Quantum Golden Ratio

Posted by Scott

I’ve posted on this subject before and its implications are certainly debatable, but last week’s announcement that researchers had discovered the presence of the Golden Ratio in the quantum world had me thinking there might be more to it than anyone has yet realized.

“Researchers from the Helmholtz-Zentrum Berlin für Materialien und Energie (HZB), in cooperation with colleagues from Oxford and Bristol Universities, as well as the Rutherford Appleton Laboratory, UK, have for the first time observed a nanoscale symmetry hidden in solid state matter. They have measured the signatures of a symmetry showing the same attributes as the golden ratio famous from art and architecture.”

Dr. Radu Coldea — the principal author of the paper — describes how the ratio was observed in magnetically linked chains of atoms: “Here the tension comes from the interaction between spins causing them to magnetically resonate. For these interactions we found a series (scale) of resonant notes: 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.”

Pretty amazing to think that something we seem to have an innate appreciation for and which occurs on such a comparatively massive scale can also be observed in the smallest components of our world.

Image via Minarai

25 Comments Leave A Comment


Fábio Martins says:

January 14, 2010 at 7:04 am

Wow! Really impressive! I’ve seen so many discussions on the Golden Ratio and usually most people go to the opposite opinion: they tell you that it’s only a visual habit of ours.

Thanks for posting this, Scott.


Troy Hanson says:

January 14, 2010 at 7:59 am

Wouldn’t it make sense for the golden ratio to be present in the most basic elements of nature (i.e. atomic structures, wave forms, etc.)? Everything in the universe is built from these basic components, so if the golden ratio is present at the basic level, of course it’s going to manifest itself in more complex structures… like living things, and the way living things see the world.

Condensed: maybe the golden ratio looks “right” to us, and recurs (often subconsciously) in the way we shape our world, because it’s a part of us on the most basic level.


marc says:

January 14, 2010 at 8:07 am

Dang! I heard them talking about this on NPR but they never mentioned that they were aligning in the golden ratio… Maybe I just needed to see the visual to connect it. Wow. Very cool. Makes me want to pull out my old design book and look over the golden ratio.


Alex / HeadUp says:

January 14, 2010 at 12:40 pm

There are definitely some powerful secrets hiding within the golden ratio, there is much more at play than we can realize. I really hope it helps us figure out how to make flying cars and fly faster than light.


Ryan Le Roux says:

January 14, 2010 at 12:43 pm

Ah yes — the topic of the golden ratio. It’s astonishing to see all the related topics and how it plays a major role in organic things.

I myself try to apply that ratio to all my work — sometimes easier said than done!


Dave says:

January 14, 2010 at 2:05 pm

Mere coincidence or there really is something to it? Nice to think there could be a real science behind it though….


Jason Warth says:

January 15, 2010 at 9:22 am

The significance of the Golden Ratio cannot be overstated, in my opinion.

- The more “novel” aspect of this ratio is that humans seem to have a subconscious predisposition of attraction towards it—including physical proportion, aural proportion (i.e. harmonies), and who knows what else.

- The more significant observations of the golden ratio—in my opinion—relate to its role in “optimizing” the physical world. In nature (i.e. biology), this ratio—sometimes most easily recognized via the Fibonacci Sequence.

——- Go outside and look at a plant: measure the angle of rotation between the point where sequential “branches” sprout from the stem. You fill find the golden ratio when you compare the angles. The amount of sunlight that reaches the leaves of a plant is maximized by the plant’s leaves sprouting at precise angles of rotation relative to the previous leaf.

——–Look at a tree: notice any numerical patterns in the number of branches that split off from the trunk… and then re-split? You may, because the Fibonacci sequence often reveals itself in this context (i.e. one branch, then 2 splitting off at he same time, then 3, then 5, 8, 13, and so on.) Ever notice that the “branches” of lightening look just like a tree’s branches? Ever try to draw a tree or lightening… unless you’re in tune with this system (consciously or subconsciously), it will likely turn out looking a bit fake. Now you know why.

——-Look at a peacock’s tail feathers when he spreads out his tail. Notice the interweaving spiral patterns formed by the “eyes” of the feathers? (note: the same patterns can be found in pinecones, and other elements of nature). Count the spirals one way, then count the spirals the other way. The two numbers you just arrived at will be sequential numbers in the Fibonacci Sequence. (e.g. 5 and 8, or 8 and 13, or 13 and 21, etc.)

——-Look at your knuckles—the proportions and ratio (there is a difference between those terms) of all the sections of your fingers.
- – - – - – - – - – - – - – - – -

My point is this: The Golden Ratio / The Fibonacci Sequence (Phi), isn’t just a “neat thing,” it’s THE MOST EFFICIENT SYSTEM FOR THE GROWTH OF THE UNIVERSE AND ALL THAT’S IN IT.

The Golden Ratio = Life Itself. So no, it cannot be overstated. ;-)


John Noble says:

January 16, 2010 at 4:33 am

Um, this is all just stuff you’ve read on the internet. It’s nice to believe, but most of it isn’t true.

If you’ve actually done these measurements yourself then accept my apologies and please post your results here. However:

- Measuring a plant’s leaves. Well, I have a plant in my bedroom that I just took a look at. I can already tell that it’s in a different position than this morning; plants move as the day progresses, and the position of the leaves will also depend on the weight of dew, etc. I don’t have a protractor so can’t measure the angles but I’m pretty confident if I did I would not find the ratio.

- No trees near me just now, so I’ll skip that. If you have any photographs on the web that you could show us that demonstrate this point that’d be great.

- The peacock. Here’s a nice picture of a peacock I found on Google:
Now, I don’t know about you, but I’d have a very hard time differentiating distinct spirals in that pattern. Let me know if you think differently.

- My knuckles. This is tricky. From which point do I measure? My hand is flat and I’m going from my best estimate of the “middle” of each knuckle.
* Tip of finger – 1st knuckle = 2.2cm
* 1st – 2nd knuckle = 2.4cm
* 2nd – 3rd knuckle = 2.9cm

I see no evidence of the golden ratio in those numbers. I’ve seen enough hands to know that everyone’s are different – to claim that this ratio holds true for them all seems, on the face of it, to be ludicrous.

I’m not trying to be a killjoy here (okay, I am). I’m just trying to point out that a little reason and logic is required when people make these sorts of claims, or they – like this one – become urban myths very quickly.

The internet is a great disseminator of information but in this broader instance the information it claims does not stand up to analysis.

I am, of course, happy to be proven wrong – but only with actual facts, not prose. Thanks.


Anonymous says:

January 16, 2010 at 6:35 am

I think you guys are missing the point… And why are you even arguing about it?

Yea the golden ratio is cool and all. So is the speed of light in a vacuum, or the gravitational constant, Napier’s constant(e), plank’s constant, √2, electron mass, pi etc. I could go on and on. These numbers do manifest themselves in nature, though significantly less the higher and higher you go in scale due to entropy, thus making it harder for us to observe them in our everyday life.

The article isn’t about the golden ratio. It’s about finding a solution to the Einstein field equations (or finding a new system that cooperates with them), and understanding the nature of our existence. All the theoretical physicists went crazy for a few decades, and in the past few years that insanity has actually begun to give us results. Discoveries such as this put us one step closer to the answer. Think about the bigger picture, the implications of a significantly higher understanding of our universe, what that would do for technology, then society, and then future generations.

The problem is so much greater than ourselves, try not to think about it in such simple terms.

The universe deserves more respect…


Anonymous says:

January 16, 2010 at 8:04 pm

No, John Noble – you are wrong. I’m not trying to be a killjoy here either.

The importance of phi, Fibonacci, and the golden ratio – all 3 concepts – does exist in nature and is important. No one refutes that.

But you are right in some ways. No, it is not found in ALL plants. No, the patterns in peacocks are not generally visible to the naked eye.

The simple fact that you said all peoples’ fingers couldn’t possibly fall under the golden ratio shows you misunderstood the previous poster. The golden ratio IS seen in an individuals knuckles – IF you measure the total proportion of THAT person’s knuckle’s to the length of THAT person’s fingers. Your numbers even prove it.

Want proof? Here it is. Golden ratio is .618, or 61.8% of the whole.

The top section of your finger – by your own numbers – is 2.2 + 2.4 = 4.6 cm. The total length of your finger – by your own numbers – is 7.5 cm.
4.6/7.5 is .613 – close enough to .618 to pass muster.

And lest you chide me for using .618 instead of 1.618, the golden ratio is actually 1/.618 which actually equals .618. Yeah, it’s the same thing. And it’s the only ratio that does that. By the way, tracing our way backwards algebraically, your finger length (7.5 cm) divided by 1.618 = 4.6 cm.

So the length of your finger divided by the golden number equals the length of your fingertip to your 2nd knuckle. Cool, right? I just measured my skinny fingers and guess what? My finger length times 1.618 = the distance from my fingertip to my 2nd knuckle too. Har har. We’re all brothers!


Anonymous says:

January 16, 2010 at 8:24 pm

Sorry, in above reply I meant to say golden ratio is 1/.618 = 1.618. So yes, the golden ratio equals the golden number. .618 is the only number whose reciprocal is equal to it plus one.

Bottom line, the ratio of your fingertip to 2nd knuckle vs. the total length of your finger should equal .618.


Anonymous says:

January 16, 2010 at 8:24 pm

Sorry, in above reply I meant to say golden ratio is 1/.618 = 1.618. So yes, the golden ratio equals the golden number. .618 is the only number whose reciprocal is equal to it plus one.

Bottom line, the ratio of your fingertip to 2nd knuckle vs. the total length of your finger should equal .618.


Hegemoney says:

January 17, 2010 at 8:24 pm

I have a friend who is doing his dissertation work at The University of Arizona on the implications of the Golden Ratio in linguistics. His discoveries are astounding. So it’s not just the physical and quantum world that bends to the ration, but also our cognitive and linguistic functions as well.


Norfolk N Chance says:

January 20, 2010 at 2:30 pm

Golden Ratio & Sacred Geometry.

hey folks…… grab yourselves a UK £10 note,look on the queens head side,bottom lefthand corner.


Also check the E/R SURROUNDED BY 4 PYRAMIDS in amongst the sacred shapes.

5 golden ratio shapes all facing one way then an elizabeth 2nd emblem surrounded by 4 pyramids followed by another but inverted symbol…….


Jason Warth says:

February 2, 2010 at 4:52 am

Was working on a project when the golden ratio came to mind (as it often does), which reminded me of this post. In response to John Noble:

Are there misconceptions about the Golden Ratio? Certainly. Was I trafficking in them? No. It’s not “all just stuff [I] read on the internet.” It’s a combination of things I’ve learned about based on my passion for the subject. Has some of it been on the internet? Of course. But much more of what I know has come from books on the subject itself, as well as from observing the world around me.

While the anonymous posters below you did a nice job of setting you straight, there are a few items that I’ll address directly:

Specifically speaking:

PEACOCK: The picture you posted is sufficient enough for me to see the spirals, but maybe the peacock and pinecone images below would help you observe this phenomenon more clearly for yourself:

YOUR KNUCKLES: To put this delicately as I know how—If your knuckles are the length that you say they are, then you would be considered “abnormal” compared to the average measurements of most human beings. My 3rd knuckle is over twice the length of my first, yet yours is only marginally larger? I think you need to re-measure, my friend. My measurements (in cm):

3rd – 5.9
2nd – 3.5
1st – 2.4

I don’t feel like explaining the whole topic to you, but if you compare those measurements the way they’re intended to be compared, then you’ll see that mine aren’t far off from the golden ratio. Note: “Not far off,” is still relevant in this case, because I have skin, tendons and muscle around my finger and can’t measure my bones with great precision. Two (of many available) forms of proof below:

(3.5 + 5.9) ÷ 5.9 = 1.593…

(2.4 + 3.5) ÷ 3.5 = 1.686…

Both of these calculations result in a close approximation of Phi (aka the golden ratio), which is 1.618. I suggest you take some new measurements and replace my data with your own.

A final suggestion: before lecturing others on the omission of reason and logic, take a stab at applying some of your own. To review: you “refuted” my post by:

a) looking at a plant and deciding not to measure it;
b) deciding that you had no trees to look at;
c) finding a random picture of a peacock on the internet;
d) failing miserably at measuring your hand (the only thing you attempted);
e) deciding that since you saw no evidence of the golden ratio, that I must be blindly regurgitating “myths” I’d found on the internet.

Since you said you’d be happy to be proven wrong with facts, I trust that you’re now satisfied.


martin fahy says:

September 14, 2010 at 1:35 pm

I;m doing my thesis on this very subject so grateful for you for posting such information. I’ll give you my result when I’ve completed in December !