
The unreasonable effectiveness of mathematics in the natural sciences (1960) [pdf] - truth_seeker
https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf
======
usgroup
I think so much maths comes from thinking about science; really self evident
with the development of calculus, statistics, LA, formal logics, etc.

It’s not like there is maths and there is science and it’s shocking that maths
applies to science because the two came up independently: they are confounded
by each other.

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whatshisface
Math is as far as we can tell a totally universal building kit for anything we
want to set up, all the way from elegant models like Newton's laws to billion-
parameter monster neural networks. The surprise is not so much the
unreasonable effectiveness of math as it is the unreasonable simplicity of
fundamental physics.

~~~
elevenoh
Example of physics' 'unreasonable simplicity'?

~~~
matt4077
Physics is the poster boy for reductionism, i. e. the ability to split any
situation into its parts, understand those, and then reassemble a complete
model that actually describes the world. Hence the jokes about spherical
chickens (the approach works, but not for chickens).

Physics has also taught us to expect absurdly simple laws as the inner
workings of seemingly complex observations. e = mcc would feel like a cruel
joke on anyone trying to grapple with how reality works pre-Newton.

This mindset, and the so obvious wins of physics in its golden age (ca
1900-1970), from the atom bomb to the moon landing, also set unreasonable
expectations for the other sciences.

Hence, people expected no less than a cure for ageing from the unraveling of
the genetic code and the decryption of the human genome. Yet, as it turns out,
biology cannot be reduced in the way that physics can. Genetics is a madman’s
den of complexity, nonlinearity, and unpredictability. It’s almost literally
what you would expect from a few million years of Perl snippets evolving. The
same is true of neuroscience, meteorology, sociology, and, to a lesser degree,
chemistry.

~~~
Frost1x
Some of that larger scale complexity may be due to irreducable emergent
relationships that reductionism alone can't explain without essentially
simulating those reductionist relationships to the scale you need from the
ground up (which defeats some of the goals of reductionism).

You may need perfect information in order to fully simulate such systems (a
snapshot of all initial conditions and perfect knowledge of physical laws).
This may be the case for many scales of relationships we're interested in.

Current reductionist theories can't tell me if I'm going to have coffee
tomorrow morning. I don't expect them to either, yet they still have very
useful purposes. They may never be able to tell me if I have coffee tomorrow
and I'm fine with that (maybe due to error propagation inherent in quantum
mechanical principles or the need for say emergent models).

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dang
2017:
[https://news.ycombinator.com/item?id=13954804](https://news.ycombinator.com/item?id=13954804)

2014:
[https://news.ycombinator.com/item?id=8520610](https://news.ycombinator.com/item?id=8520610)

~~~
vertis
I'm surprised those are the only two given it's from the 1960s. There really
needs to be a section for timeless content like this.

~~~
gwern
We have that! 'Hacker News Classics'
[http://jsomers.net/hn/](http://jsomers.net/hn/)

~~~
vertis
Amazing, I hadn't seen that.

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lordnacho
The question I'd ask is if you found a description of nature, is there any
chance it would be called not-math yet still describe the phenomenon in
question?

Is there any example of something that isn't considered math but describes
nature?

Isn't there a tendency for math to grow with science too?

~~~
Conjoiner
"Is there any example of something that isn't considered math but describes
nature?"

\- "The apple is red"

No math, describes nature.

~~~
lordnacho
Inevitably you'll become more interested in what exactly red means and you'll
end up with something recognisable as math. If you're not already there.

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kumarvvr
Is the question

"Is math behind everything or is that anything can be explained with math?"

a valid question?

Even for "chaos" we have a chaos theory. Where we cannot apply
function/formulae to physical phenomenon, math tends to use empirical
calculation and theory to study systems.

Is is that the universe bends to math or math bends to the universe?

~~~
v64
I like how Bertrand Russell viewed that:

"Physics is mathematical not because we know so much about the physical world,
but because we know so little; it is only its mathematical properties that we
can discover."

Math isn't behind everything, and not everything can be explained with math.
But it happens that the things that are mathematical turn out to also be quite
useful.

~~~
kumarvvr
> not everything can be explained with math

Can you give me any examples? I'm curious.

~~~
laszlokorte
It's the same as: There are more real numbers than you can write down.
(Everything you can write down using symbols can only be enumeratable many
(you can enumerate all symbol combinations starting with single symbols), but
there are uncountable many real numbers)

So now you say: Could you give me an example of such a real number that we can
not write down?

Answer: No such example can be given because even e or pi or any other real
number constructed by an equation is given by just inventing new (countable
many) symbols (like π) or by writing down an algorithm which consists of
countable many symbols.

So to answer your question: There could be problems that can not be explained
by math but in the same way you might not even be able express/name/describe
the problem.

~~~
chongli
_because even e or pi or any other real number constructed by an equation_

Not true. Most real numbers cannot be constructed at all [1] [2]. There is
some interest in replacing the mathematics of real numbers with computable
numbers, but this adds additional complexity to analysis (requiring a
computable modulus of convergence).

[1]
[https://en.wikipedia.org/wiki/Computable_number](https://en.wikipedia.org/wiki/Computable_number)

[2]
[https://en.wikipedia.org/wiki/Specker_sequence](https://en.wikipedia.org/wiki/Specker_sequence)

~~~
laszlokorte
Yes that's what I was trying to say with the later part of my setence you
quoted:

Only coutable many real numbers can be given by name (like pi) or by an
algorithm. But there are still many more numbers left which you can not
name/point to/give as example.

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victor106
An amazing book I’ve been reading is

[https://www.amazon.com/Infinite-Powers-Calculus-Reveals-
Univ...](https://www.amazon.com/Infinite-Powers-Calculus-Reveals-
Universe/dp/1328879984/)

The author explains the history of calculus leading up to Newton’s treatise on
Calculus and how important calculus is to modern life. It’s behind everything
you use from cell phones to containing HIV. Highly recommended.

------
_bxg1
Reminds me of this:

[https://youtu.be/HEfHFsfGXjs](https://youtu.be/HEfHFsfGXjs)

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choonway
That's because everything can be approximated with maths. Even with shoewhat
random events you can tame it with statistics.

------
air7
If ever there was a argument for Intelligent Design, this would be it.

~~~
OneWordSoln
Well, we have a universe of, perhaps, two trillion galaxies that live together
in a regularly nonuniform background radiation that can be predicted by a
mathematical model predicated upon our advanced understanding of physics and a
single point-source event we call the Big Bang, whose physics are beyond our
physical reality's description and require some serious hoops to be jumped
through (e.g. inflation) to align its progression with the state of our
universe today, and yet we have the model and it accurately predicts the
precision of our measurements of it (the CMBR) and even its non-uniformity.
The universe has a precisely-defined conversion between matter and energy
(thanks, Einstein) as well as precise laws that conserve both matter and
energy; therefore, nothing gets created and nothing gets destroyed, only
transformed, and yet some people deny that something literally "extra-
ordinary" is the Source of it all, stuff and its interrelating laws.

To say there is no "Prime Mover" is the height of hubris, for we live in a
universe with laws that bely its own creation. For we creatures -- no matter
how cognitively well-endowed we are -- to say that we are capable of
understanding everything about the Source of this creation is not only absurd,
but unscientific and logically unsound.

5/6ths of our universe's matter is missing.

The energy that keeps the universe expanding is missing.

We have no explanation for how the universe implements gravity and, thus, how
it works with respect to the other three fundamental forces.

And yet "scientists" claim there is no Creator. The interrelation of all the
dynamical systems at work in the various levels of the universe is so precise
that even a small variance of one of them -- e.g. the Fine Structure Constant
-- would not just break the entire structure; it would render it
unmanifestible.

No, we can not understand how this universe was created, because, as the time-
dependent creatures we are, the Creator of all that exists, including time
itself, is literally beyond our comprehension. Knowing that "the Unknowable"
exists should be common knowledge by now, especially for the physics
community, as they work to transform subsets of Unknowns into Knowns.

All you who downvote such opinions think yourselves better than Einstein who
himself understood that there was a Creator, even as a non-religious person
who failed to crack _all_ the mysteries of this wonderful creation. The
problem of hubris is a purely personal problem that involves a completely
different mathematics fought in a different realm.

Only by accepting the truth of reality can one successfully explore it, my
dear friends. Plugging one's ears and yelling, "Blah! Blah! Blah!" is not the
way of progress, even if it is the way of social media's self-selecting herds.
This grand experiment has shown -- among other things -- that people who can
not refute any points of an argument would simply rather make the argument go
away. Everyone who knows the history of scientific advancement knows what
became of that vast majority who ridiculed Boltzman and Einstein.

~~~
xelxebar
> ...precise laws that conserve both matter and energy; therefore, nothing
> gets created and nothing gets destroyed...

Not your main point but just wanted to point out that because of inflation,
energy actually isn't conserved! It's kind of surprising, but consider light
getting redshifted from a far away galaxy. Its frequency drops as it travels
through space and thus, so does its energy. This happens with the beam not
interacting with anything, so the lost energy doesn't really go anywhere.

~~~
OneWordSoln
Thanks! That is truly fascinating. I have never encountered that idea of it
being a consequence of the red-shift before but it does make sense. I wonder
where that energy goes. Perhaps there is an ether after all? Seeing as Planck
implies that nothing is continuous in this universe, then I wonder what the
quanta of the redshift is? Perhaps time itself causes the friction. (I
apologize for my layman's spitballing here but this universe is nothing if not
fascinating.)

And by inflation, I was referring to the brief period shortly after the BB
where the clumps of galaxies quickly separated themselves. Is that what you
are referring to here, or are you referring to the general expansion of the
universe?

