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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."
You're ALL irrational.
This really is interesting, though. The Fibonacci sequence shows up all the time in nature, but this is, to my knowledge, the first time in a non-biological function.
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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.
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...
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 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".
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 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.
Snarkiness is inversely proportional to wisdom because it emphasizes feeling right rather than being right.
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.