Measured Against Reality

Monday, March 05, 2007

Forget About Phi

For some reason, there have been a few “golden ratio” websites popping up for the past few days. I was going to let the first one go, but when the second one popped up I had to say something.

First, what is the golden ratio? It’s the ratio that you get if you divide up a line into two sections such that the ratio of the larger to the smaller is the same as the whole to the larger. This comes to about 1.618, and is often called phi. You can also approximate it by dividing two consecutive Fibonacci numbers.

What’s so important about this ratio? That’s the thing, there’s nothing special about it at all. Many claims are made about it (see the first link), but none are true. It’s not in the Parthenon, it’s not in any Renaissance paintings, it’s really not anywhere. It’s not even the most pleasing ratio to the eye, studies asking people to pick out the most pleasing rectangle (whatever that means) do not find ones involving phi to be the most pleasing.

Don’t believe me? Pick up The Golden Ratio: The Story of Phi, the World's Most Astonishing Number by Mario Livio. He discusses where phi does and does not show up, and it’s almost never anywhere sensational. It is found in certain places, such as plants and crystals. But phi was first defined because it appears in the pentagram, so it shouldn’t be entirely surprising that a geometric ratio appears in things constructed geometrically, like crystals.

As for plants, it most frequently appears in the ratios of the number of degrees between two leaves on a stalk. Livio hypothesizes that this is an evolutionary adaptation, that because phi is irrational it allows the most leaves to be exposed to the sun at once.

I can’t say so much about the second link, but since phi being pleasing optically is bunk, I’m skeptical that it’s pleasing musically as well.

Another thing to note is that nothing is ever “equal” to phi, just “close”. Often 1.6 is close enough for people to claim that phi is involved. When you think about how much wiggle room there is in measuring lengths (or times) and how many different places you can possibly measure, something “close” to phi is going to come up frequently. Don’t buy into it, it’s nothing special, just someone grasping for straws.

Besides, phi isn’t even fundamental. It’s not in any physics equation, or any equation at all (as far as I know). Marvel at pi or c or h or alpha or e or the other e, but not phi. Phi just doesn’t deserve it.

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  • "Phi isn't even fundamental. It's not in any physics equation at all..."

    Are you kidding?

    Phi is a a root of the polynomial x^2-x-1=0. It satisfies the property that its reciprocal is one less than it and it gives the limiting ratio of subsequent Fibonacci numbers.

    Do your homework next time.

    By Anonymous Anonymous, at 7:42 PM, March 05, 2007  

  • That's not a physics equation. Who cares that it's a root of a polynomial?

    And I knew both of those properties, and mentioned one. It still doesn't make phi important or interesting, it is neither.

    By Blogger Stupac2, at 7:49 PM, March 05, 2007  

  • "Besides, phi isn’t even fundamental. It’s not in any physics equation, or any equation at all (as far as I know)."

    Everyone knows that E=mc^2 and KE =
    1/2*mv^2. When the mass of a body reaches 1.6180...*m (phi*m) then its KE = mv^2, i.e the familiar classical denominator 2 has reduced to exactly unity at speed (0.6180..)^(1/2)*c. Special Relativity physics equations can involve phi.

    By Anonymous Anonymous, at 2:06 PM, April 28, 2007  

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