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If the consistency between the two is so absolute, why can we not investigate the physical nature of the universe through analysis of pure number? Particularly at the quantum scale?

danny
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Duh. Because not all of mathematics is physical. I can always make up some mathematical model that says I should float upwards instead of being pulled downwards by gravitation, but experimentation proves otherwise. Of course there is much to mathematical physics, but that is hardly all of physics.

It also seems related that Quantum physics uses many 'tricks' up its sleeve that don't seem mathematically rigorous too.

UPDATE:

Clarification. What is physics? Physics is the fundamental science. Science is based on the scientific method, which relies on experiment to test the validity of hypothesis. Thus in physics mathematics is only a tool to model the universe, not the main subject. In physics, mathematics, if to become or become accepted by physics, must make predictions, explain phenomena, and be consistent with experimentation. Thus pure mathematics investigation is NOT physics.

resgh
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  • Sorry, but not all chemistry is natural. Are you suggesting that we can't scientifically examine the nature of metals, because someone designed a motor car? – danny Dec 02 '12 at 16:27
  • ...I can't get your point. – resgh Dec 02 '12 at 16:32
  • What do you mean chemistry is not natural? And I can't see why your argument suggests that we can't study metals. – resgh Dec 03 '12 at 00:56
  • If we can't investigate physics through maths because maths has things which don't occur in nature, then the same applies to every other science.... we investigate the chemical elements using tools made from chemical elements.... and if there are no useful connections, then you can't use maths as a tool to check your physics, bbut if you CAN use maths to check your physics you are implicitly acknowledging the two are more intimately related than you explicitly think. – danny Dec 03 '12 at 23:27
  • Clarification - when I said not all chemistry is 'natural' I meant humans manipulate chemical elements into highly designed, non-natural objects. So does this make chemistry (or what it represents at least) non-natural? Because that seems to be analogous to what you said about maths. – danny Dec 03 '12 at 23:39
  • Of course we can investigate physics through math! Of course there are many extremely useful and central connectecions! Most of physics has to do with math! There's even a field called "Mathematical Physics". But we cannot investigate physics purely from a mathematical standpoint. Physics has to match with experiment, not so with mathematics. I do not understand your analogy. For one, I have not once mentioned the word 'natural' in my answer and have not implied that. Whether chemistry apparatus or anything is 'natural' anyway is a highly controversial, depending on your definition.(continued) – resgh Dec 04 '12 at 09:43
  • And we can also conduct chemistry experiments via 'natural' objects, such as observing naturally formed salts dissolve into naturally produced water. Secondly, in the chemistry analogy the relationship between the subjects are "A can be investigated via something made from A" and your question is asking whether we can "investigate A via B", so the analogy is incorrect. However if I have misunderstood you and your question is asking whether we can do calculations in physics to obtain physical answers, the answer is the obvious "D'oh, yes.". – resgh Dec 04 '12 at 09:47
  • But if there is no connection between the abstract maths and the physical real, then maths CANNOT be used to investigate physics. And if there IS a connection, it is more than coincidental..... And, further, if I predict that physical constants and phenomena can be derived from pure maths, and then there are mathematicians who publish papers about this or that "curiousity" they have found, where they can derive parts of physics from pure maths (and there are a growing number of these)... well how has the prediction NOT been confirmed? – danny Dec 04 '12 at 13:17
  • What did I say? Of course we can investigate physics through math! Of course there are many extremely useful and central connectecions! So that answers your worries. And if a theory explains constants without experiment, good. What's the contradiction? – resgh Dec 04 '12 at 14:23
  • But how can we investigate physics through math, unless they are absolutely inter-consistent? Even the most esoteric of mathematical concepts MUST adhere to 1+1=2 in order to be accepted as 'right'. Which means no matter how esoteric, they have to correspond to the physical world at their foundations - even if we haven't seen a correspondence of the whole construction. And if physics is interdependent on maths, and also absolutely connected to the nature of reality, then maths must be also. The universe does have a natural mathematicality to it, no-one denies that do they? – danny Dec 04 '12 at 16:35
  • "And if a theory explains constants without experiment, good. What's the contradiction?" -- the contradiction is that if any part of physics can be derived from pure maths, then we have some seriously new thinking to do about the rest of physics. And what maths actually represents. – danny Dec 04 '12 at 16:39
  • @danny Yes, physics and mathematics both have to be consistent. Otherwise we could prove anything. But consistency is independent of whether one thing depends on another. Next, many parts of current physics can be obtained from mathematics. The thing here is that the mathematics is only a theory and tool of physics, NOT physics. – resgh Dec 04 '12 at 17:18
  • if maths is only a theory, then so is colour. can't say it clearer than that. artists are the equivalent to mathematicians. even when someone can create beautiful abstract works of colour, it is only the manipulation of how different materials radiate/reflect electromagnetic radiation. But I'll accept you'll not agree, and leave it there. Thanks for the discussion though, it was helpful. – danny Dec 05 '12 at 01:50
  • @danny I couldn't resist debating on this. Now, math is NOT a theory. That is not what I have said. I talked about how mathematical theories are used in physics, not how math is only a theory. And what's wrong with math only being a theory? I can't see a problem. And the fact that my mom uses a computer is not equivalent to saying that she is a computer scientist. Check your own arguments. – resgh Dec 05 '12 at 03:05
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The ancient greeks did physics qualitatively & philosophically. Pythagoras asserted mystically that all was pure number. It wasn't until renaissance Italy that Galileo put these two together to create the impetus for a new physics.

So the answer to your question, thinking historically, is yes.

Mozibur Ullah
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    If you add in that it was the Aristotle theories despite experiments, adopted as dogma by the Catholic church, that kept science immobile for 1000 years the answer is NO, even historically. It was when they started again checking the data around them that enlightenment came. There were ancient greeks who observed and fitted theories to observations, as Aristarchos of Samos, but the church did not use them as prophets. – anna v Dec 03 '12 at 05:35
  • @anna v:It would be nice to find out why exactly the Catholic Church chose to rely on Aristotle. Science may have become quiscient in Europe for a thousand years, but the the Islamic empire carried the tradition on. I thought the Pope was initially quite excited by Galileos discoveries. I do realise that there were individuals in the Hellenic diaspora that carried out experiments then, but I'm just making the point that the modern enthusiasm for describing the universe as all number dates from the renaissance. – Mozibur Ullah Dec 03 '12 at 05:45
  • except I think that the questioner is talking about integers. Physics needs/uses or describing nature real numbers and complex ones and worse – anna v Dec 03 '12 at 08:21
  • @anna v: true, but wasn't it kronecker that declared that God made the integers and the rest was the work of man (read satan)?; having said that, when I think of Number, I mean it in all its manifestations - both geometrically, and algebraically; both an element of a formal system, and the formal system itself; its a moot point as to what the Pythagoras cult thought of as Number, but seeing as they lived in a time when there were gods and not a single true God, I'd like to think they had the imagination to concede that there wasn't a single true number system - the integers, but that they were – Mozibur Ullah Dec 03 '12 at 11:25
  • many such systems, even if they themselves could themselves point to no other. I get the impression that they were a mystical sect, and that they mused on the mystery of Number. – Mozibur Ullah Dec 03 '12 at 11:31
  • numbers and geometry. yes they were a mystical sect. "god continuously geometrizes" is one of their sayings. – anna v Dec 03 '12 at 11:56
  • @anna v: interesting saying, i wasn't aware of it. – Mozibur Ullah Dec 03 '12 at 12:18
  • I'm not talking just integers, I mean the whole number spectrum - but can't everything be derived from operations on integers? (I don't know) – danny Dec 03 '12 at 23:34
  • And again, a clarification about the 'abstraction' of maths: a child's ability to acquire a sense of math (not the formalised mathematics, but an understanding of basic math principles) without formal instruction shows the basics of maths are based on observation. Even more complex maths is then derived from actual observation. So how is it abstract? – danny Dec 03 '12 at 23:43
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    @danny: a child conceptualises. She already has the ability to abstract; abstraction is not only a feature of maths. But also, it is true, I think that a child observes basic maths principles, but so does the trained mathematician, to them a rieman surface is as solid as the idea of say the number 2 that you may have in your head. – Mozibur Ullah Dec 03 '12 at 23:50
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    @danny: just because eveyting can be derived from integers, or more standardly, set theory does not mean that is the best way to conceptualise. Rather than a tree of mathematical systems with the integers at the bottom, a better way may be to conceptualise it as a web of relationships between different categories of formal systems, which also has the benefit it is closer to the way mathematicians have been thinking recently. I can't vouch for the past. – Mozibur Ullah Dec 03 '12 at 23:54
  • @danny a child's ability to acquire a sense of math (not the formalised mathematics, but an understanding of basic math principles) without formal instruction shows the basics of maths are based on observation. I disagree. The logical deduction is not concrete enough :) – resgh Dec 04 '12 at 09:50
  • out of interest, does anyone disagree that 1+1=2 is an immutable law of both physics and maths? And if - if you disagree - then how can maths ever be used to validate physics? – danny Dec 04 '12 at 13:12
  • @all - thank you for the time and answers, I'm curious - not trying to be provocative. Where does that leave the difference between human experience of colour, and the electromagnetic spectrum. One is an abstract concept, the other a physical reality. But the abstract concept predicted the nature of physical reality. – danny Dec 04 '12 at 13:21
  • @namehere - perhaps 'observation' was a dishelpful term. But that a natural 'mathematicality' existed before human abstract maths, and that human maths is based on the observation of how the world around them is organised (in a natural way lol)... this can't be contradicted by physicists because it immediately cancels their entire understanding of the universe. The only human part of 1+1=2 is the symbolic representation. But the symbolic representation IS based ABSOLUTELY on observation of nature. Play with it :P – danny Dec 04 '12 at 13:27
  • @danny But the abstract concept predicted the nature of physical reality you mean explains. And my argument is that the fact that children have senses of math does not mean the basics of math are based on observation. The deduction is far from being complete. – resgh Dec 04 '12 at 14:27
  • @danny: It explained & predicted, the relationship between theory & observation is not a straight-forward one. I would disagree the 1+1=2 is an immutable law of physics & maths. In maths, you would need to state what formal system you're working in, in Z its true, but in Z/2Z its not, 1+1=0. Of course, you could say thats an implicit assumption in your question, the first formal system that anyone gets interested is (Z,+), note no multiplication. Kids understand addition earlier than multiplication. – Mozibur Ullah Dec 04 '12 at 14:56
  • @namehere: Basic maths is taught pretty much everywhere, we all have to deal with money & things. But there have been found certain peoples (tribes in the amazon?), where the relevant concept is not precise quantification, but approximation - they distinguish between nothing, one, two, & a lot. That, I think shows that basic maths is not hard-wired into us, in the same way that chomsky argues that language is. Of course that doesn't mean that these people can't distinguish between ten & twelve, of course they can, they've just don't see it as being important. – Mozibur Ullah Dec 04 '12 at 15:05
  • @namehere: and I'd bet that most children go through this phase, before they learn the name of numbers, and the numbering system. – Mozibur Ullah Dec 04 '12 at 15:06
  • @danny: The same goes for physics, there are a lots of formal systems in physics, why should I assume that you're again talking about Z? (I know its the obvious assumption to make again). There is a further problem of a kind of infinite regress, where formal systems are embedded in other formal systems. I would require you to make an infinite number of naming decisions, but we'd be both well exhausted by then :-) – Mozibur Ullah Dec 04 '12 at 15:13
  • @danny@MoziburUllah Whatever, that point was unimportant anyway. This is turning into a philosophical debate. I could easily argue with you on this for ages but that's irrelevant. So where were we... – resgh Dec 04 '12 at 15:18
  • @namehere: I assume, you're something of a platonist, I'm somewhat sympathetic to that position too, contrary to my pontifications here. But being human, does give me the freedom to be inconsistent. – Mozibur Ullah Dec 04 '12 at 15:28
  • @danny Well, I think the answer is evolution. – resgh Dec 04 '12 at 16:43
  • @namehere "But the abstract concept predicted the nature of physical reality" --- it predicted the nature of reality, not explained it. It's an evolved mechanism based on how light reflects from different surfaces in different wavelengths. Animals have a sense of colour too. They haven't got an explanation though have they? ;) – danny Dec 04 '12 at 16:47
  • @danny Really, I don't think predict means this. But ARGGGGHHH! Allow me to quote myself... Whatever, that point was unimportant anyway. This is turning into a philosophical debate. I could easily argue with you on this for ages but that's irrelevant. So where were we... – resgh Dec 04 '12 at 16:49
  • lol namehere. that's my point, how does an abstract concept evolve unless it corresponds to an aspect of the natural world which is useful to our survival? Early humans didn't sit down and 'do maths' for teh lulz. They had a concept of number and spacial relationships because the world they lived in was structured that way. (and when I use 'predict' I don't mean in a formal way. It pointed the way, it predated, it ... implied... whatever lol)... and it isn't meant to be philosophical. I'm trying hard to keep it all founded in physical truths. Circular, now there's a description! – danny Dec 04 '12 at 16:50
  • @Danny: Hmm, its the reverse of how Kant viewed this. He explained the rationality of the universe as an expression of the rationality within us, the idea of time & space are within us, they help structure our immediate impression. He called it a 'Copernican revolution' as it is the reverse of what everyone supposed then, and probably now. Of course, I now appear to be contradicting what I said earlier. Nevermind. – Mozibur Ullah Dec 04 '12 at 16:54
  • @MoziburUllah ... Z+ whuh?! :P (just read the last comment. Yes. That is what I'm trying to suggest - a reverse Kant. Our rationality is an expression of the world we live in, and the universe we evolved in. Like our maths.) – danny Dec 04 '12 at 16:55
  • @Danny: (Z,+) is math speak. Z are the natural integers, without any operations defined. You know what one is, you know what two is, but you don't know that two can be constructed from one+one. (Z,+) means to that description, you have now allowed addition. Really I should have used N, as Z includes the negative integers (which I don't think little kids are going to get straight-away) – Mozibur Ullah Dec 04 '12 at 16:59
  • @Danny: I think, when you get deeper into this problem, its really about whether you think the world is purely mental (idealism), or purely physical (physicalism). Of course you could have both, but then you have the notorious mind-body problem. I think Aquinas took your position, that the rationality of the universe imprints onto our own mind. – Mozibur Ullah Dec 04 '12 at 17:04
  • @all - thanks for replies, made me think more carefully. Of course, I still think math is the equivalent to colour, in that both developed as a way of comprehending the world around us. Which leaves the mathematicality of the universe as an equivalent to electromagnetic radiation - ie usefully investigable.@Mozibur Ullah - mentalism sounds, well, mental. I'm an absolute physicalist as you describe it: We evolved from the quirky genesis of self-replicating groups of molecules, and consciousness is an evolved 'survival' mechanism. And the ability to conceptualise math evolved as part of that. :) – danny Dec 05 '12 at 01:45
  • @Danny: Fair enough; It does doesn't it :). However as Schopenauer pointed out smugly to his detractors it was a view held by more people (Hinduism/Buddhism) than all the christians/scientists put together at the time. I kinda held your view when I was racing through the science/math curriculum. But a turning point for me, was the 'thisness' of experience. The perception of the colour red, was in no way explained by the theory of the EM spectrum, although it had exciting things to say, nor could I see how it could ever be explained. – Mozibur Ullah Dec 05 '12 at 02:37
  • @Danny:That deflated my expectations of maths/science to explain everything. And it annoyed me, because a scientist should be taught the limitations & history of his science, and we weren't being told. Too much technique to learn in todays curriculum :-(. – Mozibur Ullah Dec 05 '12 at 02:43
  • @danny math is the equivalent to colour, in that both developed as a way of comprehending the world around us I disagree. Math is more about abstract concepts, far from necessarily developed as a way to comprehend the world. – resgh Dec 05 '12 at 03:09
  • @namehere: our evolutionary acquired ability to see colour, has been around for god knows how may years, (bees see color, don't they); our ability to conceptualise everyone can do, is more recently required, probably through the subtle needs of language & spciality. But maths, who ordered that? It seems more like a side-effect than a primary evolved characterestic required for our survival. – Mozibur Ullah Dec 05 '12 at 03:22
  • @namehere: I'd suggest that rudimentary math developed for the purposes of bartering, and made more sophistacted for the administration of the first city states. Kings want to know the profit & loss. Of course some people will have just learnt to play with it too. Actually I just reread your comment properly, and we're actally agreeing. I should have aimed my comment at danny. – Mozibur Ullah Dec 05 '12 at 03:27
  • @MoziburUllah Right. Thank you. I got confused when you directed the comment at me. – resgh Dec 05 '12 at 03:51
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    @namehere: its a fortuitous serendipity that maths turned out to be possible for (a few of) us. Maybe any species that develop the ability to conceptualise neccessary will. But I doubt it, plenty of people are just as happy without it. So I can imagine a species of thinking creatures on some far off planet who conceptualise, but can neither see the point of maths, nor do it :) – Mozibur Ullah Dec 05 '12 at 03:58