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Golden Ratio Discovered In a Quantum World
FiReaNGeL writes "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."
1, 1, 2, 3, 5, Eureka!
Since we know Google is never wrong, the Golden Ratio is exactly 1.61803399, not 1.618 as stated in the summary.
...the golden ratio famous from art and architecture...
As a (former) mathematician, I would like to point out that the ratio really comes from elementary (pun intended; read on to find out more) geometry. The ancient Greeks played around with it quite a lot and Euclid mentioned it (more or less) in his Elements. The Greeks weren't interested in this because of art or how pretty it was, but because they were particularly crazy about geometry (nearly all of their mathematics was derived from it) and some seemed to think that the universe could be understood through geometry alone. Anyway, it is just the fairly simple ratio of lengths of two lines such that the ratio between the larger and the smaller is the same as the ratio of them both added and the larger, or algebraically;
(a + b)/a = a / b = phi
This can then be trivially rearranged into phi^2 - phi - 1 = 0, and then that has the one positive solution; phi = [1 + sqrt(5)]/2 (the negative solution being [1 - sqrt(5)]/2 = - 0.618... but negative lengths and ratios tend to prove problematic). As usual, Wikipedia has more information.
While it is quite interesting to see it appear in a quantum mechanical setting, it isn't particularly shocking (to me). The number is the result of a fairly simple equation (as shown above) which is why it seems to appear so frequently in nature. While I didn't get this far in my studies of quantum theories, it wouldn't surprise me if, once the mathematicians have a chance to look into this, the reason behind this appearance of phi is found to be rather trivial.
However, I am not a physicist, or an expert in this field, so I may be completely wrong.
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...
If the bodies of most organisms are anything to go by, evolution loves symmetry. The universe isn't random, it obeys rules, and when you combine random effects with structured rules you fairly often get to see patterns. Perhaps a better explanation: "The golden ratio is found everywhere in nature even to the quantum level. It is THEREFORE the most pleasing ratio to the human eye. It would be highly PROBABLE for a random universe, GOVERNED BY PHYSICAL LAWS, to create this sort of symmetry."
There are 10 kinds of people in this world: those who understand binary, and nine other kinds of people.
The golden ratio is found everywhere in nature even to the quantum level. It is also the most pleasing ratio to the human eye.
It would be highly improbable for a random universe to create this sort of symmetry.
To believe in a random universe requires a lot more mental gymnastics to reconcile the observed universe with that world view.
Which is more likely:
A) The human eye finds the golden ratio pleasing because it is everywhere in nature
B) the golden ratio is everwhere in nature because it is pleasing to the human eye
It's okay to say "I don't know."
You don't have to fill in all the gaps with "God"
[Fuck Beta]
o0t!
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 that for phi this rate is the largest possible, so the golden ratio is the hardest number to rationally approximate.