Mostly itâs just fun finding images trying to show how something is beautiful because the golden spiral is crammed in there somehow.

Ah, yes, this photo is beautiful because phi is in it. Magically.

This sentence, however, had nothing to do with the price of eggs:

Except thereâs a problem. When you do the math, the golden ratio doesnât come out to 1.6180. It comes out to 1.6180339887âŚ And the decimal points go on forever.

âStrictly speaking, itâs impossible for anything in the real-world to fall into the golden ratio, because itâs an irrational number,â

The fact that itâs an irrational number is irrelevant. Itâs impossible for the ratio of any two things to be *any* specific number, an an arbitrary level of precision. Why would a ratio of 0.5 be any easier? After all, itâs actually 0.50000âŚ to an infinitely many digits.

I bet the introduction of retina screens increased the magnitude of the phi issue by 100.

What from 2300 years ago isnât bullshit? Seriously.

Itâs irrelevant for another reason. If youâre only measuring to 1% accuracy, whatuse is the third decimal place? Racking up all those digits is nothing but a distraction; in freshman engineering we learned to discard them in favor of âplus minus.â

But the bullshit factor is more interesting. I have noticed golden spirals superimposed over dozens of pine cones and seashells that *donât actually fit the spiral.* Also, a great many ancient temples donât fit. Not just like 1% off, but like completely different.

That said, isnât a blank white sheet of 8-1/2 x 11 seductively beautiful?

I havenât replicated this experiment, but a pioneer in neuroscience Warren McCullough tells this story in his memoirs of experiments he performed, in which subjects are able to construct a rectangle by setting controls in a display. While he was a skeptic, he found that his subjects could adjust the ratio to the golden ratio with much greater accuracy than other ratios. He had no explanation, and I donât think anyone since has, but if I had to make an informed guess Iâd be looking at something priviledged about irrational numbers in terms of the dynamics, and that feedback mechanisms in our perception action loop may be able to feel that out. There are mathematical studies of the âcircle mapâ where you can show that winding ratios have a distinctive critical slowing down behavior.

Or believe the fast company guyâŚ

I am not a designer, and I certainly canât argue with the declaration in the OP that actually pleasing shapes and designs are not actually based on the Golden Ratio, but I have to object to the general trashing of the concept.

Beauty is not solely perceived by the senses. *Elegance*, as used in mathematics, exists in the realm of the ideal.

UmâŚ Archimedes developed the water screw 2300 years ago? I guess thatâs sort of cool. I mean itâs not bullshit anyways.

Also Eratosthenes was kind of a badass scientist type:

Many things particularly in mathematics, but as the article points out, the idea that this ratio is so pervasive in beauty isnât really even an ancient idea. People like Aristotle talked about the golden *mean*, the balance between excessive indulgence and restraint, and it got mixed up with the ratio later.

And yes, people have made up all sorts of nonsense about it - not just overlaying it on photos without regard to whether it lines up or makes sense, but things you shouldnât even need a picture to know are ridiculous:

There is one place, though, where the golden ratio legitimately comes up, which is in the phyllotaxis of plants. When leaves spiral around a stem, or seeds around a flower head or cone, the rotation from one to the next is very frequently in a proportion approximating the golden ratio. Sometimes very well, to the point where you get parastichies in very particular ratios like 144 to 89.

And there is solid mathematics behind why so many things converge on this irrational number, to do with things like packing or entropy. I think itâs a very interesting look at the mathematical design of living things, and itâs a shame it gets hidden behind so many other things that are completely made up.

Why would this have anything to do with there being âsomething privileged about irrational numbersâ? Most numbers are irrational. And when I say most, I mean practically all of them. Rational numbers are an infinitesimally small portion of the set of all numbers.

I thought everyone knew this. I thought it was totally obvious to anyone with a background in math or art that humans are not precise measuring devices, and while the golden ratio may be a best a stand-in for âEverything else being equal, people prefer rectangles that are not to close to a square, but not to long and skinny eitherâ, the mathematical meaning behind the irrational number phi has nothing to do with anything. You could pick pi/2 or 16/10, or any other number in that ballpark. The golden ratio is just a particular irrational number with an interesting geometric property that happens to fall in the sweet spot.

The atomic theory is older than that, and it still stands.

ErâŚ what about the atomic theory from 2300 years ago stands, exactly?

This is not going to be good for sales of my upcoming book, â1.6180: How to Use the Totally Legitimate Golden Ratio to Live a Completely Rational and Aesthetically Pleasing Life.â

Oh well. It only took 23 years to write. Plus, Iâm almost finished with my latest manuscript: âEveryone Gets Killed at the Red Wedding: A Guide to Using the Internet Without Seeing a Single âGame of Thronesâ Spoiler.â

Right; thatâs like saying âstrictly speaking itâs impossible for anything in the real world to be spherical because Pi is an irrational number.â

Sure, if you have precise enough instruments youâll find that any given bubble or planet or whatever isnât perfectly round. That doesnât mean âspherical forms occurring in natureâ is a bogus concept.

Electrons seem to be perfectly spherical, at least to our current ability to measure them.

Thank you. As a designer and artist, I have always found this to be a bunch of silly woo.

Exactly. Not sure how the spiral replaced the ratio.

Itâs also useful as an approximation in anatomy, especially for creating hand-like size stepdowns

For example, using real math and physics, you can model the growth of leaves. (Which helps one to figure out what the important factors influencing leaf shape.)

The spiral is confusing because it seems what we are really supposed to be paying attention to is all of the implied rectangle pairs. If you look at just one pair, itâs not far off from the ârule of thirdsâ and what both have in common is âwe often like the subject offset from the center.â