
The Utility of Mathematics - octopus
http://www.catb.org/~esr/writings/utility-of-math/
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lkozma
ESR doesn't mention the famous 1960 paper: "The Unreasonable Effectiveness of
Mathematics in the Natural Sciences" by Eugene Wigner.

[http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_...](http://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences)

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Pulpertank
And Richard Hamming's follow up in 1980: <http://www-
lmmb.ncifcrf.gov/~toms/Hamming.unreasonable.html>

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lkozma
I didn't know about this, thanks!

While we are at it, there is also the 2009 paper: The Unreasonable
Effectiveness of Data by Peter Norvig.

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robertk
ESR's insight is almost trivial on the surface, but reveals a deep
understanding in the same sort of way Eliezer Yudkowsky demystifies most
nonsense philosophical questions.

[http://lesswrong.com/lw/no/how_an_algorithm_feels_from_insid...](http://lesswrong.com/lw/no/how_an_algorithm_feels_from_inside/)
<http://lesswrong.com/lw/of/dissolving_the_question/>

The real problem to address is not finding the answer to "mysterious"
questions, but understanding the algorithm that makes our brain categorize
those questions as such.

I have had somewhat the same realization ESR gives here, but never so
transparently elucidated. With no irony, I translate the statement he
addresses into a mathematical like nature: "Out of formal models capable of
giving predictive powers to informal models, there exists a (unique?)
maximally such predictive model."

Proving the maximality is then easy if we simply define "maximally predictive"
to be "best we've done so far!" (I do not think it is an interesting question
to ask whether there is some sort of fuzzy idea of partial order on predictive
power, or if this partial order has multiple maximal elements.)

The existence statement is the real beautiful reduction, to me, showing the
absurdity of the original question. What ESR describes to me is precisely a
kind of selection bias; we ignore talking about "predictive formal models" for
all the situations mathematics has not come galloping in as saviour!

This latter argument is eerily similar to one of the arguments given forth by
Dawkins when I read his The God Delusion as a child and turned atheist.
Namely, the idea that I was already an atheist to every other religion out
there, so why not go one further? The power of such arguments to actually sway
and rethink my opinion as an advertised rationalist makes me tremble in their
powers, curious whether this effectiveness is deserved, or somehow a way to
hack a rationalist's brain.

I feel and believe ESR answered reasonably well the question he also posed
fairly well, but my mind can't help screaming "Is an almost trivial
reformulation really all there is to it?!" This is not so much my expression
of doubt as of awe.

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mariuskempe
This is the best essay on this subject I've ever read.

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alok-g
I have had some thoughts on why mathematics is so fundamental to nature, but
am not sure if these make any sense, or if they are ultimately cyclic.

I use words "stuff" and "things" to refer to not specifically matter but just
any concept that may exist in the universe, maybe even just space or time.

1\. The universe may comprise stuff that does not interact with other stuff in
any meaningful way. (One issue here is that by merely talking about stuff, and
more stuff, at least some aspects of set theory have already been assumed.
More on this below.) (Such stuff would be unobservable to lifeforms within the
universe so thinking about such stuff is meaningless for us.)

2\. I then invoke something like Plenitude principle to conclude that there
are things in the universe that interact with each other.

3\. Interaction between any two things in the universe, is fundamentally same
as transfer of some information between the two. In other words, these two
things appear different to us only because our language has two different ways
of referring to this.

4\. Information is meaningless if it is completely random. So there must be
some pattern to it, or else #3 above is meaningless. (In other words, it must
be possible to describe the information transferred with less "bits" than the
amount of "bits" transferred. Or the Kolmogorov complexity must be less than
the amount of information transferred.) (While I use mathematical terms to
convey the message, it is just because I need a language to say this.)

5\. Existence of any pattern whatsoever in information transferred leads to
mathematics that we then define to describe the pattern.

Note that this model readily allows for:

A. Laws of physics that are probabilistic in nature. The information transfer
must not be completely random, but this of course does not require it to be
fully deterministic.

B. Stuff that is unobservable or very weakly observable. Dark matter,
neutrinos, etc. would be examples of such stuff.

The biggest issue I know of that remains is assumption of at least some axioms
of set theory, which also is a foundation of mathematics.

There could be universe(s) where there is either none or at most one of
anything/everything. Such a universe again would not have anything observable
and is thus meaningless to us. Again invoking Plenitude principle, I assume
existence of a universe where there are more than one of something/anything.
But the moment one thinks of two things (say two particles, or even two values
of a scalar variable like time or position), aspects of set theory or number
theory have already come in.

On the other hand, and I believe for the same reason, mathematicians are
unable to define what is meant by a set or a membership to a set. (Everything
I have read on set theory starts by assuming some meaning for these two terms
and then follows with the rest.)

Would love to get feedback from others on if this makes sense, or if this is
fundamentally wrong or cyclic.

Reason for edits: Fixed some typos.

