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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.
.999... = 1 threads?
.999... and 1? .aaa...
What between
High-end ben-wah balls that reverberate to the sound of money?
Orwell: "In a Time of Universal Deceit, telling the Truth is a Revolutionary Act"
More for the spankbanks of all the readers of Dan Brown novels who truly believe Mary Magdalene is buried beneath the Louvre.
"I'd just like to emphasise that taking a million years isn't a metaphor here..." -Rich Bradshaw
This article confuses me. Would someone be kind enough to explain it to me with a car analogy?
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.
Maybe what we can see is just the surface of a deeper reality, and below that something deeper again, etc. etc.. So this appearance of a golden ratio is actually an artefact of a continued fraction i.e. 1 + 1/(1+1/(1+1/(1+1/(.....
threadeds blog
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 might have a point if the golden ratio were an entirely arbitrary number and not one derived from a simple geometric relation. Pointing to the golden ratio as evidence for the existence of god is like pointing to occurrences of pi in nature, or the Fibonacci sequence. It isn't god's fingerprints, it's math's fingerprints.
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.
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"
just to nitpick (I like irony): Fibonacci sequence IS a golden ratio in its essence; more specifically Fib(n+1)/Fib(n) -> golden_ratio :)
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']
God did it! God teir troll that man is.
Yes, but the fact that you can't do this in practice is exactly the parent's point, I think. In THEORY, if you knew absolutely everything variable involved in the airflow, the balls, the thing they were contained in, etc., you could predict which ball would be chosen. It's not random, just complicated. However, it's sufficiently complicated that it may as well be random, from the human point of view. It's a significant distinction when we're talking about the potential randomness of the universe, though.
this is a point of view physicists had in the 19 century. we now know that it's incorrect due to the uncertainty introduced by quantum mechanics.
Since, at a minimum, you can't solve for the state of the lottery lady
Huh, I rather thought that particular philosophical chestnut is still mostly considered an open question.
sic transit gloria mundi
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.
You picked a good authority comparison. Hawking is sort of known as a black hole guy. The same approach that rejects randomness also rejects black holes. I never paid much attention to Hawking but I would expect he was an Aristotle type while Einstein was a Platoist. So this is the real difference. And I think it is pretty easy to make fun of reductionists.
Does the belief in a universe that is not random necessarily imply a belief in God?
Your brain is not a computer.
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!
Offtopic??? - I have points but have already commented elsewhere.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
It isn't god's fingerprints, it's math's fingerprints.
What is an abstract concept like mathematics doing getting its grubby fingerprints all over physical reality? Some would say that only God could do that. Or are you trying to assert that the universe is just as abstract and unreal as the number 2, and we're trapped in it?
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.
"To believe in a random universe requires a lot more mental gymnastics to reconcile the observed universe with that world view."
Yes, the universe is far stranger than fiction, it's also more usefull.
And did you exchange a walk on part in the war for a lead role in a cage? - Pink Floyd.
eh... symmetry is easier for evolution to work with. I don't know about "loves", but you've got the idea.
Perhaps it was foolish to personify evolution in a response to a religious post; I assure you my intent was imagery and not theology ;)
There are 10 kinds of people in this world: those who understand binary, and nine other kinds of people.
You are thinking about quantum mechanics backwards. The true things that exist do so in many “classical” states simultaneously, i.e. the true nature of the “particle” is really a wave. We are the quirks in the system because our wave functions are so highly entangled that we perceive the universe as if it were deterministic. When we “measure” a quantity, what we are doing is forcing something that is in many states to tell us which state it is in. However, this is actually a nonsense question because the true thing is not necessarily in any “classical” state. Thus, something weird has to happen.
According to pure quantum mechanics --- that is, independent of which interpretation you choose --- the dictated evolution is for both observer and observee to become entangled so that the observer/observee system exists simultaneously in multiple states, but in a way such that in each state of the full system the observer sees the observee in a different particular classical state. The only problem with this is that things get even weirder when *you* are the observer; at that point, pick whatever interpretation you wish to explain what happens. The fundamental point, though, is that regardless of which interpretation you pick, the perceived non-determinism is inevitable and arises not from a incomplete understanding of the universe but rather from the fact that we are forcing it to answer a question for which there is truly no meaningful answer.
Snarkiness is inversely proportional to wisdom because it emphasizes feeling right rather than being right.
This is a nitpick, but technically the world is not stochastic but rather our perception of it is. When you run an experiment where you can't observe what's going on, it evolves in a perfect deterministic manner. Only the act of forcing an experiment that ends in multiple states to pick one of those states introduces the perceived non-determinism.
Snarkiness is inversely proportional to wisdom because it emphasizes feeling right rather than being right.
New properties emerge which are the result of an effect known as the Heisenberg's Uncertainty Principle.
I see neither these properties emerging as a result of the Heisenberg Uncertainty Principle nor the 'effectiveness' of this mere principle.
I rather think that the properties exist independent of any principle and we label our discovery of such as a principle [and both the properties and the principle (albeit an artificial construct) lie outside our observation of such].
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.
http://en.wikipedia.org/wiki/Anthropic_principle
Especially the variant "we observe our Universe as it is because beings like wouldn't exist in a different one"
One that hath name thou can not otter
"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."
The golden ratio is a relationship in the universe and mathematics, found by us. If it happens everywhere, even at quantum levels, it may signify "deeper" laws than the ones we are operating with now, because we currently have different laws on such vastly different scales. In this light, this find is highly interesting to say the least.
Why it is pleasing to the human eye? Can it be because it has symmetry between one level of scale and the next? I dont see the causation of its occurence in nature and level of pleasure. Many patterns occur all the time to our eye, and we find it boring and mundane. The Golden Ratio is actually pretty rare compared to other, more "random" ratios, and is more often found in biology and more complex processes. I find it more interesting that the Golden Ratio has this symmetry of binding different scales in harmony, something we humans sorely lack at this present stage. We need to find more harmonious energy sources and modes of development, rather than rape this planet and have a goldrush all the time.
Not sure how you would define a random universe. Either we can consider its input universally unknown, or governed by some higher level of existence. Usually science will occillate between these, and we may never truly find the original source. But certainly a true random generator would be just as amazing as God as a universal old bearded caucatian male. Where would such a random generator operate, and with what? If you think about it, it really doesnt explain anything at all. The flying spaghetti monster could just as well be the source then, because you can fantasize whatever you want to be "outside the universe". In addition, the Vedas says the universe / God is self-contained, which is a logical explanation in the light of this, and may be more useful in order to understand more.
A more universal definition of "physical laws", would be "vibrational limitations". Vibrations play with the Golden Ratio all the time, and is a more universal theme (pun intended) for our surroundings than the "law and order" we try to impose on it.
Personally, I think the Vedas are correct when it says everything is vibrations, and what we experience, is just the ever-changing limitations of the infinite possibilities of the universes substratum.
God then would be more a collective consciousness, rather than an old bearded caucatian male, and you could just as well call Him/Her by many names: the universe, love, all that is, etc. - also postulated by the Vedas, which never constrained "the one and only God" into anything else than the very existence that we experience. The other "Gods" / demigods etc. were just different aspects of the one universal principle.
Well I guess I lost 99% of /. readers by now, so I leave the rest as an excercise to the reader :-)
Key word: "abstract". With all the ratios in physical descriptions of reality we won't know to their exact value, it's also clear it doesn't map quite so neatly.
One that hath name thou can not otter
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.
Interesting. Now how do you write the Twilight Zone theme Da da da da just doesn't cut it IMHO.
Which brings me to the point of all this - How come only a very few scientists ever ask 'Why is this so?'.
All they seem to do is to observe and record.
What relationship is there between the Parthenon, quantum physics and nano tech?
Why 1.618 and not 10/7 or any other semi-mystical ratio???
Don't be apathetic. Procrastinate!
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.
http://www.youtube.com/watch?v=Xfqht0LEOWQ
note that golden ratio is found in many celebrated works of art. a lot of artists in history used it knowingly in their masterpieces. such pieces of art are known to appeal to human's liking more. liking, appreciation, all subjective concepts. human psyche is something we havent been able to approach with any tangible, usable definite method up to this date.
now we find this ration in quantum mechanics.
this is practically the first solid link in between something that is numeric, defined and clear cut and human psyche.
Read radical news here
Does this ratio show up in any texts? Specifically the word breaks, paragraphs, etc?
1:4:9, at least for the first 3 dimensions?
You don't understand quantum mechanics. For QM the world is fundamentally stochastic, not just pseudo random.
This theory states that it is deterministic, it is just that it is impossible to know enough detail to make the predictions.
The first artificial signal we've received via a medium we're only just discovering, perhaps? :)
The Copenhagen interpretation sucks. I for one favor the Skoal interpretation of QM.
Correct. And don't forget multi-state lotteries!
What's more, no one said the universe was "random", at least not in the sense of having no rules or structure. There's just a gap between, "having rules, structure, and rationality" and "being consciously designed by a loving creator."
And then even beyond that, I don't know anyone who claimed that this universe was "probable". Maybe this universe, with all its symmetry, is highly improbable. Even highly improbable things might happen once.
>Now, give an example of a phenomenon which exists and can't be measured.
Your stupidity?
My favorite comic writer Terry Moore has a series going on now that is tightly wound around the golden ratio. It's called Echo. Check it out. The ISBN number of the first trade paperback is 978-1892597403.
And yes, this is a plug. I like it enough to have a subscription so neener, neener! I'll plug all I want! ;)
The real question is, can anything in the quantum world really involve a non-rational number (or even a non-terminating decimal)?
Sure - non-rational numbers correlate to the uncertainty principle.
I think.
Made me laugh!
-kgj
Since, at a minimum, you can't solve for the state of the lottery lady
I don't see anything which makes it impossible to in principle measure her first, then include her as part of the machine's state.
You'd probably need to model everything she interacts with, transitively, so you have to model the entire universe, which is rather impractical if you're limited to being inside the universe.
But maybe you can measure and model to within a crazy high precision?
http://www.gootar.com/gravityboy/docs/fluxi.html Arrangement of Axis Unit Flux 10-D It has ten diagonals, nine with the force of light, one minus the charge or plus gravity (the normal state). They are composed of one dimensional (1-D) infinitesimal width string or tube like objects arranged in a ten dimensional Dodecahedron axes pattern terminating on vertices or the set of twenty points... (+-x/y, +-xy, 0) where y = (5+1)/2 ( +-xy, 0, +-x/y) x = G /(20 * 3)
( 0, +-x/y, +-xy) G = 1/(10 * 26 - 1)c
( +-x, +-x, +-x)
y = (5+1)/2 = 1.61803398875 = the golden ratio.
This diagram and description is clearer, but does not mention any of the other ratios found. https://www.helmholtz-berlin.de/aktuell/pr/pm/pm-archiv/2010/quantenwelt_en.html
Indeed the Copenhagen Interpretation sucks and I prefer the Everett Relative State interpretation.
Yet again someone who just doesn't get what QM shows.
The evolution of the State Vector is unitary and therefore deterministic. That is a consequence of unitarity, as all the probabilities must add up to one. Any quantum experiment you perform can only return a probabilistic result. This is independent of whatever interpretation of QM you prefer and is not dependent on the Copenhagen Interpretation.
Einstein did not like the elimination of determinism from physical theory and believed a theory showing hidden variables that would establish determinism might be developed. He and his co-workers Podolsky and Rosen (EPR) developed a thought experiment designed to act as a reductio ad absurdum of a non-deterministic QM.
Von Neumann provided a mathematical proof that eliminated all local hidden variables theories of QM. Einstein disliked non-local deterministic theories of QM more than non-deterministic ones as the principle of locality is essential to relativity.
Later it was realized that the EPR thought experiment could be developed into a real experimental test of QM via the Bell inequality. Experiments have been carried out with QM confirmed and Einstein proved wrong. Hidden variable theories that restore determinism have been shown to be impossible.
The physical world we live in is fundamentally stochastic and it is one of the consequences of QM.
Has any discussion taken place linking this article to this one?
Perhaps the detection of E8 symmetry could lend credibility this this theory?
http://www.telegraph.co.uk/science/large-hadron-collider/3314456/Surfer-dude-stuns-physicists-with-theory-of-everything.html
Now that we have at long last discovered the reality of the golden mean in quantum mechanics and high energy physics, we should recall the true history of this momentous discovery of one of the most amazing principles ever found combining art and science on a fundamental level. It was Mohamed El Naschie who discovered the fundamental role of the golden mean in high energy physics for the first time using golden geometry he was able to explain rationally the two slit experiment. A book which just appeared in World Scientific summarizes all this discoveries. The book is entitled: The Mathematics of Harmony. The author is academician Alexey Stakhov, the renowned mathematician and engineer. It is edited by the American Philosopher Scott Olsen. Some have proposed Stakhov for a Nobel prize based on this publication. Another noteworthy book based on Mohamed El Naschie’s work is that of Leonard Wapner entitled: The Pea and the Sun published by A.K. Peters Ltd, Wellesley, Massachusetts. It is only fair to mention that Mohamed El Naschie’s discovery would have been unthinkable without the work of Garnett Ord and Laurent Nottale in fractal spacetime. The profound question is now how did the golden mean enter into fractal spacetime. The answer is extremely simple. It is through Maulden Williams theorem. This theorem was used for the first time in quantum mechanics by El Naschie. The theorem states that a random cantor set will always have with a probability equal 1 the golden mean as the Hausdorff dimension. Since spacetime is nothing but an infinite collection of random cantor sets, it follows that the mathematical building blocks of quantum mechanics and quantum gravity is the golden mean. It sounds unlikely, esoteric or even crazy, but it is not. If it would be it wouldn’t have been discovered experimentally.