Darth Vader, Mona Lisa, and The Golden Mean :: Margins of error

I made this video earlier

Which shows that the Golden Mean is used even more extensively in Darth Vader’s helmet design than Mona herself, who is famous for it.

Darth Vader Golden Mean
Mona Lisa Golden Mean

The point (that I never get to in the video) behind all this, is not that Darth Vader is related to Mona Lisa… but that there is a margin of error in artistic applications of the golden mean. It’s not big… I’d say (at a guess) it’s around 3%. In a later post, I’ll collect a medium-ish sample-size of examples and figure out exactly what it is.

A couple of things alerted me to this… one is the nautilus shell which is always being used as an example…

Now that ain’t the golden mean. The exact ratio is closer to 290.5/219.4 = 1.324 (18% wrong)… which is miles out. Now… the measurements on Darth or Mona’s faces are nowhere near as inacurate as that – but they’re still not 100%… As I say, I’m guessing they’re about 3%. I think people operate a confirmation-bias when it comes to golden-mean stuff, so the nautilus (and others) get cited as examples… when really, they’re quite a long way off.

The other thing that makes me suspect that there’s a margin of error is the recent fuss about the iCloud logo conforming to the golden mean

They say 1.6… but 1.6 isn’t the golden mean (it’s 1.1% out)… 1.618 is closer…

So I got an official version of the iCloud logo…

The RHS circle measurements are 232.7 / 194.2 = 1.2 —–> 25%
The LHS circle measurements are 194.2 / 114.3 = 1.7 —–> 5%

Which is miles out.

Now to be fair to whoever originally blogged about this… the logo they used was different

The RHS circle measurements are 278.0 / 172.2 = 1.614 —–> 0.25%
The LHS circle measurements are 188.2 / 117.2 = 1.605 —–> 0.8%

Which is pretty close to be honest. Apple’s designers obviously went “oh noes, we’ve been rumbled. Change it, quick”.

I’m guessing that the average margin of error in oft-cited examples of golden-mean-dom is about 3% though… so to all intents and purposes, the golden ratio is between 1.67 and 1.57

Which isn’t that much… the middle one is 1.618.

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