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This questions started with a question I had about gravity. If two objects of different weights fall to the earth at the same rate of acceleration, then it seems to me that gravity is in some ways 'calculating' the weight of each item and applying the appropriate force to each item so as to have it fall at the same rate of acceleration. Is this true (or at least close to the truth)?

This got me think that perhaps this is what all of the mathematical equations of physics are really saying - namely that there are mathematical equations that are getting applied to the real world in one way or another.

Is this right? If not, why not?

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I'm starting to think I should have closed this as off topic (philosophy), although perhaps it's too late now? –  David Z Apr 11 '11 at 13:24
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I understand that this has philosophical implications and I am interested in those philosophical implications, but it seems to me that this is fundamentally (also) a physics question. Indeed, the Feyman lecture that Approximist sent me to discusses this very question. –  Moshe Apr 11 '11 at 14:12
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Off topic, in my opinion. This is not a concrete answerable question but an invitation to a discussion. My understanding is that this is discouraged, lest the site turned into a forum. I also have my opinion on philosophy practiced by non-philosophers, but that is a secondary concern. –  user566 Apr 11 '11 at 15:58
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I don't personally understand how Professor Feyman can address this question but this forum can't. I asked this question because I wanted an answer, not a discussion. –  Moshe Apr 11 '11 at 20:03
    
the problem is, this question has no answer in the meaning of Physics, at least to the knowledge of everyone participating in this discussion so far (if I may be so bold to read and assume that) –  Tobias Kienzler Apr 12 '11 at 8:11
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closed as not constructive by Moshe R., Marek, mbq Apr 11 '11 at 17:00

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6 Answers

This is a very philosophical question. Some pointers from giants:

Timothy Gowers' has an excellent description

As does Feynman.

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+1 for feynman... as always :) –  BjornW Apr 11 '11 at 10:08
    
Thanks - I'm working my way through the Feymman videos now and hope to take a look at Gowers description soon. –  Moshe Apr 11 '11 at 12:20
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Plato pondered the relationship between physical reality and mathematics 2500 years ago. He used the allegory of his cave to show that we see traces of structure in the physical world, but we do not see the full picture. I don’t particularly hold to the idea of Platonia, but the idea is food for some thought. It certainly suggests that we may never know the answer to whether reality is ultimately some sort of mathematics which is reified by some means. Penrose has suggested this reification is the existence of mind, where a mind is a way that this Platonia has to become aware of itself and observes this system as “reality.” Again, I don’t know whether it is worth embracing this as Truth, for I see no way it can ever be verified.

Tegmark has proposed some ideas along these lines. He argues that mathematics, or that set of it which is first order and halting and non-halting if it converses to some describable set, in his mathematical universe hypothesis defines the entire set of reality. The ensemble has some statistical weight to its elements which defines the probability the mathematics exists in some “universe” or exists in some reality. Of course the problem is that this set is infinite. An infinite set is one which admits a bijective map from the set to any nontrivial (finite) subset. Such a set of maps will include the Cantor diagonalization and as a consequence the Godel incompleteness issue. So it would appear that Tegmark’s system is computed within the Chaitan halting probability function, which is itself not computable. We may then never know if this system has any bearing on reality.

It seems that a determination of the truth value of these conjectures require that we somehow access information or knowledge which is outside of physical reality. Without doing that this question might amount to chasing one’s own tail endlessly. It is very unlikely this question will be satisfactorily addressed, even as a hypothesis supported by some data set, by ordinary means of science. So in general this question is best something thought about in evening over scotch and cigars.

To conclude one might ask whether reality is fully based on mathematics, or whether on some deep level it is based on magic. By magic we might mean supernaturalism or some theological imposition of an infinite will. If physics is not fully based on mathematics, then there is ultimately some sort of magic deep down in the “rivers of hidden funk.” The question might not be resolvable, but the negative seems far more disturbing.

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good answer, but also a strong indication that this question were better off at philosophy.SE (not existing yet) –  Tobias Kienzler Apr 12 '11 at 8:14
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From my point of view, the equations are "only" used to model the observed reality. You can fine-tune your equations and constants, construct new models and try predicting phenomena beyond current observations, but since one probably will never be able to examine the real "sourcecode" of the universe, you can only iterate and never tell when convergence is actually achieved.

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I understand that they are models, but don't the models imply a certain type of reality - indeed, a sort of source code or DNA (if you will) for the laws of physics? Our models may not be perfect or maybe in need of perfecting, fine-tuning or even a more radical reworking, but does not the fact that physics continuously finds mathematical models that correspond to a certain extent to observed reality have implications about what is happening in reality? –  Moshe Apr 11 '11 at 11:02
    
@Moshe: as said, every refinement of models does get "it" better. So if you are content with something like "99.99% agreement with the observed reality is reality", then yes. Beyond that only speculation is left of course –  Tobias Kienzler Apr 11 '11 at 11:20
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As Tobias wrote in his answer, the equations we have are just models. They describe the observed relationships between measured (or measurable) quantities, that's all.

If you're asking whether nature actually goes through the process of doing calculations to figure out, say, how much the force between two objects is, that question is outside the scope of physics.

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Why is that question beyond the scope of physics? If the laws imply some sort of implementation process then why can't physicists work on discovering that process. Perhaps the answer is that there is no such implication, fine, but if there is why would it be outside the scope of physics? Perhaps it's outside the scope of today's instruments and methodologies, but that is something else. In other words, if there is reason to believe that the natural world is somehow or other "calculating" it's laws when applying them then isn't that within the scope? –  Moshe Apr 11 '11 at 11:30
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@Moshe: I'm referring to some implementation which is inaccessible to experiment and thus fundamentally undiscoverable - for example, if gravity is the result of some intelligent entity plugging numbers into a calculator and applying forces. Is that what you were suggesting? –  David Z Apr 11 '11 at 13:19
    
Hello David, No - no more than a computer makes calculations. I am referring to a more fundamental mechanism which is operating. Feyman discusses and immediately rejects one such proposed mechanism for gravity and then proceeds to discuss the fact that this problem is universal to most laws of physics (at least, that is my initial understanding - I need to finish the series and then watch it again). –  Moshe Apr 11 '11 at 14:16
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@Moshe: well yes, the laws of physics can tell us something about the underlying mechanisms if by "mechanism" you mean a more fundamental mathematical model. In other words, when a high-level model results from a lower-level model, we can often use the high-level model to figure out something about the lower-level model. But your question seemed to be to be getting into something beyond that. –  David Z Apr 11 '11 at 14:35
    
I don't think that Feyman meant a more fundamental mathematical model when gave a proposed theory for how gravity actually works. He talked about a physical phenomenon - he rejected it simply because the proposed theory didn't actually work in the real world. –  Moshe Apr 11 '11 at 20:01
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A mathematical description of an observation does not say how the observed was created.

Draw a perfect circle of radius a. Do the ink points "know" that a compass and your hand was used to make this mathematical description: r=a , into a perfect circle?

There are many referential levels, meta levels, in any mathematical description. Sometimes known by construction as in the circle example, sometimes as in your gravity question still a point of research. The referential level of two objects dropping are different from the level of the gravitational equations of general relativity which are the ultimate at the moment mathematical model for gravity. The earth is not calculating anything, in the same sense that the points on the circle were not calculating the r=a. The equations of motion of bodies is a mathematical model of observations.

Edit: When one says "Nature does this or that" a level of anthropomorphism enders. It certainly belongs to metaphysics questions and not to physics. My almost metaphysical view is that mathematical forms exist , the way 2+2 exists, and matter as we know it, given the appropriate conditions "crystallizes" out following the energy levels etc. of the mathematical equations. Our mathematical models are successive levels of approximations to these ideal equations. No calculations by nature or anybody are involved, imo.

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Let me rework your analogy of drawing a circle and then ask a question. I can attempt with paper and pencil to draw a perfect circle. I may even get quite good at it after a while with practice. However, if I measure that circle I'll probably see that it's not really perfect - so I can use a tool to help me draw a more accurate circle, such as a compass. Or, I could even write a computer program to do a better job. Someone else can then come around and write a better program than I write. –  Moshe Apr 11 '11 at 11:08
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@Moshe :) . The point is that the matter points that comprise the circle have not calculated anything. It is all at the levels of the drawer's actions that create the circle. –  anna v Apr 11 '11 at 11:21
    
I had to run out while writing the previous comment - here is the continuation of that comment... In short, the more accurate the circle, the more accurate the tool needed. As such, while we may not know the actual method used, do not the mathematical laws imply something more fundamental is going on? Note, I'm not saying that the earth is calculating anything, I am saying that involved in the force of gravity, relativity and other mathematical models is the idea that there is some means of implementing those models into reality (to the extent that the models accurately reflect reality). –  Moshe Apr 11 '11 at 11:24
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@Moshe If you read my edit above you will see that I do not disagree about this. But it is at the point of going into philosophy of physics,not physics. –  anna v Apr 11 '11 at 12:57
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The fact that some of the laws describing very complicated and chaotic systems are in fact very short and 'elegant', and that any other description of the phenomenon in equations must be many orders of magnitude longer, seems to me to be a very good indicitor that Nature does infact follow some of the laws we currently know exactly. And that these equations are not just some human invented thing to explain phenomenon.

Ofcourse we can never prove which laws Nature follows and if it does so, but likewise we can never prove there aren't exact laws governing Nature, which some people here seem to think.

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In case that last paragraph refers to David's and mine answer, you're probably reading too much here, I do not believe there aren't exact laws but simply state that someone claiming there are didn't get the point. Just as you say, it cannot be proved, and philosophy is not my metier –  Tobias Kienzler Apr 11 '11 at 10:26
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