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Math and Reality. What is the deep connection? 
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#55
Mar2611, 05:51 PM

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By the length of your reply, I think at least your unconscious brain agrees. And you have sought to answer the question. We should be aware of the language barrier between us now. But I will try to work through your reply, anyway. Essentially though, what it seems like you're saying is what I've said here before, that mathematics is type of logical clay. So my point, in response to the OP's "look, math doesn't work" is that "we'll fin d a way". As you have demonstrated yourself: 


#56
Mar2611, 06:36 PM

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And as usual, you are making a nonreply. No points I raised have been addressed. Instead you say my unconscious somehow secretly agrees with you. If so, it must be horribly confused as well. . 


#57
Mar2611, 07:14 PM

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As I said, I still have to work through your reply.
Be patient, sheesh 


#58
Mar2611, 07:57 PM

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At least you have signalled your conclusion. Now you are just working on the argument that gets you there. I can see my patience will be rewarded. 


#59
Mar2611, 08:01 PM

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I do so adore when lovers spat...



#60
Mar2611, 08:20 PM

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#61
Mar2611, 08:26 PM

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Wrt the thread title, what do you mean by "deep connection", and how would you know if there was one?
Wrt reality, all we have is our private and shared sensory experience. Physical models all ultimately reduce to statements about the qualitative behaviors of objects in our sensory experience. Which can be quantified. We count things, and relate the quantities via various models of 'reality'. It would be quite strange if math 'wasn't' effective in modelling reality, imho. 


#62
Mar2611, 08:45 PM

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Math working with measuring length and volume makes sense.. for example. the pythagorian theories work it's just trigometry. Here it is intuitive math is part or reality because you can obviously see how length add up to the total when measured. Math is also intuitive in calculating trajectories because you can use calculus. But when it comes to Gauge Theory where the gauge bosons arise from the symmetry inherent in the theory. It's no longer about length and volume. It acts as though length and volume don't even exist as SR shows us. But then, SR is simple to visualize, just treat space and time as dynamic and not fixed. About QM, it's just about objects just existing probabilistics. Now when you combine them in the Dirac Equation. It predicts the existence of antimatter for example. Any familiar with the derivation of the Dirac Equation. How does the equation give rise to the positron? Does it use the simple fact that space and time are dynamic and the quantum is probabilistic? Combined, why does the equation work at all. Is reality with dynamical spacetime and probabilistic quantum enough to make it tally with the equation??
What I'm saying or inquiring is whether dynamic spacetime and probabilistic quantum is enough to pull off those Dirac Equation stunts. Or whether all of this has to be processed and calculated in some kind of processor in the 2D surface in Beckenstein Holographic Principle where our 3D is just projection.. or whether all of our reality is just output from a computer program. We can use deduction and elimination to at least get an idea what is behind this all. If dynamic spacetime and probabilistic quantum is enough to model reality. Then so be it. Projections from 2D surface and Matrixlike virtual reality is not needed. 


#63
Mar2611, 08:53 PM

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#64
Mar2611, 09:05 PM

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#65
Mar2611, 09:08 PM

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Like Cantor's approach to infinity, what seems patently unreal as ontology has a strange way of becoming instead an ontological fact simply because an epistemological stance proves so effective. (OK, I admit some physicists do talk as if they think this is an ontologically realistic view, rather than a statement about models, but there are plenty of loopy physicists out there. Some of them will believe absolutely anything.) There is a good SciAm article that talks about how it is models to models. http://homepage.mac.com/photomorphos...ments/qpdf.pdf It winds back from the crazy stuff as you can see.... 


#66
Mar2611, 09:19 PM

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Another thing. I was supposed to title this thread "Why does the Dirac Equation work".. but at the last seconds, I changed the title to "Math and reality, what is the deep connection?" as this is a philosophy forum and didn't want the thread deleted for out of topic so changed it suddenly without thinking. Anyway. After all the answers and reflections. The more appropriate title should be "Physical models and Reality: What is the deep connection?" 


#67
Mar2611, 09:26 PM

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#68
Mar2611, 09:27 PM

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You on the other hand express the voice of doubt and pessimism (or honest appraisal you would say). We may think we know a lot, but it is all an edifice of invention, and we know that we can never really know "the thing in itself". I see mathematic's claims of specialness as just a social oneupmanship. Another example of the attitude caught my eye today. http://www.physicsforums.com/showpos...43&postcount=5 We are so mysteriously clever because we are in touch with the rationalist paradise of Platonia. We have left the logical clay of lesser mortals behind to touch the mind of god. etc. etc. Maths doesn't like being told it is just standard metaphysical wisdom being worked out as formal computational structure, with the important bit (the axioms, the global constraints) frozen and left to one side for the moment. 


#69
Mar2611, 09:33 PM

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Irreducibly orthogonal measurements at the fundamental level are exactly what the systems approach predicts. QM had to be a theory about complementary properties because systems have no choice but to be organised that way. 


#70
Mar2611, 09:49 PM

P: 1,414

I wrote this:
@ rogerl Ok, so you're not really asking about a deep (reality) connection, which would be meaningless. And you're not asking why mathematics is effective in modelling theoretical/mathematical constructs, which is obvious. Or even why some theoretical/mathematical constructs are difficult to reconcile, which is difficult. What you're asking is how these constructs are translated into the language of instrumental behavior. Is that right? Then I noticed this: 


#71
Mar2611, 09:53 PM

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#72
Mar2611, 09:59 PM

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I don't think you understood a word that TT said, adn I surely don't understand your point if there is one. 


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