
A naturalist account of the reasonable effectiveness of mathematics in physics [pdf] - rndn
http://arxiv.org/pdf/1506.03733.pdf
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AnimalMuppet
The laws of physics are time-varying? That seems like... well, let's at least
call it not a mainstream opinion.

> The universe exists apart from being evoked by the human imagination, while
> mathematical objects do not exist before and apart from being evoked by
> human imagination.

Smolin says this in his conclusion. But when people talk about the
unreasonable effectiveness of mathematics (at least when I've heard it),
_this_ is what they're talking about - not that mathematical objects exist in
some nonphysical platonic space, but that they exist _in our heads_ as a game
we play - a formal axiomatic system. The question is, why does our formal
game, which we think is mostly abstract, suddenly and surprisingly turn out to
work so well to model the physical universe? (We don't find that chess works
as a model, for example.)

Smolin answers that, sort of. He says that since the basics of mathematics are
in nature, it's reasonable that as math progresses, it will continue to
correspond to nature. But it seems to me quite a stretch to say that, because
the natural numbers correspond to the existence of countable things in nature,
and natural objects take up space, therefore pseudo-Riemannian manifolds will
correspond to general relativity. To say that is reasonable, it seems to me,
requires making a mysticism around nature.

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inscrutablemike
The simple fact is that mathematics is derived from nature first by
observation of countable entities and then a process of abstraction from those
observations. The natural numbers don't merely correspond to countable things
- countable things are the original source of the much more abstract idea of
"natural numbers". Whether or not any further baste actions are a useful tool
for measuring and describing the physical world is an entirely separate
question from the nature and source of mathematics as a field of study.

It would probably be best to do away with the term "mathematical truth"
altogether. It's confusing and sloppy. Mathematics has no separate truth from
the physical world - it's just a field of epistemological methods.

~~~
cristianpascu
> mathematics is derived from nature

And where does 'derivation' come from?

~~~
eli_gottlieb
It's taking place in the brain of the mathematician.

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rndn
I just saw that this was a submission to the FQXi contest on "Trick or Truth:
the Mysterious Connection Between Physics and Mathematics". I've only read 1st
and 2nd place and this piece by Smolin yet, but I'm sure a lot of the other
submissions are worthwhile to read as well:

[http://fqxi.org/community/forum/category/31424](http://fqxi.org/community/forum/category/31424)

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adam930
The essay by David Hestenes is a worthwile read. Especially the comments where
Geometric Algebra is discussed.

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socceroos
> everything that exists is part of the natural world, which makes up a
> unitary whole.

That would cause problems for super-string theory, the big bang and many other
models of the origin of the universe.

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CurtMonash
I got a couple pages in before giving up. The question of existence/non-
existence of theorems simply isn't as important as he makes it out to be, and
I say this as somebody who's read a fair amount of relevant philosophy.

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eli_gottlieb
Oh, this is just _excellent_.

