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tommac
2009-Jun-16, 10:57 PM
Is math useful for clarification of an idea?
Or
Is math the only way to understand an issue in physics?

PraedSt
2009-Jun-16, 11:03 PM
Not this again. :)

For physics you need the maths Tommac. Especially for the Relativity stuff that you're interested in.

alainprice
2009-Jun-16, 11:05 PM
Math is fundamental in many aspects. Math essentially leads to physics, not the other way around.

Look at General Relativity. Einstein spent many years with mathematicians before he could even write out GR. Before that came Special Relativity, based entirely on 2 simple ideas and math. Even SR wouldn't have been possible if it weren't for Maxwell, an excellent mathematician with a keen sense of discovery.

Have you done calculus to the point of 2nd order and higher calculus as well as partial derivatives? All those years of working on math leads to a simple understanding of many things.

robross
2009-Jun-16, 11:07 PM
Is math useful for clarification of an idea?
Or
Is math the only way to understand an issue in physics?

Math is a way to create abstract, self-consistent models of reality. It's not really an issue of "does this equation describe reality" as is the question "does this equation allow us to make predictions about the future?" If it does, it's a useful tool in itself.

There's really nothing quite like math for being able to predict the future. Without it, you're back to the pre-scientific method of determining "truth", and you might as well go back to trying to use sheep's entrails to predict the orbits of the planets.

Rob

tommac
2009-Jun-16, 11:08 PM
Not this again. :)

For physics you need the maths Tommac. Especially for the Relativity stuff that you're interested in.

Agreed ... But you can understand some of the concepts without understanding the complicated math. Even by design I believe that Einstein avoided the math ... but Grossman tricked him into using it for GR.

I guess a better way to word the problem is ... how to approach a problem, start with the math or start with logic?

tommac
2009-Jun-16, 11:09 PM
Math is fundamental in many aspects. Math essentially leads to physics, not the other way around.

I disagree with this. Without us trying to figure out how things work there would be no math.

KaiYeves
2009-Jun-16, 11:09 PM
Math is to Science as Grammar is to Writing.

The boring stuff you have to know before you can get to the fun stuff.

tommac
2009-Jun-16, 11:10 PM
This is an interesting take ... basically you are saying that math allows you to extrapolate and deduce ...

However in order to do that you need to understand the problem in logic first. Or do you just think in math?


Math is a way to create abstract, self-consistent models of reality. It's not really an issue of "does this equation describe reality" as is the question "does this equation allow us to make predictions about the future?" If it does, it's a useful tool in itself.

There's really nothing quite like math for being able to predict the future. Without it, you're back to the pre-scientific method of determining "truth", and you might as well go back to trying to use sheep's entrails to predict the orbits of the planets.

Rob

alainprice
2009-Jun-16, 11:13 PM
Other examples include quantum mechanics, Fourier analysis(I'm a speaker buff, so yeah), actuarial science(insurance and so forth), statistics(this one is HUGE).

A lot of great discoveries are made when someone makes a crazy claim, someone else formulates it mathematically and makes predictions with it, and then it's tested and proven. Schrodinger wasn't proud of his now famous equation. The 'poisson' spot in diffraction was an attempt by Poisson to discredit Fresnel wave theory of light. Einstein developed a lot of the ideas used in QM, yet didn't take it seriously enough.

alainprice
2009-Jun-16, 11:19 PM
I don't know where you got the idea that Einstein was bad at math, or avoided it.

In reality, like a good programmer, he was excellent at taking a coherent idea and translating into equations on paper. He could do stats, as he discovered that energy levels are quantized in the search for cavity radiation. He even formulated planck's constant but didn't realize it had any meaning yet.

Tim Thompson
2009-Jun-16, 11:31 PM
Even by design I believe that Einstein avoided the math ... but Grossman tricked him into using it for GR.
Not by a long shot. The popular myth of Einstein being somehow lousy at math is just that, a popular myth. He was in fact quite good at it. It was Einstein who was the driving force behind the mathematical development of GR, going to Grossman and others for help when he knew he needed new tools to develop the necessary math. Newton solved the problem by inventing calculus for himself. Einstein did not need to do that, he only needed to find the right tool already in the hands of mathematicians.


I guess a better way to word the problem is ... how to approach a problem, start with the math or start with logic?
Logic & math are inseparable, at least in the context of the natural sciences. Math is the natural language of logic, so in order to understand the logic at any level beyond the most rudimentary, you must do the math.


But you can understand some of the concepts without understanding the complicated math.
For the most part, this too is a popular myth. You may think you "understand" an idea without the "complicated math" (which is often not really all that complicated, ust specialized). But in reality there are always key points left out or skipped over because the math, complicated or not, is still missing. This is something I have come to learn from years of trying to design talks and articles explaining those very ideas to totally non mathematical audiences. I have become quite skeptical & critical of almost all of the popular explanations I see because they are so over simplified that they just get it wrong, or get it so misleading as to make it essentially wrong.

if you can't or don't do the mathematics then you have literally no hope at all of ever really understanding general relativity, or really any other aspect of modern physics, beyond the legendary "cave man" level.

PraedSt
2009-Jun-16, 11:49 PM
Agreed ... But you can understand some of the concepts without understanding the complicated math. Even by design I believe that Einstein avoided the math ... but Grossman tricked him into using it for GR.

I guess a better way to word the problem is ... how to approach a problem, start with the math or start with logic?
Maths will limit your understanding of physics Tommac.

Judging by your threads, you seem to love physics; so why don't you take the time to learn some more maths? You'll probably get more out of it than any of us.

(And Grant will be relieved). :D

Gillianren
2009-Jun-17, 12:04 AM
I can't tell you how thrilled I am that this conversation is happening again. Someone needs to keep a Binary-Man style of list.

tommac
2009-Jun-17, 12:40 AM
Even for statistics ... you dont need to know math. What I mean by this is that you can understand the concepts without having to work through the detail. Like a lognormal distribution for example ... You dont need to know how to calculate the 99 percentile mark to understand that something may resemble a log normal distribution and that at some point you know that it is fairly unlikely that an event will happen.


Other examples include quantum mechanics, Fourier analysis(I'm a speaker buff, so yeah), actuarial science(insurance and so forth), statistics(this one is HUGE).

A lot of great discoveries are made when someone makes a crazy claim, someone else formulates it mathematically and makes predictions with it, and then it's tested and proven. Schrodinger wasn't proud of his now famous equation. The 'poisson' spot in diffraction was an attempt by Poisson to discredit Fresnel wave theory of light. Einstein developed a lot of the ideas used in QM, yet didn't take it seriously enough.

tommac
2009-Jun-17, 12:48 AM
From Kip thornes book.

I dont have the exact quotes but it stated that he tried to resist any complex math. Also that he was lazy when it came to math. I think second chapter or there abouts





I don't know where you got the idea that Einstein was bad at math, or avoided it.

In reality, like a good programmer, he was excellent at taking a coherent idea and translating into equations on paper. He could do stats, as he discovered that energy levels are quantized in the search for cavity radiation. He even formulated planck's constant but didn't realize it had any meaning yet.

tommac
2009-Jun-17, 12:50 AM
But einstein was relatively weak in math .... his main strength lies in his ability to reason and think through a problem.

Quotes such as Imagination is more important than knowledge clearly shows which he thought was more important.


I don't know where you got the idea that Einstein was bad at math, or avoided it.

In reality, like a good programmer, he was excellent at taking a coherent idea and translating into equations on paper. He could do stats, as he discovered that energy levels are quantized in the search for cavity radiation. He even formulated planck's constant but didn't realize it had any meaning yet.

Gharlane
2009-Jun-17, 12:50 AM
Without maths no-one here would be able to tell Tommac what is so good about maths.:)

tommac
2009-Jun-17, 12:54 AM
Not by a long shot. The popular myth of Einstein being somehow lousy at math is just that, a popular myth. He was in fact quite good at it. It was Einstein who was the driving force behind the mathematical development of GR, going to Grossman and others for help when he knew he needed new tools to develop the necessary math.


I am sure he was above average ... but even here you hit on the point that I am hinting at. He knew what needed to be calculated and had someone else help him develop that. He didnt know the math. And would have failed the ATM section when some idiot would ask him to do "the maths". He didnt know and needed Grossman to help him fill in the blanks. In addition he did resist it for a while.

I never state that the math ( note no s ) is not important ... i just dont feel that either :
A) it is the driving force for anything of use
B) the only way to understand complex situations

kleindoofy
2009-Jun-17, 01:00 AM
But einstein was relatively weak in math ...
Says who?

And please don't cite that bovine excrement urban legend about him flunking out in school.


... you can understand the concepts without having to work through the detail ...
Yeah, and you can play Chopin without worrying about all those bothersome 16ths and 32nds that clutter up his pieces. Just pick out the notes you want to play. Scales? Why practice scales?

Without the math, one is and remains an amateur.

tommac
2009-Jun-17, 01:03 AM
Logic & math are inseparable, at least in the context of the natural sciences. Math is the natural language of logic, so in order to understand the logic at any level beyond the most rudimentary, you must do the math.


Hmm ... I dont know ...
I believe that they are inseparable but I dont think that you need to do the math to understand the logic ... but rather than logic represents math.

To understand that one can calculate the area under a curve or the volume in funnel doesnt mean that you cant use a curve or a funnel ... or that you cant understand how a funnel works ...

I think sometimes the math just makes things harder to picture and understand ...

Yes ... I do think that if you need to figure out the exact flow of water through the funnel ... you may need to do some math. But you can hold off until you need to do that calculation

PraedSt
2009-Jun-17, 01:03 AM
He knew what needed to be calculated and had someone else help him develop that. He didnt know the math. And would have failed the ATM section when some idiot would ask him to do "the maths".I think this is where you're going wrong. If some "idiot" had asked him to show the maths, he would have said "you're right; I'll go, get the maths, and come back with it." Which is exactly what he did really.

tommac
2009-Jun-17, 01:07 AM
What math do you want me to know? All of it? I am holding off on learning stuff until I need to. until know I have not felt the need to bolster my mathematical knowledge.

when someone posts randomly ... "Show the maths" ... who knows what they are talking about ...

If you ask me to do a particular calculation I may try to give it a shot.

more than loving physics I am a master debater ( and in fact a cunning linguist).


Maths will limit your understanding of physics Tommac.

Judging by your threads, you seem to love physics; so why don't you take the time to learn some more maths? You'll probably get more out of it than any of us.

(And Grant will be relieved). :D

tommac
2009-Jun-17, 01:09 AM
Says who?

I do. He was a much better physicist/intuitive thinker than he was mathematician.

01101001
2009-Jun-17, 01:10 AM
[...] I dont know ...
I believe [...] I dont think [...] logic represents math.

To understand [...] doesnt mean [...]

I think [...]

I do think [...] [Y]ou can [...]

Why did you stop asking Q&A questions and start making statements?

Please use your Q&A topics to ask questions. Thanks.

PraedSt
2009-Jun-17, 01:13 AM
What math do you want me to know? All of it? I am holding off on learning stuff until I need to. until know I have not felt the need to bolster my mathematical knowledge.Enough maths to understand your topic of course. And you cannot be serious about the rest of it. This thread and your GR threads are proof that "you need to", and the fact that you have so much difficulty understanding GR shows that you need to "bolster your mathematical knowledge".

I'm amazed that you can say you haven't felt the need. Why are we having this conversation then?

tommac
2009-Jun-17, 01:14 AM
Yeah, and you can play Chopin without worrying about all those bothersome 16ths and 32nds that clutter up his pieces. Just pick out the notes you want to play. Scales? Why practice scales?

I can personally tell you that you dont need to learn or practicescales or learn about or practice 16th or 32nds to play chopin. You can just focus and play it ... Sometimes it is easier to just learn the piece without thinking about it too much ... it sometimes can help you learn something but sometimes it just doesnt matter. there are many great musicians that havent been trained and learned just by loving the music.

OR you can learn to enjoy it ... maybe even get a deeper feeling of what he was trying to portray with the song that he wrote. Maybe if you closed your eyes even visualize a meaning to the music.



Without the math, one is and remains an amateur.

Sure ... but it can still be fun ...

kleindoofy
2009-Jun-17, 01:15 AM
I do. ...
Would you care to cite some references or sources?

Or are references and sources as unimportant as math and as such unnecessary for understanding the basic issues?

"I make things up, therefore I am"?

kleindoofy
2009-Jun-17, 01:18 AM
... chopin. ... the song that he wrote ...
:wall: :wall: :wall:

tommac
2009-Jun-17, 01:22 AM
Would you care to cite some references or sources?

Just ask on the board ... lets post a poll.

antoniseb
2009-Jun-17, 01:24 AM
Just ask on the board ... lets post a poll.
No, please give references. Don't palm this off on anyone else. If you post a poll on this, I will remove it.

tommac
2009-Jun-17, 01:27 AM
No, please give references. Don't palm this off on anyone else. If you post a poll on this, I will remove it.

This is an opinion ... but it is clear in Kip thorns book that he agrees ...

Cougar
2009-Jun-17, 01:28 AM
...I am a master debater...

I would argue against that proposition. Debating disallows negligently making things up and presenting them as facts.

tommac
2009-Jun-17, 01:29 AM
I would argue against that proposition. Debating disallows negligently making things up and presenting them as facts.

hah ... :whistle:

Middenrat
2009-Jun-17, 01:45 AM
Tommac already cited Kip Thorne's book, chapter Two, as evidence of Einstein's non-dominance in maths.
But Tommac, you most certainly cannot 'groove' on Chopin as you suggest. The results would be laughable, I'm chuckling as I type.

WayneFrancis
2009-Jun-17, 03:05 AM
Is math useful for clarification of an idea?
Or
Is math the only way to understand an issue in physics?

math is the language of physics. Can you understand physics in other ways? Sure but if you know the maths behind a concept you'll understand the concept even better.

Take, for example you favorite concepts, gravity and Black Holes. You have, on a number of occasions made claims that at first glance might seem probable, if you don't understand the math. When shown the facts and math most people, I would hope, would change their understanding of the universe. It hopefully will even given them a better mental picture of what is going on, without the maths.

WayneFrancis
2009-Jun-17, 03:12 AM
Agreed ... But you can understand some of the concepts without understanding the complicated math. Even by design I believe that Einstein avoided the math ... but Grossman tricked him into using it for GR.

I guess a better way to word the problem is ... how to approach a problem, start with the math or start with logic?

You can have an understanding of it....but that doesn't mean you'll make accurate conclusions based on your understanding.

Take Gravity. Many people understand the "funnel" analogy of gravity. Less people understand many of the implications of this. For example I'd wager most people still think that if our sun was a black hole that the earth would get sucked in. Look how many people are worried about the LHC producing a BH with the mass of 2 alpha particles. They have an understanding of a BH but the maths would show them that they have nothing to worry about from a BH that size.

Valkyrie801
2009-Jun-17, 03:16 AM
Math is really good at figuring trajectories of objects moving through space with object weight/densities/momentum in mind to calculate gravitational forces while circumnavigating the Galaxy...

It is also real good for giving the correct change to a customer while a cashier.:rolleyes:

alainprice
2009-Jun-17, 03:21 AM
Imagine a laser sitting in a shoebox. Each photon has the same wavelength, and is discrete. The shoebox has dimensions of your choosing. Show, using special relativity, that E=mc2.

It's a simple derivation that a high schooler should be able to solve.

Try it, and then I can try it myself if you want.

Hint: give the box a certain mass and use momentum for your calculations.

Middenrat
2009-Jun-17, 03:23 AM
Much as I hate to spoil a pithy, well-constructed and funny post with tedious detail... the cashier is using arithmetic.

WayneFrancis
2009-Jun-17, 03:27 AM
I am sure he was above average ... but even here you hit on the point that I am hinting at. He knew what needed to be calculated and had someone else help him develop that. He didnt know the math. And would have failed the ATM section when some idiot would ask him to do "the maths". He didnt know and needed Grossman to help him fill in the blanks. In addition he did resist it for a while.

I never state that the math ( note no s ) is not important ... i just dont feel that either :
A) it is the driving force for anything of use
B) the only way to understand complex situations

Have you ever read his writings? I'm sure the Einstein would pass the ATM with flying colours, you know why? Because he passed the ATM back in 1905. His ideas where ATM and he articulated the concepts very well to include complex equations.

go to The Einstein Archives (http://www.alberteinstein.info) look at his writings and then come back and tell us how he avoided maths.

I don't know where you are getting your information. Perhaps you could back up your claims with some evidence?

Valkyrie801
2009-Jun-17, 03:28 AM
our galaxy is but a tiny spec of snow in a snow-globe siting upon the desk of our creator.

astromark
2009-Jun-17, 03:35 AM
I am becoming intolerant of the argumentative position seen in this forum... I can not understand why you would want to argue about what level of mathematics the head of the maths., department had. and will now try to clear this stupidity.
As has been noted. Mathematics is the mechanics of physics. Understanding some fundermental mathematics is going to help you conceptualise or make work your theories. That space vehicle descending to orbit a gas giant does need to be slowed to achieve this. A engine burn of some duration will be required. All of which is rocket science that might make me wince at the sight of but for the adept mathematician its just another problem. With the proper mathematics its a doodle....

AndrewJ
2009-Jun-17, 03:36 AM
What math do you want me to know? All of it?

Yeah, I've wondered what's the minumum maths a layman interested in science should be expected to know - have tried and failed to teach myself calculus.:think:

Given those A-left-home-an-hour-after-B-and-they-drove-towards-each-other problems I always used trial and error, where each would be after one hour etc, and it seemed to work. This approach might not work when plotting a probe's trajectory.


more than loving physics I am a master debater ( and in fact a cunning linguist).

Good skills!

EnigmaPower
2009-Jun-17, 03:56 AM
our galaxy is but a tiny spec of snow in a snow-globe siting upon the desk of our creator.

Since we are made out of star stuff that desk must be pretty darn big.

WayneFrancis
2009-Jun-17, 03:58 AM
What math do you want me to know? All of it? I am holding off on learning stuff until I need to. until know I have not felt the need to bolster my mathematical knowledge.

when someone posts randomly ... "Show the maths" ... who knows what they are talking about ...

If you ask me to do a particular calculation I may try to give it a shot.

more than loving physics I am a master debater ( and in fact a cunning linguist).

Ummm have you forgot where you've said this



...
Man that is hard. I struggle with the words ... can anyone help me out to formulate a better way to say what I want to say here?


Clearly not the sign of a "master debater" or "cunning linguist".

astromark
2009-Jun-17, 04:10 AM
:) yes that was funny the first time I saw it... could we remember the OP ?
There is such a thing as to much mathematics... I some times turn away from discussion here for that reason. It makes my head hurt. BUT. It is essential that science fact is verifiable by testing and provable by the logic. Mathematics is part of the way that is done. If its done well.

WayneFrancis
2009-Jun-17, 06:29 AM
:) yes that was funny the first time I saw it... could we remember the OP ?
There is such a thing as to much mathematics... I some times turn away from discussion here for that reason. It makes my head hurt. BUT. It is essential that science fact is verifiable by testing and provable by the logic. Mathematics is part of the way that is done. If its done well.

I understand where you are coming. There are tons of things that the math is way over my head. When it comes to GR and SR I've been more interested in the math side after getting the concepts explained to me over and over while watching people like Prof Muller at UC Berkeley describe it. If you don't understand the concept full stop the math isn't probably going to help you but if you have a basic understanding of the concept then the math can really make the concept solid.

For example it shows you just how close to a 1 solar mass black hole you would have to get to get time to really slow down for you and then at that point why the tidal forces would be ripping you apart.

If you are really interested in the topic then the maths becomes not only easier but more enjoyable.

Note to tommac : "maths" is a valid short form of the word mathematics (it is an American saying to abbreviate the plural word mathematics" to just math). In reality when you talk about maths you are talking about different types of math. IE you might employ algebra, calculus and geometry in the solution of of a problem. Next time you try to be a grammar Nazi tommac you should actually understand the word usage you are about to criticize.

Valkyrie801
2009-Jun-17, 06:34 AM
I failed.

I can calculate the impact point of a fired artillery shell through its trajectory..

but when it comes to algebra...

I can see it in my head, but can not put it down upon paper.

DrRocket
2009-Jun-17, 06:36 AM
Is math useful for clarification of an idea?
Or
Is math the only way to understand an issue in physics?

To quote an early professor "Mathematics is the study of any kind of order that the human mind can recognize."

Mathematics is useful insofar as one's mind is capable of recognizing order and analyzing it using logic.

That makes it more useful to some people than to others.

Valkyrie801
2009-Jun-17, 06:45 AM
Were I to grasp mathematics with understanding...

I could control Time and Space!

mugaliens
2009-Jun-17, 07:44 AM
Were I to grasp mathematics with understanding...

I could control Time and Space!

Really? I guess the many who do grasp mathematics have yet to reach the "understanding" phase, commensurate with the "controlling Time and Space!" phase.

Unless Time and Space are two puppies from the same litter...

astromark
2009-Jun-17, 08:42 AM
Were I to grasp mathematics with understanding...

I could control Time and Space!

Put the understanding down and step back from the mathematics... or does the understanding want to grasp the maths... ? No Valkyrie, that's not what you want. Is it ?
Time and space can never be controlled. Understood yes.

Jeff Root
2009-Jun-17, 08:44 AM
This is what Tom is referring to. From 'Black Holes & Time Warps'
by Kip S. Thorne, chapter 2:


Minkowski, you may recall, was the mathematics professor who had
labeled Einstein a lazy dog in his student days. In 1902 Minkowski,
a Russian by birth, had left the ETH in Zurich to take up a more
attractive professorship in Gottingen, Germany. (Science was as
international then as it is now.) In Gottingen, Minkowski studied
Einstein's article on special relativity, and was impressed. That
study led him to his 1908 discovery of the absolute nature of
four-dimensional space-time.

When Einstein learned of Minkowski's discovery, he was not
impressed. Minkowski was merely rewriting the laws of special
relativity in a new, more mathematical language; and, to Einstein,
the mathematics obscured the physical ideas that underlie the laws.
As Minkowski continued to extol the beauties of his spacetime
viewpoint, Einstein began to make jokes about Gottingen
mathematicians describing relativity in such complicated language
that physicists wouldn't be able to understand it.

The joke, in fact, was on Einstein. Four years later, in 1912, he
would realize that Minkowski's absolute spacetime is an essential
foundation for incorporating gravity into special relativity.
Sadly, Minkowski did not live to see this; he died of appendicitis
in 1909, at age forty-five.

-- Jeff, in Minneapolis

Jeff Root
2009-Jun-17, 09:00 AM
I consider mathematics to be an application of logic. When logic is applied
to concepts of number or quantity or value, math is the result. It is possible
to understand principles of physics without understanding the mathematical
relations that describe the principles. A four-year-old knows that an egg
will break if dropped onto a hard floor, but will not break if dropped onto a
soft pillow. That is physics.

-- Jeff, in Minneapolis

Fiery Phoenix
2009-Jun-17, 09:49 AM
Our whole world is basically made up of numbers. We need only turn those numbers into words if we are to make sense of things. And math is the key for this.

cfgauss
2009-Jun-17, 10:19 AM
Math is to Science as Grammar is to Writing.


No, math is to physics as letters are to writing. Math is absolutely required for any physics at all. Physics without math is just philosophy, and no one builds space ships, transistors, computers, understands black holes, radiation, quarks, or builds bridges with philosophy ;).


But you can understand some of the concepts without understanding the complicated math.


No, absolutely not! That's like saying you can read without knowing letters. You can't. By definition. If you think you can, you're really doing something else.


Not by a long shot. The popular myth of Einstein being somehow lousy at math is just that, a popular myth. He was in fact quite good at it.


Yeah, you have to keep into context what scientists say. Einstein was competing with people like Hilbert to develop GR. Saying Einstein "wasn't good" at math is like saying "I don't know the bible as well as the Pope." That by no means implies that you don't know every word of it!

The only people who can possibly think he's not good at math have clearly never read (or never understood) a single one of his papers.

Edit:
I once had a first year undergrad trap me and ask "so, what math would I need to learn for string theory?"
Answer: "All of it"
"No, really, what do I need to learn?"
"Really, all of it. And most of physics."
"No, really, what topics"
"Algebra, geometry, trig, calculus, linear algebra, differential equations, advanced calculus, multivariable calculus, real analysis, ........., algebraic topology, ......, and a few other things"
"Oh."

Jeff Root
2009-Jun-17, 10:42 AM
... chopin. ... the song that he wrote ...

:wall: :wall: :wall:
Although "song" is unquestionably not the right word, can you
suggest a better word in English? I have many times been faced
with the dilemma of finding a word for chunks of music. "Pieces"?
"Compositions"? "Works"? "Numbers"? "Songs"? They are all either
too general or too specific. I don't know of any word that is much
better than "song". Should Tom have said, "the composition that
he composed"?

Is there a good term in Deutsch?

-- Jeff, in Minneapolis

kleindoofy
2009-Jun-17, 11:19 AM
... can you suggest a better word in English? "Pieces"? ...
Take my word as a native English speaker who has spent his entire life heavily involved in classical music: "piece" is the correct word in this case, i.e. for a short piece by Chopin. Just ask any pianist.

"Number" was originally used by jazz musicians who had their sheet music ordered by numbers. The band leader would call out "47!" instead of "In the Mood!"

Classical musicians rarely speak of "numbers" or "songs," except for special cases.


... Is there a good term in Deutsch?...
For this case "Stück" would be correct.

gzhpcu
2009-Jun-17, 11:32 AM
I can't believe that someone could possibly ask what is good about math.:confused:

You can not build a theory in physics without math. I have had calculus (integral and differential), LaPlace transforms, etc.

It is only ATMers who think they can come up with physics "theories" with absolutely no mathematical background. Absolutely ridiculous.

Saying that Einstein was not good at math is also absolutely ridiculous.

gzhpcu
2009-Jun-17, 11:42 AM
What math do you want me to know? All of it? I am holding off on learning stuff until I need to. until know I have not felt the need to bolster my mathematical knowledge.

when someone posts randomly ... "Show the maths" ... who knows what they are talking about ...

If you ask me to do a particular calculation I may try to give it a shot.

more than loving physics I am a master debater ( and in fact a cunning linguist).
What math? At least algebra and calculus (integrals and differentials).

You might consider yourself a master debater and a cunning linguist, but I would like to see this modest self-assessment come from an unbiased, independent source. Any takers out there on the board to confirm this?:)

NEOWatcher
2009-Jun-17, 12:27 PM
I know responding to a suspended member might be futile, but there has been a lot of bantering about Einstein and mathematics that I think need to be backed up.

According to the Nobel Prize people about Einstein (http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-bio.html), here's a few key points.


...he entered the Swiss Federal Polytechnic School in Zurich to be trained as a teacher in physics and mathematics. In 1901, the year he gained his diploma...In 1905 he obtained his doctor's degree.


So he clearly had the math background.

At the start of his scientific work, Einstein realized the inadequacies of Newtonian mechanics and his special theory of relativity stemmed from an attempt to reconcile the laws of mechanics with the laws of the electromagnetic field.
Clearly an understanding of existing math. You can't reconcile two things without understanding them clearly.

Now they don't address his early years, so here's some other facts (http://physics.about.com/lr/albert_einstein/1470/3/).
In particular, look at the misconceptions paragraph explaining how he was never poor in mathematics.

Perikles
2009-Jun-17, 12:34 PM
The only surprising aspect of this thread is that so many people bothered to post in it. Surely the question is not actually worth an answer, is it?

Argos
2009-Jun-17, 01:14 PM
What math do you want me to know?

Chiefly differential equations (http://en.wikipedia.org/wiki/Differential_equation[url).

Differential equations tutorial (http://tutorial.math.lamar.edu/Classes/DE/DE.aspx)

There´s plenty of resources on the web.

Tobin Dax
2009-Jun-17, 01:36 PM
The only surprising aspect of this thread is that so many people bothered to post in it. Surely the question is not actually worth an answer, is it?
Did you read the thread? Have you read many ATM threads? Are you aware of the understanding of and attitudes toward math and science of the people you stand in line next to at the grocery store?

The question is definitely worth an answer. Many more people than just the OP have the same question and need to see it answered.

nauthiz
2009-Jun-17, 03:37 PM
So he clearly had the math background.
Maybe he was just a bit less mathematically inclined than most other people who hold Ph.D.s in mathematics or a math-heavy field. ;)

Sort of like how I didn't fare as well as a lot of my classmates at differential equations. Sure, I wish I had earned better marks, but even so the fact that I've successfully studied differential equations means it's hard to make a case that I'm no good at math. . . just not as good at math as people who are better than me at math.

Fiery Phoenix
2009-Jun-17, 04:06 PM
Maybe he was just a bit less mathematically inclined than most other people who hold Ph.D.s in mathematics or a math-heavy field. ;)

Sort of like how I didn't fare as well as a lot of my classmates at differential equations. Sure, I wish I had earned better marks, but even so the fact that I've successfully studied differential equations means it's hard to make a case that I'm no good at math. . . just not as good at math as people who are better than me at math.

I don't know why, but this post has just really inspired me. You must be living a very happy life, fine sir.

Argos
2009-Jun-17, 04:28 PM
more than loving physics I am a master debater ( and in fact a cunning linguist)

And this is a family board. ;) :)

Jetlack
2009-Jun-17, 05:08 PM
Is math useful for clarification of an idea?
Or
Is math the only way to understand an issue in physics?

I've recently been taking A&M online maths courses which i actually find invigorating since i now appreciate it in a way i never did at school (i started working directly after high-school).

However I dont think its right to say maths is the only way to understand physics. All of Einstein's peers considered him the greatest of their era because he was very intuitive about how nature worked without always understanding the matehmatical formulation. In fact he counted on a very good friend (I dont remmeber the gentlemans name at this moment) to help him with mathematical formulations.

On the other hand i believe if one wants to develop a theory which can be falsified, and for it to meet the approval of the scientific community, maths is absolutely vital.

And i also think most everyone can get a good grasp of reasonably advanced maths if they put the time into it.

Perikles
2009-Jun-17, 05:25 PM
Did you read the thread? .Yes of course
Have you read many ATM threads? .No, and I suspect I won't bother with many if this is typical
Are you aware of the understanding of and attitudes toward math and science of the people you stand in line next to at the grocery store? Very much so
The question is definitely worth an answer. Many more people than just the OP have the same question and need to see it answered.I am just surprised that this question needs answering on this forum, that's all.

To me, the question is in the same category as, say, on a forum about Shakespeare, and somebody were to question the point of being able to understand English.

Perhaps I have not yet appreciated the full range of members here.

NEOWatcher
2009-Jun-17, 05:34 PM
To me, the question is in the same category as, say, on a forum about Shakespeare, and somebody were to question the point of being able to understand English.
Not just you, but to most of us here. That's why it's such a hot topic.

But; yes, I'm sure even on a Shakespeare board, there would be regular members (if they are considerate and patient enough) that would at least try to explain why English is important.

Celestial Mechanic
2009-Jun-17, 05:38 PM
[Snip!] To me, the question is in the same category as, say, on a forum about Shakespeare, and somebody were to question the point of being able to understand English. [Snip!]
I made a similar point here (http://www.bautforum.com/against-mainstream/40391-theoretical-physics-reviewed-2.html#post724499) about Shakespeare and English that some may find worthwhile.

I finish up that post with the following:

Likewise, if you want to understand science at a level above the popularizations, you will have to learn the math. You will have to learn the history and culture of what went before in science to understand which ideas are taken to be the premises and why, to understand which ideas have been found wanting and why, and to understand what the current speculative ideas are and what is needed to verify or refute them. To repeat: there are no royal roads to anything.

Argos
2009-Jun-17, 05:52 PM
Yes of courseNo, and I suspect I won't bother with many if this is typicalVery much soI am just surprised that this question needs answering on this forum, that's all.

I know where you come from, but I think it´s still worth discussing, because tommac has asked which branch of maths should be more useful in approaching physics, especially GR physics. Referring him to number theory or group theory would be a desservice.

grant hutchison
2009-Jun-17, 05:58 PM
Philosophy is written in this immense book that stands ever open before our eyes (I speak of the Universe), but it cannot be read if one does not first learn the language and recognize the characters in which it is written. It is written in mathematical language, and the characters are triangles, circles, and other geometrical figures, without the means of which it is humanly impossible to understand a word; without these, philosophy is confused wandering in a dark labyrinth.

Galileo Galilei (1564-1642)

Grant Hutchison

Gillianren
2009-Jun-17, 06:40 PM
Take my word as a native English speaker who has spent his entire life heavily involved in classical music: "piece" is the correct word in this case, i.e. for a short piece by Chopin. Just ask any pianist.

"Number" was originally used by jazz musicians who had their sheet music ordered by numbers. The band leader would call out "47!" instead of "In the Mood!"

Classical musicians rarely speak of "numbers" or "songs," except for special cases.

I was equally amused by the singular, myself. What's more, while I've never, so far as I remember, played Chopin (viola, not piano), I've played a lot of other things, including a very complicated piece of Tschaikovsky. I did know the scales and the notes and so forth, and it was still a bit beyond me. I had a private teacher's help, not to mention the help of the conductor of the youth orchestra in which I played it. I'm not bad at music, and I've put a great deal of study in. But I'm not as good as Mr. Meyer, or even a lot of my friends. To the kid down the street who went to Julliard, I'm sure I'd count as "not as good at music," and I'm sure he'd be right--comparatively. This would not actually stop me from writing music myself, or a great work on music theory, even.

showboat
2009-Jun-17, 06:55 PM
Grant Hutchison


Well put as usual.

And true.

But with language and math, verbal and visual symbol chimes [verbal /visual]: even science must bow to the mind's ability to comprehend such communication which apparently takes siting at a disk for a minimum 24 for years from birth day one to the end of graduation..

Very constrictive to say the least.

A more direct perception would be more convincing like vision and feel: and philosophy gets put into quibbling about math and language and duality.

kleindoofy
2009-Jun-17, 07:22 PM
@Gillianren

I think a few things are getting mixed up in this thread.

I would agree with tommac as far as to say that a layman can appreciate and perhaps even "grasp" concepts such as GR on a simplistic, basic level while standing on the sidelines as a passive spectator. Where this not the case, books like those from Hawkings certainly wouldn't be sell as well as they do.

There is however a huge difference between grasping a concept and working with it, or actually developing new theories with it. While one may get the basic idea of GR, one certainly can't hope to implement it or extrapolate it to other theories without being able to crunch the numbers.

Music isn't quite the same, but mutatis mutandis, one could attempt an analogy.

There are many excellent musicians around who's only instrument of virtuosity is the CD player. Though they may know most of Chopin's music by heart and would be able discuss its interpretation with pianists, they couldn't hope to play two measures of any of it and wouldn't be foolish enough to say they could," if they only wanted to."

However, experience shows that having played an instrument of some kind and having learned some music theory greatly enhances the appreciation and enjoyment of classical music.

Even if a conductor can't play the bassoon, he can still tell the bassoon player how to play a certain passage. However, he can only tell him how it should *sound*, not how the bassoon player should technically create that sound. That's up to the bassoon player who has practiced his little tuchas off for years on end.

So, music and physics may be the same in as much as passive appreciation can be achieved without the "math," but if you want to "play" it, you have to learn the scales.

tdvance
2009-Jun-17, 08:22 PM
Take my word as a native English speaker who has spent his entire life heavily involved in classical music: "piece" is the correct word in this case, i.e. for a short piece by Chopin. Just ask any pianist.

"Number" was originally used by jazz musicians who had their sheet music ordered by numbers. The band leader would call out "47!" instead of "In the Mood!"

Classical musicians rarely speak of "numbers" or "songs," except for special cases.


For this case "Stück" would be correct.


The band I'm in calls them "charts". Piece works well. Another word used is "work"--the work by Chopin. Also, something more specific, like the waltz by Chopin or the fugue by Bach.

To me, "song" is something that is sung.

tdvance
2009-Jun-17, 08:23 PM
I know responding to a suspended member might be futile, but there has been a lot of bantering about Einstein and mathematics that I think need to be backed up.

According to the Nobel Prize people about Einstein (http://nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-bio.html), here's a few key points.

So he clearly had the math background.

Clearly an understanding of existing math. You can't reconcile two things without understanding them clearly.

Now they don't address his early years, so here's some other facts (http://physics.about.com/lr/albert_einstein/1470/3/).
In particular, look at the misconceptions paragraph explaining how he was never poor in mathematics.

I think part of the problem is there is a lot of mathematics, and no mathematician knows it all. Einstein was weak in differential manifolds, and got help from an expert before formulating his General Relativity.

Jerry
2009-Jun-17, 08:32 PM
You can use a conceptual model to develop a mathematical model, or you can make observation and use the observations to develop both conceptual and mathematical models.

The mathematical models, if the conceptualization is correct; should then have the power to predict past, present and future events within the boundaries of the model. What should be consistent, is that all of the mathematical arguments used to explain the physical concepts should be seamless. The irony is, accepted theories are NOT mathematically cohesive: General Relativist models are time-dependant; quantum models are not; and there is no obvious high ground. So even the concept of 'grasping GR' relies upon some unimaginable conceptual compromises, mathematically:)

Valkyrie801
2009-Jun-17, 08:37 PM
Really? I guess the many who do grasp mathematics have yet to reach the "understanding" phase, commensurate with the "controlling Time and Space!" phase.

Unless Time and Space are two puppies from the same litter...

That is so beautiful,

"Two puppies from the same litter."

I see us as sisters.

We argue allot, but that is how we maintainer balances within the time/space continuum.

Gillianren
2009-Jun-17, 08:47 PM
There are many excellent musicians around who's only instrument of virtuosity is the CD player. Though they may know most of Chopin's music by heart and would be able discuss its interpretation with pianists, they couldn't hope to play two measures of any of it and wouldn't be foolish enough to say they could," if they only wanted to."

Wrong. A musician, by definition, is one who plays music. One who just listens to it is not a musician. They may be a connoisseur, but they are not a musician. Further, how do you judge anyone's ability if they have never shown what they can do? They can talk a good game, but you can't call someone "excellent" or a "virtuoso" if they've never shown their stuff, and in order to show their stuff, they have to do the work.


However, experience shows that having played an instrument of some kind and having learned some music theory greatly enhances the appreciation and enjoyment of classical music.

Assuredly true.


Even if a conductor can't play the bassoon, he can still tell the bassoon player how to play a certain passage. However, he can only tell him how it should *sound*, not how the bassoon player should technically create that sound. That's up to the bassoon player who has practiced his little tuchas off for years on end.

Ah, but a conductor can play bassoon if he's come up through the ranks like any good conductor has. It's one of the things they teach you in music school--how to play everything, so that you can help people know what to do. The conductor, unless they're a bassoonist first themselves, isn't going to be remotely as good, but a conductor who isn't also a musician is not a conductor I'd want to follow.


So, music and physics may be the same in as much as passive appreciation can be achieved without the "math," but if you want to "play" it, you have to learn the scales.

But to be considered an expert, you have to know the language. To really understand Bach, you have to know what instruments are being played, for example, and the world he lived in, and why he wrote what he wrote. (There's a reason he wrote so much church music, of course.) You can appreciate the sound, but not the music.

showboat
2009-Jun-17, 09:06 PM
@Gillianren

I think a few things are getting mixed up in this thread.

I would agree with tommac as far as to say that a layman can appreciate and perhaps even "grasp" concepts such as GR on a simplistic, basic level while standing on the sidelines as a passive spectator. Where this not the case, books like those from Hawkings certainly wouldn't be sell as well as they do.

There is however a huge difference between grasping a concept and working with it, or actually developing new theories with it. While one may get the basic idea of GR, one certainly can't hope to implement it or extrapolate it to other theories without being able to crunch the numbers.

Music isn't quite the same, but mutatis mutandis, one could attempt an analogy.

There are many excellent musicians around who's only instrument of virtuosity is the CD player. Though they may know most of Chopin's music by heart and would be able discuss its interpretation with pianists, they couldn't hope to play two measures of any of it and wouldn't be foolish enough to say they could," if they only wanted to."

However, experience shows that having played an instrument of some kind and having learned some music theory greatly enhances the appreciation and enjoyment of classical music.

Even if a conductor can't play the bassoon, he can still tell the bassoon player how to play a certain passage. However, he can only tell him how it should *sound*, not how the bassoon player should technically create that sound. That's up to the bassoon player who has practiced his little tuchas off for years on end.

So, music and physics may be the same in as much as passive appreciation can be achieved without the "math," but if you want to "play" it, you have to learn the scales.





Only if you had ten digets fingers but if 12 fingers the song math is the same but the sound would be entirely different and not better, but a mistake for doing art as to science.

So art is the same, and not dependent on Math but feel.


But the math will be revealed to the satisfaction of math guys.

PetersCreek
2009-Jun-17, 09:10 PM
General note to all:

We can continue the math metadiscussion as long as it's productive to do so. However, since the OP cannot defend his positions or otherwise reply, please address your remarks to those who can.

kleindoofy
2009-Jun-17, 09:21 PM
@Gillianren

I think we agree in pricnipal (or even in detail) with each others posts. The format of the forum is just too narrow to write the wordy explanations needed to get the viewpoints fully across.

Moonhead
2009-Jun-17, 09:33 PM
You can have an understanding of it....but that doesn't mean you'll make accurate conclusions based on your understanding.

Take Gravity. Many people understand the "funnel" analogy of gravity. Less people understand many of the implications of this. For example I'd wager most people still think that if our sun was a black hole that the earth would get sucked in. Look how many people are worried about the LHC producing a BH with the mass of 2 alpha particles. They have an understanding of a BH but the maths would show them that they have nothing to worry about from a BH that size.
The first example you give, actually is one that, imho, can be understood without understanding the exact mathematics involved. Of course that does not imply that the importance of these mathematics is overrated. But imho the concept can be understood without understanding the math (just like you don't need to know any English to understand Juliet wasn't quite happy when she awoke and found Romeo dead - when you're watching the play, that is :D).

HenrikOlsen
2009-Jun-17, 09:55 PM
Only if you had ten digets fingers but if 12 fingers the song math is the same but the sound would be entirely different and not better, but a mistake for doing art as to science.

So art is the same, and not dependent on Math but feel.


But the math will be revealed to the satisfaction of math guys.
The problem with your argument is that the octave actually does have 12 notes, not 10.
Mainly because the many factors of 12 makes the pure ratios that sounds so good come out nicely (apart from the whole temper thing that makes the modern scale a bit of an approximation).

You're forgetting that math (as opposed to numerology) pretty much ignores how numbers are written and is invariant over number systems.

And it's even worse for those wind instruments that are basically a half open tube, as they really needs 17 fingers to play:D

DrRocket
2009-Jun-17, 11:34 PM
To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once. – Richard P. Feynman in The Character of Physical Law

Hornblower
2009-Jun-18, 01:12 AM
From all of the discussion about Einstein in this thread and elsewhere, I think it is clear that unlike many would-be theorists in the ATM page, he recognized and accepted the need for mathematical treatment of his idea beyond his initial capability, and he took the trouble to spend a few years learning the necessary mathematical methods.

DrRocket
2009-Jun-18, 02:53 AM
From all of the discussion about Einstein in this thread and elsewhere, I think it is clear that unlike many would-be theorists in the ATM page, he recognized and accepted the need for mathematical treatment of his idea beyond his initial capability, and he took the trouble to spend a few years learning the necessary mathematical methods.

Any resemblence between Albert Einstein and the proponents in the ATM forum is in the haircut.

Cougar
2009-Jun-18, 02:54 AM
To summarize , I would use the words of Jeans, who said that ‘the Great Architect seems to be a mathematician’. To those who do not know mathematics it is difficult to get across a real feeling as the beauty, the deepest beauty, of nature. C.P. Snow talked about two cultures. I really think that those two cultures separate people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once. – Richard P. Feynman in The Character of Physical Law


"If the calculus comes to vibrant life in celestial mechanics, as it surely does, then this is evidence that the stars in the sheltering sky have a secret mathematical identity, an aspect of themselves that like some tremulous night flower they reveal only when the mathematician whispers." -- David Berlinski in A Tour of the Calculus

cfgauss
2009-Jun-18, 02:56 AM
Saying you can understand physics without understanding math is like saying you can understand Japanese pop music without understanding Japanese. You may think it sounds nice, but that's it. They could be singing about how the Japanese love to eat babies for all you know.

Moonhead
2009-Jun-18, 09:56 PM
Saying you can understand physics without understanding math is like saying you can understand Japanese pop music without understanding Japanese. You may think it sounds nice, but that's it. They could be singing about how the Japanese love to eat babies for all you know.

This is dependent of your definition of "understanding". If you assume the essence of pop music in general is found in it's lyrics, then I must say I cannot agree. I can hardly understand some lyrics of Crass or the Exploited, but I can pick up the general themes. And what about Philip Glass's Koyaanisqatsi (title song of the soundtrack of Godfrey Reggio's motion picture of the same name)? It's lyrics are in the Hopi language. Or what about Mike Oldfield's and Tangerine Dream's instrumental compositions? Are all these not pop music?

I'm hardly an expert on the doubtlessly broad range of Japanese Pop Music, but I'm familiar with some albums of Fantastic Plastic Machine (http://en.wikipedia.org/wiki/Fantastic_Plastic_Machine_(musician)) which feature songs in English, French and German (and none in Japanese). They are funny. (although I admit my listening experience might differ from the average Japanese listener's).

Fantastic Plastic Machine - Electric Lady Land @ Youtube (http://www.youtube.com/watch?v=gTiZw2OnDkA)

DrRocket
2009-Jun-18, 10:27 PM
This is dependent of your definition of "understanding".

Precisely.

Many people confuse a "passing acquaintence" with an "understanding". This leads to the altogether too common problem of someone who does not understand that he does not understand.

Jerry
2009-Jun-18, 11:18 PM
Saying you can understand physics without understanding math is like saying you can understand Japanese pop music without understanding Japanese. You may think it sounds nice, but that's it. They could be singing about how the Japanese love to eat babies for all you know.
There are a LOT of baseball pitchers, golfers and NASCAR drivers who have an intimate working knowledge fluid dynamics, lever arms, friction an momentum but only a cursory knowledge of calculus, if any at all. Likewise many gambling odds-makers use their heads to set odds, not actuary tables. As a discriptive qualitative language of physical events, English and other adaptible languages trump math. But if you want to know if the physical laws you are using are close approximations of the real physical world, advanced math is as essential as round cows. ('Round cows' are assumptions, because our mathematical modeling techiques are limited.)

DrRocket
2009-Jun-19, 01:58 AM
There are a LOT of baseball pitchers, golfers and NASCAR drivers who have an intimate working knowledge fluid dynamics, lever arms, friction an momentum but only a cursory knowledge of calculus, if any at all. Likewise many gambling odds-makers use their heads to set odds, not actuary tables. As a discriptive qualitative language of physical events, English and other adaptible languages trump math. But if you want to know if the physical laws you are using are close approximations of the real physical world, advanced math is as essential as round cows. ('Round cows' are assumptions, because our mathematical modeling techiques are limited.)

A classic example of not understanding that one does not understand.

hhEb09'1
2009-Jun-19, 02:11 AM
True dat. Saying a race car driver has intimate working knowledge of fluid dynamics is like saying I have an intimate working knowledge of internal medicine. :)

ETA: which I do. My wife is a physician, and we have relations. Some of them are embarrassing--the ones without serious political afflictions. When we visit them all they talk about is sports--their kids, the result of genetic inbreeding I imagine. One of them looks like a goat. Whenever I start to talk about internal medicine or fluid dynamics, they have to change their diapers, or some other excuse. They're full of excuses, or what passes for excuses. I know this because I'm an expert in internal medicine and fluid dynamics. Fluid mechanics, however, is a different story. Then, they're all over it, wondering whether I know Barry Grant or Stewart Warner or Sandra Bullock, and why is her bacon number now one? I try to explain about Loverboy, but hey who can?

WayneFrancis
2009-Jun-19, 02:46 AM
...
No, absolutely not! That's like saying you can read without knowing letters. You can't. By definition. If you think you can, you're really doing something else.
...

Funny enough this is a great analogy. Many little kids don't know how to read but you swear they could if you saw them with an open book. They've memorized the story and might even recognize the words when in the proper place but give them one of those words outside of the book they won't be able to read it. Likewise if you give them a simple word they have never seen they won't be able to sound it out.

Not understanding the math, and never doing math, means that you will never really come up with valid new idea or be able to relate to concepts together. Sure you can say you understand that 2 concepts are related but that would be just memorizing the story someone else has read to you.

WayneFrancis
2009-Jun-19, 02:55 AM
Although "song" is unquestionably not the right word, can you
suggest a better word in English? I have many times been faced
with the dilemma of finding a word for chunks of music. "Pieces"?
"Compositions"? "Works"? "Numbers"? "Songs"? They are all either
too general or too specific. I don't know of any word that is much
better than "song". Should Tom have said, "the composition that
he composed"?

Is there a good term in Deutsch?

-- Jeff, in Minneapolis

Ummm I think he is banging his head against the wall because of the "the song" as in "one piece" forgive me but off the top of my head I think he has well over 200 known pieces.

So while "song" makes the comment of

I can personally tell you that you dont need to learn or practicescales or learn about or practice 16th or 32nds to play chopin. You can just focus and play it ... Sometimes it is easier to just learn the piece without thinking about it too much ... it sometimes can help you learn something but sometimes it just doesnt matter. there are many great musicians that havent been trained and learned just by loving the music.

OR you can learn to enjoy it ... maybe even get a deeper feeling of what he was trying to portray with the song that he wrote. Maybe if you closed your eyes even visualize a meaning to the music.



Sure ... but it can still be fun ...

sound a bit more naive implying that old Freddy wrote only 1 song is even worse and not the sign of a good debater.

sirius0
2009-Jun-19, 03:05 AM
I will have to watch the ramble factor with this one. Math has been such an issue for me.

Recently (two years ago) I had an identity crisis. I had always thought that I was a Physicist (minimally qualified, I completed an BSc Physics approx ten years ago). Anyhow I had a Big Thought about GR. I proceeded to read up on GR, I purchased Sean Carroll's Book Spacetime and Geometry: An Introduction to General Relativity Started to read, the maths looked familiar enough. But then I realised that while I may have understood a fair bit during the degree and I could pass exams and I was well taught, that the understanding was not broad enough. Most proofs did not mean anything.

I was quite capable of having a Big Thought (read Smart speculation) but not a Clever Inspiration. I am not a physicist but a scummy dilettante and I needed to learn.

Since then I have revised all the classical mech of earlier, stepping through all the proofs. Lots of matrices, hermitian, eigen values eigen vectors, forms, transforms, diagonalisation, basis, R^n spaces etc. Soon I will step through differential systems with these tools. Differential calculus at least should be smoother. All these I have stepped through the proofs and I am thoroughly enjoying myself!

Soon I will go through tensors and then(maybe a year off, maybe sooner) I will return to Sean's book.

I think the amount of maths needed to be known is that amount that allows for complete logical thought about the subject at hand. Within that logic could come a well founded inspiration.
I do think speculative thoughts could be very useful but once had have to be rounded out with maths or experimented with until the appropriate maths is known. After all a bubble is only a drip if it doesn't hold air.

Forgive the long post

An example of how math changed an old idea of mine.


I used to think it would be a good idea to integrate a linear generator into a car's suspension. That way the wasted energy of the suspension's compression could be used to charge the battery. But once I really understood Hooke's law as a conservative force I realised that getting any energy out would require the car's engine to put some energy in even though the path for this energy may not be immediately obvious. (of course there may be lossy systems that this would work for but perhaps it would be better to design a better suspension!)

Regards Chris (wish me luck)

WayneFrancis
2009-Jun-19, 03:30 AM
You can have an understanding of it....but that doesn't mean you'll make accurate conclusions based on your understanding.

Take Gravity. Many people understand the "funnel" analogy of gravity. Less people understand many of the implications of this. For example I'd wager most people still think that if our sun was a black hole that the earth would get sucked in. Look how many people are worried about the LHC producing a BH with the mass of 2 alpha particles. They have an understanding of a BH but the maths would show them that they have nothing to worry about from a BH that size.

The first example you give, actually is one that, imho, can be understood without understanding the exact mathematics involved. Of course that does not imply that the importance of these mathematics is overrated. But imho the concept can be understood without understanding the math (just like you don't need to know any English to understand Juliet wasn't quite happy when she awoke and found Romeo dead - when you're watching the play, that is :D).

It can be understood on a basic level and in actuality the math is VERY simple. Yet tommac has demonstrated, multiple times, that he doesn't really understand the curve of that funnel. To be exact he keeps messing up the amount of time dilation someone would experience at different distances from the event horizon of a black hole including once where he stated a time dilation of finding 1 spot of ~1x10^200 would throw off the average space time dilation for a region of ~1x10^200 spot. Which in itself is true but he was implying that the ~1x10^200 spots would be stretched across a solar system. That would be cherry picking your data points first of and second off it doesn't change the average as much as he implies. IE (1x10^200) -1 points with the value of 1 and 1 point with the value of (1x10^200) averaged is only 2 and not some huge number like he tried to imply....because he never even did the maths to check his own claim.

I agree that I, and others, can explain concepts very well with out maths. But that explanation can only be trusted as far as you trust the person doing the explaining. Maths is the independent verifier. Come up with a idea, back it up with math and others can verify your claim. Other than that it is just philosophy.

robross
2009-Jun-19, 07:24 AM
FYI, in case you don't know, MIT has put their entire course catalog online, free of charge. The media includes video-taped lectures, lab notes, examples, etc.

http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

The math specific courses are here:

http://ocw.mit.edu/OcwWeb/web/courses/courses/index.htm#Mathematics

Although they won't give you a diploma, now *anyone* can get an MIT education. For free!

Rob

Jeff Root
2009-Jun-19, 11:52 AM
... implying that old Freddy wrote only 1 song ...
That was so trivial that I just ignored it. Either an editing error or
a clumsiness typical of Tom's expression, implying nothing whatever
about his knowledge or lack of knowledge of Chopin's body of work.

I suppose that if it hadn't been for the juxtaposition of two such
peculiar word choices right together, kleindoofy would have let it
pass as well.

Let me go even farther off-topic to clarify my earlier comments
about the word "song". In this case, terms specifically applicable
to classical music are obviously the best choice. My longstanding
problem is to find a word that suits *all* forms of music. The word
"song" is a top contender for that use in the USA.

-- Jeff, in Minneapolis

kleindoofy
2009-Jun-19, 12:13 PM
... if it hadn't been for the juxtaposition of two such peculiar word choices right together, kleindoofy would have let it pass as well. ...
No, it was the basic tone of the whole response, the assumption that one could play virtuoso piano music without ever having practiced the instrument, just by pure will. The comments on Chopin and the word "song" put it over the top.

That's like saying one could land on Jupiter if one only really wanted to and then calling moons planets. It just hurts the ears and demonstrates a certain lack of knowledge.


... My longstanding problem is to find a word that suits *all* forms of music. The word "song" is a top contender for that use in the USA. ...
Which brings us back to moons and planets. Or mathematical terminology. Why differentiate between numerals, integers, digits, etc.? Just call them all "counting thingies." ;)

grav
2009-Jun-19, 12:38 PM
FYI, in case you don't know, MIT has put their entire course catalog online, free of charge. The media includes video-taped lectures, lab notes, examples, etc.

http://ocw.mit.edu/OcwWeb/web/home/home/index.htm

The math specific courses are here:

http://ocw.mit.edu/OcwWeb/web/courses/courses/index.htm#Mathematics

Although they won't give you a diploma, now *anyone* can get an MIT education. For free!

RobThat is cool, robross. Thanks. :)

Argos
2009-Jun-19, 01:02 PM
Although they won't give you a diploma, now *anyone* can get an MIT education. For free!
Rob

Who cares for a diploma... It´s just a piece a paper; a mark of social distinction.

Jeff Root
2009-Jun-19, 01:10 PM
No, it was the basic tone of the whole response, the assumption that
one could play virtuoso piano music without ever having practiced the
instrument, just by pure will.
That is a gross misinterpretation of what he said.

If I may offer my own interpretation, he said that an understanding
of music theory is not needed to play Chopin well. Practice at making
the piano do what you want it to do is obviously required, and Tom
did not say anything to suggest that it isn't. Furthermore, his first
words in the statement lead me to believe that he was describing his
own personal observations, not an assumption. I do not have the
experience to make such a statement myself, but I understand that
many first-rate musicians in different genres were self-taught, and
did not receive instruction in music theory before winning acclaim for
their accomplishments.



I can personally tell you that you dont need to learn or practice scales
or learn about or practice 16th or 32nds to play chopin. You can just
focus and play it ... Sometimes it is easier to just learn the piece without
thinking about it too much ... it sometimes can help you learn something
but sometimes it just doesnt matter. there are many great musicians
that havent been trained and learned just by loving the music.
What Tom *actually said* is not unreasonable, and fits the facts that
I'm aware of. People who have the innate dexterity and timing can
learn to play music that they hear without knowing anything about
how theory describes that music.

-- Jeff, in Minneapolis

Jeff Root
2009-Jun-19, 01:23 PM
Re-reading what Tom wrote yet again, I don't even think his use of the
definite article was particularly clumsy-- just surprising. It isn't either
factually or grammatically incorrect.

-- Jeff, in Minneapolis

Moonhead
2009-Jun-19, 01:47 PM
I agree that I, and others, can explain concepts very well with out maths. But that explanation can only be trusted as far as you trust the person doing the explaining. Maths is the independent verifier. Come up with a idea, back it up with math and others can verify your claim.
As far as my understanding goed, I think you are right about this.


Other than that it is just philosophy.
That's probably not untrue too, but I think we should not look down upon of e.g. Democritus's ideas, and recognize the intuitive 'truishness' of several of them.

Hornblower
2009-Jun-19, 03:00 PM
An example of how math changed an old idea of mine.


I used to think it would be a good idea to integrate a linear generator into a car's suspension. That way the wasted energy of the suspension's compression could be used to charge the battery. But once I really understood Hooke's law as a conservative force I realised that getting any energy out would require the car's engine to put some energy in even though the path for this energy may not be immediately obvious. (of course there may be lossy systems that this would work for but perhaps it would be better to design a better suspension!)

Regards Chris (wish me luck)At the thought experiment level, I think you gave up on your regenerative shock absorber idea prematurely.

When a car is bouncing up and down on its suspension after hitting a bump, the energy of that vertical motion did not come from nowhere. It got there at the expense of the kinetic energy of the forward motion. In other words, the car slowed down slightly, and some extra energy from the engine is needed to restore the forward speed.

Shock absorbers as we know them use hydraulic drag to convert the bounce energy into heat, so it continues as wasted energy. In theory we could convert some of it into electricity and use it to recharge the battery. That would reduce the demand on the regular generator and thus lighten the load on the engine.

This thought experiment still shows how mathematical analysis is needed to firm up a bright idea, or to reject it as the case may be.

PetersCreek
2009-Jun-19, 03:33 PM
What Tom *actually said* is not unreasonable, and fits the facts that I'm aware of. People who have the innate dexterity and timing can learn to play music that they hear without knowing anything about how theory describes that music.

The trick is they have to hear it first. Without an understanding of the theory and language of music, however, they'll likely never play a score handed to them on paper. They won't understand all those 16th and 32nd notes, the dynamic markings, or the key changes. And with all the work they put into learning a "song" that they've heard (and likely many, many times) they are left with only that song to show for it.

Learn the language, the theory, and even the history of music and you can apply it to a work you've never heard or heard of. You can apply it to music of your own creation...and this is where the analogy really breaks down for for ATM proponents. They're trying to write new "music" without knowing what the notes mean or even how to stay in key.

You can hum a little tune 'til your heart's content but if you want to be taken seriously as a "composer" learn how to write "music".

Gillianren
2009-Jun-19, 06:34 PM
Let me go even farther off-topic to clarify my earlier comments about the word "song". In this case, terms specifically applicable to classical music are obviously the best choice. My longstanding problem is to find a word that suits *all* forms of music. The word "song" is a top contender for that use in the USA.

That's as may be, but it's wrong. "Tune," perhaps. "Song" has words.


That is a gross misinterpretation of what he said.

No. It isn't.


If I may offer my own interpretation, he said that an understanding of music theory is not needed to play Chopin well. Practice at making the piano do what you want it to do is obviously required, and Tom did not say anything to suggest that it isn't. Furthermore, his first words in the statement lead me to believe that he was describing his
own personal observations, not an assumption. I do not have the experience to make such a statement myself, but I understand that many first-rate musicians in different genres were self-taught, and did not receive instruction in music theory before winning acclaim for their accomplishments.

I do have the experience. Being self-taught is one thing. I've known some self-taught musicians. Some good ones. However, to say that you don't have to know scales or sixteenth or thirty-second notes to know Chopin is flatly wrong, whether you've taught yourself or by someone else. What's more, that's not what I would call music theory. That is an understanding of music itself. You don't have to know the principles of chords. You don't have to know Chopin's history. There are all sorts of things that you don't have to know. But even a self-taught musician must know a great deal about scales and types of notes in order to play Chopin. Even if all you're doing is playing three-chord rock and roll, you still have to know the chords and how to play them.


What Tom *actually said* is not unreasonable, and fits the facts that I'm aware of. People who have the innate dexterity and timing can learn to play music that they hear without knowing anything about how theory describes that music.

But scales are not "theory." Scales are an intrinsic part of the music. To claim that you don't have to know sixteenth and thirty-second notes to play Chopin is, bluntly, like saying you don't need to know how to add in order to do physics.

Jeff Root
2009-Jun-19, 06:46 PM
The trick is they have to hear it first. Without an understanding of
the theory and language of music, however, they'll likely never play
a score handed to them on paper.
That is almost irrelevant. Reading sheet music is an entirely different
skill from being able to play music or being able to compose music.
More than a few musicians never learned to read music. Even some
composers never learned to read or write music. Their compositions
were recorded by other means, or they have been lost. I expect
that a great deal of very good music was never recorded and has
been lost forever, in part because the composer had no way to
record what he composed. A great deal of dreck, too, of course.
And modern technology makes it much easier to record music than
it was two hundred years ago.



You can hum a little tune 'til your heart's content but if you want to
be taken seriously as a "composer" learn how to write "music".
It would be dreadful if musicians had to be able to write out their
music in order for it to be taken seriously.

-- Jeff, in Minneapolis

gzhpcu
2009-Jun-19, 07:03 PM
I do not find the comparison of music and physics relevant.

Theoretical physics has to be mathematically consistent. It is not a question of coming up with aesthetically beautiful theories, it is about coming up with theories (which might be beautiful) which are predictive and accurate.

You need math, period.

PetersCreek
2009-Jun-19, 07:09 PM
It would be dreadful if musicians had to be able to write out their music in order for it to be taken seriously.

Inconvenient, yes...for those without a skill that can be learned (by most). But dreadful? Let's translate that from the analogy to the OP subject:

It would be dreadful if physicists had to be able to write out their theory mathematically in order to be taken seriously.

Doesn't really ring true to my ear.

tdvance
2009-Jun-19, 07:21 PM
That is a gross misinterpretation of what he said.

If I may offer my own interpretation, he said that an understanding
of music theory is not needed to play Chopin well. Practice at making
the piano do what you want it to do is obviously required, and Tom
did not say anything to suggest that it isn't. Furthermore, his first
words in the statement lead me to believe that he was describing his
own personal observations, not an assumption. I do not have the
experience to make such a statement myself, but I understand that
many first-rate musicians in different genres were self-taught, and
did not receive instruction in music theory before winning acclaim for
their accomplishments.


What Tom *actually said* is not unreasonable, and fits the facts that
I'm aware of. People who have the innate dexterity and timing can
learn to play music that they hear without knowing anything about
how theory describes that music.

-- Jeff, in Minneapolis

I'd say this--understanding music theory--at a "I can feel it" level is necessary to play Chopin well--though not knowing the terms involved, like phrasing, agogic, etc. isn't so important--you don't have to know what cadence means, but you have to recognize them to get the phrasing anywhere close to right. There are plenty of people who think they can play piano well because they don't miss any notes and play at full speed, but....that's the easy part (and it's not easy!). This would be like someone who mastered the pronunciation of English words and can read through a speech, but monotone with out any expression, suggesting they might not know the meanings of the sentences.

DrRocket
2009-Jun-19, 07:25 PM
I do not find the comparison of music and physics relevant.

Theoretical physics has to be mathematically consistent. It is not a question of coming up with aesthetically beautiful theories, it is about coming up with theories (which might be beautiful) which are predictive and accurate.

You need math, period.

I am fully in support of mathematical rigor, and this is a nice sentiment.

It would be better if it were true.

The next clear and rigorous definition of the Feynman path integral will be the first one.

QFT is predictive and accurate. It is not known to be mathematically consistent. It is not even well defined from a mathematical perspective.

If theoretical physicists were really required to be truly mathematically rigorous, and theories were required to be demonstrably mathematically consistent, there would be a lot less theoretical physics. Rigor is an appropriate goal. But quite often expediency wins. It is a good thing that there are experiments to help separate the wheat from the chaff.

GeorgeLeRoyTirebiter
2009-Jun-19, 07:40 PM
It's one of the things they teach you in music school--how to play everything, so that you can help people know what to do.

That hasn't been my experience. At the music school I attended (a state university with an excellent music program) only the music education majors were required to learn to play everything. Everyone else (the performance and musicology/composition majors) only needed to master a primary instrument and show basic proficiency in two others; one of the three had to be piano.

We learned the peculiarities of each instrument and group in orchestration class, but we didn't have to try playing them all.

kleindoofy
2009-Jun-19, 07:49 PM
... "Song" has words. ...
Except for Mendelssohn's "Song without words." :lol:

Let's not take the music/physics analogy too far. It's a bit limpy and was only meant as a passing remark for a certain aspect of the main argument: "what is math worth?"

Having said that: practicing scales is to Chopin (more or less) as practicing multiplication tables is to math. The scales help teach you how to move your fingers across the keyboard in a technical manner which you need when playing Chopin, perhaps not so much for Boogy-Woogy. Multiplication tables help train your mind for the relationship of numbers beyond the ten fingers.

@GeorgeLeRoyTirebiter

By "everything" I think Gillian meant different *kinds* of music, not all instruments.

Gillianren
2009-Jun-19, 09:03 PM
To be honest, everyone I know who majored in music majored in music education, so the people I know had to learn every instrument. (Though my high school music teacher, on learning the bassoon, was given the instructions to make sure that any kid taking it up could afford private lessons!) However, surely even not-music education majors gets at least the basics in how every instrument works!

GeorgeLeRoyTirebiter
2009-Jun-20, 12:15 AM
However, surely even not-music education majors gets at least the basics in how every instrument works!

Well, sort of. Like I mentioned, we covered much of that in the basic orchestration course (which everyone had to take). We didn't need to learn things that would only be important to the players (embouchure, fingerings, etc.), and instead concentrated on details of use to the composer or conductor. It seems like we spent a third of the semester on bowing, even though the string players are just going to ignore the written instructions anyway.

I don't recall spending much time on the basic mechanics of how each instrument works; there wasn't any I blow through here/ and the music goes down and 'round/ whoa-ho-ho-ho ho-ho/ and it comes out here. I think they expected that if we made it into the program, we already knew things like the difference between a woodwind and a brass instrument.

tdvance
2009-Jun-20, 12:33 AM
To be honest, everyone I know who majored in music majored in music education, so the people I know had to learn every instrument. (Though my high school music teacher, on learning the bassoon, was given the instructions to make sure that any kid taking it up could afford private lessons!) However, surely even not-music education majors gets at least the basics in how every instrument works!

I'd say the same for oboe--if the teacher is not close to pro level on oboe. Bad oboe players are never moderately bad. I recall the pro oboist who sits in front of me having a bad day once. He didn't sound that bad, but he didn't sound pro either that one day--but you had to hear him every day to really notice something was off.

kleindoofy
2009-Jun-20, 01:14 AM
At the conservatory we only studied our main instrument and had mandatory piano lessons. Only the people going into teaching had general instrument instruction.

However, nobody sits around in hundreds of hours of orchestra rehearsals without at least involuntarily picking up lots on how other instruments work. Even we brass players knew lots of the finer points of the strings' bowing technique, just from listening to what the conductors and concert masters told the string section to do. Not to mention exchanging instruments with friends just to try to get a noise out of them.

sirius0
2009-Jun-20, 01:24 AM
At the thought experiment level, I think you gave up on your regenerative shock absorber idea prematurely.

When a car is bouncing up and down on its suspension after hitting a bump, the energy of that vertical motion did not come from nowhere. It got there at the expense of the kinetic energy of the forward motion. In other words, the car slowed down slightly, and some extra energy from the engine is needed to restore the forward speed.

Shock absorbers as we know them use hydraulic drag to convert the bounce energy into heat, so it continues as wasted energy. In theory we could convert some of it into electricity and use it to recharge the battery. That would reduce the demand on the regular generator and thus lighten the load on the engine.

This thought experiment still shows how mathematical analysis is needed to firm up a bright idea, or to reject it as the case may be.
Yes I know the damping is currently a waste. And the idea still has some potential. The damping could be provided by the 'armature reaction. of the generator. I was only using the initial understanding of a conservative force to demonstrate how maths moved me from a speculation to a deeper understanding.

The energy put into the system is available to be pulled out again electrically. But what about pre detection of a bump? The car's suspension could lift the wheel a little prior to impact saving the work of a greater portion of the whole car's mass impact via the wheel. Then there would not be as much energy available for damping/generating but a more efficient and comfortable ride. So the maths takes the initial idea (a good band aid) and raises it to a very good idea perhaps.

hhEb09'1
2009-Jun-20, 03:54 PM
So the maths takes the initial idea (a good band aid) and raises it to a very good idea perhaps.Was there math presented about this idea, in this thread?

Jeff Root
2009-Jun-20, 05:24 PM
That was my thought exactly. No math was presented in the thread.
The regenerative shock absorber idea was analyzed qualitatively, not
quantiatively.

A lot of things can be figured out without using any math at all.

-- Jeff, in Minneapolis

DrRocket
2009-Jun-20, 05:34 PM
That was my thought exactly. No math was presented in the thread.
The regenerative shock absorber idea was analyzed qualitatively, not
quantiatively.

A lot of things can be figured out without using any math at all.

-- Jeff, in Minneapolis

You are confusing mathematics with arithmetic.

Very little has been discussed without mathematics (except music). There has been little use of arithmetic and specific numbers, but there has been quite a bit of discussion of and application of mathematical theorems. Applying conservation of energy, qualitatively is an application of mathematics.

Mathematics is quite a bit more than "finding the answer" to some equation. Mathematics is about inequalities, topological structures, geometry, ....

There are entire books, rather advanced books, written on the qualitiative theory of differential equations, for instance, and that is how one handles problems like stability. There are more problems that are not completely solvable than problems that are, but that does not stop one from applying deep mathematics to understand features of those problems -- in fact this sort of thing is what modern mathematics is all about.

sirius0
2009-Jun-21, 05:51 AM
You are confusing mathematics with arithmetic.

Very little has been discussed without mathematics (except music). There has been little use of arithmetic and specific numbers, but there has been quite a bit of discussion of and application of mathematical theorems. Applying conservation of energy, qualitatively is an application of mathematics.

Mathematics is quite a bit more than "finding the answer" to some equation. Mathematics is about inequalities, topological structures, geometry, ....

There are entire books, rather advanced books, written on the qualitiative theory of differential equations, for instance, and that is how one handles problems like stability. There are more problems that are not completely solvable than problems that are, but that does not stop one from applying deep mathematics to understand features of those problems -- in fact this sort of thing is what modern mathematics is all about.
Thank you DrRocket my thoughts exactly! I think also my intent has been misunderstood. The shock absorber idea was only an example of how I had used my understanding of the maths to get somewhere better. My post was not about the idea itself. If I start doing the arithmetic I might begin designing the system but that would be inappropiate here. I took for granted that the calibre of those on this forum who like to see the math had a similar veiew to that of DrRocket. I.e. I should be able to assume that we all undrstand that the ennergy of a spring system is the intergration of F.dr and that when x1=x0 there has been no change of energy. Of course a real system will have had some energy put in for however many cycles and will have to lose it via heat, sound, or perhaps electricity.

Now that last sentance has been put in to stop those who could 'pounce' on the flaw.

I wonder if perhaps Tommac had a point with "How much do I need to know?" Perhaps it is a case of how much you all need to know of what I know before you have a level of trust?

Many papers make similar assumptions of their readers. Remember if I started throwing figures into my statements I prove nothing but a single case. See now I am assuming the worst of the knowledge level of other readers. We should, i think assume the best of anyones level here until they prove otherwise. I mean car suspension is hardly ATM :). Perhaps if I start saying I can run the car forever on the energy derived from the suspension THEN ask me for the maths...OK?

mugaliens
2009-Jun-21, 11:37 PM
Here's something else to think about while pondering the question, "What good is math?"

Well, for one, our computers, monitors, and networks would be utterly impossible without math, to the point where we wouldn't be having this conversation, at least not over the Internet. Everything from the complex shrinkage patterns that result when the plastic frames surrounding your monitors cool after they're released from the mold, to the complex interactions of the millions of nodes within the various PCUs and other integrated circuits in your computer, monitor, network card, printer, router, etc., all require math, both to be understood, but also to design and manufacture!

No math --> no computers.

I find it interesting in that even the earliest computers, such as the Antikythera mechanism (c. 150-100 BC), the equitorium ((1015 AD), the castle clock (1206 AD), and Wilhelm Schickard's calculating machine (1623) all required math for their design and constuctrion. Indeed, John Napier's observation that multiplication and division could be done by adding and subtracting the numbers' logs lead to his Napier's bones, a device he used in the production of his logarithmic tables.

Through the 1800s, however, all of these machines were based on the relatively simple maths of addition, subtraction, multiplication, division. Babbage's Difference Engine took these a step further, as it could do more than multiply and divide. It solved polynomials, which are approximators of logarithmic and trigonometric functions.

Notice how there's a lot of mathematical terms, here? And our timeline is still half a century before the Civil War!

About the time Babbage was working on the design for his difference engine, Charles Xavier Thomas created a successful mechnical calculator capable of adding, subtracting, multiplying, and dividing. That was nearly 200 years ago, and many followed, remaining in use throughout the 1970s, and even into the 1980s, as mechanical cash registers. I know, as I used one, a rather elaborate and powerful one, complete with pull-handle as a source of its computational energy, in the early 1980s! Other uses of these machines include the Mark I Fire Control Computer used throughout World War II.

The earliest digital electronic computers used vacuum tubes, which were designed using math. The knowledge for designing magnetic tape (indeed all magnic storage devices) requires advanced mathematics. Error-detection and correction, critical in all applications of modern computing, require different branches of mathematics, as does encryption.

So where would we be without math? At best, discussing a need for math over scones and tea at a local pub. More than likely, however, we'd be under a mud-walled, thatched-roofed hut somewhere in a forest.

WayneFrancis
2009-Jun-22, 01:30 AM
...
What Tom *actually said* is not unreasonable, and fits the facts that
I'm aware of. People who have the innate dexterity and timing can
learn to play music that they hear without knowing anything about
how theory describes that music.

-- Jeff, in Minneapolis

But this isn't the issue in my mind. tommac thinks that he can have a great understanding of physics without math.

Sure someone, like me, can learn a few pieces of music without the underlying theory. They'll never master the field and in many cases won't even understand most of it. While there will always be savants that don't need to learn underlying principals in a given area we should not use that as a rule to not learn.

Music is probably a bad example because most people have a good enough ear to appreciate good music. Physics isn't always intuitive. Probably why we don't see idiot savants in the fields of things like particle physics.

I can play a handful of songs on the piano quiet well but I can assure you that I wouldn't claim to have any real understanding of music as a whole beyond "knowing what I like". The songs I can play sound good and to me, and my friends, when I play them they also sound good. I'm sure that if someone with real training in music came along and heard me play they might cringe a fair bit.

tdvance
2009-Jun-22, 01:32 AM
3000 BC--math needed to design and build the pyramids. You could make and use levers without math, but to plan in advance how big a lever you need to do a certain job....nope. To plan much of anything, for that matter, you need math. Cities could not exist without math. The earliest cities had to take into consideration inflow of food and water and outflow of waste.

Trade without math means the other tribe that has math will get rich off the suckers who can't do accounting.

Given natural selection, this seems to imply a law of nature:

If a species can develop math, it will.

Tobin Dax
2009-Jun-22, 01:34 AM
Here's something else to think about while pondering the question, "What good is math?"

Well, for one, our computers, monitors, and networks would be utterly impossible without math, to the point where we wouldn't be having this conversation, at least not over the Internet. Everything from the complex shrinkage patterns that result when the plastic frames surrounding your monitors cool after they're released from the mold, to the complex interactions of the millions of nodes within the various PCUs and other integrated circuits in your computer, monitor, network card, printer, router, etc., all require math, both to be understood, but also to design and manufacture!

No math --> no computers.
This reminds me of one of the most, um, interesting things I've ever seen online. A poster on another forum went off on a rant about how math should be banned and no one should ever have to learn it. This rant about how useless and inconvenient math is was made on an internet forum using a computer. The sheer ignorance in that post is still mind boggling.


So where would we be without math? At best, discussing a need for math over scones and tea at a local pub. More than likely, however, we'd be under a mud-walled, thatched-roofed hut somewhere in a forest.
And we'd have to barter for it, since the cashier couldn't make change. :)

nauthiz
2009-Jun-22, 05:41 AM
Trade without math means the other tribe that has math will get rich off the suckers who can't do accounting.

Good point. Much of the reason why the Medici family managed to amass so much wealth and power is that the dynasty's founder is the guy who introduced double-entry bookkeeping to Florence.

sirius0
2009-Jun-22, 06:52 AM
I wonder though if the average level of wealth of forum members with some mathematical competence is higher than those with lower mathematical prowess? Anecdotaly I doubt it.

gzhpcu
2009-Jun-22, 07:55 AM
But this isn't the issue in my mind. tommac thinks that he can have a great understanding of physics without math.

You can read books for the layman, like those written by Brian Greene on string theory, and manage to gain some understanding about what the theory claims, without having a knowledge of math.

However, in order to say "I don't believe it", or come up with an ATM theory contesting say, Quantum Mechanics, you need to have a solid mastery of math to both understand it and to formulate the ATM theory.

astromark
2009-Jun-22, 08:52 AM
Not that this has much to do about this threads subject... but I agree with Sirius0... Money and your brains efficiency are not a given... Its who you know and what doors that you open... :) life's like that...
As to the subject at hand... Yes mathematics, arithmetic, algebra, calculus. are very important... so is spelling...
and I can't get that right all to often. You can not avoid these things. They are facts. That in this society we need to be educated. A working knowledge, or at minimum a understanding of basic arithmetic and language skills will assist you in your life. Some very clever people have designed the modern cell phone, computer, mp3, gps and and all those must have objects. None of them are possible without a great deal of math.... If you are not an achiever and can live with lower levels of income or stability. Then follow this no math path... but. Be warned. Its a rocky path.

astromark
2009-Jun-22, 09:09 AM
Or... :) you can let some other cleaver clogs do all your math for you. I have noted a trend for that to happen.
You can get by on very little actual application of mathematics. A good general knowledge can get you through. With maturity will come the realisation that. You could have done better.... if only you stayed switched on at school.

Perikles
2009-Jun-22, 09:31 AM
You can get by on very little actual application of mathematics. I agree. Having spend some miserable years coaching teenagers in maths who clearly had no mathematics braincells at all, I have concluded that the vast majority of our society can manage quite well with basic arithmetic only.

The only aspect of maths which ever comes into the lives of most people is in connection with mortgage payments, and the banks do this calculation anyway, with virtually no customer really understanding it.

The problem these days seems to me to be a failure even to train people in basic arithmetic. I have just this minute returned from a shop having bought an item for 11.15 euros. Not having a 10 euro note, I placed 21.15 euros on the till, waited for the cashier to fiddle with his calculator, and he finally gave me something like 7.56 euros change. I challenged this, but he was puzzled because I disagreed with his calculator.

I think the pocket calculator has had a disasterous effect on the ability of the general public to be able to cope even with the simplest of calculations. They should be banned from schools.

neilzero
2009-Jun-22, 11:54 AM
In my opinion banning calculators in schools would be a mistake, but it would be appropriate to occasionally give a test where calculators, slide rules and abacus were not allowed, to make sure the students were not over dependent. I typically use a calculator to confirm the mental estimate or manual calculation. When they disagree significantly, I try both again. Failing that, I try a different approach or order of steps. Neil

kzb
2009-Jun-22, 12:08 PM
Maths as used in the natural sciences is reductionist. Equations always have to make simplifying assumptions and assume this that and the other are negligible. An equation is an attempt at a model, usually derived long before the age of computer models.

I believe the maths as used in physics/chemistry courses represents a certain psychology of looking at the world, one that will slowly be replaced.

cjameshuff
2009-Jun-22, 12:20 PM
I think the pocket calculator has had a disasterous effect on the ability of the general public to be able to cope even with the simplest of calculations. They should be banned from schools.

That's nonsense. Your anecdote there doesn't even support your belief...it was misuse of a calculator that caused the problem, not use of one. Forcing students to slog through pages of arithmetic by hand if they want to try an idea out only discourages exploration, reinforces the impression that math is boring, and teaches nothing about math.

Hornblower
2009-Jun-22, 12:34 PM
I agree. Having spend some miserable years coaching teenagers in maths who clearly had no mathematics braincells at all, I have concluded that the vast majority of our society can manage quite well with basic arithmetic only.

The only aspect of maths which ever comes into the lives of most people is in connection with mortgage payments, and the banks do this calculation anyway, with virtually no customer really understanding it.

The problem these days seems to me to be a failure even to train people in basic arithmetic. I have just this minute returned from a shop having bought an item for 11.15 euros. Not having a 10 euro note, I placed 21.15 euros on the till, waited for the cashier to fiddle with his calculator, and he finally gave me something like 7.56 euros change. I challenged this, but he was puzzled because I disagreed with his calculator.

I think the pocket calculator has had a disasterous effect on the ability of the general public to be able to cope even with the simplest of calculations. They should be banned from schools.

That cashier apparently did not understand what he was putting into the calculator. As early as 3rd grade, meaning age 9, I would have seen instantly that the change would be exactly 10 euros (or whatever currency your country used in 1957). My teacher did an excellent job in explaining how the decimal system worked in doing multiple-column arithmetic.

The calculator is a two-edged sword. It eases the drudgery of crunching big numbers the old way, but it enables one to bypass the learning of techniques that are valuable error catchers. I think we should continue teaching kids how to do the arithmetic the old way, with periodic tests to make sure they do not forget, and to admit calculators for crunching big, messy numbers in applications.

Tobin Dax
2009-Jun-22, 02:38 PM
I think the pocket calculator has had a disasterous effect on the ability of the general public to be able to cope even with the simplest of calculations. They should be banned from schools.
Calculators have their place in the classroom, and there's nothing wrong with using them in appropriate situations. Your statement is overreacting.

nauthiz
2009-Jun-22, 03:53 PM
There's a point at which forcing students to do all the calculation by hand is simply exposing them to the risk of losing points due to arithmetic mistakes in courses where arithmetic is really not what's being taught. That doesn't seem particularly fair. The fact of the matter is, arithmetic calculation is notoriously time-consuming and error-prone, which is the whole reason why people whose job is to do math have relied on calculation aids since more or less immediately after the dawn of time.

When I was taking linear algebra, for example, we did the entire exam in Mathematica and submitted our answers electronically in the form of a Mathematica notebook. This wasn't about giving us a crutch, it was because if the purpose of the exam is to make sure that the student understands the mathematical concepts involved then it's a stupid and useless waste of time to force them to do the thousands of calculations that might be involved in solving one of the exam questions by hand.

Celestial Mechanic
2009-Jun-22, 04:05 PM
[Snip!] I believe the maths as used in physics/chemistry courses represents a certain psychology of looking at the world, one that will slowly be replaced.With what? ESP? A bunch of new age touchy-feelie holistic dogma?

cfgauss
2009-Jun-22, 04:23 PM
Calculators have their place in the classroom, and there's nothing wrong with using them in appropriate situations. Your statement is overreacting.

Yeah, this is basically the fallacy of the antecedent.

Calculators can work very well, but the important thing is to make sure people understand the structure of math. Once you understand the structure, you can figure anything else out.

I was never good at arithmetic as a kid. It wasn't until much later, when I learned why arithmetic works as it does did I get any good at it. And then I could figure out all by myself all the neat tricks to doing math in my head; adding to find change instead of subtracting, approximating results, adding 0 / multiplying by 1 to simplify, etc.

In fact, playing with calculators in middle school is what lead me to learn some of this structure (gods know it was not taught to me in school).

When I was in high school I got a TI-89, and that taught me a lot more algebra and complex number stuff and calculus than anything else until I read books about junior and senior college math classes!

Calculators can really enhance understanding and curiosity for students who're curious enough, or for teachers who're good enough to know to focus on big ideas and how those lead to specific calculations, rather than just making kids do menial problems, or thinking about things too abstract for them.

I taught arithmetic to calculus at a community college when I was 16, at a "study center" where students could learn stuff on their own from books, watch taped lectures, or talk to us, and then take tests that we'd grade for them (so more involved than a TA/tutor, but less than an instructor).

Teaching there, where most students were in their mid 30s, was really interesting. A lot of the students there really liked me, because I was one of the only people who would talk about thinking about how to solve the problem, instead of just applying rules without thinking. People who I saw really try to do the former did really well, and people who did the latter would be solving "2x+1=3" for practice, take a test, turn it in blank, then complain that nothing like "-2x-1=-3" was in the assignments. (Well, they also liked be because, as I was told / overheard several times, "if that kid can do this, so can I!")

But reading most books, they tend to focus not on thinking about structure or ideas, but about solving specific problems over and over again, which is really sad. Not that problems aren't helpful, but they're hardly everything.

Gillianren
2009-Jun-22, 04:50 PM
I wonder though if the average level of wealth of forum members with some mathematical competence is higher than those with lower mathematical prowess? Anecdotaly I doubt it.

What has that to do with anything? Someone I know suggested that the true value of a school was judged in how much its graduates made, suggesting five years down the line as a starting point. Well, of course, my alma mater turns out a lot of teachers and so forth, and of course med school students haven't even finished school five years after graduation with a Bachelor's. And I expect a lot of people with higher "mathematical competence" ("prowess" and "competence" are very different things) are also doing what they love, not to mention that which benefits society, no matter what they're making.

Fiery Phoenix
2009-Jun-22, 04:52 PM
I think the pocket calculator has had a disasterous effect on the ability of the general public to be able to cope even with the simplest of calculations. They should be banned from schools.

Completely disagree. Sorry!

Perikles
2009-Jun-22, 06:06 PM
That's nonsense. Your anecdote there doesn't even support your belief...it was misuse of a calculator that caused the problem, not use of one. Of course it is, and the anecdote shows it. But a student will always choose the path of least resistance, so if he has a calculator he will use it for the simplest calculation. I have seen it time and time again. The misuse cannot be controlled. Do you think that it is acceptable for a child to use a calculator to multiply 6 by 7? I've seen it many times.

The calculator also prevents the child from gaining a feel for numbers. I have experienced asking a child I was coaching the product of something like 6 and 7 and getting an answer like 698.4563, because there is no feeling for the impossibility. You cannot restrict the use of calculators without banning them.

cfgauss
2009-Jun-22, 06:16 PM
Of course it is, and the anecdote shows it. But a student will always choose the path of least resistance

Yes, this is why kids always lay comatose in bed all day, instead of doing difficult things, like sports, computer games, or socialization.

Ken G
2009-Jun-22, 06:27 PM
Of course it is, and the anecdote shows it. But a student will always choose the path of least resistance, so if he has a calculator he will use it for the simplest calculation. I have seen it time and time again. The misuse cannot be controlled. Do you think that it is acceptable for a child to use a calculator to multiply 6 by 7? I've seen it many times. I agree with the general feeling on this thread that simply banning calculators misses the opportunity they present. Your objections to them are certainly valid as far as they go, but your conclusions about the source of the problem may miss the mark, and so your solution may not be the best one. Indeed, behind every problem there is an opportunity to use that problem for some good purpose.

For example, it's not very clear to me that memorizing multiplication tables is that much different than learning to use a calculator, so to me, the problem with 6 X 7 = 42 is not so much the method used to solve it, but rather, the lack of understanding what it means. It's true that you'll always have your brain, and you won't always have access to a calculator, but I echo cfgauss' point that math is above all a way of thinking about things, and neither memorizing multiplication tables, nor using calculators, by itself can substitute. It's nice to know the tables, it's nice to have a calculator, but neither are mathematics. Perhaps the problem you allude to is actually an entry point to address this much more important lesson?


The calculator also prevents the child from gaining a feel for numbers. I have experienced asking a child I was coaching the product of something like 6 and 7 and getting an answer like 698.4563, because there is no feeling for the impossibility. You cannot restrict the use of calculators without banning them.Why isn't that anecdote a perfect opportunity to teach the feeling for that impossibility? Note that memorizing a multiplication table also doesn't teach rules about how numbers have to work, unless you take the next step and notice things about the numbers you are memorizing. The same "next step" can be applied to using calculators too. So the problem is not the calculator, it is the way we teach people to use them-- we say, "here, take this, follow these steps, and you won't have to think". The exact same attitude can be taken with memorizing multiplication tables, with the same bad outcome. It's all an entry point for learning a lesson about what a calculation is, that transcends the medium for performing the calculation.

Gillianren
2009-Jun-22, 06:29 PM
You cannot restrict the use of calculators without banning them.

Of course you can! What an odd statement. Now, I think calculators should be banned until perhaps third grade; when you're that young, all you're doing is basic arithmetic, and it's important that you learn to do that without a calculator. However, when I was in seventh grade, we were allowed to use calculators for some tests and not for others. Surely that's restricting their use!

kleindoofy
2009-Jun-22, 06:32 PM
... Someone I know suggested that the true value of a school was judged in how much its graduates made, suggesting five years down the line as a starting point. ... I expect a lot of people with higher "mathematical competence" ... are also doing what they love, not to mention that which benefits society, no matter what they're making.
I agree.

While I can't support the following with any statistics, my experience with people I know (and know of) shows that many so-called "highly gifted" people don't go into high paying areas or "fulfil the potential" that the lesser gifted might expect them to.

This usually isn't because they *can't* fufil it or because they can't cope with it, it's simply because they don't want to. They don't need it. They already have enough intellectual wealth and are perfectly content to persue their own goals without persuing a theoretical maximum of monetary income.

This is something many people don't understand. They say: "he/she has the potential to do/earn so much, why doesn't he/she use it? what a waste."

No, no waste. It's above and beyond that. They are using it, but not for the goals others might expect. The goals are often invisible to others.

Perikles
2009-Jun-22, 06:38 PM
Of course you can! What an odd statement. Now, I think calculators should be banned until perhaps third grade; when you're that young, all you're doing is basic arithmetic, and it's important that you learn to do that without a calculator. However, when I was in seventh grade, we were allowed to use calculators for some tests and not for others. Surely that's restricting their use!I agree with you entirely - an age under which they should not be used (not quite sure what 3rd grade is) and restriction after that. I never meant a complete ban at any age. This does not correspond to what I experienced in the UK where there seems to be no restriction on their use at all. Perhaps other here have more direct experience.

Perikles
2009-Jun-22, 06:48 PM
It's nice to know the tables, it's nice to have a calculator, but neither are mathematics. Perhaps the problem you allude to is actually an entry point to address this much more important lesson?
Why isn't that anecdote a perfect opportunity to teach the feeling for that impossibility? Note that memorizing a multiplication table also doesn't teach rules about how numbers have to work, unless you take the next step and notice things about the numbers you are memorizing. The same "next step" can be applied to using calculators too. So the problem is not the calculator, it is the way we teach people to use them-- we say, "here, take this, follow these steps, and you won't have to think". The exact same attitude can be taken with memorizing multiplication tables, with the same bad outcome. It's all an entry point for learning a lesson about what a calculation is, that transcends the medium for performing the calculation.I agree with all this, and several other posts. My original post was really referring to the level of maths which the vast majority of the population actually needs - in my view just basic arithmetic. The calculator comes into force after that, and eliminates a lot of tedium. The posts disagreeing with my ban of the calculator all refer to a level of maths which only a small minority of the population achieves, a level at which the calculator is entirely appropriate.

Ken G
2009-Jun-22, 07:12 PM
The posts disagreeing with my ban of the calculator all refer to a level of maths which only a small minority of the population achieves, a level at which the calculator is entirely appropriate.You are probably right about that, but perhaps this is itself the problem-- maybe such a small proportion achieves a level where math starts to make sense, because we don't teach them that math should make sense (indeed, it is all about making sense). Being competitive in the modern marketplace may have something to do with asking people to understand some things that at present are relegated to a minority.

astromark
2009-Jun-22, 07:18 PM
Mathematics, arithmetic. Lazy minds... So its how to teach the young to learn. Find there way. Only use the machine when you need to. Its a big ask. From my own honest down to earth logic. I will let those around me do the arithmetic for me... the show of's seem to enjoy it., and I will let them have their moment... I am that lazy mind who will let others do the work. I can now argue that makes me the cleaver one... you are free to disagree.

mugaliens
2009-Jun-22, 08:43 PM
...it's not very clear to me that memorizing multiplication tables is that much different than learning to use a calculator, so to me, the problem with 6 X 7 = 42 is not so much the method used to solve it, but rather, the lack of understanding what it means.

Exactly! I knew the answer in first grade, but didn't understand that if you have six piles of beans, with seven beans in a pile, you have forty-two beans total.

It wasn't until third grade that I learned the meaning behind 6 x 7 = 42, and by way of a similar illustration as the multiple piles of beans.


Good point. Much of the reason why the Medici family managed to amass so much wealth and power is that the dynasty's founder is the guy who introduced double-entry bookkeeping to Florence.

Are you sure it wasn't because he kept two sets of books? Not exactly what's meant by double-entry accounting, but...


I wonder though if the average level of wealth of forum members with some mathematical competence is higher than those with lower mathematical prowess? Anecdotaly I doubt it.

Across the US this holds true, more so with math, from what I understand, than any other college curriculum (ie average salary correlates positively with the highest level of math taken in college).

kleindoofy
2009-Jun-22, 09:00 PM
... Are you sure it wasn't because he kept two sets of books? Not exactly what's meant by double-entry accounting, but ...
No, it was, indirectly, the double-entry accounting.

The Medici introduced semi-modern government administration in a time when that was rare. It allowed them to build up and keep tabs on a state that had a much stabler basis than your average feudal system. (The building is still there: the Uffizi [= "Office"], which is now a museum.)

Instead of just counting your 42 beans, double-entry accounting, among other things, lets you keep track of those beans throughout their stay in your possession, either as something your ordered (credit), have stored (passive capital), have sent to the kitchen (active capital), want to plant (layback investment), sell (debit), etc.

Double-entry accounting is a royal plain in the glass, but it's great for keeping things in order.

sirius0
2009-Jun-22, 10:17 PM
What has that to do with anything? Someone I know suggested that the true value of a school was judged in how much its graduates made, suggesting five years down the line as a starting point. Well, of course, my alma mater turns out a lot of teachers and so forth, and of course med school students haven't even finished school five years after graduation with a Bachelor's. And I expect a lot of people with higher "mathematical competence" ("prowess" and "competence" are very different things) are also doing what they love, not to mention that which benefits society, no matter what they're making.
Yes I agree. I was just being factitious about the post just prior.

In fact equating 'value' with 'money' is probably the worst maths mistake we could ever make!

Gillianren
2009-Jun-22, 11:00 PM
I agree with you entirely - an age under which they should not be used (not quite sure what 3rd grade is) and restriction after that. I never meant a complete ban at any age. This does not correspond to what I experienced in the UK where there seems to be no restriction on their use at all. Perhaps other here have more direct experience.

I'm not sure what the not-US equivalents would be. Agewise, probably about nine. (It varies from kid to kid, in that I was held back a year based on my birthday--it's six days after their cutoff for entering kindergarten.) We were learning division that year; it's one of the only things I remember vividly from that teacher other than that he thought people wouldn't eat food that doesn't appeal to the eye as well. We agreed that he had clearly never eaten in our school's cafeteria.

WayneFrancis
2009-Jun-23, 01:52 AM
You know what I think a lot of this comes down to is the attitude the majority of people have with learning. Please no one take offense to this but most of us where not taught how to learn properly and thus this effects our outlook later on in life. We try to rationalize why we don't need to know math to have a deep understanding of physics. We are happy to think that without doing the hard work that we can know something better then those that put in all the effort.

This doesn't only apply to maths and physics. Go to any sporting event and watch the many fans yell at the players for being stupid while they are sitting there 50 pounds over weight, eating hot dogs and drinking beer.

I realize many people will think my son is an exception because he is "Gifted" but while his genes might predispose him to be better than average academically I strongly believe much of his "Gift" comes from the environment he grew up in where I always promoted him to think about the world around him. Start learning colors before he was a year old, count before he was 2, do simple addition and subtraction, that many adults can't seem to do before he was 4, multiplication and division before he was in school and before he was 6 you could have him multiply 2 two digit numbers together in his head.

He's no math savant. It is all just encouragement and spending the time. Car drives where always filled with talking about something to do with learning. Kids are not stupid as many people treat them as. Get them learning early and they'll thrive. Just look at kids that grow up in multilingual homes. They learn 2 languages just fine often with very different grammar rules without mixing them up. This same learning ability, in my opinion, can extend to other topics like maths.

If a child starts learning maths early then they'll naturally be better at it as they get older for many reasons. The better you are at something the more enjoyment you get when doing it. Thinking that maths can be enjoyable just like sports or performing can be.

Much of the world has a problem in that education has played less and less of a role over the years. It became uncool to be smart. Parents don't get actively involved with their kids education and think their role is limited to parent teacher nights once a year and signing report cards. You'll find many parents that think being involved with your kids is limited to taking them to and watch them play in little league baseball or play soccer. I applaud parents that do this because it is more then many parents do these days and I know much more then my parents ever did with me. But they should think about doing the same with learning. Sit down with your toddler for a half hour or an hour a day to do some educational stuff. The more effort you put in early in their life the more benefit they gain overall.

If you are reading this and saying to yourself "But my kid isn't very academic so it would be wasted" then you are just making excuses for yourself.

My boy might be "Gifted" but I'm a strong believer that much of his gifts where learned behavior and I'd rather him be "less gifted" and more of his talents be "learned" because he'll have more of a drive to use his talents.

So argue that you don't need maths to know physics. It's just lying to yourself so you can feel better about your ignorance. If it doesn't interest you then fine. Maths and physics isn't for everyone. But I imagine that everyone on these boards has an interest in a bit of physics. So if you think you can have this superior knowledge about astronomy and physics without doing the fundamentals then you are only fooling the fools.

All this said don't use the "But my parents didn't encourage me when I was young and it is to hard now" excuse. There are plenty of people out there that have been unfit and overweight their whole lives and then decided to put in the effort. Sure it is harder for them then it is for someone that was fit and active their whole life but it can still be done if you want it.

I'll get down off the soap box now.

sirius0
2009-Jun-23, 06:58 AM
For me when I was learning arithmetic in primary school the turning point was an abacus. This was one of those toy ones but the teacher turned it sideways giving it columns with a base ten number system. Excellent because it taught me the concept of base ten weighting, showed me a certain symmetry between numbers of any power of ten. And demonstrated the concept of the zero place holder. I am getting a Russian abacus (http://images.google.com.au/images?gbv=2&hl=en&sa=1&q=%2B%28russian+abacus%29+-chinese+-lee+-japanese&btnG=Search+images&aq=f&oq=) soon for my daughter. I think this would be a great tool for children in the early arithmetic years.

mugaliens
2009-Jun-23, 07:08 AM
No, it was, indirectly, the double-entry accounting.

LoL, you're right. However, my comment about two sets of books leading to the Medici's riches was only partially a joke...


Instead of just counting your 42 beans, double-entry accounting, among other things, lets you keep track of those beans throughout their stay in your possession, either as something your ordered (credit), have stored (passive capital), have sent to the kitchen (active capital), want to plant (layback investment), sell (debit), etc.

Double-entry accounting is a royal plain in the glass, but it's great for keeping things in order.

Yes, it is. One of the varied things I've done was taking a turn as the "chief" (read "only") accountant for a small manufacturing concern (filled in for the owner's son when said son got a job in the big city). I love accrual-based accounting, kicked the payroll's but with Lotus 1-2-3, think the depreciation schedules put out by the IRS are a joke, and detest GAAP as being ridiculously over-complicated. In its defence, GAAP is but a small subset reflecting our incredibly bloated end-all/be-all tax code.

Cougar
2009-Jun-25, 02:11 PM
"I began to view Nature as an intelligence test to which humanity as a whole has been subjected..." -- Gerard 't Hooft

tsumrall
2009-Jun-25, 02:41 PM
I remember when Apollo 13 (the movie anyways) was in trouble and Tom was having trouble with trusting some numbers. 3 or 4 people at mission control grabbed thier physics books? No! that reached for thier sliderules. The physics part was done already they only needed to apply the specific math

My point is knowing physics does not mean you can apply it to a specific event. That takes math. Burning kerosene provides thurst, physics. How much thurst will I get from 1 gallon, math.

John Mendenhall
2009-Jun-25, 04:27 PM
How much thurst will I get from 1 gallon, math.

A thurst for 1 gallon of kerosene will certainly generate enough thrust to get you into heaven.

mugaliens
2009-Jun-25, 04:38 PM
No, it was, indirectly, the double-entry accounting.

The Medici introduced semi-modern government administration in a time when that was rare. It allowed them to build up and keep tabs on a state that had a much stabler basis than your average feudal system. (The building is still there: the Uffizi [= "Office"], which is now a museum.)

Instead of just counting your 42 beans, double-entry accounting, among other things, lets you keep track of those beans throughout their stay in your possession, either as something your ordered (credit), have stored (passive capital), have sent to the kitchen (active capital), want to plant (layback investment), sell (debit), etc.

Double-entry accounting is a royal plain in the glass, but it's great for keeping things in order.

I'm actually quite familiar with the term, "double-entry accounting," having taken it throughout high school and college, and having worked a stint as an accountant.

What I'm referring to by "two sets of books" has nothing to do with double-entry accounting. It has to do with keeping one set of books for the government, and a second set which shows one's real profits, including all under-the-table payments and off-the-record deals/work done. The set for the government will show a modest net taxable income, thereby making you look like a respectable, marginally-successful businessman, while the second allows you to keep track of your Villa in France...

By the way, Peachtree uses double-entry accounting. Quickbooks does not.

I use Peachtree for my business.

kleindoofy
2009-Jun-26, 12:22 AM
... What I'm referring to by "two sets of books" has nothing to do with double-entry accounting. It has to do with keeping one set of books for the government, and a second set which shows one's real profits ...
Yes, in quoting you I was referring to nauthiz' original comment on the Medici who's somewhat revolutionary introduction of modern accounting and administration to a Renaissance state helped make Florence one of the major forces of its day.

Now, the "two sets of books" you mean should only ever exist on paper (or where ever) in the official version. Writing down the other version is tantamount to delivering yourself to the prison gates. Just ask Al Capone.

grav
2009-Jun-26, 01:26 AM
Double-entry accounting is a royal plain in the glass, but it's great for keeping things in order.Don't you mean a pane in the glass? Just kidding, couldn't resist. :)

HenrikOlsen
2009-Jun-26, 06:31 AM
Of course it is, and the anecdote shows it. But a student will always choose the path of least resistance, so if he has a calculator he will use it for the simplest calculation. I have seen it time and time again. The misuse cannot be controlled. Do you think that it is acceptable for a child to use a calculator to multiply 6 by 7? I've seen it many times.

The calculator also prevents the child from gaining a feel for numbers. I have experienced asking a child I was coaching the product of something like 6 and 7 and getting an answer like 698.4563, because there is no feeling for the impossibility. You cannot restrict the use of calculators without banning them.
But you're equating calculating with mathematics.

Getting past numbers to actual mathematics is the main hurdle, mindless drilling of calculation actually gets in the way of that.

Using a calculator to find 6*7 frees the mind to look at the real problem.

nauthiz
2009-Jun-26, 06:40 AM
6*7 is one that's never stuck in my head. For whatever reason, I have to take a detour through either 6*6+6 or 7*5+7 instead.

Perikles
2009-Jun-26, 07:53 AM
But you're equating calculating with mathematics.

Getting past numbers to actual mathematics is the main hurdle, mindless drilling of calculation actually gets in the way of that.

Using a calculator to find 6*7 frees the mind to look at the real problem.I think there is a clear difference between the task of multiplying, say, 6.3475 * 7.64796 and the integers 6*7. My comments were in the context of school children unable to perform even the basic arithmetic. For most of the population, this is what mathematics is. If you need a calculator for 6*7 you are very unlikely to see a mathematical problem beyond that.

Tobin Dax
2009-Jun-26, 11:00 AM
6*7 is one that's never stuck in my head. For whatever reason, I have to take a detour through either 6*6+6 or 7*5+7 instead.
6*7 could take some Deep Thought. Do you know the answer to "What is six by nine?" ;)

antoniseb
2009-Jun-26, 11:26 AM
... Do you know the answer to "What is six by nine?" ;)

Do you mean in base thirteen?

Tobin Dax
2009-Jun-26, 01:43 PM
Do you mean in base thirteen?
Hmm. Apparently I do.

NorthernBoy
2009-Jun-26, 03:29 PM
Upon noting, further down the thread from where I posted, that we are now short of an OP, this is now edited to say...

Take the simple situation of a pendulum, swinging freely. Without the maths, you can't even work out how long its period is. You'd probably be quite surprised, too, to find out that for small perturbations, the period is independent of the displacement.

Taking a simple example a bit further, the maths tells you what happens when the displacement is not "small", and what difference you will get when it starts swinging on bigger arcs.

If you cannot approach even this most basic problem without the maths, then how can anyone hope to make a new and serious contribution to physics?

NorthernBoy
2009-Jun-26, 03:50 PM
FYI, in case you don't know, MIT has put their entire course catalog online, free of charge. The media includes video-taped lectures, lab notes, examples, etc.

It seems to start off at a very, very basic level. For example, it explains vector addition in one of the lectures. Surely this is assumed knowledge before university level, isn't it?

Despite not doing the additional maths at high school that others did (it was not offered at mine), I was certainly comfortable with dot and cross products, how to calculate the closest approach of two lines in 3d space, angles between arbitrary vectors, and so on, long before university.

The first lecture I ever sat down in was a "refresher" on vector calculus, where they ran over the definitions and standard proofs (i.e. What is div.grad(v)) very quickly before launching straight into the more serious stuff.

NorthernBoy
2009-Jun-26, 04:01 PM
Good point. Much of the reason why the Medici family managed to amass so much wealth and power is that the dynasty's founder is the guy who introduced double-entry bookkeeping to Florence.

And, although it is maybe not the best time in history to mention this, it is also the reason why many of us deserted physics for finance.

If we could leave aside the, er, unpleasantness exploded on the world by a small percentage of my former colleagues, maths was absolutely essential to everything that we did, including understanding exactly to how much risk we were exposed.

From understanding how to most efficiently locate and fix the source of a Cholesky error in a covariance matrix, through to both visualising and managing all of the partial derivatives of a price which was a function of fifteen different underlyings, it would have been inconceivable to become a succesful trader in recent years without really being very familiar with university level maths.

So its use, of course, goes far beyond "just" physics.

If the OP were still here, maybe the understanding that he would be equipping himself for a brighter future would encourage him to put in the hours of study that he eschews.

NorthernBoy
2009-Jun-26, 04:12 PM
The problem these days seems to me to be a failure even to train people in basic arithmetic. I have just this minute returned from a shop having bought an item for 11.15 euros. Not having a 10 euro note, I placed 21.15 euros on the till, waited for the cashier to fiddle with his calculator, and he finally gave me something like 7.56 euros change. I challenged this, but he was puzzled because I disagreed with his calculator..

OK, last anecdote, I promise, but...

A few of my friends and I used to work on the checkouts in a supermarket. By the time I left, we had the modern scanners, but at the start it was electronic tills with buttons, so you typed the cost of each thing in by hand. On the whole, you never looked at the buttons, but just shifted the items off the belt with the left hand, and typed in the prices with the right.

Sometimes, rarely, you'd make a mistake with the buttons, such as typing in £21.56 instead of £2.15. The accepted methodology to fix this was explain what you'd done (you'd feel the mistake happening when you hit two buttons at once) to look over the remaining items on the belt, and then to come up, quickly, with something like;

"I'll put your dog food, flowers, wine and milk through for nothing, and your beers for 65 pence to correct the mistake."*

Then on you'd go with the rest of it.

Admittedly, we were all reasonably bright lads, but everyone was able to do this with no problem.

We all slowed when scanners were introduced, as the limiting factor became orienting the goods with the bar code down, as opposed to just passing them from the belt to the bagging area.

Ah, happy days...

*yes, we could have cancelled the incorrect price, but that required a supervisor, so was slower, and where on earth is the fun in doing it that way?

Jeff Root
2009-Jun-26, 04:25 PM
Take the simple situation of a pendulum, swinging freely. Without the
maths, you can't even work out how long its period is.
I don't understand. What do you mean by "work out" how long
the period is? Do you mean predict what the period of a pendulum
will be, given the length and so forth? I can generally estimate
the period of a pendulum by watching it. No math is involved.
If I want to be more precise I can use a stopwatch. Still no math.



You'd probably be quite surprised, too, to find out that for small
perturbations, the period is independent of the displacement.
That's pretty obvious, to a rough approximation, anyhow, just by
playing with a pendulum for a few minutes. I'm sure Galileo wasn't
the first to discover the relationship.



If you cannot approach even this most basic problem without the
maths, then how can anyone hope to make a new and serious
contribution to physics?
What "basic problem" involving pendulums did you mean to say can't
be approached without maths?

-- Jeff, in Minneapolis

tdvance
2009-Jun-26, 07:56 PM
But you're equating calculating with mathematics.

Getting past numbers to actual mathematics is the main hurdle, mindless drilling of calculation actually gets in the way of that.

Using a calculator to find 6*7 frees the mind to look at the real problem.

Really? Using a calculator for 6*7 wastes valuable seconds when one could just think, 42, and have the bigger problem half solved by the time the calculator has the answer.

tdvance
2009-Jun-26, 07:59 PM
Upon noting, further down the thread from where I posted, that we are now short of an OP, this is now edited to say...

Take the simple situation of a pendulum, swinging freely. Without the maths, you can't even work out how long its period is. You'd probably be quite surprised, too, to find out that for small perturbations, the period is independent of the displacement.

Taking a simple example a bit further, the maths tells you what happens when the displacement is not "small", and what difference you will get when it starts swinging on bigger arcs.

If you cannot approach even this most basic problem without the maths, then how can anyone hope to make a new and serious contribution to physics?

Probably not the best example, as Galileo determined the period of a swinging light at the Sistine Chapel (in heartbeats) and that it was independent of displacement, without math. Now it took Newton to show, with math, why that was the case. I think Galileo did come up with the formula for period versus length with math.

tdvance
2009-Jun-26, 08:00 PM
It seems to start off at a very, very basic level. For example, it explains vector addition in one of the lectures. Surely this is assumed knowledge before university level, isn't it?


Not anymore, as I learned when I TA'd calculus at UVA. We had to reteach a fair amount of algebra in the sections for non-math-science majors.

tdvance
2009-Jun-26, 08:05 PM
OK, last anecdote, I promise, but...

A few of my friends and I used to work on the checkouts in a supermarket.

When I was a grocery sacker, the scanners were new. The older workers knew the prices of the most commonly bought items, but the younger workers did not, and if the scanner failed, had to type, very slowly with one finger, the price in.

Oh, and errors DID have to be canceled (we didn't require supervisor approval, though I know that opens up an avenue for fraud by customer-cashier collusion--though best we could tell, that wasn't where the bleeding was. It was shoplifting.) mainly to reduce the number of times a by-hand inventory had to be done.

tdvance
2009-Jun-26, 08:07 PM
Not anymore, as I learned when I TA'd calculus at UVA. We had to reteach a fair amount of algebra in the sections for non-math-science majors.

I just thought of something--isn't University Level something different in Europe than in the US?

cjameshuff
2009-Jun-26, 08:40 PM
6*7 is one that's never stuck in my head. For whatever reason, I have to take a detour through either 6*6+6 or 7*5+7 instead.

I tend to take the 2*(3*7) approach.



Really? Using a calculator for 6*7 wastes valuable seconds when one could just think, 42, and have the bigger problem half solved by the time the calculator has the answer.

Or it can waste you far more time when you misremember and use the incorrect result for a page full of calculations, or when you're constantly cross-checking yourself to avoid such errors.

Plus, the calculator is a useful tool for learning that 6*7 = 42. If you're unsure, it's a couple moments of button-pressing to find the correct answer, which is far more effective at reinforcing that association than dropping what you're doing and working out the answer through other means, or ploughing ahead in the hopes that you're right.

You can and certainly will make errors while entering stuff into a calculator as well, of course. But you do get a feel for what the correct answers should be, and without cramping up your hand, using up sheets of paper, and constantly making trips to the pencil sharpener. Blind trust in the machine is in large part a sign of inexperience with the machine...or perhaps more likely in this case, just not particularly caring if the result is correct. Neither of these is going to be helped by banning calculators from classrooms. The idea that mechanical aids are somehow a cause of innumeracy is just pure nonsense.

Calculators should not be banned, not at any grade level. In fact, I think they should be provided at the earliest preschool level. Specialized for the audience, of course, with things like verbal feedback, games and exercises for teaching numbers and math, etc., but powerful ones, complete with programmable and with graphical capabilities.

Gillianren
2009-Jun-26, 08:43 PM
I just thought of something--isn't University Level something different in Europe than in the US?

I've never used the term to describe any level. There's college level, which is the four years it takes to get a Bachelor's, and there's grad school, which is anything above that.

Tobin Dax
2009-Jun-26, 09:37 PM
I've never used the term to describe any level. There's college level, which is the four years it takes to get a Bachelor's, and there's grad school, which is anything above that.
I never heard this on the West Coast, but out here "college physics" is at the algebra and trigonometry math level while "university physics" is at the calculus level. That, to me, implies a "university level," which might be synonymous with "college level" for the most part.

kleindoofy
2009-Jun-26, 09:50 PM
... out here "college physics" is at the algebra and trigonometry math level while "university physics" is at the calculus level. ...
Errr, we had all three in High School (in Massachusetts).

The major difference between the US and Europe is that in Europe one only studies the major and minor subject at the university, from the first semester onward. Accordingly, "high school" lasts one to two years longer. The "general curriculum" subjects associated with (parts of) the freshman and sophmore years at US colleges/universities are all completed beforehand. In the US, this can be called the "Associate of Arts" degree.

This is why, in general, a US high school diploma is not enough qualification to be admitted to a European university.

Gillianren
2009-Jun-26, 10:12 PM
I never heard this on the West Coast, but out here "college physics" is at the algebra and trigonometry math level while "university physics" is at the calculus level. That, to me, implies a "university level," which might be synonymous with "college level" for the most part.

What about all the people who took physics in high school? (Yes, I knew some people who took AP physics, though I don't know who took the test or who passed it. But still.)

tdvance
2009-Jun-26, 10:41 PM
I tend to take the 2*(3*7) approach.




Or it can waste you far more time when you misremember and use the incorrect result for a page full of calculations, or when you're constantly cross-checking yourself to avoid such errors.

uh...who's going to misremember 6*7? I'd say punching a wrong button on a calculator is FAR more likely (I've graded so many papers with silly nonsensical answers--answers that defy common sense if you even think while you work--that were obviously punched into a calculator with a digit incorrect somewhere--calculators have their uses, but using them to avoid thinking is a real problem among Freshmen, as I know from seeing it in action).

mugaliens
2009-Jun-26, 11:50 PM
6*7 could take some Deep Thought. Do you know the answer to "What is six by nine?" ;)

Sure - it means your CB has been overtuned and is above the legal power limit of 4W on your SWR meter!

cjameshuff
2009-Jun-27, 02:09 AM
uh...who's going to misremember 6*7?

Anyone and everyone who does a lot of calculations. Are you saying you've never screwed up basic arithmetic? Yeah, right.



I'd say punching a wrong button on a calculator is FAR more likely

Perhaps more likely for simple problems, but still more easily detected, and more quickly corrected.



(I've graded so many papers with silly nonsensical answers--answers that defy common sense if you even think while you work--that were obviously punched into a calculator with a digit incorrect somewhere--calculators have their uses, but using them to avoid thinking is a real problem among Freshmen, as I know from seeing it in action).

A student giving an answer does not mean that student believed that answer to be correct. Even if they are interested and want to give a correct answer, there's not always time to find the error. Making them do it all by hand certainly isn't going to help with that.

I also don't believe you can easily spot errors made due to blind reliance on a calculator. It's too easy to make the same errors grinding out numbers with pencil and paper. From writing the wrong digit down or mis-reading a poorly written digit to outright omitting or doubling digits, to screwing up borrows and carries, etc...it's a notoriously slow and error prone process. Drills on mental arithmetic with small numbers are useful, but beyond that it's both a waste of time better spent learning real math, and conditioning of students to avoid anything that resembles math.

BlueCoyote
2009-Jun-27, 06:21 AM
but beyond that it's both a waste of time better spent learning real math, and conditioning of students to avoid anything that resembles math.

I like to call real maths - mathematics

and simple addition and subtraction - arithmetic.

Are you guys familiar with the term arithmetic?

I don't here many people from North America using this term.

gzhpcu
2009-Jun-27, 09:59 AM
I like to call real maths - mathematics

and simple addition and subtraction - arithmetic.

Are you guys familiar with the term arithmetic?

I don't here many people from North America using this term.

Right. Arithmetic is where you perform the basic operations on numbers.

When you start working with equations using variables into which you can insert numbers, then math. This is mostly algebra.

Then when you start with calculus you start really using math.

NorthernBoy
2009-Jun-27, 11:03 AM
I don't understand. What do you mean by "work out" how long
the period is? Do you mean predict what the period of a pendulum
will be, given the length and so forth? I can generally estimate
the period of a pendulum by watching it.

No you can't, it is in a spaceship which is accelerating at 2g, a long way away, it is 2 metres long, and the mass per metre down its length is given by mass per metre = (distance^2)+1

So, what's the period of that, without using any maths?

NorthernBoy
2009-Jun-27, 11:06 AM
I just thought of something--isn't University Level something different in Europe than in the US?

I'm not sure if it is different at the beginning, but I'm pretty certain that the courses here give a more in-depth knowledge than in the US, as the course tends to be a coherent whole, where you must cover the subject for the whole time (we don't have any "minor", and we don't get any credits for unrelated subjects), so, for example, if you do a physics degree, it is four years of physics (with, of course, the maths that you need as well), and nothing else.

cjameshuff
2009-Jun-27, 12:08 PM
Are you guys familiar with the term arithmetic?

I don't here many people from North America using this term.

Er...?
This seems a very odd question, considering that I used it earlier in the sentence you quoted and specifically contrasted it with "real math". But yeah, arithmetic = glorified counting, memorization and practice of algorithms for performing hand computations. While both useful in and a product of math, arithmetic itself barely qualifies as math. It's that symbolic manipulation where the real interesting stuff is. (algebra, trigonometry, calculus, geometry, logic, etc)

I think it'd be very helpful to introduce students to algebra and formal reasoning much earlier, right alongside basic arithmetic, and focus less on mindless churning through page after page of of addition, subtraction, multiplication, etc. Not only would it give them an idea of what real math is like, but those reasoning skills are valuable in mental shortcuts and cross-checks for arithmetic...like the examples given above for breaking 6*7 into simpler operations.

BlueCoyote
2009-Jun-27, 12:58 PM
Er...?
This seems a very odd question, considering that I used it earlier in the sentence you quoted and specifically contrasted it with "real math".

So you did my mistake

Gillianren
2009-Jun-27, 06:07 PM
Okay, I'm confused, actually. When I grew up, "arithmetic" was basically treated as a subset of "mathematics." Is that not true? We had math books, not arithmetic books. (Or if the cover called it arithmetic, certainly possible, everyone, teachers included, just called it math.)

Cougar
2009-Jun-27, 06:40 PM
I think it'd be very helpful to introduce students to algebra and formal reasoning much earlier...

Absolutely. Especially 'formal reasoning', or simple mathematical logic. I think young kids would love ~B->~A.

And yeah, an early introduction to and long familiarity with just the rudimentary idea of algebra should make it much more broadly palatable when students get to Algebra I.

Jeff Root
2009-Jun-28, 01:54 AM
I don't understand. What do you mean by "work out" how long
the period is? Do you mean predict what the period of a pendulum
will be, given the length and so forth? I can generally estimate
the period of a pendulum by watching it.
No you can't,
Yes I can.



it is in a spaceship which is accelerating at 2g, a long way away,
No it isn't. There is no such pendulum or spaceship.

You are describing an imaginary pendulum in an imaginary spaceship.



it is 2 metres long, and the mass per metre down its length is given
by mass per metre = (distance^2)+1

So, what's the period of that, without using any maths?
It has no period because it doesn't exist.

You are asking for a prediction of what the period would be if
it were built and subjected to the conditions you specify, as I said.

Your first post was just poorly worded. You meant to say that one
cannot predict what the period of a pendulum would be, given a set
of physical parameters, without using maths. If one can see the
pendulum swinging, there is no need of maths to determine its period.

-- Jeff, in Minneapolis

Jeff Root
2009-Jun-28, 02:57 AM
Gillian, and everyone,

The very first volume of the fabulous Life Science Library is 'Mathematics',
published in 1963. If you haven't seen it, look for it in your library.
(The home version has a weak binding. The library binding is much better.)
Chapter one is "Numbers: A Long Way from One to Zero". Chapter two
is about geometry, chapter three is about algebra, chapter four is about
analytic geometry and trigonometry, chapter five is about calculus, chapter
six is about probability and statistics, chapter seven is about mathematics
developed in the 19th century-- what some here might call "real" math,
chapter eight is about math of the twentieth century. Lots of pictures,
as you'd expect from a Life publication.

I looked in it hoping to find something to quote that would help the
discussion, pertinent to Gillian's comment, but I haven't found anything
specific. The book as a whole is excellent.

-- Jeff, in Minneapolis

NorthernBoy
2009-Jun-30, 06:35 PM
Your first post was just poorly worded. You meant to say that

It is the height of arrogance to tell me what I meant. Please don't do it.

And I don't agree that my post was poorly worded. I said that you cannot work out the period. "Work out" is a synonym for calculate. I still say that you cannot do this without maths.

You may disagree, but that isn't of particular concern to me.

DrRocket
2009-Jun-30, 07:11 PM
uh...who's going to misremember 6*7? I'd say punching a wrong button on a calculator is FAR more likely (I've graded so many papers with silly nonsensical answers--answers that defy common sense if you even think while you work--that were obviously punched into a calculator with a digit incorrect somewhere--calculators have their uses, but using them to avoid thinking is a real problem among Freshmen, as I know from seeing it in action).

Absopositively correct.

Reliance on calculators is most revealing of the lack of thought among some students. Appalling is the word.

They are pretty useful for eliminating a need to look up trigonometric functions in tables (same for logarithms), but they are too often used as surrogate for thinking. For instance I have seen things along the line of this : given a triangle with two sides length 3 and 5 and an included angle of 27 degrees find the length to the remaining side -- following some key punching a length of 9,327,435 is offered, with not a hint of a thought that such an answer is ridiculous.

Calculators are useful in physics and engineering classes, and a help in eliminating a need for table look-ups. But fundamentally calculators are counter-productive for most mathematics classes.

Frankly, I would prefer slide rules for trig and log functions, if they were available any longer. They get the job done, but the student has to think enough to know where the decimal point goes.

True slide rule story. When the HP 35 calculator first came out (first calculator that could handle trig and logarithms) a young physics professor, who figured he was pretty hot stuff, bought one for about $350 (1970 dollars, and $350 then was quite a bit of money). Figuring that some "lesser light" could make use of his old Pickett slide rule he put a note on the bulletin board and set it out for sale. An older gentleman saw the note and purchased the slide rule, figuring that it would meet his needs. It did. That "lesser light" was Eugene Wigner.

Ken G
2009-Jun-30, 07:20 PM
Here's another problem with calculators, in addition to how they can substitute for thinking about the meaning of numbers: they can substitute for thinking about the meaning of formulae too. If we say the force of gravity is GMm/d2, in calculatorese that formula says nothing more than "look up G, insert M, hit multiply, insert m, hit multiply, insert d, hit square, and divide". Like a recipe for cooking stew. But what a formula like that is really trying to tell us is, what does the force of gravity depend on, and how does it depend on it? What will happen to the force if we change various things in various ways? If you ask a student what happens to the force if you double the distance, and they say, "OK, well according to my recipe, the first thing I need to know is G", you know they are thinking in calculatorese. I think we should allow students to use calculators as needed, but make sure that they are only using the calculator to calculate for them-- not to think for them.

Gillianren
2009-Jun-30, 08:54 PM
You know, people who fail to think because they have calculators are probably not experts at thinking full stop. As it happens, there are a few very simple multiplication figures I regularly forget; I don't look them up on a calculator, but it delays me a minute while I stop to remember them. No, I'd never give some wildly improbably answer because I'd entered it into a calculator wrong, but that's because I'm a basically intelligent person who doesn't rely on others to think for me. That's true in other fields, as well.

As another example, spell check is a valuable tool for the average person. Everyone makes typos or just can't spell certain words, and it's helpful for that. You can tell when someone's relying on it too much, however, when their paper/post is full of homophones and various words that are spelled similarly to what they mean but aren't anywhere close in, well, meaning. The problem is not with the tool.

Jeff Root
2009-Jul-02, 04:04 AM
It is the height of arrogance to tell me what I meant. Please don't do it.
It isn't the height of arrogance. I've seen far worse. In any case,
what I said was correct.



And I don't agree that my post was poorly worded. I said that you
cannot work out the period. "Work out" is a synonym for calculate.
I still say that you cannot do this without maths.
Obviously one cannot calculate a mathematical value without using
mathematics. However, one can construct a pendulum and measure
its period without using any mathematics. That is working out the
period every bit as much as doing the calculation.



You may disagree, but that isn't of particular concern to me.
I could tell.

-- Jeff, in Minneapolis

WayneFrancis
2009-Jul-02, 05:48 AM
Er...?
This seems a very odd question, considering that I used it earlier in the sentence you quoted and specifically contrasted it with "real math". But yeah, arithmetic = glorified counting, memorization and practice of algorithms for performing hand computations. While both useful in and a product of math, arithmetic itself barely qualifies as math. It's that symbolic manipulation where the real interesting stuff is. (algebra, trigonometry, calculus, geometry, logic, etc)

I think it'd be very helpful to introduce students to algebra and formal reasoning much earlier, right alongside basic arithmetic, and focus less on mindless churning through page after page of of addition, subtraction, multiplication, etc. Not only would it give them an idea of what real math is like, but those reasoning skills are valuable in mental shortcuts and cross-checks for arithmetic...like the examples given above for breaking 6*7 into simpler operations.

agreed, this is why my son does maths at 2-3 years above his grade level. It isn't because he know 67 * 45 = 3015 but that 67 * 45 =( (7*45) * 10) - 135. There are a few kids doing higher level maths in his class (they are in a class for gifted kids), but he's still does better then all but on kid when doing math competitions because if the others don't know a formula for something they are kind of stuck while he has learned how to solve the underlying problems himself. His teacher says he's got the best divergent skills of the bunch. This isn't a "gift" he had as much as much of a talent that was nurtured.

I to believe that more kids should be exposed to concepts like algebra early on. Less time spent on multiplication tables and more time on what multiplication actually means. I'd say a good 30% of the students out there could probably "perform" at the the top 5%-10% of current students if they did this. Of course then you'd have people complain about the "divide" that would be caused by those students and the ones that naturally struggle with simple addition.

Can anyone tell I'm passionate about childhood education?!?!?! :)

DrRocket
2009-Jul-02, 06:09 AM
agreed, this is why my son does maths at 2-3 years above his grade level. It isn't because he know 67 * 45 = 3015 but that 67 * 45 =( (7*45) * 10) - 135. There are a few kids doing higher level maths in his class (they are in a class for gifted kids), but he's still does better then all but on kid when doing math competitions because if the others don't know a formula for something they are kind of stuck while he has learned how to solve the underlying problems himself. His teacher says he's got the best divergent skills of the bunch. This isn't a "gift" he had as much as much of a talent that was nurtured.

I to believe that more kids should be exposed to concepts like algebra early on. Less time spent on multiplication tables and more time on what multiplication actually means. I'd say a good 30% of the students out there could probably "perform" at the the top 5%-10% of current students if they did this. Of course then you'd have people complain about the "divide" that would be caused by those students and the ones that naturally struggle with simple addition.

Can anyone tell I'm passionate about childhood education?!?!?! :)


That may work for some very good students. But for most it would be nice if they knew enough by rote to be able to do arithmetic easily and not have arithmetic be a stumbling block to learning more advanced mathematics.

For instance, it is not uncommon for students to have trouble with fractional exponents, not because they don't understand powers and exponents, but because they can't add fractions.

You need to be able to do arithmetic in your sleep before trying to really learn and understand algebra and more advanced mathematics. Otherwise there is a tendency to just learn "symbol pushing" -- this is a common problem with students who learn their calculus in high school.

Gillianren
2009-Jul-02, 04:35 PM
Can anyone tell I'm passionate about childhood education?!?!?! :)

I do hope you're teaching him grammar. Or, rather, how not to end sentences.

tdvance
2009-Jul-02, 07:42 PM
don't end a sentence with a smiley. Got it!!!??!?!?!...

Ken G
2009-Jul-02, 08:47 PM
Where are you supposed to :) put them?!

GeorgeLeRoyTirebiter
2009-Jul-03, 01:10 AM
The problem's not the smiley, it's that you should be using an interrobang:

mugaliens
2009-Jul-03, 01:34 AM
"Interrobang?"

Nice!

I think..?

WayneFrancis
2009-Jul-03, 02:12 AM
I do hope you're teaching him grammar. Or, rather, how not to end sentences.

:) He's advanced in all areas but I leave most of his English to his English teachers. I do proof read his work and comment on his writing. Funny enough when he was 3-4 I was thinking about trying to teach him to read but the ladies at child care told me not to because I could screw it up. I shouldn't have listened to them. But he started reading a lot once he got into kindergarten.

When posting I write like I talk. Using punctuation like "?!?!?!" is a literary device. :)

So what do people use to indicate a sentence is both a statement and a bit of a rhetorical question?
I like the ?!?!?!
The longer longer it is the more my emphasis is.

Gillianren
2009-Jul-03, 03:43 AM
So what do people use to indicate a sentence is both a statement and a bit of a rhetorical question?
I like the ?!?!?!
The longer longer it is the more my emphasis is.

They use a question mark and let the words demonstrate the rest, or else they clearly phrase it as a question and end it with a period. (I prefer the former.) However, you get one punctuation mark to end a sentence. Using more than one is like using both x and * at the same time to represent multiplication. It's wrong and silly-looking.

And trying to write without a fundamental understanding of grammar is like trying to do physics without a fundamental understanding of arithmetic. You may be on the right track, but at the heart, you're still wrong.

ETA--oh, yeah. And "proofread" is one word.

PraedSt
2009-Jul-03, 04:03 AM
From understanding how to most efficiently locate and fix the source of a Cholesky error in a covariance matrix, through to both visualising and managing all of the partial derivatives of a price which was a function of fifteen different underlyings, it would have been inconceivable to become a succesful trader in recent years without really being very familiar with university level maths.I disagree. Although pleasantly. I consider myself successful trader, and some of my employees are also successful traders. We don't use, and never have used, any maths higher than simple arithmetic. There are many ways to trade, as I'm sure you know.

PraedSt
2009-Jul-03, 04:09 AM
Obviously one cannot calculate a mathematical value without using mathematics. However, one can construct a pendulum and measure its period without using any mathematics. That is working out the period every bit as much as doing the calculation.This pendulum back and forth (heh) is puzzling me. Just out of curiosity Jeff, how do you mean to measure it's period without doing at least some maths in your head? Even observation requires some counting.

Jeff Root
2009-Jul-03, 05:01 AM
What mathematics do you think I would need to do? Here, I'll measure
the period of a pendulum... Just a moment... about 1-3/4 seconds for my
little Swiss Army knife hanging on a thread. What math do you think I
used to get that result?

-- Jeff, in Minneapolis

PraedSt
2009-Jul-03, 05:08 AM
Ok, now that seems like a trick question. Which probably explains why I haven't been able to understand the interchange. Arithmetic is not mathematics?

Jeff Root
2009-Jul-03, 05:55 AM
What arithmetic do you think I used? I'm not aware that I used any.

-- Jeff, in Minneapolis

WayneFrancis
2009-Jul-03, 06:21 AM
They use a question mark and let the words demonstrate the rest, or else they clearly phrase it as a question and end it with a period. (I prefer the former.) However, you get one punctuation mark to end a sentence. Using more than one is like using both x and * at the same time to represent multiplication. It's wrong and silly-looking.

And trying to write without a fundamental understanding of grammar is like trying to do physics without a fundamental understanding of arithmetic. You may be on the right track, but at the heart, you're still wrong.

ETA--oh, yeah. And "proofread" is one word.

Thanks for being the grammar police for me! :)

WayneFrancis
2009-Jul-03, 06:26 AM
This pendulum back and forth (heh) is puzzling me. Just out of curiosity Jeff, how do you mean to measure it's period without doing at least some maths in your head? Even observation requires some counting.

No no no no! <- note only 1 punctuation. Though I think using the word "no" 4 times does not meet the requirements of a sentence either.

Anyway, is there a rule about starting a sentence with that word? you can measure thing by gut feel like Verschuur measures correlations between WMAP data and local neutral hydrogen and doesn't care if his gut feel isn't actually supported by the numbers.

PraedSt
2009-Jul-03, 03:54 PM
What mathematics do you think I would need to do? Here, I'll measure
the period of a pendulum... Just a moment... about 1-3/4 seconds for my
little Swiss Army knife hanging on a thread. What math do you think I
used to get that result?

-- Jeff, in Minneapolis
You've counted, and operated on, rational numbers.

PraedSt
2009-Jul-03, 03:57 PM
No no no no! <- note only 1 punctuation. Though I think using the word "no" 4 times does not meet the requirements of a sentence either.

Anyway, is there a rule about starting a sentence with that word? you can measure thing by gut feel like Verschuur measures correlations between WMAP data and local neutral hydrogen and doesn't care if his gut feel isn't actually supported by the numbers.Sounds to me like you're saying someone doesn't need maths when forming an opinion about someone else's maths.

pg_chelsea
2009-Jul-03, 05:27 PM
Perfessor language, I like the use of !? I see nothing wrong with ??? or !!! and surely you agree with the use of ...

And I think, yes, you do need math. It's a tool that helps with abstracting. I suppose you could ask the same about language.
I'm sure that without language or math, one could develop some talent playing piano or predicting pendulum periods by changing different variables. But the lack of these tools would be a great hindrance.

agingjb
2009-Jul-03, 05:56 PM
I'm puzzled.

Yes, the periods of pendulums that are to hand can be observed. But it is the accumulation of such observations that enables a predictive theory to be formed. That theory enables a formula to be constructed that will yield an estimate of the period of a pendulum given its length.

I would have said that this involved mathematics - isn't the substitution of a value into a formula mathematics?

(And the theory is also backed up by an applied mathematical theory of pendulums, although this is not required in standard cases.)

Gillianren
2009-Jul-03, 06:00 PM
Perfessor language, I like the use of !? I see nothing wrong with ??? or !!! and surely you agree with the use of ...

It's wrong. It doesn't matter if you like it or not. As to that last, it's the ellipsis. It is a separate punctuation mark (oddly, yes, it's considered one mark), and it doesn't end a sentence. If you are ending a sentence with it, you have to put a period at the end. For heaven's sake, why are people so snippy about an expectation that they at least attempt correct grammar? We fight all sorts of ignorance here, but I am expected to keep quiet about the very one that we need most--proper communication.

agingjb
2009-Jul-03, 06:08 PM
Gillianren: I often see usages that I would hope to avoid. But one reason for never drawing attention to them, at least in the context of a forum, is that they provide me with so much reliable information about the writer.

tdvance
2009-Jul-03, 06:56 PM
Wot? I has a PH Friggin D in the maths!.!.!

Gillianren
2009-Jul-03, 07:05 PM
Gillianren: I often see usages that I would hope to avoid. But one reason for never drawing attention to them, at least in the context of a forum, is that they provide me with so much reliable information about the writer.

I have had more than a few people disagree with this sentiment and thank me for the work I put in on the subject, including several who have asked me to correct them every time.

agingjb
2009-Jul-03, 07:43 PM
Well yes, if someone were to ask me, then I'd help (always assuming I knew enough to help), but my experience of forums suggests that many, perhaps most, people don't want to be corrected. I've never dared anyway, but I've seen such furious reactions that I'll continue to leave well alone (and learn).

Of course, people whose first language is not English are far more likely to be positive about offered corrections, but I would still wait to be asked. In any case I am neither a professional writer nor a teacher, so my opinions are not always reliable.

agingjb
2009-Jul-03, 07:54 PM
On the topic of the forum, I do wish I knew enough mathematics to be in a position to understand the Mainstream fully - a basic criterion for proposing something Against the Mainstream if I ever wanted to. (I don't.)

Let me mention "The Road to Reality" by Roger Penrose as a work that, whatever its merits or otherwise, has a level of mathematical content that I think is a fairly good guide to what would be required of a serious proposal contesting current theory.

Jeff Root
2009-Jul-03, 09:40 PM
What mathematics do you think I would need to do? Here, I'll measure
the period of a pendulum... Just a moment... about 1-3/4 seconds for my
little Swiss Army knife hanging on a thread. What math do you think I
used to get that result?
You've counted, and operated on, rational numbers.
I have??? I don't remember counting anything. I don't remember
performing any operation. What do you think I counted? What
operation or operations do you think I performed?

Also: Does counting count as mathematics?

-- Jeff, in Minneapolis

nauthiz
2009-Jul-03, 09:48 PM
Also: Does counting count as mathematics
I'd go so far as to say it's the very beginning of mathematics.

1. 0 is a natural number.
2. For every natural number x, S(x) is a natural number.

DrRocket
2009-Jul-03, 09:55 PM
I'd go so far as to say it's the very beginning of mathematics.

1. 0 is a natural number.
2. For every natural number x, S(x) is a natural number.

You need to tell them that 1 is not S(x) for any naturan number x. And that if you have a set A with the property that 1 belongs to A and if whenever x is in A then so is S(x) then A is all of the natural numbers.

With that you, basic logic, the usual notions of a set you can build all of the usual number systems -- integers, rationals, reals and complex numbers. (See for instance Foundations of Analysis by Landau).

Throw in the axiom of choice, and you can build virtually all of modern mathematics.

Yep, arithmetic is pretty fundamental.

Merkin Muffley
2009-Jul-04, 10:52 PM
In any case I am neither a professional writer nor a teacher, so my opinions are not always reliable.

I'm not either, but I was one once, and my opinions weren't always reliable then either.

WayneFrancis
2009-Jul-06, 02:24 AM
Sounds to me like you're saying someone doesn't need maths when forming an opinion about someone else's maths.

I guess I should have preceded that with a /sarcasm

Verschuur made a claim based on a purely visual comparison. When someone else crunched the numbers the results where within statistical norms. Verschuur then basically said he doesn't care what the numbers say and, sadly, he's an astronomer.

mugaliens
2009-Jul-06, 03:14 AM
They use a question mark and let the words demonstrate the rest, or else they clearly phrase it as a question and end it with a period. (I prefer the former.) However, you get one punctuation mark to end a sentence. Using more than one is like using both x and * at the same time to represent multiplication. It's wrong and silly-looking.

Yes, 3 x* 2 is wrong and silly-looking, as it's never done in practice. The punctuation at the end of this sentance, however, is not, as it's commonly seen throughout modern literature!!!


And trying to write without a fundamental understanding of grammar is like trying to do physics without a fundamental understanding of arithmetic.

What about beginning sentences with "And?" My teachers (all of them) taught me that was improper grammar.


ETA--oh, yeah. And "proofread" is one word.

I believe the this sentence of yours exemplifies what's going on, here. People speak informally. They do not speak formally, as they would write. Furthermore, the development of the Internet as an online social community has meant a change in the nature of online communication, a migration from formal writing reflecting the way people used to write, to information communication along the lines of the way people normally speak.


I have had more than a few people disagree with this sentiment and thank me for the work I put in on the subject, including several who have asked me to correct them every time.

If I'm not mistaken, I believe I was one of those individuals, a while back. ;) As a result, several critical errors which had crept into my writing have been removed; not all of them, mind you, just most. I'm a better writer for it, and I thank you for your efforts!


As to that last, it's the ellipsis. It is a separate punctuation mark (oddly, yes, it's considered one mark), and it doesn't end a sentence. If you are ending a sentence with it, you have to put a period at the end. For heaven's sake, why are people so snippy about an expectation that they at least attempt correct grammar? We fight all sorts of ignorance here, but I am expected to keep quiet about the very one that we need most--proper communication.

I would support an amendment to Rule 3 to include prohibiting language shortcuts as are commonly used in chat forums, and an encouragement to use proper spelling and grammar.

I would argue, however, that "proper spelling and grammar" should be inclusive of what is commonly experienced in information, face-to-face communication - in short, shop talk. Unless one is an exceptional grammarian, requiring formal grammar can prove to be as much of an impediment to good communication as allowing chat shortcuts.

In closing, if you allow yourself the occasional sentence fragment, I hope it wouldn't be too much to ask if you'd allow us the occasional missing fourth dot which completes an end of sentence ellipse and its subsequent period.

Thank you.

Tobin Dax
2009-Jul-06, 04:47 AM
Yes, 3 x* 2 is wrong and silly-looking, as it's never done in practice. The punctuation at the end of this sentance, however, is not, as it's commonly seen throughout modern literature!!!
Please provide some examples. (I seriously want to see them, as I can't recall seeing any myself.)



I would support an amendment to Rule 3 to include prohibiting language shortcuts as are commonly used in chat forums, and an encouragement to use proper spelling and grammar.
You would support the 24-hour of someone who posts before reading the rules just because they wrote "u" instead of "you"? That's a bit over the top, and a good way to easily scare off new members.

Perikles
2009-Jul-06, 07:50 AM
That's a bit over the top, and a good way to easily scare off new members.What is the position of the forum on splitting infinitives, or need I ask? :)

Jeff Root
2009-Jul-06, 08:41 AM
In the 1972 anthology, 'Again, Dangerous Visions', edited by Harlan Ellison,
cartoonist Gahan Wilson contributed a story titled "http://www.bautforum.com/attachment.php?attachmentid=10399&stc=1&d=1246867900".

-- Jeff, in Minneapolis

.

agingjb
2009-Jul-06, 08:47 AM
The forum prefers "miniscule" (in 500 posts) to "minuscule" (in 270 posts).

I was going to put in a word for Group Theory as an essential component of Mathematics.

antoniseb
2009-Jul-06, 09:56 AM
Are we getting a little off topic here? How far back do I need to look to find something specifically about the relative merits of math?

robross
2009-Jul-06, 10:01 AM
Are we getting a little off topic here? How far back do I need to look to find something specifically about the relative merits of math?

Probably right before tommac was suspended. After that this thread definitely took a turn...to somewhere else. :)

Rob

Jeff Root
2009-Jul-06, 11:00 AM
The principle direction was to define mathematics = everything.

-- Jeff, in Minneapolis

agingjb
2009-Jul-06, 11:07 AM
Sorry, but my excuse is simply that any attempt on my part to show why mathematics does have relevance to physics is getting absolutely nowhere against those who think that it does not. It wouldn't surprise me if others have had the same experience.

It is certainly arguable that a thread on the use and abuse of English within BAUT might have some value in its proper place.

Jeff Root
2009-Jul-06, 11:29 AM
agingjb,

I don't recall anyone, in my entire life, ever expressing the idea that
mathematics does not have relevance to physics. Certainly not here
on BAUT. Certainly not in this thread!

-- Jeff, in Minneapolis

Tobin Dax
2009-Jul-06, 02:06 PM
What is the position of the forum on splitting infinitives, or need I ask? :)
Check my user name. It gives me a good excuse to boldly split infinitives. :)