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2002-Nov-27, 01:56 PM
I ran a search on board re:the Drake equation it didn't find anything.

So what is the boards take on:
the Drake equation?(You know there are perhaps mill-yons of technologically advanced civilizations populating planets? )With apologies to Dr. Sagan.

Granted Just because they may exist does not automatically imply they are abducting my crazy wisconsin aunt with the tin- foil headgear./phpBB/images/smiles/icon_biggrin.gif

As to why haven't they contacted us? We have only been broadcasting in the RF for what a little over 50 years or so?

And then Just, out of curiousity, What do you think is going on with cattle mutilations? What are we? A drive (fly?) thru restaurant? Complete and udder (sorry) Hoax? Thankyou Linda Howe-mouton!

ToSeek
2002-Nov-27, 03:02 PM
The closest discussion we've had is The Rare Earth Hypothesis (http://www.badastronomy.com/phpBB/viewtopic.php?topic=1256&forum=2), which I'm largely in agreement with. I think the universe is probably lousy with bacteria, but there are few places available where anything more sophisticated can evolve. In Drake Equation terms, I believe that Fi, the fraction of places with life that go on to develop intelligence, is very, very small.

However, I know John Kierein has some distinctive views on the topic, which I hope he'll share.

JS Princeton
2002-Nov-27, 04:54 PM
I am of the opinion that L (lifetime of communication) is surpressed from considerations of the Copernican principle. If you take the opinion that there is nothing special about us, then wherever you measure yourself to be should be somewhere in the middle of an epic. Richard Gott talks about this idea in his book Time Travel in Einstein's Universe. In it, he talks about his prediction that the Berlin Wall would fall. He took a trip to the Berlin Wall in the 60s and predicted that the Wall would stand for at least 3 more years and at most 130 more years (I can't recall the exact numbers, but you get the idea). All he did was take the amount of time that the wall had been standing and consider, well, I'm likely to be in no place special during the life of this wall, so I take a confidence interval on the age of the wall (assuming I was at either at the high end of the age or at the low end of the age) and I get a range estimate for the lifetime of the entire event.

So, let's take communication. We've only had interstellar communication for of order 100 years. If we are at the 95% confidence interval that means we are likely to have radio communication for at least roughly 5 more years, but roughly no more that 2000 more years. That means we can access effectively in our communication lifetime a range of 2000 light years, but if you want a round trip communication, you're going to get 1000 light years at most. That's not a lot of space to consider. For simple detection, you can take the fraction of 2000 years that is the age of the life-inhabitable universe (which, if you say we need heavy elements and appropriate ISM mixing, is roughly 10 billion years or so) and realize that it's a factor of 10^7 surpressed, which means that for any given civilization our rough chance for detecting them is on the order of 1 part in 10^7 or 0.00001%. This means that even if there is are 10^7 intelligent civilizations out there, our chances of detecting them are not very good. And that's a best case scenario for the 95% confidence interval.

Now, I've given you a decent estimate for the L value in the Drake Equation (which everybody has said is hardest to come by). Even liberal estimates of N=L for a lifetime that is 10^-7 surpressed will mean that detection is very difficult.

GrapesOfWrath
2002-Nov-27, 05:17 PM
Gott said that in a book?? Gees, you'd think he'd've learned by now. All he does is say that something that has existed for a while is not going to disappear immediately, and it's liable to be around for quite a while longer.

Just imagine all the people who visited the Berlin wall in the couple years prior to its demise. I guess they'd have to say, well, we must be in the lower twentieth?

Bottom line? Gott's analysis gives you nothing, except the age of the object--which you had in the first place. I can't understand why that's not obvious.

John Kierein
2002-Nov-27, 07:00 PM
look here
http://www.geocities.com/CapeCanaveral/Galaxy/7827/

JS Princeton
2002-Nov-28, 02:15 AM
Actually, Grapes, before you knee-jerk respond angrily to an idea, it's best to consider it carefully. Gott's idea is sort of mundanely profound (to coin a paradox) because it has got to be right if the Copernican Principle applies. Of course, the Copernican Principle doesn't always apply. You have to measure at a "non-special" time and place. That means making the confidence interval measurement of the length of a marriage at the time of a wedding is stupid because it is a special time. However, making a measurement of the length of time our civilization will be around is fine because there is probably nothing special about when we are making the measurement. Making the measurement after worldwide nuclear war had broken out would be stupid because then we're living at a special time.

It is a nuanced argument and certainly not iron clad (it is, after all, confidence intervals and subject to error), but it is just as reasonable as any other conjecture out there and does have some interesting things to say about where we are in the universe.

One argument he made, for example, is that humans will never colonize space in vast numbers (like in the trillions) just because if that were true it would be more likely for you to find yourself existing at a time when it were true as a space colonizer (if there were more of them in number) since there would be so many people there. That's not foolproof, you could be in a special time, but the confidence interval would still be good because the MAJORITY of people who ever lived would measure it to be correct, you just happened to not go along with the majority at that particular instance. It is also not surprising you are alive when the most people ever have inhabitted the globe because if you aren't special you expect to be found in a confidence interval where most of the people through time will be found.

It is a disconcerting argument, but it is not bunk. The people that made the measurement at the Berlin wall in, say 1986 would have been wrong, but that Gott never said it was a perfectly fool-proof method. For the majority of the wall's existence such a method accurately predicted the fall of the wall (if for nothing else because the error bars were so big on the estimate).

Basically the main idea is this: things that are old stick around longer than things that are new regardless of what the thing is. Sounds stupid, but it actually does give us some insight, I feel.

roidspop
2002-Nov-28, 03:05 AM
I encountered the concept of ultra-wideband communications not too long ago; I'll instantly admit that I have only a sketch of an idea about how it is supposed to work. But it seems that a signal is broken up into discrete bits and scattered over the spectrum to be reformed at the receiver.

The question I would pose JS et al is whether such a system would fox our attempts to detect an alien civilization which happened to use it exclusively (presuming such a thing is possible or desirable). We might see a lot of 'noise' across parts of the RF spectrum, but could we determine that a non-random signal was present?

JS Princeton
2002-Nov-28, 05:40 AM
Uncooperative aliens broadbanding their signal might very well be a problem, except no one ever said it would be easy to detect these things. In principle, if it's been decomposed we should be able to recompose it.

There is a lot in this question about intelligence: how do we define it and how do we know it when we see it. This is a tricky question. Pulsars were at first thought to be intelligence because they seemed to exact to be natural, but we think we've got those things pretty much figured out.

Now I'm just guessing, but I'd say barring some CONTACT-like discovery, it'll take some significant teasing to get out the fact that there is intelligence behind the signal, and even then it probably won't be conclusive.

xriso
2002-Nov-28, 07:06 AM
My view on the whole Drake eq thing: Life supporting planets are rare. Life will rarely arise on such a planet. Intelligent-life supporting planets are Really rare, and intelligent life will rarely arise from one of these planets.

Basically, I think there is exactly one civilisation we will encounter. Oh, hey, that's us!

xriso
2002-Nov-28, 07:15 AM
Oh, while we're on the subject of the predictions, here's a similar little thing (from some scifi book or another, I forget which): A strong indication that humanity has impending doom

Humans have been increasing in number at a seemingly exponential rate. Let X be the number of humans that have ever existed up to today. If this exponential trend continues, then after some time T there will be 999X more people that have been born. That means that given any human out of the total 1000X, only 1/1000 of them will have lived during our time or before. Therefore it is quite improbable that I should find myself during this portion of human history rather than later, when there are so many more people.

Unless, of course, humanity is extinguished sometime in the near future. Then it is not so unlikely that I would exist now rather than later. So, plugging in some numbers, it is highly probable that all humanity will die in a couple hundred years.

I think this idea is quite silly, and I have many reasons. What do you think? /phpBB/images/smiles/icon_smile.gif

<font size=-1>[ This Message was edited by: xriso on 2002-11-28 02:19 ]</font>

John Kierein
2002-Nov-28, 12:55 PM
The Drake equation is too pessimistic for intelligent life since it pre-supposes this life must be on planets around stars. The big black dust clouds of carbonaceous material are everywhere in all the galaxies, incuding ours, and these contain not just dust, but planet sized bodies.
Then there are these recent experiments:
http://www.space.com/scienceastronomy/survive_space_021126.html

GrapesOfWrath
2002-Nov-28, 04:09 PM
On 2002-11-27 21:15, JS Princeton wrote:
Actually, Grapes, before you knee-jerk respond angrily to an idea, it's best to consider it carefully.
O, I have. I wrote a response letter to a magazine when his idea appeared in it ten years ago. I'll dig it out when I get home.

Gott's idea is sort of mundanely profound (to coin a paradox) because it has got to be right if the Copernican Principle applies.
Right. You start with one piece of information, the age of the object, and the only way you add information is to make unfounded assumptions. You cannot possibly tell, from within the system, whether or not you are in a "special" time or not. That can only be judged after the fact. Ultimately, his analysis is pure speculation. Sorta like the Drake equation. /phpBB/images/smiles/icon_smile.gif

It is a disconcerting argument, but it is not bunk.
I think the only thing disconcerting about it is that anyone would take it seriously. It is fun to speculate, no doubt about it. And I like science fiction, so I enjoy things like the Drake equation analysis. But Gott's stuff is pure speculation also, couched in language that makes it seem that it is not just speculation.

John Kierein
2002-Nov-28, 05:01 PM
According to my wife, the salmonella on the T'day turkey will survive a gamma ray burst.

Argos
2002-Nov-28, 05:12 PM
JS Princeton wrote:

Richard Gott talks about this idea in his book Time Travel in Einstein's Universe. In it, he talks about his prediction that the Berlin Wall would fall. He took a trip to the Berlin Wall in the 60s and predicted that the Wall would stand for at least 3 more years and at most 130 more years (I can't recall the exact numbers, but you get the idea). All he did was take the amount of time that the wall had been standing and consider, well, I'm likely to be in no place special during the life of this wall, so I take a confidence interval on the age of the wall (assuming I was at either at the high end of the age or at the low end of the age) and I get a range estimate for the lifetime of the entire event.


JS, Gott’s words appear to be a philosophical exercise, only. What’s the empirical basis for those assertions? Has it been submitted to experimental confirmation? Does it explain the course of all - or at least the majority - historical events? It’s easy to see that it does not.

This phrase “I'm likely to be in no place special during the life of this wall” summarizes the problem. Why should one consider the point of view of a (single) person for extrapolating the results? And why not to use another standard (during the "life" of a mountain, for instance? Or during 3 orbits of Jupiter?). This - disturbingly - seems to be somehow related to the strong anthropic principle – taken to the ultimate consequences, in this case.

In my personal opinion technological civilization is communication. So, L has the value of the best estimate for the life span of a technological form of life. It can be very little (we ourselves are about to terminate), but, given some appropriate causal chain, a technological civilization may last for millions of years.


<font size=-1>[ This Message was edited by: Argos on 2002-11-29 05:51 ]</font>

xriso
2002-Nov-29, 05:49 AM
On 2002-11-28 07:55, John Kierein wrote:
The Drake equation is too pessimistic for intelligent life since it pre-supposes this life must be on planets around stars. The big black dust clouds of carbonaceous material are everywhere in all the galaxies, incuding ours, and these contain not just dust, but planet sized bodies.
Then there are these recent experiments:
http://www.space.com/scienceastronomy/survive_space_021126.html



Brr... must be cold out there.

GrapesOfWrath
2002-Nov-29, 03:41 PM
I'm not home yet, but I think I have a good counter-example to Gott's arguments. Let's look at atomic decay. Take two atoms of the same element, one twice as old as the other. Since atomic decay is entirely not dependent upon past history, we are not in a "special time" for either atom, so Gott's criteria is satisfied, but Gott's analysis sets different expectations for them--even though we know that the expectation for decay is identical for both.

In order to get any meaningful conclusion from the data, you need other information about the system, but Gott assumes you don't.

John Kierein
2002-Nov-29, 03:57 PM
On 2002-11-29 00:49, xriso wrote:


On 2002-11-28 07:55, John Kierein wrote:
The Drake equation is too pessimistic for intelligent life since it pre-supposes this life must be on planets around stars. The big black dust clouds of carbonaceous material are everywhere in all the galaxies, incuding ours, and these contain not just dust, but planet sized bodies.
Then there are these recent experiments:
http://www.space.com/scienceastronomy/survive_space_021126.html



Brr... must be cold out there.

But planet-sized bodies with moons like Europa could have hot volcanoes to warm you up from tidal heating. You have to be intelligent to get near the fire in competition with everybody else trying to get there.

VanBurenVandal
2002-Nov-29, 04:33 PM
It seems that filling the skies with radio waves is a rather messy way of communicating, especially over long distances. Let's say our little planet is actually very far behind in its development. If some other race was using a highly-focused communication, who says we'd ever hear them? Then SETI would only be able to detect signals between an alien invention of radio and a better invention. Then, there could be intelligent life relitivly close by, we just don't hear them.

JS Princeton
2002-Nov-30, 01:29 AM
On 2002-11-29 10:41, GrapesOfWrath wrote:
I'm not home yet, but I think I have a good counter-example to Gott's arguments. Let's look at atomic decay. Take two atoms of the same element, one twice as old as the other. Since atomic decay is entirely not dependent upon past history, we are not in a "special time" for either atom, so Gott's criteria is satisfied, but Gott's analysis sets different expectations for them--even though we know that the expectation for decay is identical for both.

In order to get any meaningful conclusion from the data, you need other information about the system, but Gott assumes you don't.


This is a good example for how knowing too much can harm you. It doesn't disprove the Copernican application of confidence intervals.

Say atom A and B have half-lives of 1 second. Say you are looking at atom A at 1 second into it's life and you say (without knowing anything about atom A other than it's been around for one second), I give it a confidence interval that this atom will be around for at least .1 more seconds but no more than 9 more seconds (for a 90% confidence interval).

Now you look at atom B which has been around for, say 1 year. You say, I give it a confidence interval that it will be around for at least 1 month more but not more than 9 years more. Of course, if atom B has a half-life of 1 second, you're apt to be proven wrong. BUT...

BUT...

Atom B happened to be a very special (and difficult to find) atom with a half-life of one second it would be very difficult to find one that was that old. Of course, the half-life is the same no matter how old the atom is, but in this case that atom is not representative of the general population. To that end, you have a special atom (one that you won't find 90% of the time as the confidence interval states). Therefore, the confidence interval is still valid because ON THE WHOLE, if you made this same estimate many times you would find it is exactly right (simply because most atoms you choose that aren't special will be around in a proper distribution to get you the right predictions).

If you know nothing about the decay process of atoms or even what the atoms are (or whether they are the same) then an atom that has been around longer is much more likely to stay around longer than the one that isn't around longer. That's because you expect that atoms on the whole that are older have longer half-lives.

It is a statement about generalized statistics only and has nothing to do with what kind of "events" take place. The concept is absolutely mundane to the point of being a non-issue, because even when proven wrong it is proven right (since these are only confidence intervals and most everything, we assume has a finite life, therefore at any given point in the lifetime of a thing the confidence interval for the lifetime of teh object will be correct unless you end up with something in the tails).

It is not a rigorous scientific theory: it's more of a game than anything else, a game that requires two things: absolutely having no a priori knowledge about what your measuring or mechanisms and an assumption that you are not at a special place in the measurement. If those two things are satisfied then the system works.

And it must work. It will work for all things that have a finite lifespan. Try it out. Take something that was around a long time and chose a random time to do the confidence interval test. It will tend to give you a larger confidence interval for the lifetime of the thing then something that is around for a short time. It absolutely must be the case for things that have a finite lifetime and are not special.

ljbrs
2002-Nov-30, 03:41 AM
This is a good example for how knowing too much can harm you. It doesn't disprove the Copernican application of confidence intervals.

Say atom A and B have half-lives of 1 second. Say you are looking at atom A at 1 second into it's life and you say (without knowing anything about atom A other than it's been around for one second), I give it a confidence interval that this atom will be around for at least .1 more seconds but no more than 9 more seconds (for a 90% confidence interval).

Now you look at atom B which has been around for, say 1 year. You say, I give it a confidence interval that it will be around for at least 1 month more but not more than 9 years more. Of course, if atom B has a half-life of 1 second, you're apt to be proven wrong. BUT...

BUT...

Atom B happened to be a very special (and difficult to find) atom with a half-life of one second it would be very difficult to find one that was that old. Of course, the half-life is the same no matter how old the atom is, but in this case that atom is not representative of the general population. To that end, you have a special atom (one that you won't find 90% of the time as the confidence interval states). Therefore, the confidence interval is still valid because ON THE WHOLE, if you made this same estimate many times you would find it is exactly right (simply because most atoms you choose that aren't special will be around in a proper distribution to get you the right predictions).

If you know nothing about the decay process of atoms or even what the atoms are (or whether they are the same) then an atom that has been around longer is much more likely to stay around longer than the one that isn't around longer. That's because you expect that atoms on the whole that are older have longer half-lives.

It is a statement about generalized statistics only and has nothing to do with what kind of "events" take place. The concept is absolutely mundane to the point of being a non-issue, because even when proven wrong it is proven right (since these are only confidence intervals and most everything, we assume has a finite life, therefore at any given point in the lifetime of a thing the confidence interval for the lifetime of teh object will be correct unless you end up with something in the tails).

It is not a rigorous scientific theory: it's more of a game than anything else, a game that requires two things: absolutely having no a priori knowledge about what your measuring or mechanisms and an assumption that you are not at a special place in the measurement. If those two things are satisfied then the system works.

And it must work. It will work for all things that have a finite lifespan. Try it out. Take something that was around a long time and chose a random time to do the confidence interval test. It will tend to give you a larger confidence interval for the lifetime of the thing then something that is around for a short time. It absolutely must be the case for things that have a finite lifetime and are not special.


WOW! WONDERFUL!

ljbrs /phpBB/images/smiles/icon_biggrin.gif

ljbrs
2002-Nov-30, 03:56 AM
On the topic of intelligent life: Earth has had intelligent life crawling around for a long, long time. However, it has only been during the recent centuries when humans have freed themselves long enough from ideas which prevented scientific development to create the methods for communication of any kind over vast distances.

Simply because we are unable to communicate with other intelligent civilizations in the Universe before they blast themselves to oblivion (as our civilizations are prone to do if given the chance), does not disprove the existence of such alien, otherworldly civilizations or intelligent beings.

There have been many intelligent beings here on Earth which have not been capable of such communication. However, many such intelligent civilizations existed.

It is a tremendously huge Universe (at least the portion of it that we can detect with our marvelous instruments). I hardly think that we humans constitute a special case above all other possible special cases. Whether or not we are able to detect anything at all is a problem created by the vast distances and the limitations of our instruments. Is our judgment of *intelligent beings* determined by scientific advancement only. Was William Shakespeare (or whoever wrote those beautiful plays) intelligent? Was Wolfgang Amadeus Mozart or Ludwig von Beethoven intelligent? After all, it was not so long ago that humans here on Earth were burned at the stake (Giordano Bruno, for example) for even suggesting that there might be intelligent beings elsewhere in the universe. Does scientific capability alone determine the intelligence or non-intelligence of civilizations?

ljbrs /phpBB/images/smiles/icon_wink.gif

2002-Nov-30, 07:33 PM
On 2002-11-28 02:15, xriso wrote:


Humans have been increasing in number at a seemingly exponential rate. Let X be the number of humans that have ever existed up to today. If this exponential trend continues, then after some time T there will be 999X more people that have been born. That means that given any human out of the total 1000X, only 1/1000 of them will have lived during our time or before. Therefore it is quite improbable that I should find myself during this portion of human history rather than later, when there are so many more people.

Unless, of course, humanity is extinguished sometime in the near future. Then it is not so unlikely that I would exist now rather than later. So, plugging in some numbers, it is highly probable that all humanity will die in a couple hundred years.



<font size=-1>[ This Message was edited by: xriso on 2002-11-28 02:19 ]</font>

I think I follow your math xriso, but this probability doesn't take into account human will and choice??

GrapesOfWrath
2002-Dec-01, 07:12 PM
On 2002-11-29 20:29, JS Princeton wrote:
This is a good example for how knowing too much can harm you. It doesn't disprove the Copernican application of confidence intervals..
Well, it shows how worthless they are.

Atom B happened to be a very special (and difficult to find) atom with a half-life of one second it would be very difficult to find one that was that old. Of course, the half-life is the same no matter how old the atom is, but in this case that atom is not representative of the general population. To that end, you have a special atom (one that you won't find 90% of the time as the confidence interval states). Therefore, the confidence interval is still valid because ON THE WHOLE, if you made this same estimate many times you would find it is exactly right (simply because most atoms you choose that aren't special will be around in a proper distribution to get you the right predictions).
I understand that, that was my entire point. Gott doesn't seem to understand that.

It is not a rigorous scientific theory: it's more of a game than anything else
That's what I said, it's pure speculation, with no ability to make any more conclusion than the life of whatever you're analyzing--but that's the input, so you get no new information from it--as you'd naturally expect. TNSTAAFL.

a game that requires two things: absolutely having no a priori knowledge about what your measuring or mechanisms and an assumption that you are not at a special place in the measurement. If those two things are satisfied then the system works.
But worthless.

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2002-12-01 14:14 ]</font>

Chip
2002-Dec-01, 09:13 PM
On 2002-11-29 22:56, ljbrs wrote:
"Does scientific capability alone determine the intelligence or non-intelligence of civilizations?"

Interesting question. As an analogy, take for example organized insect societies on earth, such as ants, bees, or wasps. Imagine an alien civilization (they need not look like earthly "insects") functioning sort of like an ants nest, plus "industry," tools, and "advanced" instrumentality, like radio or atomic energy. Their instruments developed from an entirely different set of needs than our reasons for developing technology. An organized society not only without human cultural characteristics, but without an equivalent of human cultural characteristics. Would we be able to communicate with them, and if so, what?

<font size=-1>[ This Message was edited by: Chip on 2002-12-01 16:15 ]</font>

JS Princeton
2002-Dec-02, 04:42 AM
Grapes --

Whether something is "worth" something or not is a complete value judgement. You are entitled to your opinion and I am entitled to mine. If you don't think that the Copernican principle can be applied because of some belief you have, then you are perfectly fine in keeping that belief. However, if it does apply then the analysis stands.

Furthermore, I wonder how you can criticize Rich Gott and say what he does or does not understand without reading his work... or maybe I missed that part.

GrapesOfWrath
2002-Dec-02, 12:40 PM
On 2002-12-01 23:42, JS Princeton wrote:
Whether something is "worth" something or not is a complete value judgement.
I said before that it is equivalent to speculation. But it is worthless logically. Your analysis of the atomic example is right on: sometimes the analysis is wrong. How often? About as often as you'd expect--given information that you don't have access to at the time you apply the argument. If you know the half-life of the two atoms before you apply the argument, you may as well ignore the argument anyway--the half-life info gives you more and better information about what may happen.

In other words, the information that you don't have is going to determine how often you are wrong, and how much you can trust your conclusions--which is pretty much all you can say about speculation, in general.

You are entitled to your opinion and I am entitled to mine. If you don't think that the Copernican principle can be applied because of some belief you have, then you are perfectly fine in keeping that belief. However, if it does apply then the analysis stands.
If it does apply? How the h*ck are you going to show that it applies? It seems to me that the whole argument assumes it applies, that is, the argument is speculation. And such speculation is wrong about as often as you'd expect--if you could analyze it after the fact, after you knew the answer. The problem is, you don't know the answer. In the atomic example I gave, you don't know the half life--if you did, you wouldn't need Gott's argument.

Furthermore, I wonder how you can criticize Rich Gott and say what he does or does not understand without reading his work... or maybe I missed that part.

Yep (http://www.badastronomy.com/phpBB/viewtopic.php?topic=3025&forum=2&24&start=11), although I haven't yet found the letter I wrote, or the issue of the magazine in which his argument appeared.

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2002-12-02 08:01 ]</font>

Argos
2002-Dec-02, 05:19 PM
On 2002-11-29 11:33, VanBurenVandal wrote:
It seems that filling the skies with radio waves is a rather messy way of communicating, especially over long distances. Let's say our little planet is actually very far behind in its development. If some other race was using a highly-focused communication, who says we'd ever hear them? Then SETI would only be able to detect signals between an alien invention of radio and a better invention. Then, there could be intelligent life relitivly close by, we just don't hear them.



I'm inclined to consider this. Indeed, when we talk about communications we refer to the modulation of the electro-maghnetic field. At least in theory there are manners of using the modulation of other fields/forces to communicate. Aliens might be modulating gravitational waves, for instance. In fact, if they really want to turn "public" they affairs, across long distances in space, GW would be the best medium.

JS Princeton
2002-Dec-02, 07:18 PM
Grapes==

You are right. The argument hinges on the Copernican Principle as an assumption. Thing is, sometimes that's all the information we have to go on. For example, in the lifetime of the species, we have no other information because there is simply only one data point.

Also, this argument will fail according to the confidence interval you choose. It will not be "wrong as often as it is right". It will always work as along as the Copernican Principle applies and the Copernican Principle has been shown to apply in the vast majority of measurements made.

GrapesOfWrath
2002-Dec-02, 07:37 PM
On 2002-12-02 14:18, JS Princeton wrote:
Also, this argument will fail according to the confidence interval you choose. It will not be "wrong as often as it is right". It will always work as along as the Copernican Principle applies and the Copernican Principle has been shown to apply in the vast majority of measurements made.

I'm not so sure of that. Weren't you saying that he'd applied it to the Berlin wall? If it's going to be applied in such mundane situations, there's going to be many many times when it doesn't apply at all.

In particular, it has not been shown to be applicable to the Drake equation. It's just assumed--but then you have an assumption which drives your conclusions.

traztx
2002-Dec-02, 09:51 PM
I think the drake equation is mental opium to sedate you from the other uncomfortable options of being alone in the universe or being surrounded but completely ignored.

Ilya
2002-Dec-02, 11:31 PM
It will work for all things that have a finite lifespan. Try it out. Take something that was around a long time and chose a random time to do the confidence interval test. It will tend to give you a larger confidence interval for the lifetime of the thing then something that is around for a short time. It absolutely must be the case for things that have a finite lifetime and are not special.


Well, how long have humans been around? If you are talking Homo Sapiens, about 30,000 years. If you are talking genus Homo, at least 2 million years. The problem with applying Gott's principle to evolving systems is that they do not have a definable beginning OR end, and thus a definable lifespan.

There once was an amphibian during early Paleozoic. It was a little like a salamander and a little like a lungfish. Amphibians just like it no longer exist - in fact, have been extinct for since before dinosaurs appeared. But this particular amphibian was the ancestor of a line which got stuck with too-dry climate and evolved rough water-holding skin. Thus it was an ancestor of all reptiles, and by extension of all birds and mammals that ever lived. So even though that paritucular amphibian genotype probably lasted about as long as "species" do on the average (4 million years), its line has survived far longer than that. And since WE are a part of that line, I could argue we've been around for 300 million years.

Same thing holds true for civilizations. Every human civilization lasted only a few hundred years on the average. But that does not mean that when civilization, be it Assyrian, Egyptian, Roman, whatever, ended, all of its individuals died. Instead, they became absorbed into, or gave rise to, another civilization. In fact, with few exceptions of deliberate (and even fewer successful) genocide, I can not think of any civilization which literally died. Someone always survives and propagates the line.

Every physical object, be it an atom, a mountain, or Berlin Wall has finite lifespan. But evolving entities such as species - or civilizations, - are potentially immortal. And curiously, if an entity has a potentially infinite lifespan, it is always at the very beginning of its life (i.e. a "special time"), no matter how old it is. Because any finite expired time span is infinitesimally smaller than infinity.

<font size=-1>[ This Message was edited by: Ilya on 2002-12-02 23:08 ]</font>

JS Princeton
2002-Dec-03, 06:01 AM
On 2002-12-02 14:37, GrapesOfWrath wrote:


On 2002-12-02 14:18, JS Princeton wrote:
Also, this argument will fail according to the confidence interval you choose. It will not be "wrong as often as it is right". It will always work as along as the Copernican Principle applies and the Copernican Principle has been shown to apply in the vast majority of measurements made.

I'm not so sure of that. Weren't you saying that he'd applied it to the Berlin wall? If it's going to be applied in such mundane situations, there's going to be many many times when it doesn't apply at all.

In particular, it has not been shown to be applicable to the Drake equation. It's just assumed--but then you have an assumption which drives your conclusions.


It absolutely applied to the Berlin Wall. All you have to do is say, give me a random point in time during the lifetime of the wall. Then do the test, you will find that within the confidence interval the Berlin Wall fell. That's just a natural result of the "nonspecialness" of the measurement and the fact that the wall had a finite lifetime.

There are two subtleties here. Do things have finite lifetimes? (hard to say when you can't see the future) and Are we at a special point in the lifetime of a particular thing? (also an assumption, but not a horrible one). If both are satisfied, then we have a go as we saw from the Berlin Wall problem.

Randomly choose a date during which the Berlin Wall was around. I mean random. Have a computer do it. Do the confidence interval test. Then do it for enough tests to get a histogram. You will find that the test gets the right answer exactly as often as you expect it should just because of the nature of the question.

We don't know what the factors are that are involved in the lifetime of a civilization. Some people might have some ideas, but saying you had none. If you agree that our civilization tain't special and the time we're living in tain't special then the confidence interval is perfectly reasonable as long as you think that the lifetime is finite.

This isn't that complicated. It's just a simple result of statistics really.

JS Princeton
2002-Dec-03, 08:09 AM
On 2002-12-02 18:31, Ilya wrote:
But evolving entities such as species - or civilizations, - are potentially immortal. And curiously, if an entity has a potentially infinite lifespan, it is always at the very beginning of its life (i.e. a "special time"), no matter how old it is. Because any finite expired time span is infinitesimally smaller than infinity.


Except, if the species should get more and more members then it would be highly unusual for us to find ourselves at a part of the history of the species where there weren't very many members. The Copernican Principle might also convince us that we are living at the height of human civilization simply because we aren't special. Now, there is a chance we ARE special and humanity will expand on into the stars, but chances are that if such a thing happened and trillions or quadrillions of our species would inhabit the stars you would have found yourself as one of those people and not one of the paltry 6 billion alive here on Earth today.

This is rather mindblowing stuff and not at all comfortable since it involves predictions of the future... but it also allows room for error (we always have the "tails" as a way out... and in fact if you are an optimist you would have to believe we are in the tail).

JS Princeton
2002-Dec-03, 08:20 AM
One more thing, Ilya, your comment about evolution does make things a bit more interesting. It could simply be that we are "special" since evolution is constantly changing the "we". For the purposes of any practical discussion you establish a date of initiation and work from there.

Now if you want to classify things like intelligence we have a hard time. Why? Because we have no other examples of intelligence "ending". This is rather uncomfortable: we don't know how intelligence behaves. However, we can see other attributes beginning and ending in various species. Take land-dwelling, for example. Some animals moved back into a sea establishing a "lifetime" that a given "line" will live on the land. With intelligence the argument might be made that we are special because we don't see anything else that is intelligent around. Fine. You can have that point. However, if we take it AT ITS SIMPLEST, assuming there will be a point where we as a species (or descendents of our species) won't be intelligent, then we have a finite lifespan. If we further decide that we aren't special then we can simply slapdab the confidence interval on an estimate with the confidence that we will be right for any given measurement as often as the confidence interval we set tells us. Of course there are two problems 1)we could also be wrong and 2)we don't have many opportunities to make this particular measurement so in principle you'll never be able to measure that I'm actually telling the truth. However, it simply must be the truth if the assumptions hold.

Circular logic? Of course! Then again, our entire existence is circular or at least chicken-and-the-egg-type. These answers may be fundamentally unanswerable but who said we couldn't grope around in the dark?

GrapesOfWrath
2002-Dec-03, 08:41 AM
On 2002-12-03 01:01, JS Princeton wrote:
It absolutely applied to the Berlin Wall.
Sure, once the lifetime of the Wall is known. That's how the statistics are computed. On the other hand, I didn't say it didn't apply to the wall--I said that it doesn't apply to radioactive decay. For an individual atom, the age of the atom gives you no information about when it will decay. Trying to use Gott's analysis to assign probabilities to when it will decay is bogus. Once you have a unique object, as opposed to a population of objects, the analysis is worthless. And we are unique, so far. /phpBB/images/smiles/icon_smile.gif

This isn't that complicated. It's just a simple result of statistics really.

Exactly.

JS Princeton
2002-Dec-03, 03:59 PM
Therein lies your beef, Grapes. Uniqueness. You are allowed to have a unique item as long as the assumption that that unique item is not special holds. This works just as well with decaying atomic nuclei. If we take a unique, non-special decaying atomic nuclei, the system will work. So this all depends on whether or not you think we're special or not for all the possible conformations of intelligent beasts in the universe.

GrapesOfWrath
2002-Dec-03, 04:13 PM
On 2002-12-03 10:59, JS Princeton wrote:
If we take a unique, non-special decaying atomic nuclei, the system will work.
I'm not sure that uniqueness is my beef. I think my beef is another "u" word, utility.

What do you mean by "unique, non-special decaying atomic nuclei". Can you give me an example?

JS Princeton
2002-Dec-03, 09:23 PM
"Unique" is a synonym for singular or exactly one. In other words, I'm simply referring to a particular atom rather than a generalized atom, an abstract atom, or an atom that we say is likely from statistics of atoms. By specifying unique I am demanding that the dice be cast and the measurement be taken. It's like in quantum mechanics where measurements give you back one of the eigenstates although before the measurement is made the quantum particle exists in a superposition of states. A unique measurement will give you only ONE state. I am measuring ONE atom.

As for utility, the whole endeavor itself is suspect. Is there any hope whatsoever to gain any utility from a discussion of when those aliens are going to show up? I'd say you could make a pretty good argument for either side. It's not the confidence interval method, though, that is the problem; it's simply the situation itself.

GrapesOfWrath
2002-Dec-04, 11:20 AM
OK, now what is a "non-special" decaying atomic nuclei? I think I understand the last three terms, but non-special seems to be at the crux of this.


On 2002-12-03 16:23, JS Princeton wrote:
As for utility, the whole endeavor itself is suspect. Is there any hope whatsoever to gain any utility from a discussion of when those aliens are going to show up? I'd say you could make a pretty good argument for either side. It's not the confidence interval method, though, that is the problem; it's simply the situation itself.

Gott gives lots more credance to the method, though, and that's what I think is the problem.

JS Princeton
2002-Dec-04, 03:51 PM
Non-special just means that it was chosen at random. How do we know an atom was chosen at random? Well, if we choose an atom blindly, we have basically simulated choosing an atom at random because there was nothing special about this choice. This doesn't mean we don't end up with an atom that isn't in the tails, but setting ourselves up so that we get an atom that is special isn't fair.

How would one choose a non-special atom? Well, let's take a box of atoms with a half-life of a second and let them sit for a year. Then open the box and choose an atom that's left. Ah ha! You've chosen a special atom because all the atoms that are left in the box have been selected in such a way that their lifetimes are long. This isn't a fair way to choose because you've polluted your sample with artificially inflating the lifetime of teh atoms. You would measure the confidence interval to be very long and find that it didn't work for most of these atoms because their half-lives are so short... or, more mundanely, because you chose special atoms instead of non-special atoms.

I'm going to go to Gott's office hours today to ask him about this conversation, Grapes. Do you have anything you'd like for me to ask him?

Zathras
2002-Dec-04, 04:22 PM
The problem with this analysis is that we do not know the underlying rules that govern the behavior.

The most important assumtption is that, in order for your rule to hold, the behavior of the phenomenon investigated must be stochastic, i.e. not depend on what has happened before. The atomic decay example is stochastic because the half life of the atom in question will be unchanged, no matter how much time has gone by. To take a non-stochastic example, look at a person's life expectency. The number of years a person can expect to live after age 20 is more than the number of years a person can expect to live after age 80.

It turns out that Communism had the same problem. The USSR was able to sustain itself immediately after World War II, but the bureaucracy also experienced a similar "aging" process, so that the USSR that was able to sustain its power in 1956, 1968, and 1980 was not able to do so in 1989.

With regard to ability to make radio contact with aliens, we do not know the rules that govern its life expectency. The prosperousness that has accompanied the digital age might prove to be self-sustaining, so that it would be virtually impossible for this off once it is established. This could be seen by the rise of technology which is parallel to ability to make communication both to discover endless energy and to remove the necessity of conflict.

Alternatively, it could be ultimately self-defeating, so that the "communication age" will ultimately cause its own destruction. This is what many people believed a couple of decades ago, a "Cold War scenario," where there is a certain inevitability to the destruction of, if not the human race, at least the ability for radio communication.

Finally, it could be neither be self-sustaining nor self-destructing, so that only a freak event could cause it to cease.

Of these three scenarios, only the last is even approximately stochastic. The other two are definitely nonstochastic, as the buildup toward either sustainability or destruction necessarily relies on what has occurred before.

Which one is true? I have no idea, but one thing it certainly depends on is the psychology of the species. Just because we may be in the first category does not mean that alien species might not be in the self-destructive category, or vice versa. The Drake Equation glosses this issue over, but it is unavoidable in this calculation.

<font size=-1>[ This Message was edited by: Zathras on 2002-12-04 11:25 ]</font>

GrapesOfWrath
2002-Dec-04, 04:28 PM
On 2002-12-04 10:51, JS Princeton wrote:
How would one choose a non-special atom? Well, let's take a box of atoms with a half-life of a second and let them sit for a year. Then open the box and choose an atom that's left. Ah ha! You've chosen a special atom because all the atoms that are left in the box have been selected in such a way that their lifetimes are long. This isn't a fair way to choose
What if you took a box big enough to include the entire Earth? Then every atom we can get our hands on is "special", right?

You should see, then, that every single choice of atom is going to be such that Gott's analysis does not apply, right? That's pretty much what I said earlier.


I'm going to go to Gott's office hours today to ask him about this conversation, Grapes. Do you have anything you'd like for me to ask him?

Tell him R. M. Mentock sent you. He'll have no idea who you're talking about.

ToSeek
2002-Dec-04, 04:40 PM
On 2002-12-03 03:09, JS Princeton wrote:

Except, if the species should get more and more members then it would be highly unusual for us to find ourselves at a part of the history of the species where there weren't very many members. The Copernican Principle might also convince us that we are living at the height of human civilization simply because we aren't special. Now, there is a chance we ARE special and humanity will expand on into the stars, but chances are that if such a thing happened and trillions or quadrillions of our species would inhabit the stars you would have found yourself as one of those people and not one of the paltry 6 billion alive here on Earth today.


On the other hand, if any civilization expands to the stars there's still a time when it's Earth-bound and all those alive then can make the argument you're making. I just don't see drawing conclusions from this argument with much confidence (which, of course, the very broad confidence intervals suggest).

AgoraBasta
2002-Dec-04, 05:03 PM
Expecting advanced alien civilizations to communicate by radio is kinda like the SF writers in the 1950's were expecting the future advanced computers to use vacuum tubes... Gibberish.

ToSeek
2002-Dec-04, 05:30 PM
On 2002-12-04 12:03, AgoraBasta wrote:
Expecting advanced alien civilizations to communicate by radio is kinda like the SF writers in the 1950's were expecting the future advanced computers to use vacuum tubes... Gibberish.


I think most of them figured that something better than vacuum tubes had to come along, though very few came up with the sort of distributed computing (think Internet) that we have today. Most figured that technology would lead to bigger and better but more centralized computers, not a lot of little ones everywhere.

_________________
"... to strive, to seek, to find, and not to yield." - Tennyson, Ulysses

<font size=-1>[ This Message was edited by: ToSeek on 2002-12-04 12:31 ]</font>

JS Princeton
2002-Dec-04, 09:59 PM
Grapes... you're missing the boat. Making the box as big as the Earth is fine as long as your box is a closed system and you know that every atom that is in the box was around since the time when the box was constructed. We have no knowledge like that for our Earth so the only thing we can assume is that we have no knowledge and therefore the atoms we collect will not be special. They will have been created by other processes unseen to us and will have existences that are consistent predictors of their future behavior.

I talked to Gott about other matters today since you didn't really seem to have a substantive question to offer. I mentioned the conversation to which he nodded. Apparently there have been others like you who were similarly outraged by his most mundane of analyses. I can't think of a good argument against it other than the fact that you don't know how to establish whether something is "special" or not. But see, on the whole, that works out in the wash too because if the Copernican Principle applies to our situation, then we should expect that we will not get an overabundance of special things.

Zathras
2002-Dec-04, 10:29 PM
Brief mathematical explanation of what I said above:

The probability that an even will occur during the x_nth time interval can be expressed as a function of what occurs during the previous time intervals and itself:

P(x_n)=f(M(x_1),M(x_2),M(x_3), . . .,M(x_n-1),x_n)

I am using the letter M to connote measurement, as this is what occurs over each ith time interval. If P(x_n) depends just on x_n, and not on the M(x_i), then the measurement is stochastic, otherwise it is non-stochastic.

Even if the situation were stochastic, you and Gott are making assumptions about the underlying proability density that may or may not be viable. Suppose, for example, that you were examining something that has been in existence for 10 years. Under your analysis, it should be in existence for between 6 months and 200 years. But suppose the underlying probability density for the event "ceasing to exist" has sharp peaks which lie outside this range-before the period, after the period, or even both. Then your analysis would be wrong.

I'm just saying you need to know more about the underlying rules of the game before you can jump to conclusions about particular events' lifetimes.

Zathras
2002-Dec-04, 10:52 PM
One more example. Suppose you have an atom of lead-206, which had been previously been polonium-210 until the polonium atom spit out an alpha particle 10 minutes ago. According to your analysis, JS, the lead should live between 30 seconds and 200 minutes, but guess what! Lead 206 is stable! How do fit this into your analysis?

traztx
2002-Dec-04, 11:02 PM
Maybe the true reason why we don't pick up alien communications is because any alien who openly broadcasts ends up invaded/decimated within a few hundred years, a very short L factor, no?

The surviving intelligent aliens are the stealthy ones.

And they're coming...

boron10
2002-Dec-05, 12:30 AM
I'm just saying you need to know more about the underlying rules of the game before you can jump to conclusions about particular events' lifetimes.This basically ties in with Grapes' utility issue.

The other problem (as Grapes of Wrath pointed out) is the criterion of a non-special time in the object's life. If our example doesn't fit the prediction, we must have caught it at a special time in its life, eh?

GrapesOfWrath
2002-Dec-05, 12:31 AM
On 2002-12-04 16:59, JS Princeton wrote:
Grapes... you're missing the boat.
Which boat was that? /phpBB/images/smiles/icon_smile.gif

I can't think of a good argument against it other than the fact that you don't know how to establish whether something is "special" or not.
When I asked (http://www.badastronomy.com/phpBB/viewtopic.php?topic=3025&forum=2&start=38) "what is a "non-special" decaying atomic nuclei?" you gave me, as an example, a box of special atoms, so apparently it's not just me that doesn't know how to establish whether something is "special" or not, but you're the one whose argument depends upon understanding the term. You really do have to define your terms, so I can test 'em.

GrapesOfWrath
2002-Dec-05, 12:42 AM
On 2002-12-04 19:30, boron10 wrote:
The other problem (as Grapes of Wrath pointed out) is the criterion of a non-special time in the object's life. If our example doesn't fit the prediction, we must have caught it at a special time in its life, eh?

Welcome to the board.

Yeah, it appears that what Gott is misunderstanding is that his conclusion is equivalent to the lifetime. In other words, if there's nothing special (here I'm going to assume that this just means we have no other information) about the object, and he tells me the error bars, then I can tell him the lifetime.

Unless "special" means something else, we have produced no new information, we have just transformed it. What else would you expect? He appears to take the lifetime (or equivalently the error bars) as meaning something significant, but clearly it does not unless "special" means something else.

Except I'm feeling awful old.

boron10
2002-Dec-05, 01:03 AM
Welcome to the board.Thanks.
Except I'm feeling awful old.Well, this statistical analysis should provide some comfort for you: I (a strapping 25 year-old male) have a 95% chance of dying anytime between the ages of 26 and 1000. Since my birthday is in January, I don't think I really learned anything with this exercise (except, perhaps, how to use my calculator a little better).

GrapesOfWrath
2002-Dec-05, 01:16 AM
I guess that means I could live to be 2000. /phpBB/images/smiles/icon_smile.gif

JS Princeton
2002-Dec-05, 03:11 PM
boron10 has it exactly right. The confidence interval works because it's just so broad in its application. We can see the analysis holds true for boron10's lifetime simply because we've taken the measurement of something we expect to have a finite lifetime and at a non-special time.

You ask what non-special means. It really is defined in the negative sense. It is simply something that is not special. I described to you special objects because those are ones that cannot be used. In principle, nonspecial objects are things that we have where we have no a priori knowledge that they were treated specially. As long as we don't know whether they were treated specially or not, we have no reason to doubt the analysis.

This isn't to say the analysis will not be wrong, it is just to avoid people doing things like, say, taking one's sample population to be a newly arrived group on a maternity ward. Of course, we can always apply the confidence intervals to a nonspecial group and it might land on some newborn babies, but in that case they end up in the tails of the distribution and fail the test because of the fact that we know it's a confidence interval instead of a strict and fast measurement.

It seems also that some of you are concerned about the fact that it is time that is used as a delimiter in the argument. It seems that some people think there is no way for us to know that our time is "non-special" or indeed that the Copernican Principle should apply to time. Well, we assume it applies to space and get some very nice results out of it, so why not time? In fact, if you consider the time right now to be nonspecial and take measurements of the liftetimes of whatever you will (how long you will own your house, how long your current marriage will last, how long you will own the shirt you are currently wearing, how long before you clean your bathroom again, how long before you go back to sleep) you will find that most of the things you can measure will fall in the appropriate confidence interval. What is so difficult to accept about this?

Zathras
2002-Dec-05, 03:47 PM
On 2002-12-05 10:11, JS Princeton wrote:
. . .
It seems also that some of you are concerned about the fact that it is time that is used as a delimiter in the argument. It seems that some people think there is no way for us to know that our time is "non-special" or indeed that the Copernican Principle should apply to time. Well, we assume it applies to space and get some very nice results out of it, so why not time? In fact, if you consider the time right now to be nonspecial and take measurements of the liftetimes of whatever you will (how long you will own your house, how long your current marriage will last, how long you will own the shirt you are currently wearing, how long before you clean your bathroom again, how long before you go back to sleep) you will find that most of the things you can measure will fall in the appropriate confidence interval. What is so difficult to accept about this?

The problem with this is when it is used in place of analyzing the deeper issues that are present in a phenonmon. This can occur in space as well as time (a photon has been emitted from the sun and has traveled 10e6 km--it most likely will be travelling much much further). In my example with the decay of polonium to lead, there is nothing special about a particular lead atom that stays around forever--they all do that.

This is especially dangerous when trying to use this to predict patterns in science. Can you use it to predict the maximum speed that a microprocessor will achieve? Can you use it to predict the maximum distance that a person will be away from the earth in a spaceship?

You tried to apply this principle to the ability to make radio contact with aliens. I think you can say there is much evidence that we are at a "special time" of reference, as you say. People are planning projects that go years and decades in the future. The attitude of scientists is that we are at the infancy of what we can achieve and what we will achieve. It may still take thousands of years to reach the stars, but many believe that it will be done. For you to state that you are 95% certain of a maximum cap on the technological age without apply any knowledge of the underlying rules that might govern the advance of techonology is extremely naive.

<font size=-1>[ This Message was edited by: Zathras on 2002-12-05 10:49 ]</font>

<font size=-1>[ This Message was edited by: Zathras on 2002-12-05 10:54 ]</font>

JS Princeton
2002-Dec-05, 04:08 PM
Zathras, I agree with most of your previous post, and while I may disagree with the opinions you submit (such as we may live in a special time after all), you are certainly entitled to have them.

There is one small technicality: the 95% interval will be wrong 5% of the time. Since we really only have one measurement to do, there's really no way for us to know decently into which regime we fall. That is why there are the assumptions tied to the idea. IF we are non-special folk in a non-special time and IF we have a finite lifetime for communication THEN I can apply the analysis.

The discerning reader is free to take issue with either IF statement.

As to lead atoms as daughter atoms: again, you've demonstrated the problem of chosing a specific sample you know to be special. This is equivalent to doing the analysis on the lifetimes of babies in a maternity ward. Since the lead atoms are "new" then its unfair to take them as a representative sample since lead is stable and there must be many more lead atoms around that decayed at arbitrarily earlier times. The other problem is that lead may not have a finite lifespan, in which case you violate the second condition.

GrapesOfWrath
2002-Dec-05, 04:43 PM
On 2002-12-05 10:11, JS Princeton wrote:
You ask what non-special means. It really is defined in the negative sense. It is simply something that is not special. I described to you special objects because those are ones that cannot be used. In principle, nonspecial objects are things that we have where we have no a priori knowledge that they were treated specially.
There ya go, that should be your question for Gott during his next office hours: "What does 'special' mean?"

I suspect that the reason that it is so hard to define, is that once you define it, you immediately deflate any utility of the method. It appears that right now it means "anything that doesn't fit the method", which doesn't do much for actually applying the method, does it?

John Kierein
2002-Dec-05, 05:42 PM
Life begins in volcanic vents, like on the floor of the ocean. On Europa.
http://news.bbc.co.uk/2/hi/science/nature/2541393.stm

JS Princeton
2002-Dec-05, 07:07 PM
On 2002-12-05 11:43, GrapesOfWrath wrote:
There ya go, that should be your question for Gott during his next office hours: "What does 'special' mean?"

I suspect that the reason that it is so hard to define, is that once you define it, you immediately deflate any utility of the method. It appears that right now it means "anything that doesn't fit the method", which doesn't do much for actually applying the method, does it?


Now we're getting somewhere. "Special" definitely has to do with selection functions. Some selection functions tease out tails of the distribution (in other words, it chooses things that are special). For example, a selection function on marriages that chose only couples that had been married for less than a week would be a problem: the selection function is biased towards a tail of the population (if what we're measuring is the length of the marriage).

The problem is, we don't always know what the selection functions are. The Copernican Principle is an assumption that when we don't have an empirical measure for the selection function we can assume it to be random. For example, just deciding now to use the confidence interval method to predict the lifetimes of whatever thing you chose to measure at this arbitrary (non-special) time will work. If you don't believe me, try it and see.

GrapesOfWrath
2002-Dec-07, 12:30 PM
On 2002-12-05 14:07, JS Princeton wrote:
Now we're getting somewhere.
I suppose. /phpBB/images/smiles/icon_smile.gif

The problem is, we don't always know what the selection functions are.
I'd just like to know what you mean by special. Is it merely what I assumed in this post (http://www.badastronomy.com/phpBB/viewtopic.php?topic=3025&forum=2&start=51)?

Zathras
2002-Dec-07, 04:27 PM
JS:
Perhaps the concept of Chaitin's constant (http://www.wikipedia.org/wiki/Halting_probability) would be more rigorous for your analysis:

Argos
2002-Dec-07, 05:18 PM
Grapes X JS

One of the most vigorous discussions I've witnessed in this board.

GrapesOfWrath
2002-Dec-07, 06:04 PM
On 2002-12-07 12:18, Argos wrote:
vigorous
Smile when you say that! /phpBB/images/smiles/icon_smile.gif

I'm not doing too bad for an eighty-nine year old.

JS Princeton
2002-Dec-07, 06:15 PM
Zathras, you make an excellent point. I am do not come from the CS end of things, so I was unaware of Chaitin's constant. Of course, people may object to the supposition that the universe can be ultimately reduced to a computer program. I don't know whether making the argument any more rigorous will make it better because you end up limitting the regimes you can operate in. But for the fact that, mathematically, the exponential construction of the constant speaks to the general statistical analysis of any random distribution of lifetimes there doesn't seem to be much more I can add. Perhaps you could give it a shot?

Grapes, I can't find where you specifically define "special". Really the word can be considered one of two things: one) it can be considered a criteria... ANY criteria really... by which specific instances are selected that have a direct influence on the lifetimes of the instances or two) it can be considered a way of defining away problems with the method.

This is an analogous criticism (but by no means the same) that comes into play with Set Theory and mathematics. (Again we come back to the end of Zathras encyclopedia post with the Incompleteness Theorem). We know that we do not have a consistent solution because we can imagine instances of objects that are self-contradictory and therefore unsuitable sets. The way around this is to exclude these sets from set theory OR deal with them differently. Perhaps it is helpful to look at "special" as this very type of object.

The problem then is that you can never know with 100% certainty whether you have a "special" object or not. This is the beauty of using confidence intervals: you don't need to be 100% certain, only certain enough to determine your confidence interval!

GrapesOfWrath
2002-Dec-07, 06:37 PM
On 2002-12-07 13:15, JS Princeton wrote:
Grapes, I can't find where you specifically define "special".
At that link (http://www.badastronomy.com/phpBB/viewtopic.php?topic=3025&forum=2&start=51), I basically assume that special means that we have other information.

Really the word can be considered one of two things: one) it can be considered a criteria... ANY criteria really... by which specific instances are selected that have a direct influence on the lifetimes of the instances or two) it can be considered a way of defining away problems with the method.
Both of those fit my approach.

The problem then is that you can never know with 100% certainty whether you have a "special" object or not. This is the beauty of using confidence intervals: you don't need to be 100% certain, only certain enough to determine your confidence interval!

Nope. Gott needs 100% certainty. If you were less certain, the error bars would be different. But he would be in worse trouble than trying to define "special"--what would the effect of being only 99% certain be? If you give me an object of age X, I can confidently tell you that it will expire sometime between now and the end of the Universe (whatever that would be). That's without knowing the value of X. Once I know X, and nothing else, I come up with Gott's figures. The age X and the figures are equivalent--no new information.

I'm still trying to figure out why there is a reason you think that the race of humanity has to be finite (http://www.badastronomy.com/phpBB/viewtopic.php?topic=3138&forum=2&16&start=16).

<font size=-1>[ Fixed code, added link ]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2002-12-07 13:43 ]</font>

JS Princeton
2002-Dec-07, 06:54 PM
Well, at 100% certainty you don't have an analysis. 100% certainty says that either this is the last instant of the lifetime or that the lifetime will extend indefinitely. If you don't understand that, then you've missed the whole point of the analysis.

As far as the finite age of human beings are concerned... we might assume it from any number of arguments. None of them are rigorous, but the argument itself isn't rigorous. We know that humanity will end eventually if the universe has to end eventually. If we think we are not special, then we actually should expect to find ourselves at a time when most of the human beings in the world exists. However, we don't know for CERTAIN whether we are special or not, this is true.

The analysis works because it balances the fact that when you don't know you can assume you are not special (or at the center of the distribution, if you prefer) which is known as the Copernican Principle AND statistical sampling. You need to be much clearer as to what your actual beef is, if indeed you have one, because you haven't done a good job explaining it to me or providing a counter-example that makes any sense.

GrapesOfWrath
2002-Dec-07, 08:53 PM
On 2002-12-07 13:54, JS Princeton wrote:
Well, at 100% certainty you don't have an analysis. 100% certainty says that either this is the last instant of the lifetime or that the lifetime will extend indefinitely. If you don't understand that, then you've missed the whole point of the analysis.
The certainty under discussion was whether we were certain of the objects "nonspecialness". That nonspecialness seems to be one of Gott's requirements for applying the method. If you have any reason to doubt the nonspecialness, then you really can't apply the method, can you? Whatever information you have that makes the object special would make the method inapplicable, to that degree.


As far as the finite age of human beings are concerned... we might assume it from any number of arguments. None of them are rigorous, but the argument itself isn't rigorous. We know that humanity will end eventually if the universe has to end eventually.
I'll grant you that much, but beyond that, I am skeptical. /phpBB/images/smiles/icon_smile.gif

The analysis works
I think that is what is being contended.

You need to be much clearer as to what your actual beef is, if indeed you have one, because you haven't done a good job explaining it to me or providing a counter-example that makes any sense.

Careful. I haven't seen a definition of "special" or "nonspecial" yet (except my own, but we're ignoring that one), and that's crucial to finding a counter-example that makes sense--or even to the application of the method. That's my beef (http://www.badastronomy.com/phpBB/viewtopic.php?topic=3025&forum=2&start=57).

JS Princeton
2002-Dec-07, 09:49 PM
I think you need to give us some empirical proof that the analysis DOESN'T work, Grapes. You seem to like debating, but I have yet to see from you a concrete example of where the analysis didn't work. It worked for radioactively decaying atoms, it worked for the Berlin Wall, it works for predicting how long a marriage will last, it works for how long you will live. Please, give us an example where it doesn't work.

As for a definition of "special"... "Specialness" is the attribute of things that are sampled preferentially for their residence in the tails of a distrbution that is trying to be measured.

Under Dog
2002-Dec-07, 10:40 PM
Special time? how do you define special time? Your example of making the calculation to determine how long our civilization will exist after a nuclear war is flawed. We are always at a "special time". Sadam's got a form of smallpox that a vaccine cant prevent, wouldn't this be a special time thus not a good time to make the estimate? Hitler marched on Europe with his massive war machine determined to wipe out non "arian" races when the world was in a depression and European and American armies were barley existent making that violent dictator a dangerous threat to humanity abroad, wouldn't this be a special time? The Outbursts of fascism in Germany and Italy during the 30's made that decade a special time as well. For that matter the cold war after WWII was yet another "special time". Shall I continue? The world is constantly on the brink of destruction as you can see. Their is no such thing as a "special time". That's why making the calculation after a nuclear war would be as good a time as any. The same could be applied to the likelihood of us contacting alien life (if any) or any other time span of something you can think of. I think the idea of using math to predict events in the real universe, society, politics, anything is silly since the variables used are never the same at any one point. If we detect civilizations out their other then our own it will be completely on chance.

GrapesOfWrath
2002-Dec-07, 10:53 PM
On 2002-12-07 16:49, JS Princeton wrote:
I think you need to give us some empirical proof that the analysis DOESN'T work, Grapes. You seem to like debating,
Detest it, but that's not relevant to the discussion.

but I have yet to see from you a concrete example of where the analysis didn't work. It worked for radioactively decaying atoms, it worked for the Berlin Wall, it works for predicting how long a marriage will last, it works for how long you will live. Please, give us an example where it doesn't work.
Work? As far as I can tell, it "works," but it gives you no useful information. The output is equivalent to the input--the input is a single piece of information, and there is no synthesis. Yet when I presented my example of atomic decay, your answer seemed to be that we had chosen special atoms--so naturally it didn't apply. That's not the same as "working."


As for a definition of "special"... "Specialness" is the attribute of things that are sampled preferentially for their residence in the tails of a distrbution that is trying to be measured.

OK, take two atoms of some element, any two. Those are non-special right? Do their ages differ? Certainly. So, Gott (http://www.astroleague.org/al/awards/alaward/alawards.html)'s analysis would give us different expectations for each atom, but we know that it is actally the same for both.

So, it seems that the method doesn't actually work for atomic decay, contrary to your claim. Or did I misunderstand your definition of special?

JS Princeton
2002-Dec-07, 11:59 PM
Okay, so we have two atoms of the same element and their ages are different... I don't know whether they are radioactive or not. You didn't specify so we will not assume.

Gott's analysis does indeed tell us that the one that is younger is less likely to be around longer than the one that is older.

Since you didn't state the conditions whereby these atoms are found, this analysis will tend to be true. What destroys an atom? Well, many things do. It so happens that atoms that have been around longer will tend to stay around longer for whatever reason.

Now let's say you have a sample of atoms that are well-shielded and they are radioactive. Why, then, yes, you still get many different measurements for each of the atoms. Only these measurements have huge threshholds on them and you will find that the sizes of these threshholds means that the lifetime of the atoms fall within the confidence interval. More than that, these atoms will have lifetime distributions that mean that they will give us correct estimations because if their lifetimes are finite, they will decay before too long. We can do one better with careful observation and maybe some quantum mechanics and calculate better lifetime probabilities than crude measurement I'm talking about, but as a first order test, this method works well. Therein lies its utility.

One thing that may be confusing you, Grapes, is the concept of determinism. We only know to a particular certainty what things happen when. The certainty of our measurement is arguably MORE important than the measurement itself. When you compare this analysis on two or three or a millioin different atoms, what you will find is that the threshhold falls exactly on the distribution predicted by the method. In other words, if you chose a 90% threshhold, 90% of the atoms you measure NECESSARILY fall into the category that they decay within the prescribed times (and note, no more than and no less than times will be different depending upon how old the atom is) and 10% will not. It's as simple as that.

What's the utility of this? Why, two things: it's simple and it correctly describes nature. Things that are older DO have staying power. The proof is in the pudding.

For example, when the seven wonders of the world were compiled in the 2nd Century BC, what was the oldest wonder? The pyramid of Khufu. What's the only wonder left standing?

Now I'm being anecdotal, but the statistics are what really prove it to us. If you've ever looked at a probability distribution, you know what I'm talking about. To a first order EVERYTHING is a Gaussian!

If you think that it isn't true that older things stay around longer than newer things, demonstrate it. We know that atoms that are around a certain period of time tend to stick around longer than atoms that are around for far less or far more time. These are really order of magnitude estimates, if you will. We are saying that the lifetimes of objects tend to be within a few orders of magnitudes of their present ages otherwise we would be in a special part (that is, in the tail of the probability distribution) of their lifetimes.

Zathras
2002-Dec-08, 12:16 AM
On 2002-12-07 18:59, JS Princeton wrote:
Okay, so we have two atoms of the same element and their ages are different... I don't know whether they are radioactive or not. You didn't specify so we will not assume.

Gott's analysis does indeed tell us that the one that is younger is less likely to be around longer than the one that is older.

Since you didn't state the conditions whereby these atoms are found, this analysis will tend to be true. What destroys an atom? Well, many things do. It so happens that atoms that have been around longer will tend to stay around longer for whatever reason.

Now let's say you have a sample of atoms that are well-shielded and they are radioactive. Why, then, yes, you still get many different measurements for each of the atoms. Only these measurements have huge threshholds on them and you will find that the sizes of these threshholds means that the lifetime of the atoms fall within the confidence interval. More than that, these atoms will have lifetime distributions that mean that they will give us correct estimations because if their lifetimes are finite, they will decay before too long. We can do one better with careful observation and maybe some quantum mechanics and calculate better lifetime probabilities than crude measurement I'm talking about, but as a first order test, this method works well. Therein lies its utility.

One thing that may be confusing you, Grapes, is the concept of determinism. We only know to a particular certainty what things happen when. The certainty of our measurement is arguably MORE important than the measurement itself. When you compare this analysis on two or three or a millioin different atoms, what you will find is that the threshhold falls exactly on the distribution predicted by the method. In other words, if you chose a 90% threshhold, 90% of the atoms you measure NECESSARILY fall into the category that they decay within the prescribed times (and note, no more than and no less than times will be different depending upon how old the atom is) and 10% will not. It's as simple as that.

Not true at all. If I have two atom of any particular substance--Carbon 14 say, they each have the exact same half-life as each other, no matter which one has been around longer. An atom that has been around for 3,000 years has the exact same expected life expectancy as one that has been around for 10 minutes (notice I said life expectancy, not lifetime. The first has an expected lifetime of exactly 3,000 years - 10 minutes longer than the second one). I think any pair of radioactive atoms will follow the same pattern.

I do note that your analysis might be more correct when the atoms are unknown, i.e., the first atom is element x and the second atom is element y. But then, there is that pesky possibility that the atom has an essentially infinite 1/2-life. This is not a "special" possibility, as the vast majority of the atoms in the universe are non-radioactive and therefore have an expected infinite lifetime.

JS Princeton
2002-Dec-08, 12:18 AM
On 2002-12-07 17:40, Under Dog wrote:
Special time? how do you define special time? Your example of making the calculation to determine how long our civilization will exist after a nuclear war is flawed. We are always at a "special time".... The world is constantly on the brink of destruction as you can see. Their is no such thing as a "special time". That's why making the calculation after a nuclear war would be as good a time as any. The same could be applied to the likelihood of us contacting alien life (if any) or any other time span of something you can think of. I think the idea of using math to predict events in the real universe, society, politics, anything is silly since the variables used are never the same at any one point. If we detect civilizations out their other then our own it will be completely on chance.



What you illustrate UnderDog, is two things: one that deciding whether something is "special" or not is difficult. This is why there is an important perspective that needs to be gained. As with all measurements, it is the intent with which you exercise your selection that matters.

Let's say I wanted to measure the lifetime of the human race. I decide to make my measurement every time a World Wide Nuclear War breaks out. Why, that's an unreasonable selection function because the human race is much more likely to end itself much sooner. This is a rather cumbersome example, because we can't do the test over and over and over again, but let's say we could with many other "intelligent" civilizations. Why then, if I chose to make the measurement at a time when these folks were embroiled in a Nuclear War, then I would be choosing a "special" time. Why? Because it is preferentially biased toward the end of the lifetime of the civilization.

This is more easily seen if I take a more mundane example of atoms. If I have my selection function be "atoms that haven't decayed after 1 year" this is creating a problem that I may be teasing out a tail of the distribution function. My method might statistically fail. It is important that I maintain a random sample if the method is to work as well as I claim it will work.

Let's get back to the civilization destroying itself. If it is indeed, as you said, ALWAYS on the brink of destruction then there is no problem. The time is therefore "non-special" and go ahead an make your measurement. I don't think I'm very special, so making the measurement for my lifetime seems a perfectly reasonable thing to do. All that I have to do is choose the threshhold and I'm done.

Sometimes (dictated by the confidence interval) I will happen to land in a tail of the distribution function anyway. That's the nature of the game. The Berlin Wall might fall tomorrow, our civilization might end tomorrow. If I blindly choose marriages to guess how many more anniversaries the couple will see together, a certain fraction of these marriages will be found to be on the wedding night and the method will have a good chance of failing for that individual measurement. ON THE WHOLE, though, these errors don't matter and in fact are PREDICTED by the very fact that we have a confidence interval (say, of 90%) that means that 1 out of 10 times we try to get something that's in the middle-part of its lifetime we'll get something that is in the beginning or the end. This is just the way the statistics work.

You may be math-phobic and think that we can simply apply math to predict events is unreasonable, but believe me, you do it everyday. You watch the gauge on your car and predict when you will run out of gas. You know something about microwaving and use mathematical skills to estimate how long you're going to radiate your food. You use math all the time to make predictions whether you are conscious of it or not. To deny the fact that it is useful or that it happens is not correct.

The beauty of the method Gott outlines is that it sidesteps all the "variables" that you insist we need to get hung up on. It is simply the order of magnitude estimate on a lifetime, nothing more. In a way, Grapes is right when he says that it doesn't "add" to our knowledge. This, however, can be said of all attempts science makes to predict things. Science and statistics use past observations to predict the future... they don't "add" anything to our body of knowledge, they only presuppose that what happens in the past is a predictor of the future. You may take issue with that, but time and again this technique has proven itself useful.

The variables of politics and society or even of physics! are inconsequential when you are trying to come up with your order of magnitude estimate for a lifetime of a random thing. Your error bars will be huge, but that's okay. What matters as long as the Copernican Principle holds and we find ourselve measuring a finite lifetime is the observation of the amount of time that has transpired since the initial point of reference.

<font size=-1>[ This Message was edited by: JS Princeton on 2002-12-07 19:39 ]</font>

Zathras
2002-Dec-08, 12:24 AM
On 2002-12-07 13:54, JS Princeton wrote:
. . .
As far as the finite age of human beings are concerned... we might assume it from any number of arguments. None of them are rigorous, but the argument itself isn't rigorous. We know that humanity will end eventually if the universe has to end eventually. If we think we are not special, then we actually should expect to find ourselves at a time when most of the human beings in the world exists. However, we don't know for CERTAIN whether we are special or not, this is true.

The analysis works because it balances the fact that when you don't know you can assume you are not special (or at the center of the distribution, if you prefer) which is known as the Copernican Principle AND statistical sampling. You need to be much clearer as to what your actual beef is, if indeed you have one, because you haven't done a good job explaining it to me or providing a counter-example that makes any sense.


But we <u>do</u> know something about the issue regarding the lifetime of the universe. We have GR which tells us the universe will end if omega is less than 1 but will not if omega is greater or equal to 1. Right now there is scant evidence about which way it goes. We might as well say that there is a 50/50 chance the universe will last forever. Therefore, there is no special-nonspecial distinction to be made.

When there is a non-negligible likelihood that there will be no termination (as we do know from GR), this analysis necesarily fails.

JS Princeton
2002-Dec-08, 12:31 AM
On 2002-12-07 19:16, Zathras wrote:
Not true at all. If I have two atom of any particular substance--Carbon 14 say, they each have the exact same half-life as each other, no matter which one has been around longer. An atom that has been around for 3,000 years has the exact same expected life expectancy as one that has been around for 10 minutes (notice I said life expectancy, not lifetime. The first has an expected lifetime of exactly 3,000 years - 10 minutes longer than the second one). I think any pair of radioactive atoms will follow the same pattern.

Your analysis of halflifes and expected-lifetimes for them is dead-on, Zathras, but that doesn't invalidate the technique I outlined and everything I said was absolutely true.

While it is true that the past lifetime of a radioactive atom is no predictor of its future behavior if you have one (a unique, or specially selected) atom, what we're talking about is something more delicate. We're talking about choosing an atom that isn't special. A Carbon 14 atom that has only been around for 10 minutes is downright RARE compared to ones that have been around between one and ten thousand years. Therefore, given a random atom (non-special)you measure, you are much more likely to get one that is near the halflife. Now, it is absolutely true that the method is likely to fail for the ten-minute old C-14 atom for a 90% confidence interval, but that's made up for by the fact that you don't find many of those 10 minute old C-14 atoms unless you are in some regime where you preferentially select these. In fact, the 10-minute-old C-14 atoms are pretty much in the 10% tails of the distribution function. We never said that anything more than 9 out of 10 would work if you use a 90% threshhold. I could go out to an arbitrary threshhold where we can get the 10-minute old Carbon-14 atom in there to include its actual life-expectancy, but that's more of a game of "how certain do I want to be?" The fact of the matter is, if I'm 90% certain then you better believe my random pick of a 10-minute-old C-14 atom was pretty ridiculously unlucky in the tail of the distribution. Failure happens 1 out of 10 times!

The method works because we assume most things we look at are going to be in the bulge of the distribution function and not at the tails. I've said this all before, though, in this very thread.

JS Princeton
2002-Dec-08, 12:35 AM
On 2002-12-07 19:24, Zathras wrote:
But we <u>do</u> know something about the issue regarding the lifetime of the universe. We have GR which tells us the universe will end if omega is less than 1 but will not if omega is greater or equal to 1. Right now there is scant evidence about which way it goes. We might as well say that there is a 50/50 chance the universe will last forever. Therefore, there is no special-nonspecial distinction to be made.

When there is a non-negligible likelihood that there will be no termination (as we do know from GR), this analysis necesarily fails.


Depends on what you mean by "end". I think a Heat Death is a pretty effective ending, if you ask me.

The analysis still holds up (trying to figure out why you like to argue so much Zathras, but no matter) because it is simply based on statistics. If "humanity" has a finite lifetime and if it is fine to assume that you and I don't occupy a special time in that lifetime, then the confidence interval gives us a meaningful prediction.

Now, maybe you think there is some way around finite lifetime for "humanity". That's the philosophy behind the method and is an interesting question in its own right. I don't know how a human being can survive if the horizon is such that we lose energy reserves.

GrapesOfWrath
2002-Dec-08, 01:00 AM
On 2002-12-07 18:59, JS Princeton wrote:
Now let's say you have a sample of atoms that are well-shielded and they are radioactive.
Let's say you have two of them.

Why, then, yes, you still get many different measurements for each of the atoms.
You get, two of them.

Only these measurements have huge threshholds on them and you will find that the sizes of these threshholds means that the lifetime of the atoms fall within the confidence interval.
You're guaranteeing that both atoms will decay within the Gott's confidence interval? That's not right.

More than that, these atoms will have lifetime distributions that mean that they will give us correct estimations because if their lifetimes are finite, they will decay before too long. We can do one better with careful observation and maybe some quantum mechanics and calculate better lifetime probabilities than crude measurement I'm talking about, but as a first order test, this method works well. Therein lies its utility.
The method gives two different answers, and we know that is wrong.


One thing that may be confusing you, Grapes, is the concept of determinism.
Nope, that's not what's confusing me.


What's the utility of this? Why, two things: it's simple and it correctly describes nature. Things that are older DO have staying power.
I doubt you'll continue to believe that as you mature. /phpBB/images/smiles/icon_smile.gif

If you think that it isn't true that older things stay around longer than newer things, demonstrate it.
Do you think I claimed it?


On 2002-12-07 19:18, JS Princeton wrote:
The beauty of the method Gott outlines is that it sidesteps all the "variables" that you insist we need to get hung up on. It is simply the order of magnitude estimate on a lifetime, nothing more. In a way, Grapes is right when he says that it doesn't "add" to our knowledge.
What I meant was that it doesn't change the knowledge--there is no synthesis. The amount of information is no different than the actual age of the object.


This, however, can be said of all attempts science makes to predict things. Science and statistics use past observations to predict the future... they don't "add" anything to our body of knowledge, they only presuppose that what happens in the past is a predictor of the future. You may take issue with that, but time and again this technique has proven itself useful.
So now we're anti-science too?

Those past observations are estimators of those other variables that you are trying to sidestep.

Under Dog
2002-Dec-08, 01:20 AM
But things like a gas gauge and how long you should microwave your popcorn are definite figures. Predicting the outcome of a civilization would have to be based on indefinite figures. We would have to know what very person is thinking, what every person is feeling, what every person is about to do to perfectly determine the outcome of a civilization only a frame of time ahead of the time it is now. And that's just for starters, we would have to know what every microbe is doing, if the programs that control ballistic missile launches are working, literally what every molecule is doing in the entire universe to predict time accurately ahead just one time frame (whatever the smallest measure of time is) As we get farther away in time from that first calculation the prediction for the selected time period gets less accurate, I'm guessing it would double in inaccuracy after every time frame starting with the first inaccurate one times the amount of the smallest sub atomic particles (known or unknown to exist) in the whole universe. (just an example, not based on any real numbers) I.E, the probability of bob eating a jelly doughnut 5 minutes after the calculation being made is lets say 90%. Bob does eat the jelly doughnut after 5 min. The calculation says bob will drink a coke in 20 days with the probability being less then 90%. Bob does drink a coke but its a diet coke since the calculation hasn't been updated for 20 days so the predicted outcome in 20 days from that calculation has changed ever so slightly due to no further calculations being done to update the predicted outcome. I seemed to have strayed a bit off topic but this should prove that math cant be applied to outcome because a calculation would have to be made every time frame to determine what will happen in the next time frame.


<font size=-1>[ This Message was edited by: Under Dog on 2002-12-07 20:33 ]</font>

JS Princeton
2002-Dec-08, 01:53 AM
Fine, have two atoms that are picked at random. You can do some Baysian statistics to determine what the liklihood for the technique to work on both of them is. For a confidence interval of 90%, 81% of the time the technique will work for both atoms. That's all the confidence interval does. If you want to be more certain, take a higher threshhold. At a 95% interval, 90% of the time both of the atoms lifetimes will be predicted correctly. This is the way the analysis is supposed to work. Now, I'm confused, why is this a counterexample?

The method may give two different intervals, but that doesn't matter. It is still right as much as it claims to be. No more and no less.



What I meant was that it doesn't change the knowledge--there is no synthesis. The amount of information is no different than the actual age of the object.


No, there IS more information, namely that the object is likely to be in midlife. That is additional information. And it is likely to be in midlife BECAUSE of the Copernican Principle and the fact it has a finite age.


Those past observations are estimators of those other variables that you are trying to sidestep.

No, I'm not sidestepping anything. I'm simply making a rather crude approximation.

This is akin to when doing a back-of-the-envelope approximation I write down the volume of a sphere to go as r^3. I'm off by corrective factors but the order of magnitude of the estimate depends only on the radius and not on the prefactors.

Likewise, the order of magnitude of any given object's predicted longevity that is in the middle of its current lifespan is determined solely on the basis of how long it has been around. We assume we just don't have enough information to say anything else. And we don't for the value "L" of the Drake Equation, for example.

JS Princeton
2002-Dec-08, 02:36 AM
But things like a gas gauge and how long you should microwave your popcorn are definite figures.

No, they also have error bars on them. There is no EXACT amount of time that you have to nuke your popcorn for. You have an interval of time that you can do it for. Again, this goes back to determinism. There is no such thing as a measurement without an error bar.


We would have to know... [a lot of things]

No, you're missing the point entirely. We simply assume things pile up to create an even distribution. You are allowed to think that this assumption isn't true, that we somehow are not piled up in a nonspecial point in time and space, but the reason I think that is because I think that the Copernican Principle can be extended to time and doesn't just apply to space. This is, I'll admit, where the assumption lies. It does not lie, however, in the meat of the analysis.

Let's take your example of the length of a jelly-doughnut fast. In order to do it right, we have to know the length of the current fast. Now of course, in our sample we'll probably end up with some people that haven't eaten a jelly doughnut in years (like myself). Why on average, their confidence intervals will be much larger (often larger than their lifetimes) than those people who are jelly-doughnut addicts. We know that people who eat a lot of jelly doughnuts are likely to eat one again, and those that don't are not likely too.

Of course, the problem is how do we measure it for people that NEVER eaten or have even NEVER SEEN jelly doughnuts? For example, does a nine-week-old baby really only have a nine-week-old Jelly Doughnut fast? Why, no, the baby doesn't. In fact, there is no adequate measurement for jelly doughnut fasts for people who have no initial point of the fast (the last time they ate a jelly doughnut). Once you eat a jelly doughnut, though, and don't touch another one, your fast begins and then we can start measuring.

A bigger issue you might think of is Magical Jelly Doughnuts of Shangrila! What if there is one and only one Magical Jelly Doughnut of Shangrila and you eat that and then ask to measure the expected lifetime for all people who are on the Magical Jelly Doughnut of Shangrila fast. You will never again have a chance to eat the Magical Jelly Doughnut of Shangrila. No matter how long ago it was, the confidence test fails. Why then, does the method fail? After all, the chance is exactly zero that you will ever eat it again.

Turns out that the Magical Jelly Doughnut of Shangrila is a pretty special Jelly Doughnut. In fact, it's as special as they get and by choosing it you have basically thrown off the data. If you were to look at a broader catagory you would find that you having eaten that special jelly doughnut made yourself an isolated case and therefore not statistically random.

You might believe that we are the only civilization in the universe. If that's the case, then the method will not work because we are special (not statistically random). Our very existence is unique and therefore our ability to look at our past to predict our lifetime is subject to the Magical Jelly Doughnut of Shangrila problem.

However, if we are NOT unique as many SETI-enthusiasts believe, then we might assume we are an average civilization that will live an average lifespan and have an average run at the game. That means the analysis will hold. Since we don't have evidence one way or the other at this point, you are free to dismiss the method as being valid. But in that case you surpress some of the other variables in the Drake Equation and you're going to have to deal with the fact that we're alone!

One more thing, UnderDog, you seem concerned about the inherent "unpredictability" of random physical processes. Chaos theory is indeed an interesting thing to consider, but is probably not relevant. Why? Because our assumption of the Copernican Principle puts us smack in the middle of a distribution that basically has existence on a time-continuum. So, yes, on Tuesday a robber may rob a bank which will lead to the discovery of an ultimate energy source, but in the end the net effect of all these chance divergeances and convergeances of chaotic structures and fractal geometries is to make a coherent whole of which we have been privvy to witness the entire past. For some reason we haven't gone completely berserk and it's not snowing in New York in the middle of July (this is from the classic example of the weather computer that was turned off and then turned on again and fed slightly different outputs which drastically changed the expectations for the future). All we know is that things have conspired to this point to keep us around for so many years. If we are truly NOT SPECIAL... if our civilization is truly picked at random from all the civilizations of the universe, then we expect the confidence interval test to be valid. Now realize, we might still reside in the tails. After all, we could be in that 10% failure. In fact, the optimist in me hopes that we are.

GrapesOfWrath
2002-Dec-08, 06:40 PM
On 2002-12-07 20:53, JS Princeton wrote:
Now, I'm confused, why is this a counterexample?
It gives two different answers for identical atoms.

The method may give two different intervals, but that doesn't matter. It is still right as much as it claims to be. No more and no less.
Well, there is a claim on the table that the method says something profound. I've noticed that many of the websites reference that Nature article in the early nineties, that must have been the article I read and responded to. I'll try to dig up a copy of it. I don't remember it saying anything about the Berlin wall, but the details of it are fuzzy so it may have.

That's one of the problems that I have with the analysis. No one predicted the dismantling of the Berlin wall and it is a fairly famous example of the lack of prediction by everyone, so it irks me that someone should try to go back and say, in hindsight no less, well, this method would have predicted it.

What would the method say about the lifetime of the office of homeland security? No, wait, it may be right about that. /phpBB/images/smiles/icon_smile.gif

No, there IS more information, namely that the object is likely to be in midlife. That is additional information. And it is likely to be in midlife BECAUSE of the Copernican Principle and the fact it has a finite age.
I think that the Copernican Principle is an assumption, not more information.

No, I'm not sidestepping anything. I'm simply making a rather crude approximation.
Well, on On 2002-12-07 19:18, you did say "The beauty of the method Gott outlines is that it sidesteps all the 'variables' that you insist we need to get hung up on."

We assume we just don't have enough information to say anything else. And we don't for the value "L" of the Drake Equation, for example.
There is more information out there. For one thing, humans have a lot more sophisticated tools than any other species we've ever known. That alone allows us to control our own environment--and our own evolution, to a certain extent. The method sidesteps that.

JS Princeton
2002-Dec-08, 07:33 PM
On 2002-12-08 13:40, GrapesOfWrath wrote:


On 2002-12-07 20:53, JS Princeton wrote:
Now, I'm confused, why is this a counterexample?
It gives two different answers for identical atoms.


It most certainly does not. It gives the same answer for identical atoms.

But again, you are getting hung up on determinism. Let's say we have two C-14 atoms. One has been around for 5000 years. One has been around for 4000 years. Now we know what the 1/2 life is for C-14. Chances are that one of them is going to decay in the next 5000 years, say. Well, do the analysis and you'll see that the threshhold is such so that either one may be the one that decays in the next 5000 years. It doesn't say anything about WHERE along the threshhold we expect it to occur, just that we expect the ending to occur sometime within the confidence interval. Just because your confidence intervals are different doesn't mean that the measurments are drastically different. In fact, they are compatible and comparable measurements.

Therefore you have not given me a counterexample, but merely an example of how you don't understand what the method is telling you. It is not deterministic.... it merely says that the probability that a random atom that I pick out is going to be around is related to the lifetime it has already had. This HAS to be true for any decay process and any natural law that gives us a distribution.



Well, there is a claim on the table that the method says something profound. I've noticed that many of the websites reference that Nature article in the early nineties, that must have been the article I read and responded to. I'll try to dig up a copy of it. I don't remember it saying anything about the Berlin wall, but the details of it are fuzzy so it may have.


The reference to the Berlin Wall is from Gott's Book, Time Travel in Einstein's Universe. I'll quote it here in brief:


In 1969, at the time of my visit to the Berlin Wall, it had been standing for 8 years. People wanted to konw how long the wall was going to last. Some people thought it would be a temprorary aberration, while others thought it would remain a permanent fixture of modern Europe. I reasoned, using the Copernican principle, that since there was nothing special about my visit, I was simply observing it at some random point during its existence--somewhere between its beginning and end. If there was nothing special about the location of my visit in time, there was a 50 percent chance that I was observing the wall sometime between the middle two quarters of its existence. If I was at the end of the middle two quarters, the three quarters of its existence had passed and only one quarter lay in the future. Thus, there was a 50 percent chance that the future longevity of the was was between 1/3 and 3 times as long as its past longevity.... I predicted to a fried, Charles Allen, that there was a 50 percent chance that the future longevity of the wall would be between 2 2/3 years and 24 years. I made no prediction of why the Berlin Wall would end, just how much longer it was likely to last. My prediction could easily have been incorrect. The Berlin Wall could have been destroyed by a nuclear weapon milliseconds after my prediction had been made (this was during the Cold War, after all), or it could have lasted for thousands of years.

But 20 years later, I called my friend. I said, "Chuck, you remember that prediction I made about the future longevity of the Berlin Wall?" He did. "Well, turn on your TV because Tom Brokaw is at the wall now, and they are tearing it down!" When the wall came down in 1989, after 20 years, in agreement with my original prediction, I decided that I should write this up.



That's one of the problems that I have with the analysis. No one predicted the dismantling of the Berlin wall and it is a fairly famous example of the lack of prediction by everyone, so it irks me that someone should try to go back and say, in hindsight no less, well, this method would have predicted it.

Well, you see, Grapes, you are dead wrong there.



I think that the Copernican Principle is an assumption, not more information.


Once you decide to make the assumption, the assumption gives you information. Just like the Cosmological Principle that the universe is homogeneous and isotropic gives us information when we are tryin to model the universe.



Well, on On 2002-12-07 19:18, you did say "The beauty of the method Gott outlines is that it sidesteps all the 'variables' that you insist we need to get hung up on."

Yes, we do sidestep the mechanisms, but it's not done maliciously. It is simply because the mechanisms don't matter.



There is more information out there. For one thing, humans have a lot more sophisticated tools than any other species we've ever known. That alone allows us to control our own environment--and our own evolution, to a certain extent. The method sidesteps that.

So, this is something to take into consideration. It may be that our technology is somehow a saving grace, is that want you want to say? I would say it's at best a wash because technology also has the capacity to destroy us. We may wish to control out evolution and longevity, but we may end up wiping ourselves out. In the end, I think we don't have enough information to say how technology will help or harm the longevity of the human race.

GrapesOfWrath
2002-Dec-08, 07:53 PM
On 2002-12-08 14:33, JS Princeton wrote:
It most certainly does not. It gives the same answer for identical atoms.
Then I don't understand how you are applying the method. In my example we have two atoms of the same element, which naturally have two different ages. Are you saying the method gives the same results for both?


But again, you are getting hung up on determinism.
Other way around. That's the whole point of quantum mechanics--no hidden variables, total indeterminacy. We have no idea when the atom will decay, its past history gives us no clue.

Therefore you have not given me a counterexample, but merely an example of how you don't understand what the method is telling you. It is not deterministic.... it merely says that the probability that a random atom that I pick out is going to be around is related to the lifetime it has already had.
And quantum mechanics says differently. The expected lifetime of the atom is not related to its age.

You can't apply the method to everything in every way, you've already admitted that. I think it came up in the discussion about nonterminating decimals--because of our knowledge of how the decimals are constructed. This is just an another example of where you do not want to apply the method.

Well, you see, Grapes, you are dead wrong there.
Gott's account makes it clear that he did not go on record, right? If I had a thousand dollars for every football upset I've predicted, I'd own Bill Getes.

Once you decide to make the assumption, the assumption gives you information.
Well, it leads you in the direction you wanted to go, yes.

JS Princeton
2002-Dec-08, 08:46 PM
On 2002-12-08 14:53, GrapesOfWrath wrote:
Then I don't understand how you are applying the method. In my example we have two atoms of the same element, which naturally have two different ages. Are you saying the method gives the same results for both?


In effect, yes. Since you we expect the atoms to be distributed in the middle of their lifetimes, the method will give results that are, if not absolutely identical, then to the threshhold comparable which is all we ever said the method was supposed to do in the first place. If you want a better method, invent it yourself.




But again, you are getting hung up on determinism.
Other way around. That's the whole point of quantum mechanics--no hidden variables, total indeterminacy. We have no idea when the atom will decay, its past history gives us no clue.

No, for an atom that is chosen at random from a distribution, the past life time most certainly DOES give us a clue as to how long the atom will stay around.

It's simple for atoms that are different. Let's say you have a short-past lifetime and a long-past lifetime nucleus. Knowing nothing else I would say that it is far more likely that the short-past lifetime is probably going to decay more quickly than the long-past lifetime nucleus. You would say that we don't know anything because we don't know the details of the decay processes. Therefore you would say that the two atoms are equally likely to decay. Guess who would be proven right more often than the other?

Now take identical atoms. As long as we don't choose real young ones or real old ones preferentially we will tend to get middle-aged ones. Again, the past lifetimes will predict the future lifetimes. NOT EXACTLY, but to the threshhold. I don't care if one is around for 2353 years and the other is around for 5235 years. This is because it is only the ORDER OF MAGNITUDE that gives me the threshhold the actual details of the size of the confidence interval are inconsequential. That's because I might have found the atoms were around for 3.23 second and 1.42 second which would be on a completely different scale.

I must admit I'm getting tired of rehashing this over and over and over again just to come to the realization that you refuse to sit down and actually consider what I'm saying without pushing your agenda that the analysis has "GOTT" to be wrong.



And quantum mechanics says differently. The expected lifetime of the atom is not related to its age.


This is absolutely untrue, as I showed above. Atoms that are generally found to be 1 millisecond old and not selected for their youth tend to be less stable then atoms that are generally found to be billions of years old. How is this hard to understand?



You can't apply the method to everything in every way, you've already admitted that.

You can apply the method when the criteria are met. I'm not telling you what the criteria are again.


I think it came up in the discussion about nonterminating decimals--because of our knowledge of how the decimals are constructed. This is just an another example of where you do not want to apply the method.

Non-issue. Non-terminating decimals are not finite. End of story.




Well, you see, Grapes, you are dead wrong there.
Gott's account makes it clear that he did not go on record, right? If I had a thousand dollars for every football upset I've predicted, I'd own Bill Getes.


So, I give you the evidence and you simply balk at it? Why don't you email Charles Allen and see what he says? You are just being difficult, Grapes, because you know that you're wrong on this point. YOU were the one who said "nobody did it at the time," not me. It was not "postdated" as you seemed to declare.

I can't for the life of me decide what made you so ornery on this subject. You obviously just want to argue.

<font size=-1>[ This Message was edited by: JS Princeton on 2002-12-08 15:49 ]</font>

GrapesOfWrath
2002-Dec-08, 10:35 PM
On 2002-12-08 15:46, JS Princeton wrote:


On 2002-12-08 14:53, GrapesOfWrath wrote:
Then I don't understand how you are applying the method. In my example we have two atoms of the same element, which naturally have two different ages. Are you saying the method gives the same results for both?


In effect, yes.
Yes? So, if the two atoms had ages of one and two units respectively, the method would produce the same confidence intervals? That's not the way I understood it.

Since you we expect the atoms to be distributed in the middle of their lifetimes, the method will give results that are, if not absolutely identical, then to the threshhold comparable which is all we ever said the method was supposed to do in the first place. If you want a better method, invent it yourself.
OK, so they are not the same?

No, for an atom that is chosen at random from a distribution, the past life time most certainly DOES give us a clue as to how long the atom will stay around.
We're talking about predicting radioactive decay, right?


It's simple for atoms that are different.
Sure, but that's not the example.

Let's say you have a short-past lifetime and a long-past lifetime nucleus. Knowing nothing else I would say that it is far more likely that the short-past lifetime is probably going to decay more quickly than the long-past lifetime nucleus. You would say that we don't know anything because we don't know the details of the decay processes. Therefore you would say that the two atoms are equally likely to decay.
Therefore??? That's a pretty big leap. Why would I say that? That's a strawman, really.

I must admit I'm getting tired of rehashing this over and over and over again just to come to the realization that you refuse to sit down and actually consider what I'm saying without pushing your agenda that the analysis has "GOTT" to be wrong.
You've come to realize that I've not actually considered what you're saying? How did you do that?




And quantum mechanics says differently. The expected lifetime of the atom is not related to its age.

This is absolutely untrue

And you accuse me of pushing an agenda?


I can't for the life of me decide what made you so ornery on this subject. You obviously just want to argue.
That's irrelevant, and wrong. Let's leave off the personal insults.

JS Princeton
2002-Dec-09, 01:53 AM
The confidence interval test will not be identical for atoms of different lifetimes, but there's no reason we should consider that they should have to be. This is because if you choose an atom at random you would expect to get something in the middle of the distribution and the order of magnitude is correct. That's all the confidence interval is good for in any case (as I've said before).


So, absolutely, the technique works EXACTLY as advertised. No better and no worse. You might be able to map out a better distribution using different techniques, but that's only for the second order of the expansion, if you will. To understand the general behavior of things of finite lives you can determine the confidence interval and get your estimate and you will see that it works.

Maybe I should reiterate: the method works. If you don't think it does, demonstrate how it doesn't. Show me that two different atoms taken at random that are found in the middle of the distribution do not on average fall into the lifetime determined by the confidence interval. In fact, if you actually think about the problem for more than a few seconds you will realize that they both will give good estimates because they are on an order of magnitude and manifestly not concerned about the actual boundaries. It's like drawing two different lines, one that's a mile long and another that's a mile and twelve yards long. The overlap between the two lines is far more important than the divergeance.

Quantum mechanics still applies, it just doesn't have an effect on the analysis as I've demonstrated.

GrapesOfWrath
2002-Dec-09, 11:27 AM
On 2002-12-08 20:53, JS Princeton wrote:
The confidence interval test will not be identical for atoms of different lifetimes, but there's no reason we should consider that they should have to be.
Quantum mechanics is a good enough reason for me. /phpBB/images/smiles/icon_smile.gif

The point is, we already know enough about the world and how it works--extra information--to know that the expected lifetimes of two identical atoms should be the same. That's a little bit of a different sort of information from the nonfiniteness of decimal expansions that keep us from applying the method to pi, for instance, but it is something that we know for sure.

The example was only to counter the claim that the method applies to almost everything.

You might be able to map out a better distribution using different techniques
Well, I don't think there's any doubt about it.

Maybe I should reiterate: the method works. If you don't think it does, demonstrate how it doesn't. Show me that two different atoms taken at random that are found in the middle of the distribution do not on average fall into the lifetime determined by the confidence interval.
This is starting to remind me of the argument that Gott used in that Nature paper. I will look it up as soon as I can.

Zathras
2002-Dec-09, 04:57 PM
On 2002-12-07 19:35, JS Princeton wrote:


On 2002-12-07 19:24, Zathras wrote:
But we <u>do</u> know something about the issue regarding the lifetime of the universe. We have GR which tells us the universe will end if omega is less than 1 but will not if omega is greater or equal to 1. Right now there is scant evidence about which way it goes. We might as well say that there is a 50/50 chance the universe will last forever. Therefore, there is no special-nonspecial distinction to be made.

When there is a non-negligible likelihood that there will be no termination (as we do know from GR), this analysis necesarily fails.


Depends on what you mean by "end". I think a Heat Death is a pretty effective ending, if you ask me.

Even if you do include the possibility of a heat death, it would be so far out to be completely outside the confidence interval defined under your analysis by the present age of the human race. As I said earlier, if there is a non-negligible likelihood that there will be no termination, or a termination that is substantially further out of the confidence interval, your analysis necesarily fails. This is a simple idea, and you haven't dealt with it yet.



The analysis still holds up (trying to figure out why you like to argue so much Zathras, but no matter) because it is simply based on statistics.


Emphasis on "simply." It is an assumption that a lot of time does not hold true. Does it hold "most" of the time? I have no idea, and I think it is naive to assume that it does.



If "humanity" has a finite lifetime and if it is fine to assume that you and I don't occupy a special time in that lifetime, then the confidence interval gives us a meaningful prediction.

Now, maybe you think there is some way around finite lifetime for "humanity". That's the philosophy behind the method and is an interesting question in its own right. I don't know how a human being can survive if the horizon is such that we lose energy reserves.


See above. Any heat death is many billions of years away. If you are looking at the age of an atom, it is my understanding that a hydrogen atom, or any other stable atom at the time of the "big freeze," will continue to live forever (the possibility of interacting with another object becomes vanishingly small).

JS Princeton
2002-Dec-09, 10:10 PM
Grapes -- you are right that when you know more information you can do a better job. That's not what I'm arguing here. I'm arguing that when you don't know, you can still do a passable job.

Take, for example, approximating pi. You can approximate pi as three and be fairly decent with crude estimates. Likewise you can measure lifetime expectancies based on past lifetimes and be fairly decent with crud estimates. Sometimes (or many times) you just don't have the time and don't want to put in the effort to explore the ins and outs of considerations. That's why this method works, because it's a first approximation. You are the one who seems to think it should be better than it is. It's not up to you to decide how good the method has to be, it's up to the methods error bars to decide that.

Zatras-- you indicate that if there is a finite probability that something will last beyond the confidence interval, then the method fails. Actually, this is absolutely false. The finite probability the method will fail is the tail that's beyond the confidence interval. In that way, the method predicts exactly what you say.

What's the chance that humans survive to the end of the universe? Pretty slim because there's lots of things that can happen to get rid of us non-special insignificant things in the meantime.

So again, you have not shown the method to be false but have missed the fact that the confidence interval tells you EXACTLY WHAT ONE EXPECTS given a random selection function observation of a time during the lifetime of a particular thing.

And that's all she wrote.

You seem to think that it will fail MORE than is indicated by the method, but you see, Zatras, that's ONLY correct if your sampling is skewed by not choosing a random time in the lifetime of the thing OR by choosing something that doesn't have a finite age. You admit that it's finite, but then you want to say, "but it's so far in the future it might as well be infinite."

Huh uh, sorry. If you think we are special then we might be early in the lifetime of humanity then we are measuring in the tails. There is a finite probability that this should be the case, but it's no means the most likely scenario. The most likely scenario is that we're in the middle of the lifetime of humanity. Again, that's most likely. That's all that is being said. How can you possibly argue with it?

SeanF
2002-Dec-09, 10:11 PM
Guys, I've gotta say, I've been having a blast reading this thread. /phpBB/images/smiles/icon_smile.gif And, I've finally found something I want to comment on.

JS quoted Gott as saying (or writing):



I predicted to a fried, Charles Allen, that there was a 50 percent chance that the future longevity of the wall would be between 2 2/3 years and 24 years.


I'm sorry, but that's not a prediction. You don't predict probabilities; you calculate or estimate them. You can then use the probabilities to predict outcomes.

And this example is 50%! If there was a 50% chance the wall would come down during the stated time interval, then there was a 50% chance that it wouldn't. Thus, Gott's apparent pride in the wall coming down during his interval seems a little silly to me . . .

"I predict a 50% chance this quarter will come up heads (and thus, 50% chance it won't) -- FLIP -- Look at that, it's tails! I was right!" /phpBB/images/smiles/icon_smile.gif

JS Princeton
2002-Dec-09, 10:33 PM
There, you're getting into the spirit now, SeanF... only your criticism isn't true. Any prediction that is made has error bars, just like any measurement. You are thinking deterministically now, which is problematic. In science, predictions are always made in a "most likely" fashion. This is the conservative nature of the game.

You're right that your coin flipping 50% prediction hasn't been proven WRONG. (That's different from being proven right, of course... in a real sense science can't do that because of falsification, but that's another story). As far as induction is concerned, if you haven't been proven wrong you can't criticize the hypothesis no matter. You make a prediction with a given probability because that's the best you can do. It happens to be a prediction that can be falsifiable (go out and make the measurement). You might have an unfair coin and find out that both sides are tails which would give you a different answer than you expected, so fairness is important. Another problem is you only made one measurement. If you do the test over and over and over again, that's how you can verify the prediction of probability.


Now take this on a grander scale. Let's predict the length of a marriage. Why there's all sorts of lengths to marriages and there's all sorts of reasons for marriages to end. So, one thing we can do is we give an estimate based on statistics. We say, 60% of marriages break up. Not all, just 60%. That's a prediction for the future. On average, knowing nothing about the couple, 60% of the time the couple will divorce. Now, that doesn't mean that a couple will get a 60% divorce, of course. It simply means that for every 10 couples, 6 will end their marriage in a divorce. It may not be DETERMINISTIC for a single, unique, and isolated measurement, but it is still a prediction.

The confidence interval is even more basic than that. All it says is that I can use the idea that I'm somewhere in the middle of the distribution on the timeline to estimate the total lifetime of a given event. For example: a marriage. I can estimate the total length of the marriage if I'm simply observing at a nonspecial (random) location on the timeline to be distributed as lifetimes are, in some sort of length distribution. If I'm in the middle, I can use basic statistics to offer a probability that the marriage will be longer than one length but shorter than another. I could be wrong, as can most predictions that are involving different outcomes (existence vs. nonexistsence). After all, I'm only given a percent likihood as above. But the idea is if I took this same measurement over and over and over again for lots of different lifetimes (and I actually need not restrict myself to marriages) I'd find I was right as much as my confidence interval says I should be.

All this says is there's nothing particularly special about any event duration or any observation made therein. This is true for any and all things with finite liftimes. Period. Why? Simply because if you aren't at the ends you've got to be in the middle. We can say that lifetimes in general behave a certain way when I observe them at a random point in between. This is a tautology, in fact. If I observe at a random time I'm not likely to be near the beginning or the end. However, every once in a while I can be unlucky and find myself there.

This is why the method works and how it makes predictions. The probabilities just tell us how often we expect to be right and wrong, and they work for all events. If we could get an unbiased sampling of lifetimes we'd find that we were most of the time in the middle of the lifetimes and the method would adequately predict the future longevity of the majority of our sample determined by the confidence interval we choose.

JS Princeton
2002-Dec-09, 10:36 PM
Thus, Gott's apparent pride in the wall coming down during his interval seems a little silly to me . . .


Well, in all fairness, he wouldn't have had pride if the wall hadn't come down in time. /phpBB/images/smiles/icon_smile.gif which as you point out rightly was a distinct possibility.

We are all only human and get excited when something we bet on wins (especially if the odds are 50/50). Wouldn't you brag about winning a coin toss? Just a little?

<font size=-1>[ This Message was edited by: JS Princeton on 2002-12-09 17:37 ]</font>

Zathras
2002-Dec-09, 10:42 PM
On 2002-12-09 17:10, JS Princeton wrote:
. . .
Zatras-- you indicate that if there is a finite probability that something will last beyond the confidence interval, then the method fails. Actually, this is absolutely false. The finite probability the method will fail is the tail that's beyond the confidence interval. In that way, the method predicts exactly what you say.


Selective misquotation. I did not say "finite probability." I said "non-negligible probability." In this context, that means more than 10%.

I can tell how much you like Gaussians, and they do make certain calulcations simpler. But not everything's a Gaussian, even to first order.

I'd like to see some numbers on this, by the way. Pick a reasonable estimate of how long man has been around, and then give me what you consider to be the 95% confidence intervals. Or give me the function for which I ask below.



What's the chance that humans survive to the end of the universe? Pretty slim because there's lots of things that can happen to get rid of us non-special insignificant things in the meantime.

So again, you have not shown the method to be false but have missed the fact that the confidence interval tells you EXACTLY WHAT ONE EXPECTS given a random selection function observation of a time during the lifetime of a particular thing.

And that's all she wrote.

You seem to think that it will fail MORE than is indicated by the method, but you see, Zatras, that's ONLY correct if your sampling is skewed by not choosing a random time in the lifetime of the thing OR by choosing something that doesn't have a finite age. You admit that it's finite, but then you want to say, "but it's so far in the future it might as well be infinite."

Huh uh, sorry. If you think we are special then we might be early in the lifetime of humanity then we are measuring in the tails. There is a finite probability that this should be the case, but it's no means the most likely scenario. The most likely scenario is that we're in the middle of the lifetime of humanity. Again, that's most likely. That's all that is being said. How can you possibly argue with it?


You are being very imprecise when it comes to a definition of random. "Random" does not have to mean it has the normal distribution of a Gaussian. It is of course a syllogism to say that an event is 95% likely to fall within the 95% confidence interval for the event. What you are assuming is a very particular form of the selection function, one that does not necessarily hold.

To be clear on this, give me a function that you think would relate the width of the outer bounds of the confidence interval to the age of the item being studied. Without this, your analysis is too vague to say much more about.

Also, let me give you a more specific example. Suppose I have a nucleus that was formed 10s ago, but I don't know what it is.* Does that tell me that it will likely live a short time? NO! The vast majority of nuclei formed in the universe are completely stable nuclei, such as Helium, Carbon, or even Iron. Therefore, we can expect this nucleus to be around for much, much longer then what (I think) your analysis would say. Without some more specificity on your part, I cannot say for sure.

*BTW, you still have not answered my question when we know the atoms are the same. An atom of Carbon 14 that is 3000 years old has the exact same expected lifetime as an atom of Carbon 14 that is 2 months old.

SeanF
2002-Dec-09, 10:46 PM
On 2002-12-09 17:36, JS Princeton wrote:


Thus, Gott's apparent pride in the wall coming down during his interval seems a little silly to me . . .


Well, in all fairness, he wouldn't have had pride if the wall hadn't come down in time. /phpBB/images/smiles/icon_smile.gif which as you point out rightly was a distinct possibility.

We are all only human and get excited when something we bet on wins (especially if the odds are 50/50). Wouldn't you brag about winning a coin toss? Just a little?

<font size=-1>[ This Message was edited by: JS Princeton on 2002-12-09 17:37 ]</font>


Oh, heck yes! At the place I used to work at, we had an afternoon ritual where a bunch of us would get together and flip quarters to get an "odd man out." That person would then have to by a Coke for everybody who participated. It always felt good to win, even if it was just random chance.

However, by his own recounting of the story, Gott didn't say, "The wall will come down during this time interval." He simply said, "There's a 50% chance the wall will come down during this time interval." My point was that he would be entitled to the same amount of pride either way - and I don't feel any pride in losing the coin toss! (Especially when I have to buy eight cans of Coke because of it!)

/phpBB/images/smiles/icon_biggrin.gif


<font size=-1>[Editied because the Smilies Code won't let you do a grin and a wink on the same face!]</font>
_________________
SeanF


<font size=-1>[ This Message was edited by: SeanF on 2002-12-09 17:48 ]</font>

JS Princeton
2002-Dec-10, 04:08 AM
On 2002-12-09 17:42, Zathras wrote:

Selective misquotation. I did not say "finite probability." I said "non-negligible probability." In this context, that means more than 10%.



The onus is on you to demonstrate that is more than 10%.



I can tell how much you like Gaussians, and they do make certain calulcations simpler. But not everything's a Gaussian, even to first order.


But measurements during anything that has a finite lifetime has to be a Gaussian if it has a lifetime. This is because there is only one parameter for time.



I'd like to see some numbers on this, by the way. Pick a reasonable estimate of how long man has been around, and then give me what you consider to be the 95% confidence intervals.

Human civilization has been around for 6000 years say. That means we expect it to be around at least 300 more years or 120,000 more years for a 95% confidence interval.



You are being very imprecise when it comes to a definition of random. "Random" does not have to mean it has the normal distribution of a Gaussian.

No, random is a difficult thing to define. All I'm saying is our choice of an observation in time might as well be random for a given event.


It is of course a syllogism to say that an event is 95% likely to fall within the 95% confidence interval for the event.

Indeed.


What you are assuming is a very particular form of the selection function, one that does not necessarily hold.


I will cautiously agree to this statement. It might be that somehow people who use this analysis might fall only in the tails of the distribution causing it to always fail! This would certainly be a pretty strange conspiracy, though.



To be clear on this, give me a function that you think would relate the width of the outer bounds of the confidence interval to the age of the item being studied.

The function is defined simply by the percentage you give as I outlined on the very first page of this post. If you have an issue with it, spell it out plainly. We use something that simple because time marches on in a "linear" fashion for most of us, and we don't think a particular "instant" is any more special than any other.



Without this, your analysis is too vague to say much more about.


I have been arguing that the argument is vague and we might as well stop arguing about it. After all, it gives as big an estimate for the projected age for humanity as you want... determined simply by what you choose your confidence interval to be. I guess people just get upset when you put percents on things they feel strongly about (like humanity).



Also, let me give you a more specific example. Suppose I have a nucleus that was formed 10s ago, but I don't know what it is.* Does that tell me that it will likely live a short time? NO!

Yes it does. You know why? Because the vast majority of nuclei that are observable are much older than this. You have chosen a nuclei that is very young and therefore are more likely to be sitting on one that has a lifetime in the order of magnitude of seconds rather than millenia. This is just because you'd expect to see the nuclei in the middle of its life rather than the beginning.


The vast majority of nuclei formed in the universe are completely stable nuclei, such as Helium, Carbon, or even Iron.

This is true, but if you are picking things as they are formed it is like predicting the length of marriages at the time of the taking of vows. You need to pick an object that isn't special: namely, you cannot exclude nuclei that are of any age. They all have to be included. If you do that, most nuclei you find will not be a few seconds old!

Now, we run into some interesting problems if you DEMAND that we restrict our sample to these special groups. Then it's a more difficult question. I cannot predict how long a marriage will last for just newlywed couples without looking at overall distributions. This is where quantum mechanics comes into play for nuclei. The method isn't applicable for nuclei that are "just born". It is only applicable for generalized nuclei... nuclei we pick not for their age but rather because we just happened to observe them in a non-special, Copernican location in space and time.


Therefore, we can expect this nucleus to be around for much, much longer then what (I think) your analysis would say.

Just as we expect marriages at the altar to last longer than the method would say. Indeed, we cannot restrict our method to special points in lifetimes or we will get wrong answers.


Without some more specificity on your part, I cannot say for sure.


This is where the assumption of the Copernican Principle MUST come into play. We have to decide whether we are at a special location or not.

It may simply be a matter of belief. I talked with someone who couldn't decide whether we were at a special location in the time of humanity's endurance. That's a perfectly reasonable thing to think, but I'm inclined to believe there isn't anything special. That's just me.



*BTW, you still have not answered my question when we know the atoms are the same. An atom of Carbon 14 that is 3000 years old has the exact same expected lifetime as an atom of Carbon 14 that is 2 months old.


True, but it's very rare in all the Carbon-14 atoms that are now around for us to find one that is 2 months old. It just doesn't happen nearly as much as we find one that is thousands of years old. That's the point of the analysis. It says nothing about individual measurements. It is talking about the generalized measurements of the same TYPE (being non-special).

JS Princeton
2002-Dec-10, 04:17 AM
However, by his own recounting of the story, Gott didn't say, "The wall will come down during this time interval." He simply said, "There's a 50% chance the wall will come down during this time interval." My point was that he would be entitled to the same amount of pride either way - and I don't feel any pride in losing the coin toss! (Especially when I have to buy eight cans of Coke because of it!)


Well, the point of the matter is when you assign the odds usually you end up choosing a side. He assigned 50/50 odds and it probably seemed at the time that the wall looked like it was going to stay around forever (it was the height of the cold war, after all). I assume what he meant was that he had a 50% chance of getting the right answer either way and he just chose the more interesting one as a validation. In all fairness he doesn't even say he was vindicated, only that he said there was a 50% probability that it come down within the confidence interval. He could have also bet that it would occur anywhere BUT in that confidence interval. Of course, that isn't as exciting, I would say /phpBB/images/smiles/icon_smile.gif

SeanF
2002-Dec-10, 02:16 PM
Good point, JS. He does say, "I made no prediction of why the Berlin Wall would end, just how much longer it was likely to last,"
which would seem to indicate he was saying it was going to fall. In that matter, though, I question the usage of the word "likely" in relation to 50% odds. /phpBB/images/smiles/icon_smile.gif

As for him feeling vindicated, I do get that impression from the his last paragraph.

traztx
2002-Dec-10, 07:36 PM
We have to be careful when we put trust in people who are good at predicting things.

A devious idea: Send out 512 letters to people predicting a certain volatile stock will go up. Send out 512 letters to other people predicting that the same stock will go down.

The next day, see which prediction was right. Then divide those people into 2 groups of 256 who get a letter saying it will go up and 256 saying it will go down.

The next day, see which prediction was right. Then divide those people into 2 groups of 128 and repeat.

Pretty soon you have a group of people who would bet their life savings on you. Now ask them to send their money and RUN AWAY!!!

(They'll eventually catch you, of course)

JS Princeton
2002-Dec-10, 09:08 PM
On 2002-12-10 09:16, SeanF wrote:
Good point, JS. He does say, "I made no prediction of why the Berlin Wall would end, just how much longer it was likely to last,"
which would seem to indicate he was saying it was going to fall. In that matter, though, I question the usage of the word "likely" in relation to 50% odds. /phpBB/images/smiles/icon_smile.gif

As for him feeling vindicated, I do get that impression from the his last paragraph.




I just talked to Gott today. When he started writing the papers for Refereed Journals he changed the confidence interval to 95% so that if he was wrong, "it would be embarassing."

In any case, he shared all kinds of anecdotes about this hypothesis and I'm nearly convinced that he knows what he's talking about.

He wrote a paper for Nature Vol 363 27 May 1993 "Implications of the Copernican principle for our future prospects" that addresses in good detail what "L" in the Drake Equation is. Check it out if you are still dubious.

By the way, he got livid when I mentioned atoms. The argument that it doesn't work for radioactive decay is "fallacious" said Gott, since observations are going to be weighted by the lifetime. He actually ASSUMES that there is some established decay rate 1/e upon tau and so forth in his argument for civilization lifetimes in the Nature paper!

JS Princeton
2002-Dec-10, 09:09 PM
On 2002-12-10 14:36, traztx wrote:
We have to be careful when we put trust in people who are good at predicting things.

A devious idea: Send out 512 letters to people predicting a certain volatile stock will go up. Send out 512 letters to other people predicting that the same stock will go down.

The next day, see which prediction was right. Then divide those people into 2 groups of 256 who get a letter saying it will go up and 256 saying it will go down.

The next day, see which prediction was right. Then divide those people into 2 groups of 128 and repeat.

Pretty soon you have a group of people who would bet their life savings on you. Now ask them to send their money and RUN AWAY!!!

(They'll eventually catch you, of course)


That pyramid scheme is a classic, to be sure, but it is manifestly not what Gott is talking about.

Zathras
2002-Dec-10, 09:29 PM
On 2002-12-10 16:08, JS Princeton wrote:


On 2002-12-10 09:16, SeanF wrote:
Good point, JS. He does say, "I made no prediction of why the Berlin Wall would end, just how much longer it was likely to last,"
which would seem to indicate he was saying it was going to fall. In that matter, though, I question the usage of the word "likely" in relation to 50% odds. /phpBB/images/smiles/icon_smile.gif

As for him feeling vindicated, I do get that impression from the his last paragraph.




I just talked to Gott today. When he started writing the papers for Refereed Journals he changed the confidence interval to 95% so that if he was wrong, "it would be embarassing."

In any case, he shared all kinds of anecdotes about this hypothesis and I'm nearly convinced that he knows what he's talking about.

He wrote a paper for Nature Vol 363 27 May 1993 "Implications of the Copernican principle for our future prospects" that addresses in good detail what "L" in the Drake Equation is. Check it out if you are still dubious.

By the way, he got livid when I mentioned atoms. The argument that it doesn't work for radioactive decay is "fallacious" said Gott, since observations are going to be weighted by the lifetime. He actually ASSUMES that there is some established decay rate 1/e upon tau and so forth in his argument for civilization lifetimes in the Nature paper!


Why is he so testy about this? It's not the first time he has become so impatient with the ignorance of another who cannot understand his brilliance:

http://physicsweb.org/article/news/4/2/6/1


Here is a good critique of his application of these ideas:
http://www.anthropic-principle.com/preprints/inv/investigations.html

TriangleMan
2002-Dec-10, 10:08 PM
When I looked at the Drake equation I found it did not account for:

1) that the civilization would be aware of outer space (cloud cover, intelligent underwater life, poor or short-sighted vision)

2) that the civilization would be inclined to explore space. Humans are a very curious species after all, an alien race could just not care about exploring space, or be technologically advanced but still steeped in cultural/religious beliefs that prevent development of space travel.

3) poorly-suited biologically for space travel (ex. biological inability to cope with zero G's)

With these factors in the equation you still get a number of alien races in the galaxy but less likelhood that they will contact/visit us.

SeanF
2002-Dec-10, 10:44 PM
On 2002-12-10 16:29, Zathras wrote:

It's not the first time he has become so impatient with the ignorance of another who cannot understand his brilliance:

http://physicsweb.org/article/news/4/2/6/1



Well, I don't know about Gott's brilliance, but Caves does seem ignorant. His proposed experiment is skewed against Gott.

Gott's hypothesis is really just simple statistics. All dogs spend half their life at less than half their dying age, and half their life at more than half their dying age, right? Ergo, 50% of all the dogs that exist right now are in the first half of their life, and the other 50% are in the second half. Ergo, if you randomly choose a dog, there is a 50% chance you'll get one in the first half of its life. Ergo, a randomly-selected dog has a 50% chance of living to twice its current age.

Caves did not randomly select the six dogs (he specifically selected them from amongst the older dogs), therefore his proposed experiment is not a valid statistical test.

Is the human race a valid statistical test for Gott's hypothesis? Take a look at extinct species. If you randomly select a species, and randomly select a time during that species' life, half the time you'll end up in the second half of that species' existence. So, if you consider the human race to be randomly selected, and today to be a random date, then there's a 50% chance that today is in the second half of our species' existence.

I can understand Grapes' concerns that there's nothing inherently useful or amazing about this, but it certainly is valid, I think.

JS Princeton
2002-Dec-11, 04:16 AM
SeanF --

Thanks for the poignant defense. I would say Bostrom is off the mark because he chooses subjective priors for Bayseian statistics he is doing.

Gott mention this to me today.

There are basically three types of priors

1) database priors. These are things that are gathered from statistical sampling. Arguably the best priors you can get in science, but unfortunately we only have ONE example of an intelligent civilization (our own).

2) vague priors. This is the prior Gott uses in his Science article in 1993 that I quoted. It gives an estimate for L that is based upon assuming nothing but the Copernican Priciple. It is a bit more complicated than the simple confidence interval because you have to find an "average" rather than an "expected" lifetime, but that's dealt with rather nicely in the article.

3) subjective priors. This is what Bostrom seems to think is the best. Only it's full of nonsense. It is basically assuming that human beings ARE special in the realm of things, that we may very well not be like all the other intelligent species in the world. While this may be true, when you bet on being special you usually tend to lose.

Basically, anyone who uses the first prior listed gets larger error bars than does Gott in his analysis and anyone who uses method 3 is basically just making things up. I have to say I think Gott has done a good job of covering his bases.

GrapesOfWrath
2002-Dec-11, 06:59 AM
On 2002-12-10 16:08, JS Princeton wrote:
He wrote a paper for Nature Vol 363 27 May 1993 "Implications of the Copernican principle for our future prospects" that addresses in good detail what "L" in the Drake Equation is. Check it out if you are still dubious.
Yeh, that's the one (http://www.badastronomy.com/phpBB/viewtopic.php?mode=viewtopic&topic=3025&forum=2&start=81) I was going to go look for, I think. There was something funny about it...


By the way, he got livid when I mentioned atoms. The argument that it doesn't work for radioactive decay is "fallacious" said Gott, since observations are going to be weighted by the lifetime. He actually ASSUMES that there is some established decay rate 1/e upon tau and so forth in his argument for civilization lifetimes in the Nature paper!

I did a websearch, and came up with this comment by Alan Dix (http://www.hiraeth.com/alan/misc/gott-nov97/gott.html) about an article that Gott must have written for New Scientist in 1997--but I don't have a copy of that article either. Did Gott make the calculation for space travel in his article, or does Dix throw that in?

Basically, it says that using the method, applied to space travel, the end of space travel is likely within 1248 years.

JS Princeton
2002-Dec-11, 02:27 PM
Yes, Gott does the calculation for space travel as well (though in a different context, not in the Science paper). Of course, it's done with a 95% confidence interval so it's not absolutely certain. Nothing ever is! Nevertheless, the point is that things with finite liftimes that are observed at non-special times tend to be observed in the middle of their existences.

GrapesOfWrath
2002-Dec-11, 02:33 PM
On 2002-12-11 09:27, JS Princeton wrote:
Yes, Gott does the calculation for space travel as well (though in a different context, not in the Science paper).
Science paper? Which paper is that? I might be able to get ahold of that easily.

JS Princeton
2002-Dec-11, 09:27 PM
Sorry, the paper was in Nature. My mistake.

Argos
2002-Dec-12, 01:02 PM
On 2002-12-10 17:08, TriangleMan wrote:
When I looked at the Drake equation I found it did not account for:

1) that the civilization would be aware of outer space


Remeber Asimov's "Nightfall"? A story of a civilization which wasn't aware of outer space because there was always two suns in the sky.

In fact, the way we perceive space has a very important role in the way we conceptualize the cosmos, in the development of philosophy.

But I think that a technological civilization would easily infer the existence of the outer space. A technology expertise like we had in the 17th century would suffice.

<font size=-1>[ This Message was edited by: Argos on 2002-12-12 08:07 ]</font>

TriangleMan
2002-Dec-12, 01:45 PM
On 2002-12-12 08:02, Argos wrote:

But I think that a technological civilization would easily infer the existence of the outer space. A technology expertise like we had in the 17th century would suffice.

<font size=-1>[ This Message was edited by: Argos on 2002-12-12 08:07 ]</font>


With only one inhabited planet to draw conclusions from (Earth) its hard to say what percentage of civilizations would be aware of space. Still, I also believe that most would have knowledge of space (Drake equation modification of .96 to .98). It was just another factor modifying the equation.

GrapesOfWrath
2002-Dec-13, 08:30 AM
I still may be able to look that paper up, maybe if I just could find my old copy of my letter (it's on a different computer).


On 2002-12-11 09:27, JS Princeton wrote:
Yes, Gott does the calculation for space travel as well (though in a different context, not in the Science paper). Of course, it's done with a 95% confidence interval so it's not absolutely certain. Nothing ever is! Nevertheless, the point is that things with finite liftimes that are observed at non-special times tend to be observed in the middle of their existences.

Well, that makes our time of space travel a lot shorter than our existence as a species. I mean, as a prediction. That's interesting. Of course, we'll be 95% certain that we'll keep going, right up until we stop, right? /phpBB/images/smiles/icon_smile.gif

boron10
2002-Dec-14, 01:25 AM
GrapesOfWrath:
Of course, we'll be 95% certain that we'll keep going, right up until we stop, right?

Yes, but 5% of us will be wrong, eh? This brings us right back to the problem of "utility." There is nothing novel about this idea, it is merely a WAG disguised as a statistical analysis.

GrapesOfWrath
2002-Dec-15, 02:10 PM
On 2002-12-13 20:25, boron10 wrote:
Yes, but 5% of us will be wrong, eh?
If we all used the method, then we'd all be wrong, at the end.

V01d
2002-Dec-16, 01:45 PM
But the Drake's equation is based on assumptions that we would expect aliens to have. Maybe thats not what exists there afterall. I mean bacteria don't know what we are, but :? maybe we're the kinds of bacteria to some other kind ??? How about an answer ??
/phpBB/images/smiles/icon_lol.gif
/phpBB/images/smiles/icon_lol.gif

GrapesOfWrath
2002-Dec-16, 01:56 PM
On 2002-12-16 08:45, V01d wrote:
How about an answer ??
What's the question?

And welcome to the BABB.

snowcelt
2003-Apr-06, 02:09 PM
This was a great read! The argument cleared up for me many points in an argument precented by John Leslie in his book THE ETHICS OF HUMAN EXTINTION. The argument is the geocentric veiw of Drake's "L" ;however, the argument works well with any imaged alien spieces as well. Have not a clue as to place those blue links, just look up human extintion and you will find some intellegent arguments both pro and con.