The golden ratio is not particularly significant "at the quantum level", though it shows up here and there, like lots of other numbers.
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The only place I've seen it appear is in "Fibonacci anyons": fermions that have fusion rules such that fusing two together gives a superposition of the vacuum state and one fermion. Chaining a bunch of such fusions together gives the Fibonacci sequence https://arxiv.org/abs/0902.3275
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Why apple?
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Interesting properties of phi More at https://www.goldennumber.net/math/ pic.twitter.com/tUISBTzCPj
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This golden rectangle has been weirdly scaled. We should see squares. You might enjoy this one:https://twitter.com/panlepan/status/878018163807404034?s=19 …
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Most of these claims are bunk. See, e.g., Markowsky's "Misconceptions About the Golden Ratio" or
@profkeithdevlin's blog post and linked talk: http://devlinsangle.blogspot.com/2017/04/fibonacci-and-golden-ratio-madness.html?m=1 …Thanks. Twitter will use this to make your timeline better. UndoUndo
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Golden ratio is awesome φ=(1+√5)/2 One can see it when they evaluate integrals. Some examples:pic.twitter.com/3eopWm7HwX
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We JUST talked about false myths of the Golden Ratio in my number theory class, couldn't you have tweeted this a few days earlier to give me a nice example of how prevalent these still are?
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Does it or are we pre programmed to see it ?
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