Freethought & Rationalism Archive

Mr. Sammi · 01-23-2003, 10:09 AM

cfgauss,

do I have to reply?

OK, I will.

Math is used to strengthen physics. It would be just as fine to say Force is proportional to mass. Acceleration is proportional to Force. Force is the cause of acceleration.

Math may be used to refine the equations, but tell us nothing about the system. If I used a math equation R = F*u. What does this mean? nothing. Only R equals F multiplied by small u.

R=F*u ; is a meaningless math equation. The equations become meaningful when the relations have a correspondence to reality. To say R implies F on the left side of the equation ; F implies m on the right side of the equation ; u implies a on the right side of the equation ; thus we have a relation with the physical world. Not a relation with some mathematical abstraction. Mathematical abstractions usually come after the observations.

The implication of what I have written in this post IS you lack depth in your understanding, and this is obvious in your treatment of the question. Your scope of knowledge is limited. Your analogies are abhorrent.

Sammi Na Boodie ()

Feather · 01-23-2003, 10:46 AM

Quote:

Originally posted by cfgauss
Neither physics nor math are simply "abstractions" or constructs of humans. They exist independently of us. If we know it or not, F still equals ma, and F=ma is defined with math.

Physics, I believe, does come from math because there's so much of physics we can derive from simply math! For example, we can get many of the laws of circular motion from purely math and some definitions. We can get all of the conservation laws from various mathematical symmetries. We can get Special Relativity from math and a few postulates. Etc. That's why those theories are so strong! Relativity only rests on a small handful of postulates, the rest is concrete math, which is cool as long as we make sure to do the math right!

Also, asking if physics comes from math or if math comes from physics is most likely asking the same thing. The only difference is a philosophical one. It's like asking if factorial is a special case of the gamma function or if gamma is a generalization of factorial.

Ummm, no?

Physics is the study of the most basic of natural phenomena. Mathematics is a useful tool to describe such things quickly and in a standard way. I'm sure mathematicians would disagree that math is "merely" a tool, but as far as physics is concerned that is indeed the case.

Mathematics is a system of logic that requires axioms to be established before discussion, and any conclusions following thereafter rely on the validity of the axioms. Any set of axioms is no more or less valid than any other set of axioms (provided that neither set contains self-contradictory statements, of course). This simply isn't the case with Physics. There are no axioms in physics. None. A theory works only as long as the observational data support it. Mathematics has no such restriction placed upon it.

Neither "comes from" the other in any way.

cfgauss · 01-23-2003, 12:27 PM

I'm really not going to give you several years of the math and physics training that you clearly don't have, but need to understand in order to have the slightest idea what one is talking about, Sammi. I doubt you even got my gamma function example, which is something that I knew about in Jr. High

.

For those of you who do actually want to listen to someone who knows physics...

Consider the derivation of time dilation in SR. Barely need any physics. All you need to know that distance = rate times time! Mathematically, you need algebra and the Pythagorean theorem. You *assume* that the speed of light is isotropic and that the laws of physics are the same in every inertial frame, and that's it! In fact, one could easily argue that you need to know no actual physics, but only to *define* that v=x/t! From no physics, just math, comes SR! So simple!

Doesn't it seem odd to you that math is the absolute perfect thing to describe physics with? Math doesn't describe anything else like that! Has there ever been an economic model made from *purely* math and definition? No. The closest thing to that is probably game theory, but you still need to add economics to it in order to yield a viable theory. Has anyone came up with a mathematical theory of psychology (let alone one that comes from math!), or one of politics? No. We can average and measure and make models, for sure; but not pure math has yielded anything there! We can only model other things with math; physics it describes perfectly, and in many cases alone.

And you can do it again and again with physics! Want conservation of angular momentum? Rotational symmetry! Want more SR? Easy! We can do this with *nothing* else!

And if you look at some theories of quantum gravity it just gets scary! Some imply things like that everything is a result of relatively simple mathematical symmetries, and such.

When you have something that *perfectly* describes something, you should worry! Just as it is odd that the integral of e^-t * t^x dt from 0 to infinity *just happens* to be x(x-1)(x-2)...1 for positive integral x, it is odd that from (ct)^2 = (ct')^2 + (vt)^2 comes SR!

Indeed, this is why many mathematicians and physicists I've talked to (the former, especially) believe in God! Things are just "too" perfect!

Goliath · 01-23-2003, 12:29 PM

Mr. Sammi,

First of all, let me say that I am a graduate student in Mathematics, and that I will have my PhD in less than a year and a half (if everything goes according to plan).

You had claimed that Mathematics is only meaningful when it has a correspondence to reality.

Consider this paper, written by my advisor.

The preprint that I have linked to is new research in Factorization Theory that looks at a lot of "classical" results in a much more general setting. This paper will open up new doors in my field of research, and thusly, in my academic opinion (which shall soon be a professional opinion) contains meaningful mathematics.

Could you please read through this paper and point out any correspondences to reality?

Sincerely,

Goliath

(edited to fix UBB code in the link)

cfgauss · 01-23-2003, 12:33 PM

they need a "smug" smiley here.....

Oxymoron · 01-23-2003, 12:57 PM

Quote:

cfgauss wrote:Consider the derivation of time dilation in SR. Barely need any physics. All you need to know that distance = rate times time! Mathematically, you need algebra and the Pythagorean theorem. You *assume* that the speed of light is isotropic and that the laws of physics are the same in every inertial frame, and that's it! In fact, one could easily argue that you need to know no actual physics, but only to *define* that v=x/t! From no physics, just math, comes SR! So simple!

Physics: the science of measurement. Distance and time needed measuring, the last time I looked. So dilation really does need physics.

Before you get carried away, remember that SR is a very limited approximation: very few real-world systems have zero acceleration. SR is, therefore, an idealised model, it is not the territory, it is the map and that is true of all theories. I am heartened by your fervour, cfgauss, but you overstate the power of mathematical modelling.

cfgauss · 01-23-2003, 01:06 PM

It is an *idealization*, but that doesn't matter. We could (and eventually will) account for every effect, but that doesn't matter. The only reason it's an idealization (beside the fact that we can never really get completely flat spacetime, which arguably has nothing to do with it being an idealization) because it makes some "hidden assumptions." Once we know these assumptions, we can account for them and do the math again. For example, Newtonian mechanics assumes that the speed of light is infinite, and that there's no limit on how precise measurement is. SR assumes that there's no limit on measurement, too (among other things). But the point is, that when these effects are smaller than experimental error, the theory is absolutely correct. And if we could know *all* of the assumptions, then we could develop a perfect mathematical description of the universe, which would decay to SR given some assumptions, to NM given others, etc.

Oxymoron · 01-23-2003, 01:24 PM

Quote:

Originally posted by cfgauss
It is an *idealization*, but that doesn't matter. We could (and eventually will) account for every effect, but that doesn't matter. The only reason it's an idealization (beside the fact that we can never really get completely flat spacetime, which arguably has nothing to do with it being an idealization) because it makes some "hidden assumptions." Once we know these assumptions, we can account for them and do the math again. For example, Newtonian mechanics assumes that the speed of light is infinite, and that there's no limit on how precise measurement is. SR assumes that there's no limit on measurement, too (among other things). But the point is, that when these effects are smaller than experimental error, the theory is absolutely correct. And if we could know *all* of the assumptions, then we could develop a perfect mathematical description of the universe, which would decay to SR given some assumptions, to NM given others, etc.

Ah, the petulance of youth

We will (I can confidently predict) never develop a "perfect mathematical model" of the universe. Go read about the N-body problem; spend weeks expanding the solutions out in power series and then figure out how to get rid of the singularities. I'll save you the bother: you can't.

Or, go solve the QED equations for a proton. Stable? Who knows?

Every non-trivial mathematical model has usually been simplified, and/or linearised and/or truncated because that's the only way to solve it. Sure, a better model might come along later, but how then does that square with your isomorphism between maths and reality if many models exist for the same phenomena?

cfgauss · 01-23-2003, 01:40 PM

Oxymoron:
I'm not meaning that we *will* come up with a real theory of everything, I'm just saying that one does exist.

And many theories are damned ugly! But my experience in math has taught me that just because something can't be solved doesn't mean it doesn't have meaning. For example, something as simple as x - sin x = y can't be solved for x! But you can still get as many decimals to the solution as you want, and, in fact, you can guess and check to find an exact answer! (Though it may take a while!)

IMO, though, I think that one can express everything in a surprisingly elegant way (or at least from elegant principals) and meaningfully use it to do things, even if you can also get things that are computationally, or in principal, difficult.

Mr. Sammi · 01-24-2003, 05:47 AM

Goliath,

I am going to do no such thing. No free reading for you.

When your paper becomes meaningful to life and real world applications become apparent THEN I may consider reading it, until then... well...

As a side issue, what is your take on the laws of physics at the dawning of the universe?

Sammi Na Boodie ()

01-23-2003, 10:09 AM	#21
Mr. Sammi Banned Join Date: Jun 2002 Location: Montr�al Posts: 367	what is needed cfgauss, do I have to reply? OK, I will. Math is used to strengthen physics. It would be just as fine to say Force is proportional to mass. Acceleration is proportional to Force. Force is the cause of acceleration. Math may be used to refine the equations, but tell us nothing about the system. If I used a math equation R = Fu. What does this mean? nothing. Only R equals F multiplied by small u. R=Fu ; is a meaningless math equation. The equations become meaningful when the relations have a correspondence to reality. To say R implies F on the left side of the equation ; F implies m on the right side of the equation ; u implies a on the right side of the equation ; thus we have a relation with the physical world. Not a relation with some mathematical abstraction. Mathematical abstractions usually come after the observations. The implication of what I have written in this post IS you lack depth in your understanding, and this is obvious in your treatment of the question. Your scope of knowledge is limited. Your analogies are abhorrent. Sammi Na Boodie ()

01-24-2003, 05:47 AM	#30
Mr. Sammi Banned Join Date: Jun 2002 Location: Montr�al Posts: 367	no such thing Goliath, I am going to do no such thing. No free reading for you. When your paper becomes meaningful to life and real world applications become apparent THEN I may consider reading it, until then... well... As a side issue, what is your take on the laws of physics at the dawning of the universe? Sammi Na Boodie ()

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01-23-2003, 12:27 PM	#23
cfgauss Regular Member Join Date: Jan 2003 Location: USA Posts: 108	I'm really not going to give you several years of the math and physics training that you clearly don't have, but need to understand in order to have the slightest idea what one is talking about, Sammi. I doubt you even got my gamma function example, which is something that I knew about in Jr. High . For those of you who do actually want to listen to someone who knows physics... Consider the derivation of time dilation in SR. Barely need any physics. All you need to know that distance = rate times time! Mathematically, you need algebra and the Pythagorean theorem. You assume that the speed of light is isotropic and that the laws of physics are the same in every inertial frame, and that's it! In fact, one could easily argue that you need to know no actual physics, but only to define that v=x/t! From no physics, just math, comes SR! So simple! Doesn't it seem odd to you that math is the absolute perfect thing to describe physics with? Math doesn't describe anything else like that! Has there ever been an economic model made from purely math and definition? No. The closest thing to that is probably game theory, but you still need to add economics to it in order to yield a viable theory. Has anyone came up with a mathematical theory of psychology (let alone one that comes from math!), or one of politics? No. We can average and measure and make models, for sure; but not pure math has yielded anything there! We can only model other things with math; physics it describes perfectly, and in many cases alone. And you can do it again and again with physics! Want conservation of angular momentum? Rotational symmetry! Want more SR? Easy! We can do this with nothing else! And if you look at some theories of quantum gravity it just gets scary! Some imply things like that everything is a result of relatively simple mathematical symmetries, and such. When you have something that perfectly describes something, you should worry! Just as it is odd that the integral of e^-t * t^x dt from 0 to infinity just happens to be x(x-1)(x-2)...1 for positive integral x, it is odd that from (ct)^2 = (ct')^2 + (vt)^2 comes SR! Indeed, this is why many mathematicians and physicists I've talked to (the former, especially) believe in God! Things are just "too" perfect!

01-23-2003, 12:29 PM	#24
Goliath Banned Join Date: Mar 2001 Location: Fargo, ND, USA Posts: 1,849	Mr. Sammi, First of all, let me say that I am a graduate student in Mathematics, and that I will have my PhD in less than a year and a half (if everything goes according to plan). You had claimed that Mathematics is only meaningful when it has a correspondence to reality. Consider this paper, written by my advisor. The preprint that I have linked to is new research in Factorization Theory that looks at a lot of "classical" results in a much more general setting. This paper will open up new doors in my field of research, and thusly, in my academic opinion (which shall soon be a professional opinion) contains meaningful mathematics. Could you please read through this paper and point out any correspondences to reality? Sincerely, Goliath (edited to fix UBB code in the link)

01-23-2003, 12:33 PM	#25
cfgauss Regular Member Join Date: Jan 2003 Location: USA Posts: 108	they need a "smug" smiley here.....

01-23-2003, 01:06 PM	#27
cfgauss Regular Member Join Date: Jan 2003 Location: USA Posts: 108	It is an idealization, but that doesn't matter. We could (and eventually will) account for every effect, but that doesn't matter. The only reason it's an idealization (beside the fact that we can never really get completely flat spacetime, which arguably has nothing to do with it being an idealization) because it makes some "hidden assumptions." Once we know these assumptions, we can account for them and do the math again. For example, Newtonian mechanics assumes that the speed of light is infinite, and that there's no limit on how precise measurement is. SR assumes that there's no limit on measurement, too (among other things). But the point is, that when these effects are smaller than experimental error, the theory is absolutely correct. And if we could know all of the assumptions, then we could develop a perfect mathematical description of the universe, which would decay to SR given some assumptions, to NM given others, etc.

01-23-2003, 01:40 PM	#29
cfgauss Regular Member Join Date: Jan 2003 Location: USA Posts: 108	Oxymoron: I'm not meaning that we will come up with a real theory of everything, I'm just saying that one does exist. And many theories are damned ugly! But my experience in math has taught me that just because something can't be solved doesn't mean it doesn't have meaning. For example, something as simple as x - sin x = y can't be solved for x! But you can still get as many decimals to the solution as you want, and, in fact, you can guess and check to find an exact answer! (Though it may take a while!) IMO, though, I think that one can express everything in a surprisingly elegant way (or at least from elegant principals) and meaningfully use it to do things, even if you can also get things that are computationally, or in principal, difficult.

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