## Golden Ratio Discovered In a Quantum World 191

*"Scientists have for the first time observed a nanoscale symmetry hidden in solid state matter. 'In order to study these nanoscale quantum effects, the researchers have focused on the magnetic material cobalt niobate. It consists of linked magnetic atoms, which form chains just like a very thin bar magnet, but only one atom wide.' By artificially introducing more quantum uncertainty, the researchers observed that the chain acts like a nanoscale guitar string. The first two notes show a perfect relationship with each other. Their frequencies (pitch) are in the ratio of 1.618, which is the golden ratio famous from art and architecture. The observed resonant states in cobalt niobate are a dramatic laboratory illustration of the way in which mathematical theories developed for particle physics may find application in nanoscale science and ultimately in future technology."*

## Re:Summary wrong (Score:5, Interesting)

You're ALL irrational.

This really is interesting, though. The Fibonacci sequence shows up all the time [world-mysteries.com] in nature, but this is, to my knowledge, the first time in a non-biological function.

## Re:Summary wrong (Score:5, Interesting)

Sort of. The golden ratio is apparently related to the E8 lie group, which shows up in string theory and supergravity. WIkipedia says the golden ratio also shows up in relation to quasicrystals.

This one is cool though. My first thought was "creepy."

PS: to the mod who gave all discussion of the irrationality of the golden ratio an offtopic mod: get a life.

## Re:Car Analogy (Score:5, Interesting)

Here's my cut at a car analogy. Notice that a naturally recurring form-factor for popular cars involves a height to length ratio of 1:1.618. That ratio shows up again in that "rise to run" ratio of windshield rake. ...and again in overdrive gear ratio... and yet again in...

## Re:Summary wrong (Score:3, Interesting)

The real question is, can anything in the quantum world really involve a non-rational number (or even a non-terminating decimal)?

Take a simple circle. A mathematical perfect circle is effectively a polygon with an infinite number of sides, and pi is infinite because of this same fact. A 'circular' object in the real universe has faceted sides, each of at least the lengths between adjacent atoms. (It's also 'fuzzy' when measured at that scale, and part of that is also QM). The whole concept of Planck length dictates minimum distances, angles and such, and objects have granularity that means an infinite number of facets or an infinitely dividable curve isn't part of the real universe.

So, isn't what's been discovered here an expression of the golden ratio to only some finite number of decimal places?

## Re:Art and Architecture? (Score:2, Interesting)

As a (former) mathematician

How do you stop being a mathematician? (you don't seem to have stopped).

## Re:Art and Architecture? (Score:3, Interesting)

How do you stop being a mathematician? (you don't seem to have stopped).

By being forced to graduate from university and getting caught up in politics [pp-international.net] and law [pirateparty.org.uk]. It must be at least 3 months since I did any proper maths (and the stuff above doesn't count - any suitably well-taught 8 year-old should be able to derive the answer; and it is all on Wikipedia anyway). But still, I guess one never quite recovers from spending 5+ years almost entirely devoted to the subject...

## Re:Oblig. Square One TV's MATHNET reference... (Score:2, Interesting)

Modded Redundant? Who else posted this? This was First Post!

## Re:Car Analogy (Score:1, Interesting)

You get a grant to analyze a car in order to find something really special about it. You measure its top speed, acceleration, etc. and spend 3 years analyzing it, but find nothing special about it, it's an average car. At this point you already spent all the money and you need to somehow justify spending all that time and money, so you start comparing all the measurements you took in order to at least find some kind of well known constant and that's when you notice that the diameter of the AC vent is 1.618 of the diameter of the cigarette lighter.

## Re:Art and Architecture? (Score:2, Interesting)

How do you stop being a mathematician? (you don't seem to have stopped).

By being forced to graduate from university and getting caught up in politics [pp-international.net] and law [pirateparty.org.uk]. It must be at least 3 months since I did any proper maths (and the stuff above doesn't count - any suitably well-taught 8 year-old should be able to derive the answer; and it is all on Wikipedia anyway). But still, I guess one never quite recovers from spending 5+ years almost entirely devoted to the subject...

Wish people would stop fussing that college actually makes them learn things outside their field of study.

If you get through college and don't understand why they made you take those classes you missed the point of college and need to go back because you still have a LOT more to learn about the world.

## Re:Looking for god's finger prints? Here it is. (Score:3, Interesting)

I believe randomness doesn't exist. In its place stands "too complicated to understand".

Take the typical state lotto. If you knew all of the variables in the machine that draws the numbers, you can solve for which numbers will land in the winning numbers area. As a result, the lottery keeps details of the machine secret. Is the ball marked 43 the same ball (with the same weight and other properties) as the 43 in the previous or next drawing? Where is the machine located and what elevation is it at? When exactly does the drawing machine go into motion? If you know the answers to these secrets, you're not allowed to play.

Take any casino card game. Shuffling is a complex possible that's hard to technically observe. Do it right and repeatedly you've got uncertainty as to what card is going to come off the deck.

Take any slot machine. It's got a PRNG but it needs a seed value. It measures the time in between button presses measured to an annoyingly tight accuracy to get the complex number to run through its complex formula to create unpredictability.

Random just doesn't exist if you're going to believe everything moves according to the laws of physics.

## Re:What are they going to use this for? (Score:3, Interesting)

Our computer memory technologies are largely based on understanding magnetizable materials at a very short length scale. The next logical step is to understand various phenomena of these materials at the nanoscale which is exactly what they are doing. The research is interesting because it hints at more going on in quantum physics that may at the least be interesting and at most useful in order to advance state of the art technology.

## Re:Art and Architecture? (Score:5, Interesting)

Yes, it's more the other way around really. The fact that the ratio between the first two frequencies measured in the spectrum was the Golden Ratio (within error), was evidence that the state had E8 symmetry, for group-theoretical reasons I can't quite explain. (I'm kind of in the opposite situation; I know QM but Group Theory was never my strongest point)

This is interesting because E8 isn't a symmetry many real physical systems have. But it's of interest for string theorists and other advanced theories, so it's interesting if they can find systems that can act as a model. The 'real' system here doesn't have E8 symmetry either. Rather it's a system of quasiparticles [wikipedia.org] created by the spins of the system which is E8, when exposed to a magnetic field at a certain critical phase-change point.

Which is why the title of the Science article calls it "emergent E8 symmetry".

## Re:Looking for god's finger prints? Here it is. (Score:5, Interesting)

I believe randomness doesn't exist. In its place stands "too complicated to understand".

David Bohm wrote a lot about that, especially later in life. He essentially believed that what we perceive as randomness is a higher degree of order. An example he liked to use is a drop of ink placed in a cylindrical tank of glycerin, with a smaller central cylinder attached to a crank. If the crank is turned slowly in one direction, the drop of ink smears out and finally becomes invisible, dissolved in the surrounding medium. But if the crank is turned slowly back in the opposite direction, the drop of ink coalesces.

The unturned ink has a low (meaning simple) degree of order, while the spread-out ink has a high (complex) degree of order that is made apparent only when we wind it back to a state we can easily grasp. He also called these states the explicate, or what is readily apparent, and the implicate, or what is waiting to coalesce. The implicate order is why we have the maxim "hindsight is 20/20"--once something has happened, it often becomes easier to see how previous events lead up to this one.

It's interesting stuff, though certainly not orthodox, especially when one starts reading about the holomovement.

## Re:Summary wrong (Score:5, Interesting)

The fact that something cannot practically be directly measured at a particular precision without creating a black hole does not mean that it does not exist at the desired precision.

## It is the "most irrational possible" number (Score:5, Interesting)

The golden ratio phi is "the most irrational number", in some sense. If you try to take better and better rational approximations to phi, obviously you need to go to bigger and bigger denominators in the fraction. In the limit as the error tolerance goes to zero, the necessary size of the denominator grows at a certain asymptotic rate. One can show [ams.org] that for phi this rate is the largest possible, so the golden ratio is the hardest number to rationally approximate.

## Re:Summary wrong (Score:2, Interesting)