
Physicists Prove Surprising Rule of Threes - digital55
http://www.simonsfoundation.org/quanta/20140527-physicists-prove-surprising-rule-of-threes/
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ipsin
The Efimov constant is only approximately ≅ 22.7. It would be a little
surprising to have a physical constant end in exactly 0.7, since it would
imply that there's something special about base 10 and bases that are a
multiple of 10.

Section 3 of this paper talks about the actual transcendental equation that
provides the constant.

[http://rsta.royalsocietypublishing.org/content/369/1946/2679...](http://rsta.royalsocietypublishing.org/content/369/1946/2679.full)

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snorkel
I vaguely recall that if a circular disc with a circumference of pi (3.14 ...)
is held at an angle of 22.7 degrees relative to a flat surface, it projects an
ellipse that has a circumference of 3.000 Coincidence? Eh, probably. Might've
also been 26.8 degrees.

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ColinDabritz
One common association of those digits with PI is the handy approximation of
22/7 accurate to three digits, off by just over .0004.

I stress that this is an approximation only! I had to explain about PI being
irrational rather than exactly equal to the shortcut approximation to a couple
co-workers, explaining some poor behaviors in their rotation function.

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ph0rque
Quite fitting...

 _“What you see is three groups, in three different countries, reporting these
multiple Efimov states all within about one month,” said Chin, who led one of
the groups. “It’s totally amazing.”_

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gpvos
How far were these groups spaced apart?

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thomasahle
“Although we didn’t see an infinite number of them, there’s pretty strong
evidence when you see three in a row,” - What a physicist thing to say :P

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ctdonath
3, 5, and 7 are prime, therefore 9 is prime.

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graycat
No: 11 is prime. 13 Is prime. So 9 is just an exception!

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GotAnyMegadeth
A teacher asks a group of students to prove that all odd numbers above 1 are
prime numbers. After a short while the students begin arguing about the best
proof.

Mathematician: "We should use proof by induction, I can show 3 is a prime
number by listing all of it's factors, and then from there I can show that 2n
+ 1 is prime ..."

Scientist: "What? that doesn't make any sense. What we need is experimental
data. Let's collect enough points, 3, 5, 7, 9, 11, 13. Six points should do,
now look, the general trend is that all of them are prime. We have one
anomaly, but it's probably just caused by a random fluctuation in..."

Engineer: "Nah, all this theory is pointless, we only need to know if they are
prime in the real world. Let's just take a few and see if they work for our
purposes. 3 - prime, 5 - prime, 7 - prime, 9 - nearly prime, 11 - prime,
surely that's good enough."

Computer scientist: "While you lot have been wasting your time arguing I have
been writing a program that will do all the work for us"

All of the students gather around the CS's computer and watch as he presses
go.

Computer: 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3
is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3 is prime 3
is prime 3 is prime 3 is prime

~~~
graycat
This whole thread is messed up because it has never even mentioned the whole
other half of the subject as in the famous monograph, _A Short Table of Even
Primes_.

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datenwolf
I wonder if this principle can also be applied to nucleons. Protons and
neutrons are each made up of 3 quarks. And there are some troubles in pinning
down the radius of the proton. If Efimov scales apply to nucleons, this would
imply that there are multiple scales in which quarks can arrange depending on
the outside potential. This could explain the differences of measured proton
radius depending on the used experimental setup. But I'm just wildly
speculating here.

~~~
Panoramix
This trick only works for bosons *Edit: I think.

At any rate, these depths of physics are quite complex and not very intuitive,
and this kind of discovery shows it is very easy to overlook things. A giant
discovery could be looming in the horizon...

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anigbrowl
In the lab. The paper contemplates the possibilities for nucleons too - it's
just harder for spin particles:
[http://www.uibk.ac.at/exphys/ultracold/projects/levt/efimov/...](http://www.uibk.ac.at/exphys/ultracold/projects/levt/efimov/SovJNucPhys12.589.efimov.pdf)

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Evgeny
_More than 40 years after a Soviet nuclear physicist proposed an outlandish
theory that trios of particles can arrange themselves in an infinite nesting-
doll configuration, experimentalists have reported strong evidence that this
bizarre state of matter is real._

I think it's quite awesome that Vitaly Efimov lived to see his theory being
proved (or, at least, to see strong evidence in its favor).

It always makes me sad when I read about scientists who made great discoveries
just to be laughed at until their days end, and then their theories are proved
after they are dead.

A classic example is Alfred Wegener, who postulated continental drift just to
be ridiculed., but of course there are many, many others.

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

Another, even more tragic story is that of Ignaz Semmelweis, who not only
pioneered antiseptic procedures in hospitals, but, to my mind, proved their
effectiveness beyond any reasonable doubt, was rejected, and died tragically.

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

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pessimizer
I swear I'm not trolling, just ignorant, but could a workable theory of local
hidden variables be based on this?

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danbruc
I am pretty sure this is not related to local realism. I would naively imagine
the situation as follows (not having read anything related in detail and not
being a physicist). The forces between particles become very weak with growing
separation but never become zero. Now imagine throwing two ping-pong balls
into a pool making ripples on the surface similar to the force field or the
probability of presence of the particles. There will be a interference pattern
and you can probably find a valley where you can place a third ping-pong ball
and it will sit there more or less stable. Now finally imagine every pair of
ping-pong balls forming the valley for the third ping-pong ball. This may of
course be incredible far off from what really happens - just making up images.

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araes
I like the ping pong balls over the surface of a pool, that's a neat analogy.
However, I am also not a physicist, but my impression is that this is
something closer to how a
[http://en.wikipedia.org/wiki/Lagrangian_point](http://en.wikipedia.org/wiki/Lagrangian_point)
(in particular, the L4 or L5 lagrange point) works. In fact, I think the size
difference thing they describe in the article is probably very similar to how
gravity, and relative object positions work out based on their mass ratios.
Kind of an equilateral force balance, with a self stable state that things
will naturally gravitate towards if the background energy level is low enough.
Course, then that makes me wonder if there's a 4-body version with a stable
tetrahedron formation?

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pavel_lishin
Interesting that they referenced 22.7 falling out as similar to pi, since 22/7
is one of the simpler approximations of pi.

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zorbo
Completely coincidental, I'm sure.

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wlievens
Obivously, since base 10 is arbitrary.

