What is the nature of math...in Nature?
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30-03-2014, 10:07 PM
What is the nature of math...in Nature?
Just curious about your thoughts on what you see as the relationship between our abstract minds, the elegant mathematical equations we come up with to describe what appear to be fundamental regularities in Nature, and "objective" reality itself. Are mathematical models intrinsic to Nature, that is, are they properties of our Universe, or are they merely human symbols that speak more to the structure of our brain's abstractions? Sorry if that is poorly worded but I hope you understand the question I'm trying to convey. (I'm on my phone so my communication skills are a bit limited at the moment.)
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31-03-2014, 04:59 AM
RE: What is the nature of math...in Nature?
Interesting question.

Math is the language of enumeration and ratio, properties of nature that exist regardless of our having named them. Pi, e, etc. are as real as atoms, they don't need us to exist for their existence.

Enumeration and ratio are so basic that the language we've developed is universal; there's no such thing as French algebra or Indonesian trigonometry. I find that amazing, considering how we fragment all our other languages right down to neighborhood dialects. But perhaps that speaks to just how intrinsic a component of nature math is.

Does the quantity five exist without a person to tick the fingers of one hand to describe it? I'd say so.
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31-03-2014, 05:08 AM
RE: What is the nature of math...in Nature?
Axioms

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(30-03-2014 10:07 PM)Pickup_shonuff Wrote:  ...
I'm on my phone so my communication skills are a bit limited at the moment.

... and there I was thinking that phones were invented to delimit our communication. Consider

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31-03-2014, 07:22 AM
RE: What is the nature of math...in Nature?
(31-03-2014 04:59 AM)Airportkid Wrote:  Interesting question.

Math is the language of enumeration and ratio, properties of nature that exist regardless of our having named them. Pi, e, etc. are as real as atoms, they don't need us to exist for their existence.

Enumeration and ratio are so basic that the language we've developed is universal; there's no such thing as French algebra or Indonesian trigonometry. I find that amazing, considering how we fragment all our other languages right down to neighborhood dialects. But perhaps that speaks to just how intrinsic a component of nature math is.

Does the quantity five exist without a person to tick the fingers of one hand to describe it? I'd say so.

That seems as strange a fact as any. I've never thought the teleological arguments for God's existence held much sway because the Universe, in most respects, is not well suited for life, and for all we know, it's just one configuration of many. However, that it can be reduced to such simple and elegant mathematical formulations, that all fit together like a grand puzzle, does seem to me at least to suggest that we live in a Universe that is rich in information displaying high marks of intelligence. That's why I'm inclined to ponder that perhaps it suggests more about us than "objective" reality. I suppose I'm ignoring some crucial factor.
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31-03-2014, 07:26 AM
RE: What is the nature of math...in Nature?
(31-03-2014 05:08 AM)DLJ Wrote:  Axioms

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(30-03-2014 10:07 PM)Pickup_shonuff Wrote:  ...
I'm on my phone so my communication skills are a bit limited at the moment.

... and there I was thinking that phones were invented to delimit our communication. Consider

One of the many ironies of modern technology, I'd say! Cool
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31-03-2014, 08:20 AM
RE: What is the nature of math...in Nature?
If you are asking why concepts that are relatively simple and comprehensible to our species also describe nature well enough to engineer systems with... well... it could have been different. We could have been velociraptors or dogs whose cognition didn't quite stretch that far. The universe might have been a little more complex than it is. We're just lucky, I suppose. How lucky is hard to say without a good basis for comparison. We may be exceptional in this regard and have a high degree of correspondence between our ideas and reality, or we may be comparatively poor at it compared to other species in our universe or beyond the universe as we know it.

I don't think it is quite appropriate to head into the quasi-mystical territory of wondering why maths specifically is a good fit to reality. Our mathematics is just a description of some of the ideas we can come up with and comprehend as written, perhaps no more fundamentally profound as other forms of language and ideas. Specific branches of mathematics correspond to particular ways that we can teach ourselves to think, and these in turn correspond to reality. But the reason we have invested in thinking that particular way is often because those ways correspond to reality and are predictive of how reality will respond to our actions.

I prefer to keep it general, high level, and clear. We are able to think and communicate with each other in ways that allow us to predict the way reality responds to our actions. How good we are at it is difficult to self assess, but for the moment we seem good enough for our own purposes.

Give me your argument in the form of a published paper, and then we can start to talk.
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