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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?

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Possible duplicates: physics.stackexchange.com/q/414/2451 and links therein. –  Qmechanic Dec 2 '12 at 15:47
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closed as off topic by Qmechanic, Manishearth, dmckee Dec 4 '12 at 19:13

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2 Answers

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.

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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 2 '12 at 16:27
    
...I can't get your point. –  namehere Dec 2 '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. –  namehere Dec 3 '12 at 0:56
    
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 3 '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 3 '12 at 23:39
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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.

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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 3 '12 at 5:35
    
@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 3 '12 at 5:45
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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 3 '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 3 '12 at 23:54
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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 5 '12 at 3:58
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