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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.
Its got the number of the beast in it. Quick, ring Robert Heinlein.
http://michaelsmith.id.au
...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...
Mod me troll, but this sort of thing really annoys me
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.
Or it could just be that the ratio comes from a very simple geometrical idea and a pretty basic equation.
Next you'll be suggesting that the fact that so many things in the universe seem to be approximately spherical is evidence of a divine being.
Oh, and just because something is improbable, doesn't mean that it can't happen. As for it being "most pleasing to the human eye", personally, I prefer the 1:1 ratio; squares have more symmetry than rectangles. Does that make me inhuman? The golden ratio looks quite nice, and is mathematically a bit interesting, but that doesn't make it magical.
This is not a 'high form of symmetry' but very basic one; a solution to a very rudimentary quadratic equation. I, for one am surprised we're not seeing such solutions more often around us.
Here's why: every semi-dynamic system tends to find a local energy minimum, which needs to be stable. A quadratic equation has always a stable minimum or it doesn't have a minimum. Well... that's all, nothing more to see here for me.
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!
You don't understand quantum mechanics. For QM the world is fundamentally stochastic, not just pseudo random. Einstein didn't like this but he was wrong.
Einstein:
"God doesn't play dice"
Stephen Hawking:
"Not only does He play dice, He does it with his hands behind his back"
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.
Ummmm....yeah...I'm gonna have to go ahead and disagree with you there. Most of those machines blow ping-pong balls around with air, which is most likely turbulent, and they are blown up into the slots when the lottery lady pulls the lever for the slot. Since, at a minimum, you can't solve for the state of the lottery lady, you can't "solve for which numbers will land in the winning numbers area."
(Never mind the outrageous accuracy of initial conditions and precision of the calculations you'd need to solve for the movement of ~4 dozen ping-pong balls being blown around by turbulent air.)
[b.belong('us') for b in bases if b.owner() == 'you']
For those of you that want to hear what this ratios sounds like, it's 833 cents, or a minor sixth plus 33 cents. This happens to be the interval used to form the aptly named Bohlen 833 cents (or A12) scale.
Mal-2
How is the Riemann zeta function like Trump rallies? Both have an endless number of trivial zeros.
That's actually not quantum mechanics but rather the Copenhagen interpretation of QM.
QM doesn't actually tell us much on whether the universe is deterministic or not, because:
A) The time-evolution of the wave-function itself is deterministic.
and
B) Because it's a philosophical question Science will never be able to answer.
You can always simply deny that it's the ultimate theory of Reality and then add a metaphysical layer explaining why it only 'appears' to be random. Or non-random.
Since, at a minimum, you can't solve for the state of the lottery lady
Easy! The state of the lottery lady is the same as the state of the lottery itself.
When our name is on the back of your car, we're behind you all the way!
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.
Your brain is not a computer.
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.
You'll probably find this line in the computer program that runs version 5 of "Life, the Universe and Everything"
public const float seed = 1.618f;
Exception Duck - may or may not contain chicken.