Objective reality

I wanted to ask you about the role of mathematical elegance. As I understand it mathematical/theoretical physicists are often driven by the underlying belief that nature is in some sense mathematically elegant.Now I am frankly too mathematically ignorant to even really know what is meant exactly by "mathematical elegance". Also "elegance" by it's very nature would seem to be a highly subjective quality. But this approach does seem to have borne much fruit. Einstein and Dirac spring to mind as two obvious examples of those who have achieved an immense amount with this abstract and highly non-empirical approach.Now I am not saying that ultimately empirical verification can be anything but the ultimate arbiter of reality. If the maths says one thing but empirical reality says another then empirical reality wins (would you agree with that?) BUT having said that.......It is my understanding that with one postulate (the constancy of the speed of light), an assumption of the universality of the equivalence principle and a notion of mathematical elegance it is possible to derive the whole of relativity (special and general) along with all of the predictions of relativity (Big Bang, black holes, gravitational time dilation etc. etc. etc.) just by sitting in a room manipulating equations. No need for a single observation or experiment or even for our mathematician in a room to have ever even expereinced gravity himself. Is that right?Now Einstein didn't exactly do that. Practicalities of human endevour are never that black and white. But he did revoloutionaise science with his approach. An approach that strongly suggests that maths can lead the investigation rather than simply model observations. And that is where this more platonic view of reality is derived from.Is that how you see it?

In other words, you are going to be an ass about it (I'm using the American spelling for "arse"). The Straggler inquisition begins. I would suggest that you consult a shrink about your obsession with conducting these inquisitions.Incidentally, none of your questions actually has very much to do with "shared subjectivity", but I'll accept that you think they do. You won't like my responses. You will think I am being evasive, though I am not. I don't think we are conjuring up a world out of nothing.One problem with the way you word the question, is that we don't really know what we mean by "material". A second problem is that many Berkeley idealists could respond "yes" to your question, as explained in that limerick usually attributed to Ronald Knox. Whatever it is that the Andromeda galaxy is doing now, it will continue to do that even if the sun expands to a red giant and wipes out all life on earth. The words "objective", "material" and "reality" are human words that have meanings only on account of how humans use the words. The question is not meaningful unless you can come up with definitions for those terms that are not inseparably connected to their use by humans. That depends on what you mean by "experience". If a person were unconscious under anesthesia, and somebody put a bullet through that person's head, then the person could be said to have experienced death with no subjective involvement. That's one meaning of "experience". On a different meaning, the person would be said to have died but to have experienced nothing. They may be wholly subjective, but I doubt that they are wholly experienced. No. That depends on what you mean by "objectify". Presumably I could provide a written report that purports to be a description of my dream. And one could say that the written report is objective. One obvious difference is that dreams are incoherent. WTF!You are asking me to compare incomparables.

No. I am asking you why you think they are incomparable.So?Edited by Straggler, : No reason given.

You addressed your question to cavediver, but I'll add my two cents so that you can have more than one opinion. If physicists believe that, then they are mistaken. One of the things Dirac did, was to use a notion of generalized functions. I think many mathematicians would view that as inelegant and half-baked. The Theory of Distributions, due to Laurent Schwartz, provides a far more elegant way of doing this. Likewise, I suspect that many mathematicians would consider Einstein's treatment of GR as somewhat inelegant.The mathematical analysis as described by Bourbaki is far more elegant than the same analysis as described by Titchmarsh, even though they are presenting the same analysis. You should think of mathematical elegance as an artistic quality that is appreciated by many, but not all, mathematicians. I am inclined to say that is wrong.For one thing, Einstein didn't start with just those assumptions. He also had Newtonian mechanics, which had proved highly effective. I look at it as finding a way to modify Newtonian mechanics to incorporate the new assumptions. It's a while since I looked over the history of that era, but I seem to recall that there were several proposed ways of modifying Newton, and I would guess that any of them could have been done in ways that were mathematically elegant.There are serious conceptual changes involved in going from Newtonian mechanics to Relativity, and there was a lot of resistance. I would guess that finding changes that could be sold to other physicists was one of the important influences on the direction that Einstein took. It ought to be obvious to anyone who seriously examines science, that mathematics is used for more than modeling observations. But you can find that as much with Newton as with Einstein. I can't comment on that, since I have never held a platonic view of reality. It has always seemed to me that the world (i.e. the universe) is a messy, disorderly place.

Comparison is a perceptual operation. We do not perceive dreams. We "experience" them in some sense, but we are not perceiving them. So comparison is out of the question.

OK. So what is an example of something that we do perceive? What is it that makes some things able to be experienced as a result of perception and some things (like dreams) not? You seem to be simply making the rather obvious statement that objective reality is necessarily perceived subjectively. A statement I would wholly agree with.Except that cannot be the case because you have previously made it quite clear that is not what you mean by "shared subjectivity". The question remains - What do you mean by "objectivity is just shared subjectivity"?Or are you going to just continue to state what it is you don't mean?Edited by Straggler, : No reason given.

If you think those are useful questions, then it is no wonder that we are miscommunicating.You seem to be in the thrall of epistemology, and are attempting to apply epistemology's definition of rationality to everything. In particular, you seem to try to expose cases where people do not appear to adhere to that view of rationality.By contrast, I think epistemology is mostly bullshit.We are pretty much guaranteed to miscommunicate.

I know this is addressed to cavediver, but I'll give it a go. I think when physicists say this, they mean something quite different to what a mathematician means. Simply because a lot of physics is not very tidy mathematically.The best way to describe it would be that we would like to derive physics as the consequence of simple but powerful ideas. Ideas that are quite short to write down mathematically, but contain a wealth of information about the physical world. An example would be Quantum Chromodynamics. If you say you want a theory which is:
1. Quantum
2. Relativistic
3. Makes sense (not self-contradictory)
4. Matches a certain experimental value (one single experiment), by getting a factor of three correct.Then basically only one theory can possibly obey this. No fixing, no real tuning, no "why wasn't it this, instead of that?". The whole of nuclear physics from three principles and one experimental constraint. That's what we want.Physics and reality gets more complicated the higher up you go, but at the deepest, lowest levels it is shockingly simple. Abstract and difficult to understand, but simple. As you mentioned, exploring the possibility that we should have simpler and less starting assumptions has lead to advancement.It's why we have the standard model. In the 1960s particle physics was in a mess, with no way to relate the observations or what they had to do with each other. However by requiring 1-3 above, only one type of theory could possibly be write, "Yang-Mills field theory". All of particle physics is based on this. Definitely.Edited by Son Goku, : Spelling.

Nwr initially writes:

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"Some (including me) would argue that objectivity is just shared subjectivity anyway".

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Yet in two threads we have seen no argument in support of this statement and no explanation of this somewhat paradoxical phrase. Instead we have seen a great deal of squirming around evading the issue and a fair degree of philosophical name dropping. You are the one that raised perception as the defining difference between subjective experiences that cannot be shared and those that you apparently believe can be shared. This would seem to be rather key to the notion of objectivity as "just shared subjectivity". No? No. You seem unable to explain what you mean with your seemingly meaningless statement. I think this is something of a trend in your contributions here. My bullshit detector combined with a propensity for tenacious arsiness compels me to expose this. Then why do you keep throwing philosophical name-drops into your posts (Wittgenstein, Kant) and participating (even starting!) threads that are philosophical and epistemological in nature? Is this your latest evasion tactic? I thought with you having identified perception as a key factor we were at last getting somewhere. I guess you are unable to follow that line of thought without contradicting your previous statements of what you didn't mean. Oh well.

Whether he did or not the question is could the whole of relativity be derived in that manner? It also seems that this was more so in Einstein's case than you are allowing for. SR LinkAnd now (so I understand) if we add in the equivalence principle the whole of GR can be derived from Special Relativity. So with 2 postulates and the equivalanece principle it is mathematically possible to derive large swathes of modern cosmology from the Big Bang to black holes and the predicted effects of gravity. I find that friggin amazing! Dirac is probably the best example (or at least the most quotable) of a physicist who held elegance and beauty in high esteem - Dirac writes

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"I think there is a moral to this story, namely that it is more important to have beauty in one's equations than to have them fit experiment. .... If seems that if one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the result of one's work and experiment, one should not allow oneself to be toodiscouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory..."

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I don't think maths leading the investigation into nature rather than following it really occurred until Einstein. Yeah those cave shadows are just no substitute for mathematical reality.

Given the success that approach brought to 20th century physics, I think I'll stick to being "mistaken" That's like pointing out Einstein's contribution to refridgeration as a counterexample to the elegance of his work in physics - the delta-function is not exactly amongst Dirac's highest achievements... Again, I think you are missing the point - it is not the treatment that is elegant but the mathematics that lies behind. It's actually correct. And is precisely how Hilbert beat Einstein to the Field Equations, by jotting down the only possibly action one morning over breakfast. No, nothing like this at all. Newton plays the role of the desired end-point - as in an r^-2 law in the weak field limit - which determines the coupling to the stress-energy tensor. But that is all. For vacuum space-times, Newton is not used at all. Then you need to check out QCD, Electro-Weak, and Gravitation more. And remember that today's world is sat at the bottom of a hierarchy of symmetry breaking. You need to get out of the trees to see the real nature of the wood.Edited by cavediver, : No reason given.

As Son Goku mentioned, you have to be clear what is meant here. Actual solutions (things that look like our world) can be exceptionally messy - the elegance is in the top level theory. Yes, though the real use of this approach was later with the application of group theory to particle hierarchies, and most successfully (as SG mentioned) with the SU(3) Yang-Mills theory of Quantum Chromodyanamics (QCD). Almost, though Einstein used the requirement that the end theory must reduce to ewton in the weak field limit to produce the correct coupling to the stress-energy tensor. However, that correct coupling is also the most trivial coupling when viewed from the action principle, so even the connection with Newton is not exactly required. Not quite - it certainly speaks to that view, but far more interesting to me is the nature of our fundemental particles and how they are pure group representations.

Please do. I get that. E=mc^2 is the most famous example I guess. Cool. Much like the whole of gravitation from a couple of postulates and the equivalence principle. "Simple but powerful ideas" as you put it previously. So we still seeking one equation that incorporates a quantum theory of all the fundamental forces. How's that going?

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All things that are collectively agreed to exist within objective reality (as defined above in this post) are testable and verifiable through the scientific method.

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I think putting 'collectively agreed' in your statement makes it meaningless. Who is to do the agreeing here?If everyone on earth collectively agreed that God exists, then your statement would imply that God would be testable and verifiable through the scientific method. This is not true.Suppose there are some genuine solipsists out there. In that case, there is nothing that is collectively agreed to exist within objective reality.Leaving aside the collectively agreed piece, I agree with Cavediver that there is some kind of objective reality to mathematical concepts. If two different species invented the concepts of integer and prime number, then the same integers would be prime numbers for both of them. I can see no way in which that could not be true.Many properties of mathematical objects are NOT verifiable by the scientific method. For example, the existence of an inifinity of prime numbers can be proved but not observed.

I am certainly no expert either, but this is the way I look at it:The roots of mathematics lie in what I would equate to almost logical rules born of observation; 1 + 1 = 2 would not only be mathematically valid, but also a tautology. More advanced mathematics are in essence based on remaining internally consistent with those underpinnings, so that while entire sections may have no manifestation (irrational numbers for instance) the field itself is firmly rooted in reality.Now what happens when we are wrong with a theory, where we have an incorrect formula? Usually we require weird constants and gyrations in order to fit our curve or answer to observations. These formula are accurate only within certain ranges, outside of which they are unreliable. A formula that is correct is correct in all cases, and usually fits nicely with other known formula.What I am getting at is that the concept of "elegance" is talking about internal consistency. Mathematics is based on being internally consistent with itself, and being based on reality the assumption becomes that reality is internally consistent as well. This appears to have born out to this point in time, and the confidence in this trend continuing is the expectation of "elegance" in formula for natural laws.