
New derivation of pi links quantum physics and pure math - bpolania
https://www.aip.org/publishing/journal-highlights/new-derivation-pi-links-quantum-physics-and-pure-math
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murbard2
Many series that calculate pi are very simple, as a result, it can randomly
appear in physical problems. See for instance
[http://ics.org.ru/doc?pdf=440&dir=e](http://ics.org.ru/doc?pdf=440&dir=e)

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sawwit
That’s a nice definition of mathematical constants: Numbers whose calculation
specifications have a Kolmogorov complexity that is low enough so that they
reappear in different contexts with high probability.

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murbard2
More precisely it would be the algorithmic probability. Not only are there
short programs that compute mathematical constants, but there are _many_ such
programs, so the total mass is even higher.

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sawwit
I'm not sure what you mean. Do you mean that a mathematical constant has
multiple different shortest programs?

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murbard2
Not necessarily shortest, but it has many short programs.

The algorithmic probability of a sequence x is the sum over the set of all
prefix-free programs u that calculate x of 2^-len(u). Think of the shortest
description length as a MAP, while the algorithmic probability integrates over
the full prior.

A constant which has many short programs can thus have a greater algorithmic
probability than another constant with a slightly lower Kolmogorov complexity.
To put it back in context, it's possible that a very short program computes
some constant, but it's unlikely to be an important mathematical constants.
What's particular about mathematical constants is that they keep appearing in
many different situations.

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keithpeter
Extended quote from original article...

 _" When Hagen started solving the problem himself, he immediately noticed a
trend. The error of the variational approach was about 15 percent for the
ground state of hydrogen, 10 percent for the first excited state, and kept
getting smaller as the excited states grew larger. This was unusual, since the
variational approach normally only gives good approximations for the lowest
energy levels."_

Rings bells from celestial mechanics. You can end up with things like a series
solution converging on an elliptical or circular orbit when you apply series
methods to simple (or 'simple' in this case - it _is_ quantum mechanics!)
systems.

I'll see if I can hack my way though their paper (linked to OA, downloadable
in full text).

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gus_massa
Pi appears in many many many quantum calculations, so the title of the press
article is very bad.

The title of the research article is much better "Quantum mechanical
derivation of the Wallis formula for pi" because as far as I know the Wallis
formula has never appear before in a QM calculation.

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stared
The game of mafia (aka Werewolf) is linked to PI (my paper:
[http://arxiv.org/abs/1009.1031](http://arxiv.org/abs/1009.1031), for a
summary: [http://boardgamegeek.com/thread/1157558/polish-paper-
werewol...](http://boardgamegeek.com/thread/1157558/polish-paper-werewolf)),
also via the Wallis formula. But so what?

Pi appears in physics roughly as often as 2 in finance. Even to describe the
simples quantum states (ground states of the harmonic potential) you use Pi
(as a normalization factor).

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4ad
Of course there is nothing special about this result. The hyped "science"
articles describing this are longer than the paper!

Lubos Motl wrote about it here: [http://motls.blogspot.co.at/2015/11/pi-found-
in-hydrogen-ato...](http://motls.blogspot.co.at/2015/11/pi-found-in-hydrogen-
atom.html)

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Garlef
What's so special about this ? I was always under the impression that quantum
physics is allready 99% pure math ;)

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nileshtrivedi
I felt the same. For example, gravity/electromagnetism force depends on
distance, hence naturally lead to circular/spherical contours, which would
involve Pi.

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fengwick3
I don't know enough about quantum physics, but from what I understand, this pi
seems to have arose as an artifact of the variational method used, rather than
quantum mechanics itself.

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Create
be floored ^1.

[https://en.wikipedia.org/wiki/Buffon%27s_needle](https://en.wikipedia.org/wiki/Buffon%27s_needle)

^1 and don't fall for phy PR

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Create
Dear Downvoter: can you tell when The Cat makes it through the crack?

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johncolanduoni
Somebody should tell these guys about hbar.

Just kidding, it is interesting that this series showed up in QM. Terrible
article title though...

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a3n
Maybe because, not being a mathematician, and certainly not a quantum
mechanic, I understand pi and circles as being lock-step mutually defining;
from what I've read, this derivation of pi doesn't seem to be described as
anything more than an interesting coincidence, and to call it a "link" is
reaching.

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dang
Url changed from [http://phys.org/news/2015-11-derivation-pi-links-quantum-
phy...](http://phys.org/news/2015-11-derivation-pi-links-quantum-
physics.html#jCp), which points to this.

