
The Unreasonable Effectiveness of Mathematics (1980) - efm
https://www.dartmouth.edu/~matc/MathDrama/reading/Hamming.html
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rndn
Wild speculation: Perhaps one could also attempt to explain the effectiveness
of mathematics the other way around: Why are the rules of physics simple
enough so that we can describe them fairly accurately? I think this stems from
the fact that complex systems are often the substrate for simpler systems.
There are plenty of examples for this: Simple lifeforms emerge from
biochemistry, planets are on elliptical orbits around stars as the result of
countless particle interactions and so on. Perhaps this can be explained by
the minimum total potential energy principle, that simple rules happen to be
the ones which are stable or at least metastable and more complex systems
would need more energy to maintain the relationships between its constituent
elements. Simple systems can be abstracted from the substrate to the degree
they are a reliable phenomenon. The human brain is a rather reliable
information processing system, but it's also rather limited in capacity (it
certainly has many times less capacity compared to the systems we are able to
reason about). However, since the rules of most physical systems happen to be
rather simple and since the language of mathematics allows us to compress
rules into efficient chunks which fit into the working memories of the
brightest humans, we are able to describe physical systems with counter-
intuitive effectiveness.

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asah
Disagree with your assumption: the universe is full of everyday phenomenon
that have confounded or ability to explain. Like say, gravity.

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smtucker
Simple doesn't necessarily mean easy to understand, particularly when the
thing doing the understanding is part of (and constrained by the rules of) the
system being analysed. It is conceivable that there are simple aspects about
our universe we will never understand because they are hidden behind some
threshold of observation.

~~~
rndn
Exactly. I was trying to say that equivalently to "the unreasonable
effectiveness of mathematics", we could also wonder at "the unreasonable
simplicity of physical laws" (simple in the sense that we are able to
understand the properties of it—at least superficially, but often also
deeply). There is perhaps also an anthropic principle here: If the systems we
find ourselves in would be much more complex, life would have likely been
unable to form as prediction and organization would have been too difficult.

It's actually hard to quantify simple systems so perhaps I should have
replaced the word "most" with "many" in my comment above. There are also typos
e.g. s/its/their/, sorry for that.

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swatow
When I mentioned I wouldn't be continuing with Economics after I graduated,
one professor asked my why. I said that I had wanted to find a theory with the
same mathematical elegance as classical economics (i.e. general equilibrium
theory) but found that there didn't seem to be such a theory left to discover.
Almost everything beyond classical economics was mathematically shallower (not
to say it was wrong or poorly thought out, just that deeper mathematics wasn't
applicable).

So while mathematics is very effective in Physics, and I believe it will
remain so, I am highly skeptical whenever I see people trying to apply deep
mathematics outside physics and chemistry. Some things just don't seem
amenable to mathematical laws.

~~~
Ar-Curunir
We just don't have a good enough model. Once (if) a good mathematical model
that takes into account enough information is created, then the 'deep'
mathematics that you speak of would once again be successful in predicting
things.

~~~
melloclello
I would disagree - the economy is anti-inductive[1] (in that it resists
attempts to understand it). As soon as you implement the results of your
sufficiently-sophisticated model, the economy will start to be influenced by
that.

Any viable model of the economy would therefore have to recursively contain a
model of the model of the economy and so on.

[1]
[http://lesswrong.com/lw/yv/markets_are_antiinductive/](http://lesswrong.com/lw/yv/markets_are_antiinductive/)

~~~
stolio
This is the second time in a week this article has come up so I read it. I've
never read anything about economics that made any less sense than that.

> As soon as you implement the results of your sufficiently-sophisticated
> model, the economy will start to be influenced by that.

This is called a feedback loop, systems with feedback loops are well
understood.

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Retra
This piece always irritates me. I don't think it's that interesting of a
question.

Firstly, Mathematics is a language for studying structure.

The reason it works is because we won't call something "mathematics" unless it
is a reliable/reproducible/communicable tool for representing structure. As it
is a language, it employs linguistic structure in an act of mimicry of
experience. This is called analogy.

Secondly, the brain -- the basic function of a brain -- is to differentiate
between experiences -- to assign meaning or to separate a signal from noise.
This is how a brain develops a notion of 'appropriateness.' We apply this
concept to linguistic analogies, and from that you can recover a notion of
'truth.' (An 'appropriateness engine' could be a suitable term for a moral
algorithm. 'Utility function' is also often used in this context.)

It is not unreasonable that math works. Math works because if some language
doesn't work, we just won't call it math. The mystery here is that anything
works at all, and to answer that you'd have to explain why anything even
exists.

