

The Golden Ratio is Evil (and why, in Clojure) - ihodes
http://copperthoughts.com/p/the-golden-ratio-is-evil/

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gjm11
Meh. It's "evil", supposedly, because if you add up the first N decimal digits
of its fractional part then, for carefully chosen N, you get 666, the Number
of the Beast.

I say we should be using binary rather than decimal -- ten is a terribly
arbitrary number -- in which case, of course, _all_ numbers are "evil" other
than a few dyadic rationals.

Here's a better reason why the golden ratio is evil. As you know, Bob, in
mediaeval times the musical interval of a tritone -- three tones, or six
semitones -- was called "diabolus in musica", _the devil in music_. It was
called that because it's a highly discordant interval; in equal temperament
(which of course they didn't have back then, but hush) it corresponds to a
frequency ratio of sqrt(2). And why does that sound highly discordant? Well,
basically because there's no simple rational number that's a really good
approximation to sqrt(2); for much much more about what's going on here, put
"William Sethares" into Google and consider buying his book. In fact, in a
certain sense sqrt(2) is the second-worst-approximable-by-rationals irrational
number, which is related to the fact that its continued fraction is
[1,2,2,2,2,2,2,...]. And what's the worst-approximable irrational number,
which would produce an even more dissonant musical interval -- a maximally
dissonant one -- something even worse than the devil himself in music?

Why, the golden ratio, of course. Continued fraction [1,1,1,1,...]. Evil
incarnate.

(Note: there are a few half-truths in the above, but only for convenience of
exposition.)

~~~
ihodes
Oh that's pretty neat! I didn't realize the connection it had to even
temperament tuning.

------
cicada
The first 144 digits of the fractional part of pi sum to 666.

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onoj
"golden ratio" nonsense. The words never link to the correct maths. It is
evil, but not rational. <http://www.lhup.edu/~dsimanek/pseudo/fibonacc.htm>

------
japherwocky
I think there are about 666 parentheses in those code examples.. I don't get
the appeal of Clojure?

~~~
ihodes
You don't really see the parens after a while. Clojure's appeal goes beyond
its syntax, as I'm sure does whichever language you prefer.

Curiously, the equivalent code in most other languages has about the same
number of parens.

~~~
substack
For fun I was whipping up some haskell one-liners as I read along.

You can just do:

    
    
        let fibs = 1 : 1 : [ fibs !! n + fibs !! (n - 1) | n <- [1..] ]
    

for the Fibonacci sequence and

    
    
        take 10 $ iterate (succ . recip) 1
    

for the first 10 iterations of the continued fraction.

To me these read much more clearly but then I haven't written anything big in
a lispy language yet.

~~~
ihodes
There are all sorts of ways to do it; for instance, I really like the
following:

    
    
        (def fibo (map second 
                       (iterate (fn [[x y]] [y (+ x y)]) [0 1])))
    

I just went with a different version for the article to show another way of
doing it that might be clearer to someone new to Clojure. As for
understanding/ease of reading, the Haskell version is a little more alien to
me, but that's because I haven't spent much time in Haskell.

Once again, for your CF ex:

    
    
        (take 10 (iterate (comp inc /) 1))
    

Which gives ratios in Clojure, not doubles. Both elegant solutions,
definitely. I just wanted to use my GCF, which could probably be made to look
a little nicer as well. This post was more about playing around with the
Golden Ratio than writing sexy code (though admittedly, I probably could have
done better in many places!)

Haskell is a really cool language: I'm making my way through Real World
Haskell right now!

