Beta
×

### Thank you!

Before you choose to head back to the Classic look of the site, we'd appreciate it if you share your thoughts on the Beta; your feedback is what drives our ongoing development.

Beta is different and we value you taking the time to try it out. Please take a look at the changes we've made in Beta and  learn more about it. Thanks for reading, and for making the site better!

# The Rule of Three Proved By Physicists

#### Soulskill posted about 5 months ago | from the omne-trium-perfectum dept.

80

An anonymous reader writes "In 1970, Russian physicist Vitaly Efimov developed mathematical proof (PDF) that any three-particle substance, referred to as a trimer, will scale up or down in size by a factor of 22.7 and that if the particles are not all of the same type, 'the scaling factor of 22.7 decreases according to the particles' relative masses.' In 2006, physicists in Austria proved that Efimov's trimers can be created in laser-cooled environments. And now, in 2014, physicists in Austria, Germany, and the U.S. have physical proof that Efimov's trimers do indeed scale by a factor of 22.7 if they are comprised of the same particles or a lower ratio relative to their particles' masses if they are comprised of a mixture of different particles (abstract 1, abstract 2, abstract 3). 22.7 — a.k.a., the rule of three — now appears to be as significant as pi."

cancel ×

n/t

### Even more amazing (-1, Redundant)

#### Anonymous Coward | about 5 months ago | (#47105917)

22/7 is a good rational approximation for pi! Next up: 22^7.

### Re:Even more amazing (0)

#### Mister Liberty (769145) | about 5 months ago | (#47106047)

No.
Pi is the volume of the box around the quarter pizza I just ate.

### Re:Even more amazing (5, Funny)

#### Sique (173459) | about 5 months ago | (#47106143)

The volume of a pizza of radius z and height a is pi*z*z*a.

### Re:Even more amazing (1)

#### LifesABeach (234436) | about 5 months ago | (#47106923)

Damit, Coffee, all, over, my, keyboard! :p

### Re:Even more amazing (0)

#### Anonymous Coward | about 5 months ago | (#47107957)

OK. That right there is why "Funny" mods deserve karma.

### Re:Even more amazing (1)

#### Gr8Apes (679165) | about 5 months ago | (#47108265)

Thanks for the funniest thing I'll probably read all day. :)

### Re:Even more amazing (1)

#### Richy_T (111409) | about 5 months ago | (#47110555)

This needs to be a t-shirt.

And by posting this, I guarantee that it already is.

### Re:Even more amazing (0)

#### Anonymous Coward | about 5 months ago | (#47117479)

Pretty sure I first saw that joke on a t-shirt.

### Re:Even more amazing (1)

#### Richy_T (111409) | about 5 months ago | (#47118701)

Indeed, there appears to be something of a selection at least one of which appears to miss the joke.

### Re:Even more amazing (1)

#### yo303 (558777) | about 5 months ago | (#47112841)

Further, if the density of the pizza is p, the Earth's mass times the gravitational constant is u, and the pizza's distance to the center of the Earth is l, the force on that pizza is p*i*z*z*a*p*u / l*l.

### Re:Even more amazing (0)

#### Anonymous Coward | about 5 months ago | (#47116883)

Only if you treat it as a point mass.

### Re:Even more amazing (-1)

#### Anonymous Coward | about 5 months ago | (#47106147)

No.
The important volume is the suction generated in the mouth of yo mama I just fucked.

--
There is no security in knowing your mom's a slut.

left out

### Damn you beta (0)

#### Anonymous Coward | about 5 months ago | (#47108403)

Sorry this is off topic, but why the fuck does beta (fuck beta btw) always cut off the titles of posts? You can see the whole title when you click reply, but it's cut off otherwise. Either fix this or warn about the length that will be displayed.

### Re:Damn you beta (0)

#### Anonymous Coward | about 5 months ago | (#47109035)

Sorry this is off topic, but why the fuck does beta (fuck beta btw) always cut off the titles of posts?

Because Beta sucks.

Sometimes the simplest explanations are best.

### infinite amounts? well yeah, if 3 is about infini (1)

#### gl4ss (559668) | about 5 months ago | (#47106061)

"Each 22.7-times larger Efimov state is also 22.7-squared times weaker, requiring the optical trap to be cooled even further to allow the new state to form. Grimmâ(TM)s group perfected its techniques and detected the state at the very edge of experimental limits."

"Meanwhile, the two other groups managed to observe three consecutive Efimov states by taking advantage of a footnote in the theory: When a trimer is built from a mixture of different particles rather than an identical set, the scaling factor of 22.7 decreases according to the particlesâ(TM) relative masses. In other words, nesting dolls made of atomic mixtures become closer in size, enabling more of them to be observed within the experimental window."

cool sure, but ""The law is a geometric progression of evermore-enormous trios of particles, spanning in a theoretically infinite sequence from the quantum scale to (if the particles were cold enough) the size of the universe and beyond. âoeAlthough we didnâ(TM)t see an infinite number of them, thereâ(TM)s pretty strong evidence when you see three in a row,â Chin said.""

yeah sure, universe size yeah why not if we have 3 smallest and every sequence is weaker...

### Re:infinite amounts? well yeah, if 3 is about infi (-1)

#### Anonymous Coward | about 5 months ago | (#47106373)

This is why a publication isn't worth anything until after it's peer review. Until the proof is verified this is meaningless. (And even if the proof holds does it hold for what it claims to hold for? A common mistake made by programmers is creating a brilliant solution that doesn't solve the problem they were trying to solve.)

### Re:infinite amounts? well yeah, if 3 is about infi (1)

#### K. S. Kyosuke (729550) | about 5 months ago | (#47110397)

I thought the proof was verified decades ago. Perhaps you wanted to say "evidence" instead?

### Enough of the Slashdot Beta crap already! (-1)

#### Anonymous Coward | about 5 months ago | (#47106241)

Stop trying to make everything flat and Metro-ish.

Whoever's in charge of this, screw you and hope you die a horrible death.

### Re:Enough of the Slashdot Beta crap already! (-1)

#### Anonymous Coward | about 5 months ago | (#47106491)

Third time's the charm. Maybe Slashdot Gamma will be better.

### Re:Enough of the Slashdot Beta crap already! (0)

#### Anonymous Coward | about 5 months ago | (#47107401)

I want to see Slashdot Ypsilon. With that name it had better be some real Daliesque shit.

### Why, of course... (-1, Offtopic)

22.7 — a.k.a., the rule of three — now appears to be as significant as pi.

Why, of course! The proof in one step: 22 / 7 = Pi /snark

### Re:Why, of course... (0)

#### Anonymous Coward | about 5 months ago | (#47106339)

Well, it's closer to 22.6942....

### Article Fails to Prove Rule of Three (-1)

#### Anonymous Coward | about 5 months ago | (#47106283)

There's nothing in the article about the monster jumping out every 3rd time the scary music plays in a movie. Just some boring stuff about really cold atoms.

### Pi? (-1)

#### normanjd (1290602) | about 5 months ago | (#47106307)

"...now appears to be as significant as pi." Wonder if this is a subtle joke or actually related to the value of pi... Pi is approximated by 22/7...

### Re:Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47106435)

It could be just a coincidence. Going from 22.7 to 22/7 is quite a leap. Correct me if I'm wrong.

### Re:Pi? (1)

#### mrbester (200927) | about 5 months ago | (#47106497)

Not much of a leap on my keyboard, / being next to . so an easy typo to make...

### Re:Pi? (3, Informative)

#### Anonymous Coward | about 5 months ago | (#47106637)

http://rsta.royalsocietypublishing.org/content/369/1946/2679.full

If you check section three, you'll be able to compute that the number in question is 22.6943825963666951931....

### Re:Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47107573)

Strange, I get 22.6943825953666951928... As supporting evidence, a Google search for 22.69438259536 gives some hits, but not for 22.69438259636.

### Re:Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47107821)

Interesting! You are right about the 5, but your last digits are also wrong...

s_0 = 1.0062378251027814890640668123429012308420481556643372852718021332089137814435579...

which gives:

22.69438259536669519286021713693337651029896890130319136482608...

### Re:Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47108141)

Look again. The last digits given by your parent match what you have.

### Re:Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47108251)

Not really. To truncate the series there, it would be properly noted as ...29...

### Re:Pi? (1)

#### BronsCon (927697) | about 5 months ago | (#47108975)

To truncate with rounding, yes. Lazy truncation, however...

### Re: Pi? (1)

#### orangesquid (79734) | about 5 months ago | (#47106523)

22.7 is 2*10^1+2*10^0+7*10^-1.
If you express the same quantity in a bar other than ten, the .7 is no longer going to be a 7 after the decimal point, 7*10^-1. Note that you multiply it by TEN to get the 7 in the denominator of 22/7. In another base, you'd be multiplying by something other than 10, so you wouldn't get 7.

### Re: Pi? (0, Funny)

#### Anonymous Coward | about 5 months ago | (#47106875)

The adorable thing about people with Asperger is that they really think they've made a contribution when they state the obvious. (This is offset by how angry they get when they don't understand something and have a tantrum over how WRONG others must be.)

### Re: Pi? (0)

#### azav (469988) | about 5 months ago | (#47107901)

People do not have "Asperger". They have "Asperger's", or "Asperger's Syndrome".

Asperger alone means nothing.

You should know this.

### Re: Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47108147)

People do not have "Asperger". They have "Asperger's", or "Asperger's Syndrome".

Asperger alone means nothing.

You should know this.

Thanks for confirming the parent's point.

### Re: Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47108071)

Considering the number of people making this connection, I would submit that this explanation is effectively "not obvious." I await your impending tantrum.

### Re: Pi? (0)

#### Anonymous Coward | about 5 months ago | (#47107609)

Yes but consider this: $\omega\infty\int\hbar$

### So the Rule of Three is 22.7? (0)

#### Anonymous Coward | about 5 months ago | (#47106521)

Boy am I going to look so smart in Trivia Pursuit now

### Re:Clueless (5, Informative)

#### hansraj (458504) | about 5 months ago | (#47107177)

I found the summary confusing but the article made more sense.

The theory was that there exist configurations of three particles that is stable in a strange sort of way. The strange part is that if a certain configuration was stable then putting the particles in the same configuration but the distances blown up by a certain factor (22.7 if the three particles were the same) gives another stable configuration. So you can keep blowing up the distances in multiples of 22.7 and would get an infinite sequence of stable configurations. These configurations are necessarily quantum and not classical since the distances involved would be much larger than the range of the forces between the particles. (Although even the initial distances are large too, if i understood correctly, you would agree that they _will_ get pretty large at some point).

Now some independent groups have shown the existence of such states with the required blowup. Since similar-particle setup required cooling things down to the limit of present day technology, only _one_ configuration was observed initially. Someone used a system of different particles resulting in a blowup factor less than 22.7 allowing them to observe _three_ of these configurations, essentially validating the theory.

### Re:Clueless (1)

#### azav (469988) | about 5 months ago | (#47107919)

Soooooo, this might explain stability of atoms in certain structures and certain distances?

Or how certain subatomic particles make stable structures and become atoms?

Am I reading into this right?

### Re:Clueless (1)

#### hansraj (458504) | about 5 months ago | (#47109063)

I don't think so.

Stability of ordinary matter is well explained by other more traditional theories (strong/weak forces for nucleus, electromagnetic for atoms and molecules, gravity for even larger structures). This theory described stable states that initially no one believed existed.

Morever, these configurations are stable but quite fragile.

### 50's monster movies vindicated! (1)

#### Thud457 (234763) | about 5 months ago | (#47108495)

So a 200-foot praying mantis is still a possibility as long as it's scaled up some power of 22.7. Got it.

### Re:50's monster movies vindicated! (0)

#### Anonymous Coward | about 5 months ago | (#47111127)

200 foot is 60.96 metres, while a praying mantis is 1.2 to 15 cm, or 0.012 to 0.15 metres (source [nationalgeographic.com] ). To get to 200 foot, you need to scale the mantis up by 406.4 to 5080 times, or 22.7^1.924 to 22.7^2.733 times. So, the only possible integer power is 22.7^2 = 515.29 times the original.

Working backwards, that means you'll need a praying mantis of 11.83 centimeters, or 4.66 inches.

### Re:Clueless (1)

#### lazy genes (741633) | about 5 months ago | (#47116529)

That the geometrical shape of the fabric of space-time or higgs field should show similar events relative to 22.7. I suggest that everything is a three body problem at its fundamental point. I ran into that number before in a dream, I was watching an neutrino travel through the fabric of space time and it needed to be passing through 2.7 or 2.6 compartments of the fabric at the same time or it would not exist. Hmm oh well.

### Re:Clueless (1)

#### jovius (974690) | about 5 months ago | (#47111697)

What I gathered is that the configuration is like mirrors facing each other. The observer of the particle configuration is somewhere in the middle of the reflections, which go from an infinitesimal small scale to the infinitely large, in a sort of continuum. The distance of one mirrored reflection from another is successively 22.7 times more (or less) than the distance from the previous reflection, depending which direction is observed.

The number 22.7 is not necessarily a constant, and it depends on the properties of the particles. In the article it is said that the scaling factor decreases according to the particles’ relative masses, for example.

### Cue the flood of numerologists ... (0)

#### Slayer (6656) | about 5 months ago | (#47106693)

That 22.7 number is going to get numerologists going. Remember, that in ancient times 22/7 was a common approximation for pi ...

### Re:Cue the flood of numerologists ... (5, Funny)

#### hawkinspeter (831501) | about 5 months ago | (#47106777)

Yes, and 22+7 is exactly equal to the number of days in a month (+ or - 2 days).

### Re:Cue the flood of numerologists ... (0)

#### Anonymous Coward | about 5 months ago | (#47111091)

22.7
22/7

a real life 42???

### No good (0)

#### Anonymous Coward | about 5 months ago | (#47106863)

Americans are too fond of pi , so they are never going to embrace being trimmer

### Re:No good (1)

#### azav (469988) | about 5 months ago | (#47107925)

Mexico has us beat.

We were #1. We were #1.

### mr. putin please do show on russian prisons (-1)

#### Anonymous Coward | about 5 months ago | (#47107261)

we know ours suck.. thank you

### Planescape (0)

#### Anonymous Coward | about 5 months ago | (#47107375)

http://en.wikipedia.org/wiki/Planescape#Rule-of-Three

### Re:Planescape (1)

#### Will.Woodhull (1038600) | about 5 months ago | (#47108305)

And I was sure they were talking about The Mathemagician's Rule of Three:

• "Just the place for a Snark! I have said it twice:
• That alone should encourage the crew.
• Just the place for a Snark! I have said it thrice:
• What I tell you three times is true."

--The hunting of the snark, Lewis Carrol [poetryfoundation.org] . Fit the First, second stanza.

#### Anonymous Coward | about 5 months ago | (#47107685)

Proof that having a threesome is not only okay, but proved to be fucking awesome by none of than science!

### 22.71415926535...? (1)

#### Ted Stoner (648616) | about 5 months ago | (#47107779)

Is it really 22.70000000 or is there some interesting splatter of digits beyond? I didn't see any more specific number in the article.

22.69438....

### As someone not schooled in this discipline (1)

#### azav (469988) | about 5 months ago | (#47107873)

Why is this relevant?

What does it teach us that a normal person could understand?

### Re:As someone not schooled in this discipline (0)

#### Anonymous Coward | about 5 months ago | (#47108175)

A certain magnitudinal order to the observable universe has been proven true to the best of our ability. This changes nothing about current applied physics, but makes certain disciplines of theoretical physics slightly less theoretical. I.e.: this will affect you in no way whatsoever, but the guys from Big Bang would be mildly interested.

### Re:As someone not schooled in this discipline (0)

#### Anonymous Coward | about 5 months ago | (#47111073)

First, I am not a physicist. However, this is yet another example of a mathematical model being proven true in the lab. Science often depends on math to find more theories.

The "anti-electron" or positron was predicted as a "negative root" to a quadratic equation. Later, they found one one by experiment.

Relativity and the Lorenz transform was a theory based on math. Particle physics have verified things about mass and the speed of light.

In this case, math showed that a three-body problem (3 particles connected by forces) had stable connections at distance X and x*22.7^n for any n. This could lead to chemical engineering breakthroughs, where the materials must be the right distance apart.

### Smaller scales (1)

#### justthinkit (954982) | about 5 months ago | (#47115935)

Our knowledge tends to be high in the middle of the spectrum.

When we try to grasp the entire Universe, we end up looking at pixels of info. We know little and speculate much.

Similarly, at the smallest scales we have to resort to atom smashing to learn a bit and speculate a lot.

This theory suggests that life is LEGO-like after all. Once we know this underlying pattern, we can look for it, and we can use it to build better models of stuff very large and very small.

I would add that these results are consistent with my own theory [just-think-it.com] .

### Article has incomplete data (0)

#### Anonymous Coward | about 5 months ago | (#47107897)

I thought this was about celebrities dying in threes.

### More Than Three? Fine, But... (0)

#### Anonymous Coward | about 5 months ago | (#47108067)

The Efimov state is the most elementary effect in few-body physics, the researchers said, but there are countless others that seem to influence the arrangements of small numbers of atoms: four-, five- and six-body interactions and so on.

I'm fine with it as long as they don't use water molecules and they keep the number of particles below nine [wikipedia.org] .

### Re: More Than Three? Fine, But... (0)

#### Anonymous Coward | about 5 months ago | (#47108741)

Nicely done sir !

below the beta state is also something I'm kind of ok with. Still pissed off tho.

### freeman (0)

#### Anonymous Coward | about 5 months ago | (#47108199)

half life 3 confirmed

### 22.7 and pi (1)

#### iguana (8083) | about 5 months ago | (#47108209)

"22.7 — a.k.a., the rule of three — now appears to be as significant as pi."

22/7 approximates pi.

Iiiinteresting...

### Re:22.7 and pi (1)

#### Gibgezr (2025238) | about 5 months ago | (#47108923)

It is pretty interesting!

I always use 355/113 as my "super quickie fractional representation" of pi. It is accurate out to 6 decimal places, which makes it useful enough for most purposes. 22/7 only gets us to 2 decimal places, unfortunately.

### Re:22.7 and pi (0)

#### Anonymous Coward | about 5 months ago | (#47109847)

If you can memorize 355/113 why not just memorize pi to 6 decimal places and save some calculation?

### 3.14159265358979323846264 (1)

#### pezpunk (205653) | about 5 months ago | (#47108881)

yay! i'm going to memorize as many digits as i can of the Rule of Three!

### And 22/7... (1)

#### GPS Pilot (3683) | about 5 months ago | (#47109039)

is a good approximation for pi.

### Re:And 22/7... (0)

#### Anonymous Coward | about 5 months ago | (#47113065)

For sufficiently bad definitions of good.

### Re:And 22/7... (1)

#### ghmh (73679) | about 5 months ago | (#47115201)

Raised to the power of grayskull.

### Can someone shed some light (1)

#### monkeyFuzz (3398671) | about 5 months ago | (#47109789)

.. on why this is significant?

### reference (0)

#### Anonymous Coward | about 5 months ago | (#47110735)

"in 2014, physicists in Austria, Germany, and the U.S. have physical proof that Efimov's trimers do indeed scale by a factor of 22.7 if they are comprised of the same particles or a lower ratio relative to their particles' masses if they are comprised of a mixture of different particles (abstract 1, abstract 2, abstract 3)"

Ah, proto-culture and the triumvirate. When do I get my hovercycle?

### Otherwise known as the Rule of 2 (plus one) (1)

There must always be a master, an apprentice, and the apprentice's secret apprentice.

### The Exact Value... (1)

#### Sigfried (779148) | about 5 months ago | (#47112523)

is most likely transcendental. According to Efimov's original paper, the magic value "22.7" (we shall M) is given exactly by e^(pi / |s0|), where s0 is a pure imaginary solution (very close to i) of an equation (9) he derives earlier and is related to the three-body problem (there are an infinite number of real solutions s1,s2...). If you define s0 = i x where x is real, then (by converting from trig to hyperbolic trig) it can be shown that the number M is given by e^(pi / x), where x is the positive real solution to:

0 = (8 / sqrt(3)) sinh( pi * x / 6) - x * cosh( pi * x / 2)

If you copy/paste the right-hand side into the WolframAlpha website, you will see that the curve has exactly two non-zero solutions, approximately (+-) 1.00624. You can ask for more digits, and it will give you x=1.0062378251027814891..., which means to eight digits, M = 22.694382595... This equation above is a transcendental equation whose non-zero solutions are neither rational nor algebraic, and very likely M itself is also transcendental. Proving these sorts of things, however is very difficult. The best we can hope for is that the number can be expressed as an infinite expansion whose terms have a nice form which converses rapidly. A few more clicks on Wolfram Alpha and I'm sure someone will work it out.

### Rule of Two is more important (1)

#### Gothmolly (148874) | about 5 months ago | (#47112881)

I'm more concerned about the Rule of Two. When Obama goes, who is there to take his place?

# Slashdot: News for Nerds

"It is easier to fight for principles than to live up to them." -- Alfred Adler