. :neutral:.]

Ken G
2005-Nov-30, 11:51 PM
You're right George, for all our bluster about "useless" or "dull" ways to express Occam, we all pretty much agree, because we understand science. As for Macco's hammer, I see some advantages to that approach but what bothers me is that if taken to the limit, it would seem that an infinitely malleable theory would not really be a theory of anything-- it could flex into a new form to accomodate anything. Doesn't a theory have to at some point stand and deliver, or face elimination? In other words, at some point you want the theory to be the hammer, not the horseshoe. And if it breaks on the anvil, then you needed a hammer made of stronger stuff. But I do see what you mean that we are kind of shooting in the dark based on limited information, so what chance do we have of making a perfect bullseye? The very fact that we try at all is really amazing, and that we sometimes succeed pretty well is even more amazing.

George
2005-Dec-01, 12:29 AM
You're right George, for all our bluster about "useless" or "dull" ways to express Occam, we all pretty much agree, because we understand science. As for Macco's hammer, I see some advantages to that approach but what bothers me is that if taken to the limit, it would seem that an infinitely malleable theory would not really be a theory of anything-- it could flex into a new form to accomodate anything. Doesn't a theory have to at some point stand and deliver, or face elimination? In other words, at some point you want the theory to be the hammer, not the horseshoe. And if it breaks on the anvil, then you needed a hammer made of stronger stuff.
Sometimes I do not express myself clearly with these analogical ideas in the sense that they are often meant more to generate a smile than to establish something of pure merit. :) Albeit, my hope is to create a few nuggets now and then.

The thought was more in line with the emphasis dgruss had of things changing toward complexity even if resistance or regret transpires; hence the hammering action reshaping a theory. The ones hammering - the scientists; the anvil - the foundational scientific method; the metal of the object - the "mettle" within the theory; the final shape - the latest version of the theory.

I just sense that metaphors are handy and popular for understanding the tougher stuff (eg methodologies).

Ken G
2005-Dec-01, 07:22 AM
I see what you are saying, you mean that GR has survived pounding from Macco's hammer because it is able to accomodate dark matter and dark energy without too much difficulty. That is a valid point. However, it is also possible that the need for these fixes is trying to tell us that we have missed something simpler. Or to follow your metaphor, perhaps Occam's razor will ultimately prove sharp enough to slice through even Macco's trusty hammer!

George
2005-Dec-01, 05:25 PM
I see what you are saying, you mean that GR has survived pounding from Macco's hammer because it is able to accomodate dark matter and dark energy without too much difficulty.
Hmmmm, that may be a better analogy than my original view, which was...the hammer comes when the theory is being reshaped in some manner due to ascending complexity (almost opposite of Occam, hence - maccO).


That is a valid point. However, it is also possible that the need for these fixes is trying to tell us that we have missed something simpler. Or to follow your metaphor, perhaps Occam's razor will ultimately prove sharp enough to slice through even Macco's trusty hammer! Yes indeed, all you need is a great deal of heat. ;) For instance, put the "heat" on Planck's raditiation equation by using reduced terms in the Taylor series solution for e^x, and voilA, you have a cut-down version equal to the old classic radiation equation. :)

Also of interest to me...this does show me that you are metaphorically malleable. IMO, you have just gained a sigma value for your tighter sync with the analogical cornjunktive (ironically, often less of a fit to scientific society). :)

Corn aside, I still suggest a metaphor needs inventing for the complexity likelyhood in modern theories. It should hint of the respect for the razor, though, somewhat, opposite. Maybe just a catch phrase will do.

Ken G
2005-Dec-02, 02:52 AM
I did not catch your occaM pun, sorry! But a good metaphor is as pleasing to me as a solid explanation, fear not. And I live in Iowa, so I'm no stranger to corn! But when we talk about the need for complexity, I think the crucial point is that complexity comes with a value and a price. The value is greater accuracy, generally, and the price is, it is not as easy to use or understand. Any researcher will constantly be walking that line. So in fact, modern research does constantly apply Occam, in the sense that theories, or models, are constantly tailored to be the simplest possible one that meets the desired accuracy need. So this may be the most complete statement of Occam that does include your maccO element: "when choosing to work with a theory as applied to a particular model, scientists always try to choose the simplest version that meets their accuracy requirements". This kind of confrontation occurs in virtually every situation, but one may distinguish a theory from a model if one wants to get technical about the differences.

George
2005-Dec-02, 04:14 AM
Yes. Another nice articulate description of sound science as it relates to Ocaam's razor.

Yet, I have a hunch there is a ripe metaphor ready for plucking which would go in the hand opposite the hand with the razor. Maybe not.

Ken G
2005-Dec-02, 01:27 PM
The metaphor you are looking for might be synonymous with the oft-heard statement "the devil is in the details". That is kind of your maccO's hammer. I suppose a fair description of science would use both approaches, a simplifying element to give us a conceptual grasp, and a mechanism for incorporating all the details needed for practical applications that require high accuracy. So when Galileo said that all objects fall at the same rate under gravity, he was following the Occam approach, but if one wants to understand the more complicated concept of terminal velocity, one would need a few pounds from that hammer o' yours. Still, in pounding out terminal speed, again you'd need that razor to shave off the rough edges, as there are many ways to model that phenomenon and one would again choose the simplest that meets the accuracy need.

George
2005-Dec-02, 02:36 PM
The metaphor you are looking for might be synonymous with the oft-heard statement "the devil is in the details".
Yes. I suppose that is clever enough to offset whatever lack of metaphor I was hoping for. The hammer is a little too crude, and the razor much sharper (sorry). :)


So when Galileo said that all objects fall at the same rate under gravity, he was following the Occam approach, but if one wants to understand the more complicated concept of terminal velocity, one would need a few pounds from that hammer o' yours.
Adding punishment, maybe Macco's laptop (you did say "terminal" ;)) would be more appropriate to modern science; much more sophisticated, and essential in chasing today's devils.


Still, in pounding out terminal speed, again you'd need that razor to shave off the rough edges, as there are many ways to model that phenomenon and one would again choose the simplest that meets the accuracy need. The emphasis for using both "tools" has been nicely stated by you, and others, in this thread.

hhEb09'1
2005-Dec-02, 06:56 PM
You obviously see it as an ineffective device. But "useless" is not the right criticism of it, for it is far from useless. Indeed, it is one of the most widely known scientific principles-- obviously it has had some positive effect. The real criticism of the "normal" way of stating Occam is the one I raised originally-- it is so often confused for a principle about what is more likely to be correct. That is the meaning to avoid. The image of theories in confrontation, like contrast, is a highly effective education tool, as evidenced by its widespread appeal.I've said before that I don't think Occam's Razor is a scientific principle--it just doesn't fit. I agree that it is useful, I've used it myself, but it's use by scientists does not make it scientific--otherwise, we'd have to say that the alphabet is scientific, since it too is used by so many. :)

Yes, it's ironic that our prose is so focused on argumentation when in fact there is a great deal of agreement.Sometimes disagreement is just a matter of defining terms :)

Ken G
2005-Dec-02, 07:43 PM
Adding punishment, maybe Macco's laptop (you did say "terminal" ;)) would be more appropriate to modern science; much more sophisticated, and essential in chasing today's devils.
Are you suggesting that terminal velocity is the speed maccO's laptop achieves if one tries to use it to read email while skydiving? Occam would be proud of such a simple definition, and maccO's laptop might be constructed well enough to withstand some pounding, but I fear that the ultimate confrontation with the ground would cause your definition to fall to pieces.

Ken G
2005-Dec-02, 07:49 PM
Sometimes disagreement is just a matter of defining terms :)
That is quite often true, I'm sure. Here the issue is, what distinguishes science from other pursuits. True enough, we may seek simplicity in many nonscientific pursuits as well, from dance to painting, or we might seek complexity, it is kind of a matter of taste. All I want to stress is that the biggest misconception about science is that it can be used to completely unravel the mysteries of existence, like untying a knot. That is not what science does, we already know the mysteries of existence are too complex for our feeble brains (insert your favorite examples here). What science is actually about, and what scientists actually do every day, is to replace the full richness of existence with a simplified model that captures its essence, to whatever is the desired level of accuracy. Thus the whole point is simplicity, or maximal simplicity within some constraint, and in this sense Occam's razor is not only scientific, it is the very heart of the scientific method. But yes, science is a human endeavor, and shares many aspects with nonscientific human endeavors, so I would not claim ownership of Occam by science, if this is what you mean by "not fitting" as a principle. It's more like a meta-principle, I grant you.

George
2005-Dec-02, 09:46 PM
Are you suggesting that terminal velocity is the speed maccO's laptop achieves if one tries to use it to read email while skydiving? Occam would be proud of such a simple definition, and maccO's laptop might be constructed well enough to withstand some pounding, but I fear that the ultimate confrontation with the ground would cause your definition to fall to pieces. Please keep in mind it is more beneficial for all if you will simply constrain dialogue to represent your true intent; this will help eschew obfuscation (uh oh) ...benefiting all who want to learn; people considerate enough to offer you their ear (oops). Shucks, I just couldn't do it, but I tried! :) You caught me off gaurd, Iowan. I ain't use to buttered counter-corn on the BAUT farm! :) "Terminal velocity" - you're Maching me, right? ;) :) [/cornjunktive]

Still, it would be nice to see a useful metaphor to compliment Occam's razor, yet in more of the opposite sense; producing a sense of reason for the value inherent in greater complexity. The better the mental pictures of any process, the easier it is to learn, appreciate, and grow.

I wonder if religion is not, somewhat, the opposite? They start with pictures and try to articulate the process. Hermeneutics has evolved, apparently, from straight interpretations to a much more comprehensive approach by identifying methodologies, I think. [ I never took religion.]

[I'll be gone at least a day..... so behave. ;) :)]

Ken G
2005-Dec-03, 07:28 AM
Still, it would be nice to see a useful metaphor to compliment Occam's razor, yet in more of the opposite sense; producing a sense of reason for the value inherent in greater complexity.
There is a kernel of truth to this...

George
2005-Dec-04, 12:02 AM
There is a kernel of truth to this...
As Charlie once said....I...must....resist....temptation! :wall:

:)

Those who can get through corn will oft find a cob of value; kind of a cobblestone that helps support their pathway (e.g. my concession stand in your 2, but maybe 3, envelope game). [Other times, the cob is worthless. :)] That, of course, is the simple version. You will need your Macco Laptop to deal with the whole enchilada. Hmmmm...Occam's Razor and the Whole Enchilada. Is that too much of a mixed metaphor (I think it is a mixed metaphor, right?)?:think:

dgruss23
2005-Dec-04, 02:12 AM
A nice summary, especially since you've dove-tailed it into the scientific method. :clap:

I believe the majority here hold this view. I also like Grant's cork screw. :)

Thank you George! :)

dgruss23
2005-Dec-04, 03:04 AM
Again, the "popular usage" is merely a device to explain the razor, not a description of an actual process of theories in confrontation. It is a guiding principle that is usually applied from the start, but not always, as was pointed out in regard of the search for the TOE, etc.

But the popular usage is a very poor device because it doesn't capture the essence of Occam's razor's role in science.


You obviously see it as an ineffective device. But "useless" is not the right criticism of it, for it is far from useless. Indeed, it is one of the most widely known scientific principles-- obviously it has had some positive effect.

But here is why we keeping talking past each other. Yes the name "Occam's razor" is widely known, but its actual utility in science is not because the description of Occam for popular consumption does not describe the real Occam's razor.


The real criticism of the "normal" way of stating Occam is the one I raised originally-- it is so often confused for a principle about what is more likely to be correct. That is the meaning to avoid. The image of theories in confrontation, like contrast, is a highly effective education tool, as evidenced by its widespread appeal.

Yes, I agree it is inappropriate to talk in term of theories more likely to be correct, but I completely disagree that the modern version of Occam is a useful educational tool. If we're trying to help students gain an understanding of how scientists evaluate two proposed theories, then we must talk about how well the predictions of those theories are supported by evidence and experimental results rather than talk about which theory is simpler. The problem with the modern version of Occam is that it describes scientists doing something they don't do! How can something that is an incorrect (not just overly simplified - but flat out incorrect) description of what scientists do be a useful pedogogical tool?


Yes, it's ironic that our prose is so focused on argumentation when in fact there is a great deal of agreement. You are simply overstating your distaste for the modern way that Occam gets stated, since you think it makes people believe that scientists are constantly facing off theories based on simplicity when in fact the battle is fought on the evidence.

I don't think I'm overstating my case at all. The modern version of Occam is an incorrect formulation. It is stated in terms of scientists comparing/choosing between/using two theories and then states that simplicity is the criteria that is used. Simplicity is not the criteria at that stage - the evidence is. So modern Occam is wrong - which makes it very difficult to overstate criticism of it.


I don't think that people have that impression, I think they understand the way the device is applied, except the business about likelihood to be correct.

Lets just say - for the sake of argument, that very few people actually are led to an incorrect understanding of theory evaluation by the Modern version of Occam. Why is that? There would be two likely reasons. First, from experience (pre or post learning Occam) they would have seen that evaluation of theories requires a look at evidence. Second they have been instructed at some point that when scientists evaluate competing theories they must look at the evidence.(Actually a third would be that the word "Occam" is so strange that they tuned out the teacher and thus never learned the thing in the first place:) ). In either case if the person learns the modern Occam they must through experience or alternate instruction learn that it is wrong. So what value is it?


Well, that is a perfectly fine formulation, I agree with it completely, but it is pretty dull. If I were to tweak it, I'd reduce the redundancy, and I'd try to breathe a little more life into it, but it certainly demonstates a good understanding of the principle. It is not necessary for me to argue against any particular valid formulation, that is your chosen position. All I have argued, throughout this thread, is that embedded in science is a love for simplicity, a love for making things comprehensible.

I'm glad that we agree on my formulation in terms of accuracy. That's a positive accomplishment for us! :clap: :)

But you've argued for more than a love of simplicity in science. You have argued for some value in modern Occam even as you seem to agree that it does not describe how scientists evaluate two competing theories. And I don't see how an incorrect formulation of the process of science can make science more comprehensible.


This means that even when a complete theory is complicated, like the motion of an airplane, it is piggybacked on layers of simpler and simpler ideas. This is what Galileo meant when he claimed that all objects fell at the same rate, even when everyone knew this is not the case. It was the core of the scientific method then, and it still is now, and is the reason many of us do science in the first place.

And its not modern Occam! :) New layers were added to the simpler ideas in spite of their simplicity because new evidence required new layers of complexity!

Gosh, I am sorry for being a pain! You like to debate because you're used to it from having a brother. I like to debate because growing up my parents and my only sibling hated to. I've got years of pent up debating to get out of my system. :lol:

Ken G
2005-Dec-04, 04:55 AM
Gosh, I am sorry for being a pain! You like to debate because you're used to it from having a brother. I like to debate because growing up my parents and my only sibling hated to. I've got years of pent up debating to get out of my system. :lol:
We both like a good argument, it's clear, but it's probably time to agree on what we agree on. Simplicity is a defining goal of science, even though it tends to get compromised as improved accuracy is needed, merging ultimately into engineering. Sometimes new observations cause a need for greater complexity, sometimes the opposite occurs (witness the wavelength shift in 180-degree Compton scattering-- classically, it is a complicated function, but relativistically, it is always a fixed redshift!) The modern statement of Occam has debatable usefulness as a demonstrative device, but is easily misinterpreted as saying either that simpler theories tend to be right, or that competing theories are generally debated on the grounds of their simplicity, rather than on their success.

dgruss23
2005-Dec-04, 04:28 PM
We both like a good argument, it's clear, but it's probably time to agree on what we agree on.

Agreed.


Simplicity is a defining goal of science, even though it tends to get compromised as improved accuracy is needed, merging ultimately into engineering. Sometimes new observations cause a need for greater complexity, sometimes the opposite occurs (witness the wavelength shift in 180-degree Compton scattering-- classically, it is a complicated function, but relativistically, it is always a fixed redshift!) The modern statement of Occam has debatable usefulness as a demonstrative device, but is easily misinterpreted as saying either that simpler theories tend to be right, or that competing theories are generally debated on the grounds of their simplicity, rather than on their success.

Very nice summary! No disagreement.

And thanks for a good debate!

Ken G
2005-Dec-04, 05:45 PM
Thanks to you as well, dgruss23.

George
2005-Dec-04, 08:58 PM
Thanks you two for the whole enchilada on Occam. :clap: [BTW, I withdraw the enchilada nomination as Occam's more effective compliment. It just sounds too cheesy!]

Ken G
2005-Dec-04, 09:02 PM
And thank you for your tasteful comments, George.

George
2005-Dec-04, 10:30 PM
And thank you for your tasteful comments, George.
Ooohhh. Of course, at this point, we are only leaving a meer razor behind; however, the cornjunktive will appear ever near when you veer, or steer, toward a jeer to my ear. :)]

mugaliens
2005-Dec-04, 11:07 PM
I always though it meant stating something then using evidence to prove or disprove it. If proved, then theory becomes fact, or law. If not, then theory may still be a theory, but less likely

Disinfo Agent
2005-Dec-05, 07:23 PM
I always though it meant stating something then using evidence to prove or disprove it. If proved, then theory becomes fact, or law.And if later disproven it ceases to be a fact?...

George
2005-Dec-05, 08:14 PM
mugaliens, I think it can be stated the scientific method does not prove anything to be true. [Disinfo Agent's answer is one good reason why.] It can, however, be useful to help prove something to be false.

Ken G
2005-Dec-06, 08:25 PM
It seems to me the issue of proof in science is a very tricky one. I've heard the claim that you can disprove a theory but not prove it, but this idea doesn't hold water for me, it has a slow leak like my pesky bicycle tire. Let us assume that all observations have been corroborated and are reliable, so we don't even have to get into the (important) issues of observational error or misinterpretation. Even so, a theory that works in every situation for which it has been observed has indeed been "proven" to work in those situations. If it fails in some new situation, or some new accuracy realm, there must be a reason why, so one would say the theory cannot be extended to that situation or to that accuracy. This does not make the theory false in the situations where it was previously tested, to the degree of accuracy to which it succeeded. It just shows you the theory's limits. Likewise, if a theory passes all tests to some accuracy level, we say it is useful in all those situations and to that accuracy, but we just don't know about other situations or other levels of accuracy. Is there really such a strong asymmetry between proof and disproof? I know this is often quoted, but I think what is really meant is, of all the current possible explanations for something, you can decide which is the most likely to be correct, or which works to the highest accuracy. You cannot guarantee that a new explanation might prove even more likely, or more accurate. So that's really the distinction between proof and disproof, it's more subtle than the "party line" in my opinion.

George
2005-Dec-06, 09:53 PM
Nice Ken. On the one hand, it seems a little unfair to say nothing can be truly proven. Establishing constraints on a given "proof" makes the term valid, if I understand your statement, and I agree.

On the other hand, a proof, within established confines, could be expressed erroneously if those confines are forgotten or ignored. The use of a proof, if allowed but restricted, requires responsibility on the part of the user. This may be the heart of the issue, maybe (I am not knowledgeable in this area, and I can prove it ;) ). Declaring "proofs" to be an impossible term takes it off the market to eschew obfuscation ;), I guess. I am a little surprised this seems to be the case, but not shocked.

However, if I'm right, and getting things off the market is important, it would encorage the idea that some things can be disproved.

Ken G
2005-Dec-06, 10:36 PM
On the other hand, a proof, within established confines, could be expressed erroneously if those confines are forgotten or ignored.

Yes, I agree this is the key error to avoid. It's not the concept of "proof" that is at fault, it is the blind application of something "proven" to a context to which it has never been proven, like saying that "an airplane is proven technology so let's just fly to Mars". But the same error can occur for "disproven" things, the Boy Who Cried Wolf being the most obvious example. I don't think we should take the word "prove" off the market, but I think we should be more careful to define the context in which it is being used. Heck, if a prosecutor can use the word, surely scientists can!

George
2005-Dec-07, 12:05 AM
I don't think we should take the word "prove" off the market, but I think we should be more careful to define the context in which it is being used. Ok. So what do we call it? Proof lite? :)


Heck, if a prosecutor can use the word, surely scientists can! Yes, no doubt (or at least not beyond a reasonable one :))It would be interesting to see an analogy between legal and scientific methodologies. It seems it is never clear (not Everclear which is 200 proof!). ;)

Ken G
2005-Dec-07, 12:13 AM
Newton's laws are a prime example of a theory that has been both proven and disproven, and is still as much physics as most college students ever learn. (And like you say, college students are experts in "proof"!) So I think we just say, Newton's laws have been "proven" to work in the context of motions of and on planets in solar systems. They don't work in atoms, and they don't work in cosmology, in those contexts the laws are "disproven". We just need a better appreciation for what laws really are (things meant to control the behaviors of other people, right?).

George
2005-Dec-07, 12:50 AM
We just need a better appreciation for what laws really are (things meant to control the behaviors of other people, right?).
Yes. :clap: Clever. :) If all people understood the term "proof" in this context, we could all use it with constrained freedom (oxyjunktive).

Ken G
2005-Dec-07, 01:09 AM
Well, I suppose it's better to be an oxyjunktive like "constrained freedom" than a corn-moron, like, well, me!

hhEb09'1
2005-Dec-07, 07:23 AM
Simplicity is a defining goal of science, even though it tends to get compromised as improved accuracy is needed, merging ultimately into engineering. Sometimes new observations cause a need for greater complexity, sometimes the opposite occurs (witness the wavelength shift in 180-degree Compton scattering-- classically, it is a complicated function, but relativistically, it is always a fixed redshift!) The modern statement of Occam has debatable usefulness as a demonstrative device, but is easily misinterpreted as saying either that simpler theories tend to be right, or that competing theories are generally debated on the grounds of their simplicity, rather than on their success.
Very nice summary! No disagreement.I'm not as much into debate as you two master debaters, but I'm going to have to disagree here. I don't think simplicity is a defining goal of science. What would define science, but the scientific method? Where is the seeking of simplicity in that? From that point of view, science is about prediction, only.

George
2005-Dec-07, 02:59 PM
Well, I suppose it's better to be an oxyjunktive like "constrained freedom" than a corn-moron, like, well, me!
Yes. I await your bounded proof within this fruitful field. :)


I don't think simplicity is a defining goal of science. What would define science, but the scientific method? Where is the seeking of simplicity in that? From that point of view, science is about prediction, only.
True, but is predictability the only goal? I suspect the distinction is semantic. If you could reduce a very complex equation without compromise to integrity, would this not be of worth? Anything that adds value to science should also be considered a worthy goal.

Ken G
2005-Dec-07, 03:32 PM
I don't think simplicity is a defining goal of science. What would define science, but the scientific method? Where is the seeking of simplicity in that? From that point of view, science is about prediction, only.
Then why don't we just do what I call "google science:" simply store the result of every experiment and observation, and when you want to predict a new one, just interpolate between what's already been done. If you can't interpolate, then guess what, no other "theory" is guaranteed to work either. The point is, science is about more than prediction, it is about understanding, and understanding involves simplification and idealization.

hhEb09'1
2005-Dec-07, 04:06 PM
True, but is predictability the only goal? I suspect the distinction is semantic. If you could reduce a very complex equation without compromise to integrity, would this not be of worth? Anything that adds value to science should also be considered a worthy goal.The marketing guys will tell you that advertising adds value to anything. But it's not a component part of science. :)

Then why don't we just do what I call "google science:" simply store the result of every experiment and observation, and when you want to predict a new one, just interpolate between what's already been done. If you can't interpolate, then guess what, no other "theory" is guaranteed to work either.Science doesn't come with a guarantee. :)

All sorts of forward predictions are made, it's the nature of hypotheses, some of them very complicated. Science is all about the testing of those predictions. In some instances, even modifications to interpolated values can be considered an extension of the theory.
The point is, science is about more than prediction, it is about understanding, and understanding involves simplification and idealization.That's where we disagree. I would say, at that point, you're getting into philosophy. It's the area that Feynman was afraid of, if ever science were to reach a limit: arbitrary and un-testable intrepretation of the results of science, in the quest for understanding.

Ken G
2005-Dec-07, 04:49 PM
All sorts of forward predictions are made, it's the nature of hypotheses, some of them very complicated. Science is all about the testing of those predictions.

Yes, but I can make forward predictions with my google science, and they will be as accurate, or probably more accurate, than any other theory you can name. Yet it would be lousy science. Don't you agree?

hhEb09'1
2005-Dec-07, 05:44 PM
Yes, but I can make forward predictions with my google science, and they will be as accurate, or probably more accurate, than any other theory you can name. Yet it would be lousy science. Don't you agree?I don't agree that you can do that, all the time. Or even most of the time. At least, I don't agree yet, I guess I'm a little vague on what you are proposing. Give me some specifics and I'll bet I can come up with a counterexample. There are all sorts of deterministic results that are completely incapable of being determined by forward interpolation from previous results, especially inexact or imprecise ones.

Disinfo Agent
2005-Dec-07, 05:58 PM
It seems to me the issue of proof in science is a very tricky one. I've heard the claim that you can disprove a theory but not prove it, but this idea doesn't hold water for me, it has a slow leak like my pesky bicycle tire. Let us assume that all observations have been corroborated and are reliable, so we don't even have to get into the (important) issues of observational error or misinterpretation. Even so, a theory that works in every situation for which it has been observed has indeed been "proven" to work in those situations.A theory that only describes what has been observed in the past (assuming we can trust our memories and our records about what the past was) is useless in most sciences.

What scientists often want is to make inferences about future, as yet unobserved realities. But you can't know whether the theory fits the future before you get there.


If it fails in some new situation, or some new accuracy realm, there must be a reason why, so one would say the theory cannot be extended to that situation or to that accuracy. This does not make the theory false in the situations where it was previously tested, to the degree of accuracy to which it succeeded. It just shows you the theory's limits. Likewise, if a theory passes all tests to some accuracy level, we say it is useful in all those situations and to that accuracy, but we just don't know about other situations or other levels of accuracy. Is there really such a strong asymmetry between proof and disproof? I know this is often quoted, but I think what is really meant is, of all the current possible explanations for something, you can decide which is the most likely to be correct, or which works to the highest accuracy. You cannot guarantee that a new explanation might prove even more likely, or more accurate. So that's really the distinction between proof and disproof, it's more subtle than the "party line" in my opinion.Would you describe Ptolemy's astronomy of epicycles as "factual within certain levels of accuracy"?


Ok. So what do we call it? Proof lite? :)Karl Popper calls it "corroboration". I, personally, don't object to the use of the word "proof" in a loose sense in the natural sciences. We are too used to that term to do away with it. As long as we never forget that a theory that has the status of "proven"(-lite) today may well be disproven tomorrow.

Ken G
2005-Dec-07, 07:07 PM
I don't agree that you can do that, all the time. Or even most of the time. At least, I don't agree yet, I guess I'm a little vague on what you are proposing. Give me some specifics and I'll bet I can come up with a counterexample. There are all sorts of deterministic results that are completely incapable of being determined by forward interpolation from previous results, especially inexact or imprecise ones.
All right, let's take Kepler's laws (please). You can notice that P^2 = a^3, a very simple result, or you can simply plot all the P against a in our solar system. Now you can predict P(a) for any object in the solar system using your plot, without ever expressing an analytic form for the expression. If you go outside the domain of observations, just extrapolate smoothly. You might be wrong, but so might Kepler, in a domain it's never been tested. (And if it has been tested in that domain, just include that test in your plot, including tests that appear in other contexts like other solar systems or planetary satellites, where you will note the dependence on the central mass, etc.) I am arguing that any analytic expression is just a way of simplifying, it has no greater validity or predictive power than an empirical relation since if it has been tested it will be included empirically, and if it hasn't, it has no greater claim to validity than a smooth interpolation. But science goes farther than this, because it doesn't just want to make and test predictions, it strives to understand.

Ken G
2005-Dec-07, 07:10 PM
What scientists often want is to make inferences about future, as yet unobserved realities. But you can't know whether the theory fits the future before you get there.

That is just as true for simple theories as complex ones, I am missing your point.



Would you describe Ptolemy's astronomy of epicycles as "factual within certain levels of accuracy"?

Yes, but the levels of accuracy are pretty stretched for some of the orbits, like that of Venus. It's so far off it isn't much use except for saying where Venus will appear in the sky from Earth, and for that it's fairly good.

Disinfo Agent
2005-Dec-07, 07:22 PM
That is just as true for simple theories as complex ones, I am missing your point.And I am missing yours. What does the complexity of a theory have to do with the issue?


Yes, but the levels of accuracy are pretty stretched for some of the orbits, like that of Venus. It's so far off it isn't much use except for saying where Venus will appear in the sky from Earth, and for that it's fairly good.Just to confirm, you would say that Ptolemy's model is factual?!
I'm not asking whether you'd grant it can be a good enough approximation in some cases. I'm asking whether you'd call it 'a fact, a law', as Mugaliens did above.

hhEb09'1
2005-Dec-07, 07:28 PM
All right, let's take Kepler's laws (please). You can notice that P^2 = a^3, a very simple result, or you can simply plot all the P against a in our solar system. Now you can predict P(a) for any object in the solar system using your plot, without ever expressing an analytic form for the expression. If you go outside the domain of observations, just extrapolate smoothly. You might be wrong, but so might Kepler, in a domain it's never been tested. (And if it has been tested in that domain, just include that test in your plot, including tests that appear in other contexts like other solar systems or planetary satellites, where you will note the dependence on the central mass, etc.) I am arguing that any analytic expression is just a way of simplifying, it has no greater validity or predictive power than an empirical relation since if it has been tested it will be included empirically, and if it hasn't, it has no greater claim to validity than a smooth interpolation. But science goes farther than this, because it doesn't just want to make and test predictions, it strives to understand.But what you said was "Yes, but I can make forward predictions with my google science, and they will be as accurate, or probably more accurate, than any other theory you can name." What if the theory I name is "Newton's laws"? If we discount relativistic effects, say, wouldn't Newton's theory results be more accurate than anything produced by your google science? I don't see how google science could be "more accurate"--especially if we were to name "Einstein's theory" instead.

George
2005-Dec-07, 07:36 PM
The marketing guys will tell you that advertising adds value to anything. But it's not a component part of science. :)
Science doesn't come with a guarantee. :)
I'm not buying your argument. :) "A goal" implicitly expresses a desirable point. [Who would suggest a detremental goal, or at least without explanation as to why?] However, other goals can also coexist. If a goal of simplificiation can be reached for a particular description of the universe, the simplified version can be more effective than a very complex approach, even if the advantage of the simple version is only found in computational time and the ability to express it to others. Of course, I am only addressing those expressions which produce identical predictability. If the simpler has less predictability, it may still be favored if accuracy tolerances are not compromised. You don't need QM and GR for deer-riffle ballistics.

Besides, aren't scientists some of the best salespeople? :) [Ok, some are the worst. :)]

George
2005-Dec-07, 07:42 PM
Karl Popper calls it "corroboration". I, personally, don't object to the use of the word "proof" in a loose sense in the natural sciences. We are too used to that term to do away with it. As long as we never forget that a theory that has the status of "proven"(-lite) today may well be disproven tomorrow.
Nice statment, although I can't see "corroboration" being user friendly.:)

hhEb09'1
2005-Dec-07, 07:52 PM
I'm not buying your argument. :) But I'd guarantee it'd be worth every penny you paid for it

"A goal" implicitly expresses a desirable point. [Who would suggest a detremental goal, or at least without explanation as to why?] However, other goals can also coexist.Sure, like "Legibility". :) But again that doesn't make penmanship scientific. As the title of this thread, the Scientific Method is preeminent in science. I just don't see any mention of Occam's Razor in that. It may be pragmatic, but that's for the engineers.

If the simpler has less predictability, it may still be favored if accuracy tolerances are not compromised. You don't need QM and GR for deer-riffle ballistics. Now you're talking engineering, not science. :)

Besides, aren't scientists some of the best salespeople? :) [Ok, some are the worst. :)]Three words: SSC :)

George
2005-Dec-07, 08:28 PM
I'm not buying your argument.
But I'd guarantee it'd be worth every penny you paid for it.
Yes. In one sense, you always make good cents, probably marketable.;)




"A goal" implicitly expresses a desirable point. [Who would suggest a detremental goal, or at least without explanation as to why?] However, other goals can also coexist.
Sure, like "Legibility". But again that doesn't make penmanship scientific. As the title of this thread, the Scientific Method is preeminent in science. I just don't see any mention of Occam's Razor in that. It may be pragmatic, but that's for the engineers. [Wow, you have me in sales and engineering. I am...your scarry. :)]
However, "The Scientific Method" is the abridged, user-friendly title. Like Principia or Origin of the Species. The verbose version for TSM, incorporating Occam and other principles, is rather lengthy and obtuse. Since its full name violates a stated tenet (ie Occam's Razor), it's now extinct. [How's that for salesmanship? :)]




If the simpler has less predictability, it may still be favored if accuracy tolerances are not compromised. You don't need QM and GR for deer-riffle ballistics.
Now you're talking engineering, not science.
True, but from whence doth it come? We can only use what ya'll give us, and the simpler, the better. ;)




Besides, aren't scientists some of the best salespeople? [Ok, some are the worst. ]
Three words: SSC Ohhh, I don't know this one. However, I can dream up many variations to this, yet they are negative. At least you are using Ocaam literally. :)

dgruss23
2005-Dec-07, 08:36 PM
I'm not as much into debate as you two master debaters, but I'm going to have to disagree here. I don't think simplicity is a defining goal of science. What would define science, but the scientific method? Where is the seeking of simplicity in that? From that point of view, science is about prediction, only.

I agree that simplicity is not a defining goal of science. My argument in the debate has been that scientists base the viability of a model/theory upon how well its predictions hold up to the latest relevant empirical evidence. I don't consider simplicity relevant in any way at that stage.

However, I agree with KenG that in developing hypotheses, scientists generally won't propose something that is more complicated than seems necessary. But you're right, simplicity is not a defining goal of science. I'm not sure why I agreed with that. :think: I guess I was focused on the later comments in that passage about Occam's razor.

Ken G
2005-Dec-07, 08:50 PM
But what you said was "Yes, but I can make forward predictions with my google science, and they will be as accurate, or probably more accurate, than any other theory you can name." What if the theory I name is "Newton's laws"? If we discount relativistic effects, say, wouldn't Newton's theory results be more accurate than anything produced by your google science? I don't see how google science could be "more accurate"--especially if we were to name "Einstein's theory" instead.
It would be more accurate because "google science" would naturally merge Newton's laws of motions directly into special relativity. There would be no need to make the distinction, it's purely empirical, and highly accurate because it already incorporates every observation that's ever been made and recorded. Of course, if we really did science this way, there would be a lot more observations to fill in the spaces that we now fill analytically. But who's to say we won't find surprises while filling those gaps? That's essentially what relativity was. Still, this is not a user-friendly way to do science, and that's the problem-- science strives to be user-friendly, often at the expense of accuracy. Basic science more so than engineering sciences, which are closer to "google science" to begin with.

Ken G
2005-Dec-07, 08:56 PM
It seems to me the issue of whether or not simplicity is a "defining goal" depends on what indeed are the goals of science. So we should start there. I would say that the goals of science include, but are not limited to:
1) understanding our universe
2) making predictions at an accuracy level that are helpful in applications (including #1 as such an application)
3) using the above to generate beneficial technologies
I may have left something out, but to me each of these is so central to the reasons we do science that I would call them all "defining goals", where #3 would have a slightly different flavor as an engineering science rather than a basic science. Simplicity falls in #1, since let's face it, humans are no Einsteins (OK, one of them was-- but even he liked maximal simplicity to help him understand!). I brought up the "google science" idea to show that #2 is not the same as #1.

hhEb09'1
2005-Dec-07, 09:36 PM
There would be no need to make the distinction, it's purely empirical, and highly accurate because it already incorporates every observation that's ever been made and recorded.You still haven't specified what that interpolation is going to be. Given two endpoints, and no matter how many supporting points, how is interpolation between those points going to be more accurate than the application of the theories? I understand that there could be some surprises, that's what we all live for, but given the track record of the theory, and the track record of interpolation, how do you say the latter would be more accurate?
It seems to me the issue of whether or not simplicity is a "defining goal" depends on what indeed are the goals of science. So we should start there. I would say that the goals of science include, but are not limited to:
1) understanding our universe
2) making predictions at an accuracy level that are helpful in applications (including #1 as such an application)
3) using the above to generate beneficial technologiesMe, I would have placed #1 under philosophy, and #3 under engineering.

I may have left something out, but to me each of these is so central to the reasons we do science that I would call them all "defining goals",But that's different. Reasons for doing science are different than what is science. You left off "#4 money"--some scientists do do science for money, but that doesn't make the money part of science.

Disinfo Agent
2005-Dec-07, 09:45 PM
Quantum mechanics (http://www.bautforum.com/showthread.php?t=35006), although I don't know much about it, seems to be a case where theory preceded understanding. It's possible that it won't ever become a 'comprehensible' explanation of subatomic phenomena. But it works! Isn't that what makes it science?

'Shut up and calculate!' (http://www.physicstoday.org/vol-57/iss-5/p10.html)

Ken G
2005-Dec-07, 11:51 PM
You still haven't specified what that interpolation is going to be.

It makes no difference, choose any reasonably smooth interpolation, lets say a spline of some kind. The point is, you can't claim that an analytic theory is accurate except at the points it has been established, but the interpolation fits those points as well. If you assert that the analytic theory interpolates better than any other interpolation, you are making a nonscientific claim because it has not been tested in detail. We are happy to assume the interpolation of an analytic theory will work, and we do fine, but strictly speaking it should be completely filled in by observations, or inaccuracy is being tolerated. Fine, we can also tolerate inaccuracy, but the same holds for any smooth interpolation.


Given two endpoints, and no matter how many supporting points, how is interpolation between those points going to be more accurate than the application of the theories? I understand that there could be some surprises, that's what we all live for, but given the track record of the theory, and the track record of interpolation, how do you say the latter would be more accurate?

It could be more accurate because it will fit the datapoints that do exist more accurately than the analytic theory, which generally involves approximation. But I don't want to argue it's more accurate in general, only that it is never less accurate, to within observational uncertainty (which is more an issue of precision than accuracy).


Me, I would have placed #1 under philosophy, and #3 under engineering.But that's different. Reasons for doing science are different than what is science. You left off "#4 money"--some scientists do do science for money, but that doesn't make the money part of science.
Well, adding value to humanity is certainly a key goal of science, and it is natural that this should be accompanied by personal gain. It is the added value to humanity that counts as a goal, just as a goal is to gain understanding. But I see that you are distinguishing reasons for doing science from the definition of what science is. So we have the semantic question of how are "defining goals" of science different from the goals of actual scientists who practice it. I wouldn't care to make that distinction, but if that is central to your point, then we are just using words differently and are probably not actually disagreeing.

hhEb09'1
2005-Dec-09, 06:46 PM
It makes no difference, choose any reasonably smooth interpolation, lets say a spline of some kind. The point is, you can't claim that an analytic theory is accurate except at the points it has been established, but the interpolation fits those points as well. If you assert that the analytic theory interpolates better than any other interpolation, you are making a nonscientific claim because it has not been tested in detail.The only claim made was yours that the interpolation would do better than the analytic theory. I'm very dubious, in this case, even though you haven't given the specifics of the interpolation method.
It could be more accurate because it will fit the datapoints that do exist more accurately than the analytic theory, which generally involves approximation.Interpoloation is usually approximation, by definition :)

But I don't want to argue it's more accurate in general, only that it is never less accurate, to within observational uncertainty (which is more an issue of precision than accuracy).You'd claimed earlier that it would be more accurate, so I think that's progress, but never less accurate? That is a real strong claim--I don't think you have a prayer of supporting that contention. :)

Well, adding value to humanity is certainly a key goal of science, and it is natural that this should be accompanied by personal gain. It is the added value to humanity that counts as a goal, just as a goal is to gain understanding. But I see that you are distinguishing reasons for doing science from the definition of what science is. So we have the semantic question of how are "defining goals" of science different from the goals of actual scientists who practice it. I wouldn't care to make that distinction, but if that is central to your point, then we are just using words differently and are probably not actually disagreeing.I am actually disagreeing. :)

I would say, the personal goals of individual scientists (or even large groups) have absolutely nothing to do with the definition, or the defining goals, of science. Even the use of Occam's Razor.

Ken G
2005-Dec-09, 08:15 PM
You'd claimed earlier that it would be more accurate, so I think that's progress,

I presume you are referring to this:


Yes, but I can make forward predictions with my google science, and they will be as accurate, or probably more accurate, than any other theory you can name

I personally feel that "probably" is an important word in this sentence that should not have been overlooked by you, but it's a nitpick.

That is a real strong claim--I don't think you have a prayer of supporting that contention.
The motivation behind this claim is that an interpolation will automatically include all the physics that was present in the observations being interpolated, whereas any analytic theory that is applied will by necessity involve idealizations that most likely will be completely applicable to none of the observations. Theory is always a limitation to accuracy, but "google science" minimizes the inaccuracy to the greatest degree possible.
That does not make it good science, however, it just makes it predictive science. This is my entire point.


I would say, the personal goals of individual scientists (or even large groups) have absolutely nothing to do with the definition, or the defining goals, of science.
You might have a hard time explaining how "science", an inanimate entity, can have "goals" at all, if they are to be completely divorced from the goals of the individuals doing the science.

George
2005-Dec-10, 10:42 PM
Theory is always a limitation to accuracy, but "google science" minimizes the inaccuracy to the greatest degree possible.
I've been wanting to ask this question, though I am not confident it is closesly related to this discussion...

Wasn't it empirical radiation data that Planck was faced with when he dreamed up the quanta idea? Is this a fair example of "google science", or am I a website off?

Ken G
2005-Dec-10, 11:33 PM
The application of google science, as I intend the term, would mean that Planck would have no need to dream up the quanta idea, at least not to explain the radiation spectrum. The idea of quanta is a simpifying concept that is totally unnecessary for predicting the result of spectral observations (it is needed for the photoelectric effect, so that's where it would appear in "google science"). Google science can predict a thermal spectrum simply by interpolating on previous frequencies and temperatures that have been observed, no need for Planck or quanta. The point being, explanation is not a necessary part of prediction, which is precisely why good science is much more than prediction. Occam's razor makes both parts easier, but it is certainly of most irreplaceable value to the former.

George
2005-Dec-10, 11:46 PM
The application of google science, as I intend the term, would mean that Planck would have no need to dream up the quanta idea, at least not to explain the radiation spectrum. The idea of quanta is a simpifying concept that is totally unnecessary for predicting the result of spectral observations (it is needed for the photoelectric effect, so that's where it would appear in "google science"). Google science can predict a thermal spectrum simply by interpolating on previous frequencies and temperatures that have been observed, no need for Planck or quanta.
That is what I thought you meant, though I see my prior post was poorly written with this intent.




The point being, [I]explanation is not a necessary part of prediction, which is precisely why good science is much more than prediction. Occam's razor makes both parts easier, but it is certainly of most irreplaceable value to the former.Nice statement.

hhEb09'1
2005-Dec-12, 06:29 PM
I personally feel that "probably" is an important word in this sentence that should not have been overlooked by you, but it's a nitpick.I wasn't overlooking it, I was just disagreeing with more than it. Not just the probably more accurate, but the just as accurate too.

The motivation behind this claim is that an interpolation will automatically include all the physics that was present in the observations being interpolated, whereas any analytic theory that is applied will by necessity involve idealizations that most likely will be completely applicable to none of the observations. Theory is always a limitation to accuracy, but "google science" minimizes the inaccuracy to the greatest degree possible.
I understand, but interpolation itself involves limitations to accuracy, and -- in this field -- the analytic results have been worked out to high precision. So, I'm dubious.


You might have a hard time explaining how "science", an inanimate entity, can have "goals" at all, if they are to be completely divorced from the goals of the individuals doing the science.True, but I was just using that phrase because others had used it before me in this thread. Wasn't it from this post (http://www.bautforum.com/showthread.php?p=616443#post616443)?

I myself like Feynman's "definition" of science: "Science is the belief in the ignorance of experts."

Ken G
2005-Dec-12, 07:54 PM
I wasn't overlooking it

Actually, you were, when you said "You'd claimed earlier that it would be more accurate, so I think that's progress". How is that not overlooking that I said it would "probably" be more accurate? But as I said, this is a nitpick-- no point in arguing about the argument!


I understand, but interpolation itself involves limitations to accuracy, and -- in this field -- the analytic results have been worked out to high precision.
Of course, analytic results are essentially infinitely precise. The question is, are they accurate. And the only way to test that is to do an observation, not a calculation. But as soon as you do that, oops, it goes into the google science interpolation. So you see, you can never beat that.



True, but I was just using that phrase because others had used it before me in this thread.
Of course, there's nothing wrong with the phrase "goals of science"! My objection was manifestly to your interpretation of that phrase as being completely separable from the goals of humans. I maintain they are not separable, because you cannot separate off the goals of an inanimate entity.



I myself like Feynman's "definition" of science: "Science is the belief in the ignorance of experts."
Well you've hit my soft spot there-- I'd never disagree with anything Feynman said, he's as close to a hero as I get. That's beautiful, as usual. Of course, it makes it clear why Feynman was always getting himself in trouble...

George
2005-Dec-12, 11:39 PM
I myself like Feynman's "definition" of science (http://Feynman's "definition" of science): "Science is the belief in the ignorance of experts." Link fails for me, but it should be interesting to see. I finally found a cd covering one of his lost lectures, I think. It was a delight to hear him.

hhEb09'1
2005-Dec-13, 10:32 PM
Ohhh, I don't know this one. SSC: Superconducting Super Collider
Actually, you were, when you said "You'd claimed earlier that it would be more accurate, so I think that's progress". How is that not overlooking that I said it would "probably" be more accurate?But I was responding to your comment "But I don't want to argue it's more accurate in general." Maybe I'm misunderstanding the difference between "probably" and "in general"? They seem to connote about the same thing to me.
Of course, analytic results are essentially infinitely precise. The question is, are they accurate. And the only way to test that is to do an observation, not a calculation. But as soon as you do that, oops, it goes into the google science interpolation. So you see, you can never beat that.Not the way it works! :)

You make the prediction before the observation, and it is the prediction that is compared to the observation. You can't (even in google science) make the observation, and then claim "see, I was right" :)

Of course, there's nothing wrong with the phrase "goals of science"! My objection was manifestly to your interpretation of that phrase as being completely separable from the goals of humans. I maintain they are not separable, because you cannot separate off the goals of an inanimate entity.I did say "personal goals". By that I meant things like hunger, greed, lust, etc., all on the personal level.

Well you've hit my soft spot there-- I'd never disagree with anything Feynman said, he's as close to a hero as I get. That's beautiful, as usual. Of course, it makes it clear why Feynman was always getting himself in trouble...Me too :)
Link fails for me, but it should be interesting to see. I finally found a cd covering one of his lost lectures, I think. It was a delight to hear him.Argg! I screwed up. I didn't include the link. It was supposed to be to the article What is Science? (http://www.fotuva.org/feynman/what_is_science.html) on the Friends of Tuva website (fotuva.org), a lecture first presented to the National Science Teachers Association in 1966. It also appears on page 171 of the book The Pleasure of Finding Things Out. The sentence appears at the end of one of the last few paragraphs.

Ken G
2005-Dec-14, 04:32 AM
You can't (even in google science) make the observation, and then claim "see, I was right" :)

My point is that the laws of physics are really just interpolation schemes, because they cannot be extrapolated into parameter regimes where they have not been tested. The way you make a prediction in google science is by first gathering all relevant existing experimental data (that's the "google" part) and then interpolating directly on the data-- no theory serves as intermediary. That's going to be pretty darn accurate. Note that if analytic theories also work, they will represent low-order interpolations (ergo, the analytic part). If you need numerical solutions to differential equations, that is just one form of interpolation. It's an interpolation that follows the logic of the universe, it's true, but that comes at the expense of idealizations (such as neglecting or heuristically treating air resistance, etc.). Google science has no need for idealizations, just lots and lots of experimental data. So it would be done more like the way engineering is done, and note that engineers typically need more accuracy than scientific researchers.



I didn't include the link. It was supposed to be to the article What is Science? (http://www.fotuva.org/feynman/what_is_science.html) on the Friends of Tuva website (fotuva.org), a lecture first presented to the National Science Teachers Association in 1966. .
Always nice to have access to Feynman lectures, thanks for the link.

hhEb09'1
2005-Dec-14, 10:29 PM
My point is that the laws of physics are really just interpolation schemes, because they cannot be extrapolated into parameter regimes where they have not been tested.I'm not sure what is intended here. I think that they are often extrapolated. Do you mean, you don't think that they should be?

That's going to be pretty darn accurate.Can we try an example, maybe? :)

It's an interpolation that follows the logic of the universe, it's true, but that comes at the expense of idealizations (such as neglecting or heuristically treating air resistance, etc.).?? I've seen air resistance treated in the theory too.
Google science has no need for idealizations, just lots and lots of experimental data. So it would be done more like the way engineering is done, and note that engineers typically need more accuracy than scientific researchers.No, engineers just overbuild. :)

How can you have more accuracy than the Hughes-Drefer experiment, for instance?

Ken G
2005-Dec-15, 04:06 AM
I'm not sure what is intended here. I think that they are often extrapolated. Do you mean, you don't think that they should be?

I mean that any time they are extrapolated, they are not laws any more. Like Newton's "law of gravity". Extrapolate this to a neutron star, and it's no longer a law of nature.

hhEb09'1
2005-Dec-15, 11:51 AM
I mean that any time they are extrapolated, they are not laws any more. Like Newton's "law of gravity". Extrapolate this to a neutron star, and it's no longer a law of nature.It hasn't been a law of nature since about 1920 or so, though. On the other hand, the physics of a neutron star has been described--isn't that an extrapolation as well, since we have no actual measurements?

Ken G
2005-Dec-15, 12:05 PM
It hasn't been a law of nature since about 1920 or so, though. On the other hand, the physics of a neutron star has been described--isn't that an extrapolation as well, since we have no actual measurements?
Actually, the physics of the neutron star has not been described, only its gravity, and for that we do have measurements. Classic example, actually of the way science almost always works--observations come first. Granted, Chandrasekhar's theory of white dwarfs was developed before the observations of them, and was a shining example of prediction, but it united two principles that had been observed-- gravity and degeneracy. Google science could have done that too-- you just do a cross-interpolation between the pressure of degenerate electrons, which I presume had been experimentally verified by then, and the force of gravity, which had been observed in many different stellar settings. And saying that Newton's laws stopped being laws is rather misunderstanding what laws are-- they are always dependent on some kind of idealization of reality, and are never required to hold in all situations. But my real point is not about accuracy, that's very much a side issue we are debating and it's not worth our time because there really is no such thing as google science, because it's not very good science at all.

This is my point, science is much more than prediction. If prediction is viewed as interpolation, it is rather trivial since interpolation is fairly easy, one doesn't need a theory to do it, and if it is viewed as extrapolation, then science gives no confidence that it's correct-- historically, there have been some dramatic successes and some big surprises too. Prediction is just kind of the way you keep science honest, so you're not just deluding yourself that you are doing anything connected with nature. But what really elevates science is its ability to couple prediction with understanding, which is why Occam is a particularly essential part of science. I am surprised you would disagree with that and then provide the link to Feynman's lecture-- it is all about understanding things, in simplifying an unifying terms, and it never even uses the word "prediction" as I recall!

Ken G
2005-Dec-15, 12:13 PM
It hasn't been a law of nature since about 1920 or so, though. On the other hand, the physics of a neutron star has been described--isn't that an extrapolation as well, since we have no actual measurements?
Actually, the physics of the neutron star has not been described, only its gravity, and for that we do have measurements. Classic example, actually, of the way science almost always works--observations come first. It's true that Chandrasekhar's theory of white dwarfs was a shining example of prediction before white dwarfs were observed, but he just united gravity, which had been observed at the stellar scale, and degeneracy pressure of electrons, which had been experimentally verified by that point I would assume. Certainly it was an extrapolation of degeneracy pressure to stellar scales, and was hotly debated at the time by the top scientists (like Eddington). Also, saying that Newton's laws stopped being laws is rather misunderstanding what laws are-- they are always dependent on some kind of idealization of reality, and are never required to hold in all situations. But my real point is not about accuracy, that's very much a side issue we are debating and it's not worth our time because there really is no such thing as google science, because it's not very good science at all.

This is my point, science is much more than prediction. If prediction is viewed as interpolation, it is rather trivial since interpolation is fairly easy, one doesn't need a theory to do it, and if it is viewed as extrapolation, then science gives no confidence that it's correct-- historically, there have been some dramatic successes and some big surprises. Prediction is just kind of the way you keep science honest, so you're not just deluding yourself that you are doing anything connected with nature. But what really elevates science is its ability to couple prediction with understanding, which is why Occam is a particularly essential part of science. I am surprised you would disagree with that and then provide the link to Feynman's lecture on "What is Science"-- it is all about understanding things, and it never even uses the word "prediction" that I can remember! (Of course, he didn't mention Occam by name either, Feynman's not going to say anything that's already been covered!)

Maddad
2005-Dec-15, 09:38 PM
Even so, a theory that works in every situation for which it has been observed has indeed been "proven" to work in those situations.The difficulty is that your current set of observations may not incorporate all possible situations, even if you think that they do. This is why for 300 years we considered Newtonian physics to be proved. Along about the turn of the 20th Century we had come up with observations that did not work for Newton. Had at that point we instead made the claim that Newtonian physics was very strong because we had failed to disprove it, then we would have not needed to explain why we had been satisfied with an incorrect model of the universe.

hhEb09'1
2005-Dec-16, 10:33 PM
Google science could have done that too-- you just do a cross-interpolation between the pressure of degenerate electrons, which I presume had been experimentally verified by then, and the force of gravity, which had been observed in many different stellar settings.Could you give a few more details about how you envision google science working in this instance? I'd like to see how google science works.
And saying that Newton's laws stopped being laws is rather misunderstanding what laws are-- they are always dependent on some kind of idealization of reality, and are never required to hold in all situations.I don't think it is misleading--it is just a different perspective. Newton's laws have been superceded by other laws, which hold in the same regimes that Newton's do, plus other regimes. It'd be different if the "new" laws didn't encompass the same regimes, but they do. I'm not arguing that Newton's laws can't be applied--just against the charge that it's misleading.
This is my point, science is much more than prediction. If prediction is viewed as interpolation, it is rather trivial since interpolation is fairly easy, one doesn't need a theory to do it, and if it is viewed as extrapolation, then science gives no confidence that it's correct--I'll agree that science is more than prediction, but I don't think science ever requires absolute confidence. Is predicting that the sun will rise tomorrow an extrapolation? If you think not, why not?

But what really elevates science is its ability to couple prediction with understanding, which is why Occam is a particularly essential part of science.I disagree.
I am surprised you would disagree with that and then provide the link to Feynman's lecture-- it is all about understanding things, in simplifying an unifying terms, and it never even uses the word "prediction" as I recall!I'm not so sure. Where does he talk about simplifying?

Mostly, it seems to me, he talks about how the world is more complex than we think it is--hence that quote, that we are basically ignorant.

Ken G
2005-Dec-17, 05:47 AM
Could you give a few more details about how you envision google science working in this instance? I'd like to see how google science works.

Google science is a device to illustrate a point. The point is that prediction is only a small part of the goals of science. Why would you want to know how google science works? It doesn't work, there's no such thing. It's hypothetical. You have to imagine a huge bank of zillions of different observations categorized in every imaginable situation where a measurement is possible. Imagine a vast pan-universal society of countless trillions of scientists, all making observations and storing them in the google science network, if you like. All that matters is that at the end of the day, you'll have a far more powerful predictive tool than what we call science, and it will not be much science at all.


Newton's laws have been superceded by other laws, which hold in the same regimes that Newton's do, plus other regimes.

Indeed, until those laws are themselves superceded in other regimes. They're all laws, they all require idealizations, and they all break down somewhere. If one law is contained in another more generally correct one, it does not eliminate the first one, because the first one might be a whole lot easier to apply (this describes the vast majority of all physical theories).


I'll agree that science is more than prediction, but I don't think science ever requires absolute confidence.

Indeed, absolute confidence is impossible, and science is possible. So I think we are approaching agreement.


Is predicting that the sun will rise tomorrow an extrapolation? If you think not, why not?

That's not an extrapolation in the sense I mean, I'm talking about parameter regimes. Of course the most fundamental assumption of science is that if you do an experiment right, and recreate all its conditions entirely, you'll get the same result again, at least statistically. So you don't need to repeat what's been done except to confirm that the experiment was done right. Without that assumption, which holds up well in practice, science would be impossible. So no, I don't say it's an extrapolation that the Sun is predicted to rise. But then, we don't need science to make that prediction-- I'd call it unrefined experience.



I disagree.I'm not so sure. Where does he talk about simplifying?

A lot of the article is about simplifying perspectives. Unification of ideas, seeing the connections, that is a very important form of simplification. If you understand that trees use CO2 and soil to build themselves, in such a way that when you burn them they go back to CO2 and ash, this is a simplifying concept because it "boils down" a lot of the complex things trees to into a very simple life cycle. Obviously trees do a lot more than that, but science is about extracting these simple essences, like distilling alcohol to get to something really potent and powerful.



Mostly, it seems to me, he talks about how the world is more complex than we think it is--hence that quote, that we are basically ignorant.
I think you are missing the flavor of why Feynman doesn't trust experts. I don't think he sees them as oversimplifying reality, and that's why they are wrong. On the contrary, I think he sees experts as people who have categorized and stored a huge amount of detailed information, but who often miss the crucial truths in what the information is trying to tell you. That is certainly the flavor of Feynman's own approach to teaching, and his Dad's too. An expert knows that friction causes shoes to wear, Feynman wants to get behind the expertise and into the simple everyday explanation, which in many cases only seems simple once Feynman has figured it out for us!

Disinfo Agent
2005-Dec-17, 02:26 PM
My interpretation of Feyman's lecture was that science is not a neat, ready-made deductive system. You don't start from well defined terms and universal axioms, and then derive whatever you need from a chain of syllogisms. You build your own terms and "laws" as you struggle to understand/predict. I agree that this is a notion that schools often fail to convey, and it's a very important one. You wouldn't have people attacking evolution with the argument that "It's just a theory", if they understood this about science.

ZaphodBeeblebrox
2005-Dec-17, 02:38 PM
My interpretation of Feyman's lecture was that science is not a neat, ready-made deductive system. You don't start from well defined terms and universal axioms, and then derive whatever you need from a chain of syllogisms. You build your own terms and "laws" as you struggle to understand/predict. I agree that this is a notion that schools often fail to convey, and it's a very important one. You wouldn't have people attacking evolution with the argument that "It's just a theory", if they understood this about science.
Yeah, I Know ...

The Next Time, I Hear Someone, Say That ...

Well, Let's Just Say, It MIIGHT Make The Evening News!

:wall:

hhEb09'1
2005-Dec-19, 07:15 PM
Google science is a device to illustrate a point. The point is that prediction is only a small part of the goals of science. Why would you want to know how google science works? It doesn't work, there's no such thing. It's hypothetical.I understand that you used it to make a point--but in making that point you made the claim that it would be as accurate. That's where I disagreed, and asked for details, how it would work. I have a feeling that it couldn't work, but I have no real basis for that, since I have no details about how it would work.

They're all laws, they all require idealizations, and they all break down somewhere.I can see that we have not achieved the Theory of Everything, but where do the current laws break down, and in what sense? You don't mean, they give verifiably false results, right? Quantum mechanics, general relativity, both have been tested and re-tested. Which tests have they failed?

If one law is contained in another more generally correct one, it does not eliminate the first one, because the first one might be a whole lot easier to apply (this describes the vast majority of all physical theories).In the case of Newton's laws, it means that they are just an approximation to the other.

That's not an extrapolation in the sense I mean, I'm talking about parameter regimes.What is an interpolation, then?

I mean, what is the difference between interpolation and extrapolation, to you?

Of course the most fundamental assumption of science is that if you do an experiment right, and recreate all its conditions entirely, you'll get the same result again, at least statistically. So you don't need to repeat what's been done except to confirm that the experiment was done right. Without that assumption, which holds up well in practice, science would be impossible.Feynman has an interesting rant about that. I've been re-reading The Pleasure of Finding Things Out, because of the chapter What Is Science? that we've been discussing in a couple threads. He claims on p.214 that the directors of the National Accelerator Laboratory were possibly destroying the value of the experiments being done at the facility because they would not allow previous experiments to be repeated, because of the expense.

Ken G
2005-Dec-19, 08:14 PM
Quantum mechanics, general relativity, both have been tested and re-tested. Which tests have they failed?
It all depends on your accuracy criteria. Quantum mechanics works on isolated particles, for example. Our universe doesn't have any of those. Does this make the theory useless? No, it is still very useful, because the universe does provide us with countless examples of very nearly isolated systems. This is what I mean about idealizations, the core of science (also related to the concept of simplicity). General relativity suffers from the opposite problem-- it is a local theory, so has to be integrated to yield useful global solutions. This requires boundary conditions-- more idealizations. See what I mean? Science is all about replacing complex realities with far simpler subsystems, but this may still be done with high accuracy, the universe has been kind to us in that regard.



In the case of Newton's laws, it means that they are just an approximation to the other.

Every meaningful statement about reality is "just an approximation", including this one.



I mean, what is the difference between interpolation and extrapolation, to you?

An interpolation is when you have a physical system that you have measured at various points, and want to extend this to make predictions of points you have not measured that lie between the points you have measured. The accuracy is limited only by how densely you've measured the system. That would be the way to do google science. Extrapolations are when you want to apply your results to similar systems, especially if they are on different scales. You have to assume some scale invariance, but if the universe has granted you that, you can also use the google science approach to making such extrapolated predictions. More likely, the universe has not granted you unlimited scale invariance, and so your predictions will begin to break down, whether using google science or principles of physics.


He claims on p.214 that the directors of the National Accelerator Laboratory were possibly destroying the value of the experiments being done at the facility because they would not allow previous experiments to be repeated, because of the expense.
I presume he was commenting on the issue of making sure the experiments were done right, not the fundamental repeatability of physics. If the latter were to come under question, it would mean a Nobel prize for someone, but probably the last one!

hhEb09'1
2005-Dec-22, 07:49 PM
It all depends on your accuracy criteria. Quantum mechanics works on isolated particles, for example. Our universe doesn't have any of those. Does this make the theory useless? No, it is still very useful, because the universe does provide us with countless examples of very nearly isolated systems. This is what I mean about idealizations, the core of science (also related to the concept of simplicity). General relativity suffers from the opposite problem-- it is a local theory, so has to be integrated to yield useful global solutions. This requires boundary conditions-- more idealizations. See what I mean?I don't think I do see what you mean. When you said they break down, then, are you saying we just haven't learned to apply them correctly in full effect? But that would seem a "break down" on our part, rather than the theory.

Every meaningful statement about reality is "just an approximation", including this one.That's an absolute comment, whereas I was talking about the relative relationship--Newton's laws are everywhere an approximation to, and are subsumed by, Einstein's. Sure, in some areas, they are a better approximation than in others, but the statement that Einstein's are better in that they give better answers is true across the board.

An interpolation is when you have a physical system that you have measured at various points, and want to extend this to make predictions of points you have not measured that lie between the points you have measured.That's the sort of definition that I would have used. So I do not see what the two points are that make our inference about the sun rising tomorrow an interpolation. How is that not an extrapolation?

I presume he was commenting on the issue of making sure the experiments were done right, not the fundamental repeatability of physics. If the latter were to come under question, it would mean a Nobel prize for someone, but probably the last one!It was neither. The comment was about making sure that the future experiments were done right. As I see it, disagreeing with "So you don't need to repeat what's been done except to confirm that the experiment was done right."

Ken G
2005-Dec-23, 04:53 AM
I don't think I do see what you mean. When you said they break down, then, are you saying we just haven't learned to apply them correctly in full effect? But that would seem a "break down" on our part, rather than the theory.

The line gets blurred when a theory can only be carried out in principle, but not in practice. That is often the case in the absence of idealizations.


Newton's laws are everywhere an approximation to, and are subsumed by, Einstein's. Sure, in some areas, they are a better approximation than in others, but the statement that Einstein's are better in that they give better answers is true across the board.

Einstein's laws are not better "across the board", they are only minutely more accurate in normal (say, solar system) applications. If they were better, they would be used more often. However, it is usually Newton's laws that are used, because they are so much simpler yet suitably accurate. The laws that are used are the better laws in practice, this again is an application of Occam's razor.


So I do not see what the two points are that make our inference about the sun rising tomorrow an interpolation. How is that not an extrapolation?

It's not because we don't count "another day" as putting us outside the existing data if there are no parameters relating to tomorrow that are not included in the bounds of what has been observed. If we had to allow for experiments that differ by nothing but when they were carried out, then even google science would be impossibly difficult, and forget about normal science.


It was neither. The comment was about making sure that the future experiments were done right. As I see it, disagreeing with "So you don't need to repeat what's been done except to confirm that the experiment was done right."
Well I'm sorry, that still sounds like the same thing to me.

hhEb09'1
2005-Dec-23, 11:40 PM
The line gets blurred when a theory can only be carried out in principle, but not in practice. That is often the case in the absence of idealizations.Still, I would only say "the theory breaks down" if it returns false results that are only false because of the theory itself.

Einstein's laws are not better "across the board", they are only minutely more accurate in normal (say, solar system) applications.But that is what I meant by "better". They are more accurate across the board, then, would be another way of putting it.
If they were better, they would be used more often. However, it is usually Newton's laws that are used, because they are so much simpler yet suitably accurate. The laws that are used are the better laws in practice, this again is an application of Occam's razor.Pretty much why I say that Occam's razor is not a part of science. It is a function of utility, not actual science.

It's not because we don't count "another day" as putting us outside the existing data if there are no parameters relating to tomorrow that are not included in the bounds of what has been observed.What is interpolation then?
If we had to allow for experiments that differ by nothing but when they were carried out, then even google science would be impossibly difficult, and forget about normal science.Extrapolation is allowed, but you said google science was just interpolation.


Well I'm sorry, that still sounds like the same thing to me.The idea was expressed in the context of experimenters performing new tests to extend old tests--but they were not allowed to perform the old tests. Feynman's point was that if the new experimenters were not allowed to perform the old tests, it wasn't clear that their technique matched the old experiments. If it did not, they might draw conclusions that extended the old results, invalidly.

Ken G
2005-Dec-24, 02:23 AM
Still, I would only say "the theory breaks down" if it returns false results that are only false because of the theory itself.

But how do you define "false"? All theories always return false results at some level, this was my point about idealizations.


They are more accurate across the board, then, would be another way of putting it.Pretty much why I say that Occam's razor is not a part of science.
And so we've come to the very heart of the matter. You see, more accurate is not the functional definition of better. Just pick up any research journal and ask yourself how many papers apply the most accurate possible treatment of their subject. Answer: next to none, if you don't count idealized initial conditions. None, if you do. This is precisely the essential importance of Occam's razor, as it plays out every single day in science research. And even more so in science education, and science reporting.

hhEb09'1
2005-Dec-26, 12:54 PM
But how do you define "false"? All theories always return false results at some level, this was my point about idealizations.If that's all you mean by false results, or breaking down, then it doesn't mean anything, then. As you say, they all do it.

I would prefer to restrict it to the scientific test. If we test a theory, and it fails the test, then I would have said the theory returns false results, or breaks down. I don't think general relativity has failed any tests, so far.

And so we've come to the very heart of the matter. You see, more accurate is not the functional definition of better.I wasn't trying to make a functional definition of better. I was just pointing out that Newton's laws are completely subsumed by by Einstein's.
Just pick up any research journal and ask yourself how many papers apply the most accurate possible treatment of their subject. Answer: next to none, if you don't count idealized initial conditions. None, if you do.None if you do count idealized initial conditions?
This is precisely the essential importance of Occam's razor, as it plays out every single day in science research. And even more so in science education, and science reporting.That saves paper. :) But, as I said, economic or personal time considerations may come into play in each and every thing we do--but that does not make them scientific, or a part of science. Same for Occam's razor.

HenrikOlsen
2005-Dec-26, 02:10 PM
It sounds like the two of you actually agree on everything except the definition of "Better" and whether it's relevant at all :)

Ken G
2005-Dec-26, 03:38 PM
Yes, we both agree on a lot of things, the essential question is what is actually part of science, and what is just the way scientists do science. I think hhEb09'1 has a kind of Platonic ideal about science which is all about making unfalsified predictions, whereas I see it as a subjective endeavor done by humans for humans, where a theory is "false" when the tests applied to it fail the subjective accuracy target. It's all about utility, and this is the reason that Occam's razor is in the center of it all, not some extraneous bit included only because scientists want to save time and paper. It is also the reason that we still refer to them as "Newton's Laws" even though we all know they are formally incorrect, this does not phase us at all.

hhEb09'1
2005-Dec-27, 01:57 PM
It sounds like the two of you actually agree on everything except the definition of "Better" and whether it's relevant at all :)I disagree :)

"Better" is subjective. In the context I used it, and as I clarified, I meant that the results are always as or more accurate. Nobody disputes that, so we all agree on that point.

Yes, we both agree on a lot of things, the essential question is what is actually part of science, and what is just the way scientists do science. I think hhEb09'1 has a kind of Platonic ideal about science which is all about making unfalsified predictions, whereas I see it as a subjective endeavor done by humans for humans, where a theory is "false" when the tests applied to it fail the subjective accuracy target.Science is an attempt to rid ourselves of the subjective component. Our brains lie to us all the time, we cannot trust our own senses. Subjective endeavors cannot be scientific--or, in the case that it is recognized that we can never rid ourselves completely of subjectivity, to that extent we are not scientific.
It's all about utility, and this is the reason that Occam's razor is in the center of it all, not some extraneous bit included only because scientists want to save time and paper.Utility is completely subjective. Utility is in the realm of engineering, not science.
It is also the reason that we still refer to them as "Newton's Laws" even though we all know they are formally incorrect, this does not phase us at all.The universe works differently than Newton could ever have imagined. I'm sure it would have fazed him. :)

dgruss23
2005-Dec-27, 02:07 PM
Science is an attempt to rid ourselves of the subjective component. Our brains lie to us all the time, we cannot trust our own senses. Subjective endeavors cannot be scientific--or, in the case that it is recognized that we can never rid ourselves completely of subjectivity, to that extent we are not scientific.

This is an important point. And that is the core of my problem with Occam's razor. It is inherently subjective to make an attempt to decide which theory/hypothesis is "simpler" or has more "utility".

Ken G
2005-Dec-27, 05:05 PM
But it is very important to be clear on the subjective, as well as the objective, elements of science. Deconstructionists went too far when they suggested that science has no objective component, and I agree with hhEb09'1 that the objective part is kind of a goal we shoot for, but the deconstructionist view was a backlash against exactly this kind of oversimplified view of science that it is entirely objective, and any subjectivity is somehow a breakdown to be avoided. I can certainly see that anyone shooting for a fully objective view of reality would not favor the use of Occam's razor, it has no place there. But this is not, and never has been, what science is all about. Not only would it be impossible, it really wouldn't be any fun. Just look at the zeal with which we address this subjective dicussion! Science is by humans and for humans, as I said, and that part the deconstructionists had right. They just didn't really understand ("hard") science, and so their ideas fell short of being anything really helpful, in my view. Humans are limited by their perceptions and their intellect, and science if forged, by necessity, in our own image, more than in the unknown image of "reality". Yet, we have learned a lot about reality, the least of which is not that the very concept is useful (again, the utility angle). The very fact that science is possible at all is the deepest mystery I know, along with consciousness itself, and neither science or deconstructionism has much to add to the mystery at present. All I can think of is that science works because it is built to be simple, in the sense of being understandable, and as such it lies in the intersection between reality and our understanding of reality. How large that intersection really is is unknown, but it does seem to be pretty large indeed.

Ken G
2005-Dec-27, 05:09 PM
The universe works differently than Newton could ever have imagined. I'm sure it would have fazed him. :)
And with that statement you make my point as eloquently as I could have. (And thanks for the spelling correction!)

hhEb09'1
2005-Dec-28, 06:37 PM
But it is very important to be clear on the subjective, as well as the objective, elements of science.That's difficult to do--"subjective" means that it might be different for different people. I don't think that is what we mean by science. Occam's razor has that problem of subjectivity--I've seen arguments where one side rejects a proposition because of Occam's razor, and the other side rejects its opposite, for the same reason.
...I agree with hhEb09'1 that the objective part is kind of a goal we shoot for,...I would leave it at that. That's our goal, however much our subjective selves get involved.

...any subjectivity is somehow a breakdown to be avoided.I would just say that subjectivity is not totally avoidable, and go on. It's not a disaster.

Just look at the zeal with which we address this subjective dicussion!I like philosophy too! :)

PS: just happened upon this quote from Einstein (The Quotable Einstein, Calaprice, quoted in Life magazine Jan. 9, 1950)
The grand aim of all science is to cover the greatest number of empirical facts by logical deduction from the smallest number of hypotheses or axioms

Ken G
2005-Dec-28, 07:56 PM
And ask the next question of Einstein.. why is that the grand aim? The aim is merely the starting point of why we do science. Note further that Einstein's quote is what I would say is entirely the spirit and intent behind Occam's razor. It is also the opposite of "google science", which is just the reason I invented that hypothetical construct. I think Einstein's quote is positively dripping with subjectivity, even as it lays out an objective definition.

hhEb09'1
2005-Dec-28, 08:02 PM
I didn't mean to imply that I thought Einstein was right. or wrong. :)

Ken G
2005-Dec-28, 08:31 PM
As with Feynmann, I understand. It is helpful to get insights from the masters, no matter which way they fall!

hhEb09'1
2006-Jan-04, 05:27 AM
Here's another, from Einstein. Via the book Einstein Defiant (!) by Edmund Blair Bolles (p.27):
Man tries to make for himself in the fashion that suits him best a simplified and intelligible picture of the world.Still, Einstein made a lot of comments about the state of humanity. In the context of the quote, science could be a tool to be used to simplify our world, without contradiction.

Disinfo Agent
2006-Jan-04, 04:54 PM
Is the cosmological principle (http://www.bautforum.com/showthread.php?t=36529) an example of Occam's Razor applied to astronomy?

hhEb09'1
2006-Jan-04, 06:09 PM
Is the cosmological principle (http://www.bautforum.com/showthread.php?t=36529) an example of Occam's Razor applied to astronomy?Hard to tell. As I am fond of saying (http://www.bautforum.com/showthread.php?p=77170#post77170) (because it always makes people wince :) ), Occam's Razor is in the eye of the beholder. The principle reminds me of Hutton's credo in The Theory of the Earth: We find no vestige of a beginning, no prospect of an end.

dgruss23
2006-Jan-04, 07:08 PM
Hard to tell. As I am fond of saying (http://www.bautforum.com/showthread.php?p=77170#post77170) (because it always makes people wince :) ), Occam's Razor is in the eye of the beholder. The principle reminds me of Hutton's credo in The Theory of the Earth: We find no vestige of a beginning, no prospect of an end.

DA,

The Cosmological Principle is a postulate that is an important part of cosmological theory. The Cosm. Princ. is a construct for developing logical arguments - and to my knowledge there are no observations that provide a compelling reason to abandon the Cosm. Prin. However, the Cosm. Princ. could in theory be abandoned if observations indicated it was an invalid postulate to reason from.

Is it an example of Occam's Razor? I agree with Grapes.

Tensor
2006-Jan-04, 07:13 PM
Hard to tell. As I am fond of saying (http://www.bautforum.com/showthread.php?p=77170#post77170) (because it always makes people wince :) ), Occam's Razor is in the eye of the beholder.

No wince from here, I like it. ;)

Ken G
2006-Jan-04, 09:48 PM
Indeed this is why many modern theories admit to multiple pedagogies, i.e., multiple ways to say the same thing. In this sense, science has a subjective character, even a philosophical one, but there is only a problem when different predictions are made. Then we must test and discard the incorrect theory. The Cosmological Principle has no competitor, there is simply no other choice that would not be completely arbitrary given that the observations are consistent with the Cosmological Principle. So yes, it is certainly an example of the application of Occam's Razor, and in this case it is a slam dunk, no matter what reasonable eyes you behold it with.

hhEb09'1
2006-Jan-05, 06:38 PM
The Cosmological Principle has no competitor, there is simply no other choice that would not be completely arbitrary given that the observations are consistent with the Cosmological Principle. So yes, it is certainly an example of the application of Occam's Razor, and in this case it is a slam dunk, no matter what reasonable eyes you behold it with.But there are theoretical investigations that are done based upon disagreement with the cosmological principle. People devise tests of those theories, and attempt to detect the differences. Are they "doing science"?

Ken G
2006-Jan-05, 06:52 PM
Of course-- I did not say the cosmological principle has to be correct, I said that given that it is consistent with current observations, there is no competitor. If observations indicated otherwise, then the simplest theory consistent with those new observations would have to be devised. And I think it's fine if people want to devote their time and energy in anticipation of such observations, I'm just glad I'm not doing it because there's a pretty high probability in my estimation that they are wasting their time. I'm sure many said the same thing about a lot of great innovators.

hhEb09'1
2006-Jan-05, 07:15 PM
Of course-- I did not say the cosmological principle has to be correct, I said that given that it is consistent with current observations, there is no competitor. If observations indicated otherwise, then the simplest theory consistent with those new observations would have to be devised. Is the simplest theory that the laws of physics hold wherever we've observed, or is it that they hold everywhere? :)
And I think it's fine if people want to devote their time and energy in anticipation of such observations, I'm just glad I'm not doing it because there's a pretty high probability in my estimation that they are wasting their time. I'm sure many said the same thing about a lot of great innovators.I'm pretty sure it was about each and every one of them. :)

One of my favorites is the general relativity theory of Alfred North Whitehead, which had a preferred reference frame. It held its own against Einstein's way up into the seventies, and even then I would say its dismissal might be a little premature. Was Whitehead wasting his time? Was Will, who devised the test that decided against it?

dgruss23
2006-Jan-05, 07:34 PM
The Cosmological Principle has no competitor, there is simply no other choice that would not be completely arbitrary given that the observations are consistent with the Cosmological Principle. So yes, it is certainly an example of the application of Occam's Razor, and in this case it is a slam dunk, no matter what reasonable eyes you behold it with.

But the reason for using the cosmological principle as a reasoning tool is that it is a postulate that appears to be consistent with our observations of the universe not because it is simple. This is a good example of what I was talking about earlier in this discussion.

It could be proposed that the universe is inhomogeneous on large scales. Which postulate is simpler - a homogeneous universe or an inhomogeneous universe? That I think is a matter of debate. But does it matter? No - what matters is that our observations of the universe suggest a homogeneous and isotropic universe on large scales. Simplicity and Occam's razor are completely irrelevant in deciding whether to accept a homogeneous or an inhomogenous universe as a postulate.

Ken G
2006-Jan-06, 05:11 AM
Is the simplest theory that the laws of physics hold wherever we've observed, or is it that they hold everywhere?
The latter, of course. The former is not a theory, it is a result.



One of my favorites is the general relativity theory of Alfred North Whitehead, which had a preferred reference frame. It held its own against Einstein's way up into the seventies, and even then I would say its dismissal might be a little premature. Was Whitehead wasting his time?
No, not if he had a reasonable chance of being borne out by observations. In my opinion, anyone basing their research career on the possibility that the cosmological principle is substantially wrong does not have such a reasonable chance of ever being supported by observation, especially given our prospects of ever going to a significantly different part of space.

Ken G
2006-Jan-06, 05:20 AM
It could be proposed that the universe is inhomogeneous on large scales. Which postulate is simpler - a homogeneous universe or an inhomogeneous universe? That I think is a matter of debate. But does it matter? No - what matters is that our observations of the universe suggest a homogeneous and isotropic universe on large scales. Simplicity and Occam's razor are completely irrelevant in deciding whether to accept a homogeneous or an inhomogenous universe as a postulate.
This is a point I am not clear on as well, because Hawking seemed to feel that the Cosmological Principle assumes more than is in evidence, yet he is aware of the isotropy of the CMB. I don't know if he is talking about parts of the universe we cannot see, or if he is wondering if the universe could have conspired to appear homogeneous from our vantage point when in fact it is not. But still, whatever aspects of the Cosmological Principle have already been shown to be correct by observation, those aspects are no longer an assumed "postulate" but rather a demonstrated rule, and have no bearing on Occam's Razor, obviously. So I am talking about what Hawking views as unproven by observations, and I would certainly argue that those aspects can only be said to be consistent with current observations. Whatever aspects dgruss23 labels as a "postulate" must also be consistent with an inhomogeneous universe, and I do not see how anyone could argue that an inhomogeneous universe with all kinds of unspecifiable degrees of freedom is not less simple than a homogeneous universe with no unspecifiable degrees of freedom. I also do not see how any other principle other than Occam's Razor can favor the homogeneous postulate.

hhEb09'1
2006-Jan-06, 02:14 PM
The latter, of course. The former is not a theory, it is a result.By that, I didn't mean that the laws of physics hold in each observation, I meant that the laws of physics hold wherever we've been able to observe. That's not an observation, or result, per se.
No, not if he had a reasonable chance of being borne out by observations.His theory matched the big four tests of Einstein's theory, which is why it hung around for so long. Will's analysis claimed that Whitehead's would have a local anisotropy in gravity that would produce measureable tides on the Earth.
In my opinion, anyone basing their research career on the possibility that the cosmological principle is substantially wrong does not have such a reasonable chance of ever being supported by observation, especially given our prospects of ever going to a significantly different part of space.As with Whitehead's theory, we might not have to leave Earth to test it though.

HenrikOlsen
2006-Jan-06, 02:50 PM
One traditional way of getting a Nobel price is to take what respected scientists say is true and prove them wrong.
Science often advances when someone asks a what if, finds a place where the what if would give a different result than current theory, then shows that result to be the one that happens.
Where the woowoo's fail is in realising that the what if must not be in conflict with already observed data.

dgruss23
2006-Jan-06, 04:28 PM
This is a point I am not clear on as well, because Hawking seemed to feel that the Cosmological Principle assumes more than is in evidence, yet he is aware of the isotropy of the CMB. I don't know if he is talking about parts of the universe we cannot see, or if he is wondering if the universe could have conspired to appear homogeneous from our vantage point when in fact it is not.

The cosmological principle says that on large distance scales the universe is homogeneous and isotropic such that the Earth does not occupy a special location in the universe. On smaller scales the universe is not homogeneous - as seen by the observations of galaxy superclusters and voids. As we have extended our observations deeper into space, the cosmological principle seems to hold.


But still, whatever aspects of the Cosmological Principle have already been shown to be correct by observation, those aspects are no longer an assumed "postulate" but rather a demonstrated rule, and have no bearing on Occam's Razor, obviously.

Then the cosmological Principle becomes less relevant each passing decade because it becomes less and less a postulated assumption and more and more observational fact.


So I am talking about what Hawking views as unproven by observations, and I would certainly argue that those aspects can only be said to be consistent with current observations.

I'd say we're talking about scale and/or distance here. What is the minimum scale at which the universe may be said to be homogeneous? What is the minimum distance at which we can confirm a homogeneous appearance? Those would be the areas that would remain "unproven".


Whatever aspects dgruss23 labels as a "postulate" must also be consistent with an inhomogeneous universe, and I do not see how anyone could argue that an inhomogeneous universe with all kinds of unspecifiable degrees of freedom is not less simple than a homogeneous universe with no unspecifiable degrees of freedom. I also do not see how any other principle other than Occam's Razor can favor the homogeneous postulate.

The only principle that matters is consistency with observations. Occam's razor is irrelevant. If someone wants to formulate a hypothesis about the universe that suggests an inhomogeneous universe in a regime in which the matter is not yet resolved by observations, it is perfectly valid to do so. Why is it any simpler to argue that because the universe is homogeneous on scale X (large scales) it is also homogenous on scale Y? We know that on small scales (Z) the universe is not homogeneous? So it could just as easily be argued that since the universe is not homogeneous on scale Z it is not homogeneous on scale Y. I fail to see where simplicity has any relevance to such a hypothesis. As long as the hypothesis is not inconsistent with current observations and can be tested by future observations, it can be as simple or complex as needed.

Ken G
2006-Jan-06, 09:30 PM
By that, I didn't mean that the laws of physics hold in each observation, I meant that the laws of physics hold wherever we've been able to observe. That's not an observation, or result, per se.

I see what you mean, that we predict the laws will work and in fact they do. But there are a lot of laws that have not been tested on Saturn, and none of them have been tested in the Virgo cluster, except that there is no smoking gun that anything is different out there. So the simplest assumption is that nothing is different, and we'll hold that until proven otherwise. That's Occam's Razor in its full glory-- don't fix something that isn't broken.


As with Whitehead's theory, we might not have to leave Earth to test it though.
This theory of Whitehead sounds interesting, I've never heard of it. No doubt it is a good thing that he came up with it, but it would certainly disappoint him to realize that his theory will be nothing but a historical footnote. And most likely the same is true for deviations from the Cosmological Principle. Still, there is value in at least anticipating other possibilities, you never know, and even a historical footnote is better than complete anonymity!

Ken G
2006-Jan-06, 09:56 PM
As we have extended our observations deeper into space, the cosmological principle seems to hold.

Of course, but Hawking would be aware of this. Yet he still holds that the Cosmological Principle makes assumptions that are beyond what is in evidence.




Then the cosmological Principle becomes less relevant each passing decade because it becomes less and less a postulated assumption and more and more observational fact.

Yes, I agree this transition occurs and is occuring here, it would seem. Still, what I'm wondering is the extent to which Hawking sees the principle as being more than observational fact, and the use of the word "metaphysics" by others in the thread. What is the weakest Cosmological Principle that we actually need to do cosmology, and how much of it is unproven by the current observations?



I'd say we're talking about scale and/or distance here. What is the minimum scale at which the universe may be said to be homogeneous? What is the minimum distance at which we can confirm a homogeneous appearance? Those would be the areas that would remain "unproven".

Those are details, I think there must be much more that is unknown than questions of scale. Let's take one alternative, for example. What if our galaxy really was at the center of a finite distribution of mass that comprises everthing in the universe? Our measly 300 km/s of peculiar motion would not matter over 3 times 10^17 seconds, it's only 1/1000 of the speed of light, so we'd have only traveled 14 million LY, a pittance on galactic scales. So let's imagine the scale parameter of the universe was not globally constant, but varied according to a spherical pattern with us at the center. By symmetry we would still see an isotropic CMB, but the cosmological principle would be wrong. It would also be completely consistent with GR, and I'll bet we could get fairly arbitrary variations in the scale parameter to still agree with all observations with some tinkering. That would really require knowing what one was doing, so I can't claim to really see how it would work out, but my money says it's possible, especially given the fudge factors already in place. If necessary, one could also allow the laws of physics themselves to vary with location in the universe, to get the observations to work out. Why doesn't anyone bother to lay out such a theory? Well, perhaps they should just for the pedagogical value of seeing the alternatives, but it would not be a serious scientific theory because it holds unnecessary degrees of arbitrariness that are ruled out by Occam's Razor, not by observations.


The only principle that matters is consistency with observations. Occam's razor is irrelevant.

See my point above. I stronly suspect you could alter the laws of physics, including the speed of light if you want, and also the nature of the expansion of spacetime, as a function of location in the universe, put us at a symmetry center, and still recover all the observations. Why would you? The key point is that physics and cosmology are not unique descriptions, they are chosen descriptions. And when the choices are made, there's Occam, every time.


As long as the hypothesis is not inconsistent with current observations and can be tested by future observations, it can be as simple or complex as needed.
But the point is, we can take the current set of observations, and come up with a billion different theories that explain them all perfectly well. Why do we settle for just one? Because it is the irreducible intersection of all those billion possible theories. It is, the simplest. Why, I can give a prescription right now for generating these theories. I will say that the equations of special relativity should include an additional term, any term you like, which only disagrees with the current form by an amount which is currently below our observational accuracy. This is a testable prediction, and could someday be shown to be correct. But why would I bother to do this until the observations compel me? If my theory were simpler and could explain existing data, you better believe I would suggest it and collect my Nobel prize. Since it is more complex, it will win me no prize unless future data requires my complication. Science is not unique, but it chooses the simplest theory that works. Without this postulate, we would be completely crippled, because we'd have to wade through as many theories as there are theorists.

dgruss23
2006-Jan-08, 05:04 PM
Ok, KenG. I think I've lost sight of what we seemed to have agreed upon before - my apologies. I'll agree that at the stage of science at which a hypothesis is proposed, scientists either conciously or unconciously apply the original meaning of Occam's razor (not multipling entities needlessly). But at the stage of testing ideas and drawing conclusions about the validity of proposed ideas, Occam becomes irrelevant - observations rule. And new observations necessarily result in more complex models because our knowledge of nature becomes more detailed. So I don't think that we can describe Occam's razor as a defining goal of science. At best it is a tool used in one stage of science to help us achieve a more complete (and complex) understanding of the universe.

hhEb09'1
2006-Jan-08, 05:54 PM
I see what you mean, that we predict the laws will work and in fact they do.No, I don't think that is what I meant. I meant, the assumption that we assume the laws work in the areas where we've been able to make any measurement at all, versus the assumption that the laws work everywhere. Which is the simplest? It appears to me that the first is the simplest, but for some reason, the second is the most common, among scientists.
This theory of Whitehead sounds interesting, I've never heard of it. No doubt it is a good thing that he came up with it, but it would certainly disappoint him to realize that his theory will be nothing but a historical footnote. And most likely the same is true for deviations from the Cosmological Principle. Still, there is value in at least anticipating other possibilities, you never know, and even a historical footnote is better than complete anonymity!We don't know yet. Will's analysis (and I have talked to Will about this, personally, on the telephone) assumed that the anisotropy would be dominated by the galactic core. In other words, the tide would be oriented towards the constellation Sagittarius. However, the tidal term is proportional to mass/distance. Within our galaxy, the galactic core easily does dominate--but the Milky Way core effect could be completely dwarfed by the effects of mass outside the galaxy, like the Great Attractor.

An Occam's Razor approach would say, ignore Whitehead's theory, it is an unnecessary complication. But it has not been proven wrong yet. On the other hand, there are aspects of Whitehead's theory that make it extremely attractive--on the basis of Occam's Razor!

That's why Occam's Razor is not scientific. It is too arbitrary, and non-discerning.

I will say that the equations of special relativity should include an additional term, any term you like, which only disagrees with the current form by an amount which is currently below our observational accuracy. This is a testable prediction, and could someday be shown to be correct. But why would I bother to do this until the observations compel me?Why special relativity? The current form is general relativity, not special relativity.
If my theory were simpler and could explain existing data, you better believe I would suggest it and collect my Nobel prize.As I said, Whitehead's theory did explain the existing data, well into the seventies. That's over fifty years--but Einstein's was first.
Since it is more complex, it will win me no prize unless future data requires my complication. Science is not unique, but it chooses the simplest theory that works. Without this postulate, we would be completely crippled, because we'd have to wade through as many theories as there are theorists.Will established a system of parameters to distinguish between various theories of general relativity, to more easily test those theories. He did wade through those theories, and was not even partially crippled by the experience. :)

When it came to Whitehead's theory, it did not fit into this parametrization. He had to develop a special parameter, the Whitehead parameter. So, from that point of view, the Whitehead theory is more complicated than all the others--and yet, from another point of view, some people have said that a Whitehead theory is simplier than even Einstein's.

Ken G
2006-Jan-08, 09:47 PM
Ok, KenG. I think I've lost sight of what we seemed to have agreed upon before - my apologies.

We agreed that Occam is critical in the early stages of the development of a theory. It's how you choose one from a host of more complex possibilities that have extraneous and unnecessary elements. Happens all the time. The Cosmological Principle, which is what we are talking about, is an absolutely classic example of Occam's Razor, and like all examples of this principle, will be adhered to until observations dictate otherwise. So far the observations are perfectly in accord, so it continues to be maintained and solidified, as you say.


At best it is a tool used in one stage of science to help us achieve a more complete (and complex) understanding of the universe.
Precisely, and what could be more important than that.

Ken G
2006-Jan-08, 09:50 PM
No, I don't think that is what I meant. I meant, the assumption that we assume the laws work in the areas where we've been able to make any measurement at all, versus the assumption that the laws work everywhere. Which is the simplest?

The latter (edit) is the simplest, because it does not require new physics every time you make a new observation. How could that not be a simplifying principle?

hhEb09'1
2006-Jan-09, 04:29 PM
The latter (edit) is the simplest, because it does not require new physics every time you make a new observation. How could that not be a simplifying principle?I don't see why it would require new physics each time, so from that point of view, the former is the simplest.

That basic disagreement between two completely reasonable points of view makes Occam's Razor non-scientific. Worse, a commitment to applying Occam's Razor could lead us to the wrong conclusion, but I don't see anything wrong with saying it is as handy as say extra money, spare time, or an easily distracted advising professor. :)

Ken G
2006-Jan-09, 05:44 PM
Science itself is handy, and that is all it is.

hhEb09'1
2006-Jan-10, 05:15 PM
I found another interesting comment in Bolles's book (http://www.bautforum.com/showthread.php?p=643119#post643119), page 143 (I'm reading slowly :) ). The chapter is discussing Einstein's Noble lecture, which he gave a little late, in 1923, after his world victory tour celebrating Eddington's confirmation of his general theory of relativity. Bolles says Einstein presented his plans for the future, what he was to be working on.

He said he was going to be working on the unification of electromagnetism and gravity, but there was a problem with that--the contradictions between the two had been resolved (mostly by Einstein), so "We are restricted to the criterion of mathematical simplicity." A telling statement.

However, Bolles says, Einstein went on to say that "simplicity as a goal 'is not free from arbitrariness.'"

Ken G
2006-Jan-10, 05:43 PM
I agree there is arbitrariness in simplicity. There is a lot of arbitrariness in science itself. It is quite common for practicing scientists to use the same equations but have very different ways of understanding them. Even the equations can be superficially different, although they have to be mathematically equivalent. But I could write down all the equations of science and I wouldn't be doing science. The act of doing science is a very arbitrary act, and that's why there are always disagreements about how to model various phenomena. Most of the arbitrariness tends to converge in time (though pedagogical alternatives never go away), but the bottom line is, it does not bother me at all that a lynchpin of science should involve some degree of arbitrariness. I think this is in a nutshell our fundamental disagreement about what aspects should be viewed as the core of science, and what aspects are statements more about scientists. To me the two are not separable-- without scientists, without humans, and without arbitrariness, there simply is no science.

hhEb09'1
2006-Jan-10, 10:59 PM
To me the two are not separable-- without scientists, without humans, and without arbitrariness, there simply is no science.You can't be Sirius? serious :)

PS: when you talk about arbitrariness in science, do you mean like wave mechanics and matrix mechanics, which were shown to be two different treatments of the same thing, or do you mean like the unpredictability of the time and direction of radioactive emissions?

Ken G
2006-Jan-14, 10:52 AM
PS: when you talk about arbitrariness in science, do you mean like wave mechanics and matrix mechanics, which were shown to be two different treatments of the same thing, or do you mean like the unpredictability of the time and direction of radioactive emissions?
I meant more like the former. I'm imagining an intelligent species on another planet that has a different looking science, partly because they may use different definitions and different concepts that overlap or are at some level equivalent to ours, and partly because they will have filled in different pieces of the puzzle. They may have different priorities about what they need to understand, like an underwater species or one that can fly. Maybe they feel it is terribly important to be stationary and at the center of their universe and have constructed laws that allow that to be the case. It depends on how they may have applied Occam's razor compared to how we do it, among other things. The same question applies for science as for intelligent life-- how different could it be, or is there some principle of convergence at work?

hhEb09'1
2006-Jan-14, 08:33 PM
But we haven't chosen between wave mechanics and matrix mechanics--both are valid (and useful--although other equivalencies may not have the same status--like Feynman diagrams and the methods of the others who shared his Nobel). Scientifically, they are on equal footing--neither can be rejected scientifically.

That's pretty much why I do not consider Occam's Razor a scientific principle.

Disinfo Agent
2006-Jan-21, 09:04 PM
But you are overlooking an obvious point, and the main reason why all of these remain interesting, but for the time being, minority viewpoints. What do we actually know about gravity? That is comes from mass. So what is the simplest, obvious answer to the question "where does extra gravity come from?" How about "it comes from extra mass"? That answer has to be either verified, or falsified, before anyone can sensibly assume that the answer lies elsewhere. Why should anyone bother with extra dimensions when extra mass works just fine? If you are "stunned", I am equally "stunned" that such a simple, obvious thing as "extra mass" is decried as unreasonable with such ferocity. I will never understand where such misguided thinking comes from.

here (http://www.bautforum.com/showthread.php?p=660922#post660922)Occam's Razor at work?

mancur
2006-Jan-23, 07:01 AM
I always viewed Occam's Razor as a guideline and a rather good one. Does it need or claim to be a 'scientific principle'?

Consider, for example a complex geometric shape, circles and lines at specific angles, forming both a work of both art and mathematics, perfectly pressed into a field of wheat.

A crop circle.

You are first on the scene, and it's never been seen before. There is no evidence for who/what created it, yet there are two theories:

1. It was created by humans.
2. It was created by an extraterrestrial intelligence.

Now, considering we have no credible physical or scientific evidence that extraterrestrial's have ever visited Earth, which of the two theories is more likely?

Here's an amusing anecdote on the subject Crop Circle Discussion (14MB) (http://www.mysteryinvestigators.com/files/sunrise_crop_circles.wmv)

Ken G
2006-Jan-23, 11:07 AM
I definitely agree that Occam's razor is the best justification for the concept of dark matter, indeed the only justification. It says, if your current theory cannot explain an observation, add the minimally violent change to your theory that is permitted by current observations, unless a complete rethinking yields an even simpler explanation (which so far has not been provided, but might include MOND ideas). But I don't see how it relates to the explanation of crop circles, because there you are searching for the most likely explanation. No scientific principle can assert the most likely explanation, other than which theory has the most supporting evidence. This should be a separate "razor" of some kind, that states, the theory with the most corroborating evidence is the most likely explanation. Unfortunately, it is not always easy to know how to "measure" evidence. Still, in many cases it is perfectly obvious, as in the case of crop circles, where there is tons of evidence that humans both exist and have the motive, ability, and opportunity to perpetrate hoaxes, and no credible evidence that extraterrestrials meet any of those requirements.

dgruss23
2006-Jan-24, 02:03 PM
I definitely agree that Occam's razor is the best justification for the concept of dark matter, indeed the only justification.

There are numerous observations that suggest that the dynamical mass derived using Newton's laws exceeds the observed mass. Assuming the observations are not incorrect - which is well established at this point - there are several possible explanations:

1. There is unseen mass that explains the discrepancy - Dark matter.
2. Newton's laws of gravity must be altered in the regimes of observations that suggest dark matter - MOND.
3. Other forces provide significant contribution to extragalactic dynamics - Plasma cosmology.

Is simplicity really the only justification for adopting the first hypothesis over the others? DM has more free parameters than MOND - so if we're trying to avoid needless multiplying of entities, then MOND would seem to have an edge. Reality is that DM - CDM specifically - is in the minds of most astronomers the explanation most consistent with the current cosmological paradigm and observations.


But I don't see how it relates to the explanation of crop circles, because there you are searching for the most likely explanation. No scientific principle can assert the most likely explanation, other than which theory has the most supporting evidence. This should be a separate "razor" of some kind, that states, the theory with the most corroborating evidence is the most likely explanation.

That's what science is --> developing and working with explanations that have the most supporting evidence.

I've emphasized that throughout this discussion such as in post #65:



I think this illustrates the whole problem with too much emphasis on simplicity and Occam's razor. What it boils down to is that theories/models/whatever in science must be consistent with the data regardless of the complexity of the model. Their predictions must hold up to new observations. Simplicity is not a deciding factor. Consistency with observations is. Too much emphasis on Occam's razor distracts from a correct understanding the scientific process.

and post #42 to provide just two of the numerous times I've made the point:


Like Grant, I disagree with this. Simplicity is not the only aspect of utility that is applicable. The ability of a theory to make testable predictions is the more important part of its utility. That's been my point - perhaps not well explained on my part. In practice scientists are focusing on the testable predictions of a model/theory and the observationals results that put the hypothesis to the test rather than the beauty of its simplicity. Simplicity would seem to be more important in the formulation of a hypothesis rather than in the ultimate decision making as to whether a hypothesis should be kept or discarded in favor of another.



Unfortunately, it is not always easy to know how to "measure" evidence.

Which is why there is debate in science. MOND researchers think that the evidence more strongly supports their hypothesis and DM researchers think the same. If simplicity has a role here perhaps it is more personal than scientific in the form of "easier". It is simpler (easier) for "me the researcher" to stick with the CDM paradigm because I've been working with it for so long that I know everything that is known about the model at this time. MOND would require me to make some nasty changes to my understanding of the universe that I'm not ready to accept until I've thoroughly bludgeoned the CDM paradigm with every last possible test that has been or might someday be thought of.

I'm not in any way suggesting in the above that there is anything wrong with choosing one theory over another for such reasons. All viable scientific avenues should be pursued to their end by those researchers that have an interest in pursuing them. But certainly simplicity of the model itself is not nearly as important as the observational side when deciding whether or not to work with a particular model.

Ken G
2006-Jan-24, 03:15 PM
There are numerous observations that suggest that the dynamical mass derived using Newton's laws exceeds the observed mass. Assuming the observations are not incorrect - which is well established at this point - there are several possible explanations:

1. There is unseen mass that explains the discrepancy - Dark matter.
2. Newton's laws of gravity must be altered in the regimes of observations that suggest dark matter - MOND.
3. Other forces provide significant contribution to extragalactic dynamics - Plasma cosmology.
The point about Occam's razor is that there is actually a fourth possibility, which is that gravity may be able to derive from something other than matter (that would be very different from MOND, which says gravity comes from matter but obeys slightly different laws). Since when is the definition of matter "that which generates gravity"? It is purely an application of Occam's razor that we do not postulate gravity sources that are not matter, simply because we don't need to. Matter, as defined by a material substance that obeys the laws of matter, is the only thing we've ever observed to generate gravity. Thus, it is simplest to expect that gravity always comes from matter. Yet I can point at every CDM equation that dgruss23 refers to and say "but how do you know it's matter, and obeys the laws of matter?" The part of the theory that says the matter behaves like matter is the part that is unconstrained by observations at the moment, and even gives a few problems like structure formation. Perhaps the stuff is something else, and obeys different laws, which we now need to figure out. How far would I get with such an approach? Not very far, since it opens up great complexity and is so far not required by observation. Only when such an approach is required will it be viewed as fruitful, and that is entirely due to Occam (which is what I meant when I said the CDM theory is entirely due to Occam). So the very use of the word "matter" in CDM is, I argue, all about Occam. Otherwise, you have to call it CDATGG (cold dark anything that generates gravity).

hhEb09'1
2006-Jan-30, 05:32 AM
Perhaps the stuff is something else, and obeys different laws, which we now need to figure out. How far would I get with such an approach? Not very far, since it opens up great complexity and is so far not required by observation. Only when such an approach is required will it be viewed as fruitful, and that is entirely due to Occam (which is what I meant when I said the CDM theory is entirely due to Occam).But such an approach could suggest tests that might produce just such observations. Such an approach is allowed, and it's scientific. If, as you say, an application of Occam's Razor would rule against it, then that clearly makes Occam's Razor non-scientific.

Ken G
2006-Feb-01, 04:15 AM
But of course any approach of the type I mention makes predictions that can be tested. Take the cosmological constant-- anybody could have come along and made a theory where the cosmological constant exists and is of magnitude 0.000000000001. Such a theory is testable in principle, but not in practice. It is only values like 0.7 that are of any value in real science, so others are not included. Why not? Why is my 0.000000000001 value any worse than simply 0? Oh yeah-- "simply". The overarching point here is simply that by convention we do not complicate our theories unnecessarily (I call that Occam's Razor). This convention is crucial, it eliminates the Tower of Babel problem in science. That's all I'm saying, we do it almost automatically, because key goals of science are to understand and communicate, not just predict. That's where Occam comes in, over and over.

worzel
2006-Feb-01, 09:10 AM
The way I see it you both have a good point. Contrary to what some seem to think, only experimental backing can choice between two competing theories, not simplicity. But before we ever get to that stage we use Occam's razor when postulating. For every theory we have, there are infinite more complex ones that are, thus far, expeirmentally indistinguishable from the standard one (Zanket's theory (http://www.bautforum.com/showthread.php?t=20008) comes to mind here), but we already applied the razor and ruled them out before they hit the drawing board. And it would be significant if someone came up with a formulation of a current theory that matched exactly in prediction but was simpler by some measure (number of postulated entities, maybe).

hhEb09'1
2006-Feb-02, 06:15 PM
The way I see it you both have a good point. Contrary to what some seem to think, only experimental backing can choice between two competing theories, not simplicity. But before we ever get to that stage we use Occam's razor when postulating.I agree that Occam's Razor is often used, I use it myself in some fashion. But I also look to philosophy, art, religion, and music for inspiration. And nature. :)
For every theory we have, there are infinite more complex ones that are, thus far, expeirmentally indistinguishable from the standard one (Zanket's theory (http://www.bautforum.com/showthread.php?t=20008) comes to mind here), but we already applied the razor and ruled them out before they hit the drawing board. And it would be significant if someone came up with a formulation of a current theory that matched exactly in prediction but was simpler by some measure (number of postulated entities, maybe).There is no measure, unfortunately, although many have tried. Without one, Occam's Razor is not even quantifiable, so in that sense Occam's Razor is anti-scientific. A principle is not much good, as science, if you can reach two opposing conclusions with it.

worzel
2006-Feb-02, 07:34 PM
Well I'm not about to argue the point with you, and I take the point that there are many other non-scientific inspirations too. But I wonder, if competing theories are expressed in the same mathematical language (and trying to do that coud be the whole problem with this idea), could not some form of relative complexity be measured using information theory?

hhEb09'1
2006-Feb-02, 07:49 PM
Well I'm not about to argue the point with you, and I take the point that there are many other non-scientific inspirations too. But I wonder, if competing theories are expressed in the same mathematical language (and trying to do that coud be the whole problem with this idea), could not some form of relative complexity be measured using information theory?I think big advocate of that is Richard Gott, but I may have him confused with someone else. I don't think there's been any success--and I think there's been a lot of persuasive argument that it is impossible. What if you applied it to matrix mechanics and wave mechanics--which turn out to be identical? Any way of quantifying the difference (none) between those two surely amounts to just a proof that they are the same theory, but different people have different opinions on their relativie complexity. Like Feynman diagrams--which are easier to use--are the same as certain other formulations that are not even used at all, what then?

worzel
2006-Feb-02, 10:25 PM
Yeah I guess if two theories are identical then if one appears more complex it can be rearranged/simplified until it is the other, and it could be argued that the formerly more complex one had more redundancy and the information content was always identical anyway. And of course, if they're not identical then they're experimentally differentialable (i.e. scientifically differentialable), at least in principle anyway.

But what about two theories that are only identical predictionwise as far as we can measure thus far, but differ beyond that. Then rearrangement/simplification could show one to be the other but with some additional terms. Wouldn't we then chose the one without the additions until they can be experimentally distinguished? Is that not scientific in your opinion?

hhEb09'1
2006-Feb-03, 08:16 AM
But what about two theories that are only identical predictionwise as far as we can measure thus far, but differ beyond that. Then rearrangement/simplification could show one to be the other but with some additional terms. Wouldn't we then chose the one without the additions until they can be experimentally distinguished? Is that not scientific in your opinion?I wouldn't have a quibble with the choice, but if someone were to choose the other, I wouldn't quibble with that either, since it would not have been ruled out experimentally. So, I guess my answer to your question is that I consider both choices scientific--but Occam's Razor (according to the way you set up the example) would not. That's why I disagree with it.

worzel
2006-Feb-03, 09:02 AM
So to play devil's advocate for a moment, if I were to come up with an alternative to GR that had hunders of extra terms in all the equations, all derived (the extra terms that is) from astrological influences say, which modified the predictions to such a small extent that my modified theory agreed with experimentation just as well as the original, you would consider my modified theory as scientific as the original?

hhEb09'1
2006-Feb-03, 09:12 AM
So to play devil's advocate for a moment, if I were to come up with an alternative to GR that had hunders of extra terms in all the equations, all derived (the extra terms that is) from astrological influences say, which modified the predictions to such a small extent that my modified theory agreed with experimentation just as well as the original, you would consider my modified theory as scientific as the original?sure and you'd be welcome to it, while I and others heaped scorn and derision on your head :)

hhEb09'1
2006-Feb-03, 09:44 AM
The point is, there are a continuum of such examples and you have trundled out one of the more extreme and egregious ones. Everybody I know, including some astrologers, would object to it, but we have to be clear about why we are objecting to it.

A less extreme example would be one of the minor variants on general relativity that have cropped up over the past (almost) hundred years. Some did not differ from the predictions of general relativity, at the time they were proposed, but almost all of them now have been shown to be wrong. I still consider them to be scientific approaches, and worthy endeavors, but they are wrong--but it would not have been scientific to reject them on the basis of over complication alone. And most scientists didn't, though they might not have even been familiar with them.

Ken G
2006-Feb-04, 02:07 AM
Of course no theory is ever rejected by virtue of complexity, what they are is shelved, or simply not spent time on. Why not? Because it is obfuscating, rather than illuminating. Illumination, as opposed to obfuscation, is absolutely a central part of science, and is not at all like using any particular inspiration in your daily scientific work.

hhEb09'1
2006-Feb-05, 07:19 PM
Of course no theory is ever rejected by virtue of complexity, what they are is shelved, or simply not spent time on. Why not? Because it is obfuscating, rather than illuminating. But the examples I mentioned earlier, the variants on general relativity, were not shelved, and people did spend time on them (Einstein, for one). Personally, I consider the work fascinating and illuminating.

Had one of them turned out to be right, everybody else would think so too. :)

worzel
2006-Feb-05, 09:43 PM
And, presuming you don't, why would you find my astrological relativity not so fascinating or illuminating? Sure you could heap scorn and derision upon it from many angles, but if you were on a science funding board and were asked to give only scientific reasons for rejecting my grant to further it, would you really have no scientific objection to it?

Ken G
2006-Feb-06, 03:36 AM
But the examples I mentioned earlier, the variants on general relativity, were not shelved, and people did spend time on them (Einstein, for one). Personally, I consider the work fascinating and illuminating.

They were not shelved because they were simply different assumptions, making different predictions. This is not the same as an application of Occam's razor, as they were substantially different theories at the frontier of the current measurements, and certainly could have been right. They were not more complicated ways of making the same predictions as the current theory, nor were they complex theories that could only make different predictions at accuracy levels we have no hope of testing in the near future. Occam's razor says, of all the ways you could choose to explain the current data, to within your own desired accuracy target (I would add), choose the simplest as your current hypothesis. This includes models of all kinds (ever read a modeling paper?). Focus your attention on testing that simplest effective hypothesis. If people want to invest their energy anticipating the failure of the hypothesis, that's fine too, but at a lower priority. If they want to come up with complex theories that make no new predictions that are likely to be tested any time soon, give them the boot. That's what I would do if I were on a funding panel.

hhEb09'1
2006-Feb-06, 04:28 AM
if you were on a science funding board and were asked to give only scientific reasons for rejecting my grant to further ithey, hey, we're supposed to be talking real-world possibilities here! :)

Nereid
2006-Feb-07, 04:21 PM
Fascinating thread, long may it live! :clap: :)

A question to Ken G, and a comment (if I may), about 'google science' (post #133 (http://www.bautforum.com/showpost.php?p=625474&postcount=133) is as good an example as any): it seems that the interpolation would involve the use of some math, possibly quite spiffy math. The choice of which tools and techniques to use - any guiding principles?

The comment: how well this google science could work, in any real world, would surely depend upon the 'amount of science' it started with, which in turn introduces the inextricable intertwining of theory and observation (there is no such thing as a 'theory-free observation'). Dig a little bit, and you arrive at the mental models critters such as (many? most? all??) Homo sapiens individuals develop, via their successful interaction with their environment.

An example: atomic spectra. Assume your observations comprise only the Lyman-beta, Lyman-gamma, Lyman-delta, Brakett-alpha, Brackett-beta, and Brackett-gamma lines of the H spectrum. How would a google scientist interpolate to find Lyman-alpha, Brackett-delta, Brackett limit, the Balmer series, Rydberg atomic spectra (e.g. HeII), etc?

hhEb09'1
2006-Feb-07, 05:24 PM
My point was that grants, personal decisions, societal support, etc. are rarely made on the basis of something we could call science. I don't have a problem with that--in the same way that I don't have a problem with a dingo eating a baby, it's just the nature of the beast. If someone wants to spend time pursuing alternatives to general relativity, I think that is OK, it's a personal decision. But it's probably not as lucrative as other choices.

worzel
2006-Feb-07, 05:58 PM
I still feel uneasy with the idea that there is nothing scientific about chosing GR (pro tem) over some currently--and possibly foreseeably--experimentally indistinguishable variant with loads of extra terms. But maybe I'm just projecting the values of scientisits onto your strict definition of scientific.

Nereid
2006-Feb-08, 11:54 PM
Returning to Occam ... in 1900, David Hilbert delivered a lecture to the International Congress of Mathematicians (http://aleph0.clarku.edu/~djoyce/hilbert/problems.html), in which he outlined 23 mathematical problems, and introduced them (modestly) as follows:
The supply of problems in mathematics is inexhaustible, and as soon as one problem is solved numerous others come forth in its place. Permit me in the following, tentatively as it were, to mention particular definite problems, drawn from various branches of mathematics, from the discussion of which an advancement of science may be expected.A century later, almost all of these "problems"* have been solved.

One of the few that haven't is number 6: Mathematical treatment of the axioms of physics. In this section of his lecture, Hilbert concludes:
The physicist, as his theories develop, often finds himself forced by the results of his experiments to make new hypotheses, while he depends, with respect to the compatibility of the new hypotheses with the old axioms, solely upon these experiments or upon a certain physical intuition, a practice which in the rigorously logical building up of a theory is not admissible. The desired proof of the compatibility of all assumptions seems to me also of importance, because the effort to obtain such proof always forces us most effectually to an exact formulation of the axioms.This 'problem' is about as far from being 'solved' as it was in 1900 (perhaps further, given that GR and QFT are so incompatible, mathematically).

But might it provide a possible path to 'reducing' Occam to a branch of math (at least as far as physics is concerned, and so by extension astrophysics and cosmology)?

A post by hhEb09'1 hints at how this might come about:
[...] we haven't chosen between wave mechanics and matrix mechanics--both are valid (and useful--although other equivalencies may not have the same status--like Feynman diagrams and the methods of the others who shared his Nobel). Scientifically, they are on equal footing--neither can be rejected scientifically.Here we have two (or is it three?) approaches to the physics, which can be shown - mathematically - to be equivalent.

Do we need a successful ToE ("Theory of Everything") before we can begin to solve Hilbert's sixth problem? Or could we begin a programme into axiomatisation now (and let Occam take a well earned retirement)?

*not all are pure 'problems', some are more like programmes. There are only two others that remain 'unsolved' - number 8 ("Problems of prime numbers") and 16 ("Problem of the topology of algebraic curves and surfaces"), at least according to Yandell ("The Honors Clas (http://www.amazon.com/gp/product/1568812167/002-3736669-4481603?v=glance&n=283155)s")

Ken G
2006-Feb-09, 07:03 AM
I think what is missing from this perspective is the way science works in practice, which is also related to the weakness of a TOE. The problem with a TOE is that, although it would be neat to have, let's say we did get such a theory. I claim it would never actually be used in science, except in regard to papers about the TOE itself. The rest of science would just carry on unaffected by the existence of such a theory. No cold gets cured, no technology is advanced, no engineering is cheaper or more effective. Real scientists would still be out there solving real problems by first trying to understand some kind of system, and the first step toward understanding and analyzing and communicating about that system would be to represent it with some simpler construct that functions in an effectively similar way, to some desired level of accuracy. That approach is the true heart of science, and will always involve the application of Occam's razor, right from the outset. TOE or no.

Nereid
2006-Feb-09, 02:01 PM
I think you've opened another window of discussion, Ken G (or maybe two)! :clap:

A lot of physics is 'done' these days, as it has to varying extents for several centuries now, by theoreticians (I expect it's similar in other fields too; I'm not as familiar with them). Does their work constitute part of the 'doing' of science, 'in practice'? (There's a very nice sentence in one of Greene's books, about him sitting in the office next to Ed Witten, listening to the physics pouring out of his laptop ... or something like that, I can't find it in my copy just now!) If so, then the kinds of things which guide the day-to-day doing of science include tractability, elegance, and scope. Some re-writing of Occam would be needed to get it to encompass this, I feel.

Of course no one would try to 'do' an extension to economic portfolio theory by developing the equations of M-Theory (if some variant were to become a successful ToE) to apply to the actors in economics! However, the acceptance of quantum theory in physics lead to changes in the 'doing' of chemistry, and so on. Maybe all this means, in the Ken G view of Occam, is that the universe of choices is both more limited (as a chemist you wouldn't seriously entertain a new, or alternative, explanation or idea that was clearly inconsistent with quantum theory from the get-go, for example) and richer (quantum theory has so much subtlety, so many delightful surprises awaiting discovery, for example) than Occam and contemporaries could possibly have contemplated.

In another sense, we all know that the actual steps by which a scientist arrives at some new conclusion can be messy, silly, weird, and so on, (as well as logical, mechanical, etc) and not at all like the caricature still so widely portrayed in the popular press. In this regard, let's hear it for beer, sleep, jogging, stray words overheard at parties, walks in the woods (or on beaches), {insert your favourites here} :) Oh, and Occam too.

[Edit: the role of math in providing guidance for at least some scientists in at least some branches was introduced in this thread (http://www.bautforum.com/showthread.php?t=34519) by Tim Thompson; maybe time to revive it and continue that discussion?]

Ken G
2006-Feb-09, 04:00 PM
If so, then the kinds of things which guide the day-to-day doing of science include tractability, elegance, and scope. Some re-writing of Occam would be needed to get it to encompass this, I feel.

I agree, it's kind of the legacy of Einstein, that you can "do" physics with gedankenexperiments. Note that Aristotle got into all kinds of trouble doing that, and essentially none of his physics survives (although the bodies-as-spheres idea was pretty good). But we've gotten better at it, and I would agree that M-theory, etc., is physics, even if it desperately needs testing. When I refer to Occam, I am thinking about an evolved version that has kept up with the times, including elements such as elegance and fundamentality in the overall meaning of "simplicity". Of course what these words really should mean is debatable, but so is everything in science.


Maybe all this means, in the Ken G view of Occam, is that the universe of choices is both more limited (as a chemist you wouldn't seriously entertain a new, or alternative, explanation or idea that was clearly inconsistent with quantum theory from the get-go, for example) and richer (quantum theory has so much subtlety, so many delightful surprises awaiting discovery, for example) than Occam and contemporaries could possibly have contemplated.

Yes, that sums it up rather well I'd say. The key point is that our goal is to understand our reality. Given the limits of the human mind, this requires simplifications and idealizations. That is fundamental to science. It's amazing we get anywhere at all with this approach, but we do. Perhaps the thread Nereid mentions is well worth reviving with these kinds of questions in mind.

George
2006-Feb-11, 04:18 AM
Are ya'll summing up? Ya'll've made Occam a deligthful effervescense. :clap: [Yet, somehow I knew it wouldn't be all that simple.;)]

hhEb09'1
2006-Feb-11, 12:51 PM
When I refer to Occam, I am thinking about an evolved version that has kept up with the times, including elements such as elegance and fundamentality in the overall meaning of "simplicity".I would relegate those words to philosophy, not science. Not that there's anything wrong with that. I like elegance as much as the next nattering nabob.

The philosophy of Mach was extremely helpful, for instance.
Of course what these words really should mean is debatable, but so is everything in science.If a researcher gets a particular result, is it debatable whether or not they actually got that result? Like, they might be dreaming or something?
Given the limits of the human mind, this requires simplifications and idealizations. That is fundamental to science.I'm less convinced of the limitations of the human mind :)

Nereid
2006-Feb-11, 01:50 PM
Ken G, I just tried to send you a PM, about google science (I wanted to ask you to expand on this concept, per my post (http://www.bautforum.com/showpost.php?p=675338&postcount=210)), but it seems your mailbox is full. :sad:

Disinfo Agent
2006-Feb-22, 04:04 PM
Here's an interesting article (http://www.bautforum.com/showthread.php?p=681373) with some connection to the subject of this discussion.