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While reading many sources and watching many video's about nature and physics I wonder if the golden ratio is really that often occurring in nature and physics ? If I look on the Wikipedia pages I see both arguments for it in sea shells and similarly it seems debunked on other pages. I believe it occurs in some animals and plants and buildings but I really wonder :

1) Is it true that golden spirals dominate the majority of logarithmic spirals in both hurricanes and spinning galaxies ? And that most hurricanes and spinning galaxies are logarithmic spirals ?

2) Is it true that the golden ratio recently occured as an important constant in investigations of relativity and quantum mechanics ?

The list of things associated with the golden ratio is unmeasurably large , it goes from black holes to evolution, pyramids, religion, chemistry and even finance and aliens.

And also it is sold as both a part of education and as 'hidden secret'. Even worse , it does not play a superimportant role in math apart from continued fractions and a few other subjects imho.

I remain very skeptical about the golden ratio in 'science' especially nonmathematical, physics and biology.

And thus I finally want the truth about it. And if it turns out to be mainly nonsense , I think we should give the golden ratio a more realistic place in both media and especially publications and education. I think it is becoming harmful. It might even give the impression towards some people that they know a bit of math and biology !?

To me it appears as a dangerous concept ! Maybe this should go to chat.

But at least I asked 2 clear questions.

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closed as primarily opinion-based by Najib Idrissi, Mice Elf, Samrat Mukhopadhyay, Zain Patel, yoknapatawpha Jul 23 at 1:41

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise.If this question can be reworded to fit the rules in the help center, please edit the question.

I presume you've seen this? –  J. M. is back. Sep 10 '12 at 16:41
See also –  Robert Israel Sep 10 '12 at 16:47
@J.M No i havent. Should i ? –  mick Sep 10 '12 at 16:55
This could possibly be cross-posted on Skeptics. –  zzzzBov Sep 10 '12 at 21:12
Markowsky's review of Livio's book. The paper Markowsky: Misconceptions about the Golden Ratio might be interesting in the context of this question, too. –  Martin Sleziak Sep 27 '12 at 6:54

5 Answers 5

up vote 10 down vote accepted

The golden ratio appears as a solution to a quadratic. It is therefore important in applications where that quadratic appears. It can also be considered to be important in applications where that quadratic appears approximately.

There is otherwise, however, no underlying physical reason as to why it should or should not appear. The ratio is merely a convenient approximation to physical scaling in many systems. However, so too is 8/5=1.6. These physical systems have mathematical properties that can lead to structures that lead to things like logarithmic spirals, and these models are based on underlying physics, but rarely do they exactly equal $\phi$.

As with many things in popular science, it has been spectacularized by unsavvy media and educators trying to make something seem "special," whereas the truly special aspects of the mathematics and the sciences are usually much more complex -- and much more interesting.

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Thats what i thought. So are you saying the answer to both questions is no ? Thanks for your quick reply. Dont you think we should do something about the problem ? –  mick Sep 10 '12 at 16:42
Among all the problems with popular journalism and public education, I think this particular issue ranks fairly low on the list. –  Arkamis Sep 10 '12 at 16:49
We have bigger fish to fry (math-wise, at least) than correcting false impressions on $\phi$, @mick... –  J. M. is back. Sep 10 '12 at 16:50
What are the biggest fish J.M ? –  mick Sep 10 '12 at 16:53
If one places points around a circle a uniform distance apart (wrapping around after doing a full circle) and wants to be able to place an arbitrary number of points without any of them being excessively close together, the fraction of a circle between points should be the golden ratio or relative thereof. If one placed points a rational number of revolutions apart, they'd repeat; with many near-rational numbers, they'd come close to repeating. With the golden ratio, however, they don't. –  supercat Jul 29 '14 at 13:38

My answer: $\phi$ appears non-trivially in......

Biology (phyllotaxis), yes.

sunflower image

Physics, no.

Art, no.

Hidden Secret, no.

Mathematics, yes.

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I don't see $\phi$... –  Fabian Sep 10 '12 at 19:28
@Fabian: See –  ruakh Sep 10 '12 at 20:47
Can you expand on that? If your “no” is in answer to the question in the title, then why not? –  Konrad Rudolph Sep 10 '12 at 21:17
No in physics ?? –  mick Oct 1 '14 at 11:19
Plz clarify @GEdgar –  mick Oct 1 '14 at 21:07

I think claims that the golden-ratio is found in nature are exaggerated.

However undeserved its recognition on the street may be, though, it is still a useful number that does pop up here and there, due to its nifty scaling-invariance property.

One instance is golden-section search, a numerical method for optimisation of a function of one variable, in which the golden number naturally arises.

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What would you consider an underrating of the golden ratio to be?

Ron Knott maintains a very detailed webpage on the phi ratio and was one of the discussants in Melvyn Bragg’s radio program on the Fibonacci series (along with Marcus du Sautoy and Jackie Stedall), which I highly recommend.

During the discussion on why the Fibonacci series recurs in nature (beginning ~24:00), Knott states, “…yes, it’s prevalent there in nature but actually in the plant kingdom. not so much in animals…” (~28:00, paraphrased)

Recently, we published a report on abduction of mouse corneal behaviors that highlights the different ways the phi spiral is used in this animal model. I can't speak to your second question but I believe our manuscript addresses many of your other concerns about the position of the phi ratio in science education. We immerse the reader into the discovery of our measurement, compose a working hypothesis that touches on a packing problem, and justify its selection via colligated discussion of existing literature. The main aim of the paper was to structure our inquiry so that we can come to convergence.

"The opinion which is fated to be ultimately agreed to by all who investigate, is what we mean by the truth, and the object represented in this opinion is the real.", ~ C.S. Peirce

One thing of which I would warn is that the phi ratio is expressed differently in different situations and the phi spiral is a very specific shape, with very constrained relations. Sometimes, the names get mixed and used haphazardly. That is, we often know in our heads what we're talking about during this conversation but the same usage may not apply in that one. This can create confusion for novices/students wanting to know.

Best, Jerry

Promoting convergence: the phi spiral in abduction of mouse corneal behaviors

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1) logarithmic spirals do occur in Nature. I doubt that exact golden spirals occur otherwise than by accident (i.e. with probability $0$), as I can see no physical law that would explain them.

2) clearly, no.

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