What is the relationship between the abstract world of mathematics and the material universe?

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Isn’t most of science, especially physics, now applied math? Sure one can talk and discuss the material world in terms other than in math, but it’s when the math comes in to play, the science becomes real. So the OP may have things backwards in a sense.
 
From Five Fingers to Infinity: A Journey Through the History of Mathematics [Paperback]
Frank J. Swetz (Editor)

Zero: The Biography of a Dangerous Idea [Paperback]
Charles Seife ( Author)

Quantum Mind: The Edge Between Physics and Psychology [Paperback]
Arnold Mindell PhD (Author)

amazon.com/Five-Fingers-Infinity-Journey-Mathematics/dp/0812691946

Does that which we describe pre-exist the description? One cannot separate reality from ones perception of it, for the one.

peace
 
The success of science is largely due to mathematical precision - which implies that mathematics and the material universe are inextricably related. Mathematics is based on logic which is not a set of arbitrary axioms and rules but truths about the material reality:
At any particular time, in any particular context
(1a) - every thing is some thing
Existence
(1b) - a thing is the thing it is.
Identity
(1c) - no thing is another thing than the thing it is.
Uniqueness
(2a) - every thing has some property.
Specificity
(2a) - a thing has or does not have a particular property.
Excluded middle
(2b) - no thing has and does not have a particular property.
Non-contradiction
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Code: 
                            [users.ugent.be/~frvandun/Texts/Logica/logic.htm](http://users.ugent.be/%7Efrvandun/Texts/Logica/logic.htm)
Logic and mathematics are mental constructs but without material things they wouldn’t exist!
 
Generally math is considered the language of natural order. Nature moves at its own self controlled rate. Abstract math communicates much of that change to humans, thus allowing humans to predict many future movements and extrapolate many past movements. Thus humans can benefit from these predictions by aligning their desires with when and where nature will provide the desired human benefit or similarly avoiding conditions in which nature will produce events undesirable to human. Humans may well enjoy a beach with sunny, 75 degree temperature, while wishing to avoid a minus 40 degree temperature, with heavy wind. While Nature produces both conditions it is math that predicts where and when both will occur.
 
tonyrey said:
The success of science is largely due to mathematical precision - which implies that mathematics and the material universe are inextricably related. Mathematics is based on logic which is not a set of arbitrary axioms and rules but truths about the material reality:
Code: 
                            [users.ugent.be/~frvandun/Texts/Logica/logic.htm](http://users.ugent.be/%7Efrvandun/Texts/Logica/logic.htm)
Logic and mathematics are mental constructs but without material things they wouldn’t exist!
Click to expand...
Consider 1a=0

peace
 
I’m no mathematician, but it seems to me we need to distinguish between two different kinds of math here.

The first I would call abstract mathematics, except I’m afraid the term probably has a different official meaning. Anyway what I mean is math that is universally true, and would have been true even if there were no universe or a radically different universe. One plus two really does equal three, for example. It can’t equal anything else.

The other would be mathematical descriptions of natural phenomena. For example Newton’s famous laws, or constants like the speed of light expressed using numbers and units. These things describe natural phenomena but one could easily imagine a universe in which they did not apply. For example, a universe at which the speed of light was different would not violate the eternal truths such as that one plus two equals three. Math of this second kind is merely descriptive and perhaps predictive in a practical way, but not in an absolute way.
 
hazcompat said:
Consider 1a=0

peace
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Not all equations refer to reality! 🙂

If you collect one object on an unspecified number of occasions you never collect the object if the number of objects multiplied by the number of occasions equals zero!
 
Mathematics, strictly speaking, has no meaning. (From the point of view of first-order logic, nothing has meaning except in its relation to other things.) It does, as tonyrey suggests, assume the truth of logical axioms and rules of inference (although so-called intuitionists do not accept the Law of the Excluded Middle); it also posits its own axioms (technically, the “nonlogical” axioms of the theory). The latter are not necessarily realized in, well, reality, although often there are such manifestations. Science, on the other hand, makes use of mathematical models of reality; these models are not reality itself, but merely approximations of reality (although they might be “isomorphic”, that is structurally indistiguishable from reality, but this is probably idealistic).

That was really a mouthful. :o But I’m happy to expand on any of it.
 
WinterLight said:
Mathematics, strictly speaking, has no meaning. (From the point of view of first-order logic, nothing has meaning except in its relation to other things.) It does, as tonyrey suggests, assume the truth of logical axioms and rules of inference (although so-called intuitionists do not accept the Law of the Excluded Middle); it also posits its own axioms (technically, the “nonlogical” axioms of the theory). The latter are not necessarily realized in, well, reality, although often there are such manifestations. Science, on the other hand, makes use of mathematical models of reality; these models are not reality itself, but merely approximations of reality (although they might be “isomorphic”, that is structurally indistiguishable from reality, but this is probably idealistic).

That was really a mouthful. :o But I’m happy to expand on any of it.
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Your post reminds me of a materialist on this forum who regards truth as an isomorph of atomic particles! 🙂
 
tonyrey said:
I was careful to specify “your post” rather than you!
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I know and I was not offended. No worries.

As for my post, well, that too is quite anti-materialist. Some would regard it as extremist, actually.
I don’t associate Catholics with (ontological) materialism but some seem to be heading in that direction…
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Unfortunately, I think that you’re right.
 
I couldn’t let this nonsense rest…
I read an excellent 700 page book on the fundamentals of Maths.
In short: numbers come from nature and nature come from invented numbers.
How come? No one knows.
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Total hogwash. Makes math look to be God.

Nature goes about its business without referring to math about which it knows nothing.

A two mile wide asteroid crashing into earth will cause more damage than a one mile wide asteroid, but not because it’s two miles wide instead of one. Number means nothing except to the human mind.
 
cho_pilo said:
Thoughts?
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It is the language of the universe! I’ve never seen it as something anti-spiritual; quite the opposite. Its interesting that multiple dimensions exist mathematically, but we only percieve in three or four (if you include time) here. Its interesting that things we take for granted, like the pythagorean theorm, are sometimes just simplified approximations of a larger formula or concept and are often only applicable in the relative space of our earth. Its humbling and inspiring to recognize the beauty of logic and its ability to explain natural pehnomena. I would assert that it does more than explain…it writes nature into existence in a way. I guess I have a strange perspective because I am always hit by the beauty of the poetry in math. Keep in mind that this is something that you will not see until you get beyond basic algebra.
 
buffalo,

How do you get so much stuff in your signature? :eek:

There’s supposed to be a 300 character limit, and my signature is nearing the limit.
 
Oh - I just want to add that, even though we will ever understand a tiny amount about it, the small glimpse that we have into this brilliant shining logic makes me want to cry with joy or get down on my knees and worship the creator of it. I know it sounds really corny, but wow, it is beautiful!
 
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