12:35 AM -:- Posted by Allen    

The Golden Ratio

Gerald Klaas comments on mine and Fred Smart's discussion of numbers, particularly the Fibonacci Sequence.

In particular, Gerald says, I was surprised that neither Fred nor Allen referred to the ratio as The Golden Ratio.

Or, as it is also known, the Golden Proportion, the Golden Section, and as I originally encountered it, The Golden Mean.

Golden or otherwise, I can't begin to describe my own amazement the first time I (wrote and) ran a little program designed to calculate F.numbers and then for each one before going on to the next, divide each pair both forward and back; and there, in the middle of my screen, these two sides of the ratio resolved toward a mirrored perfection, closer and closer to each other after the decimal as the number pairs grew in magnitude, until finally my screen ran out of room to display the minute variances tens of digits out.

I may still have the Visual Basic (or was it Quick Basic) code for that little experience, lying around on a disk somewhere, maybe holding up the odd leg of a coffee table or something.

I can't speak for Fred, but I didn't go that far with the discussion (it actually took place by email) because I didn't have all year that day to have the discussion that the subject deserves every time one thinks of it. Meaning, every time *I* think of it, in a flash within my mind I view a couple hundred universes of correlations and coincidences, and if I try to tell anyone about it, the world dissolves into Ylem (primordial superconscious foam), and I end up sitting there totally absorbed without words, much like an old friend used to do right after he'd shout out, "My God, I have to tell you this!!!", on LSD.

You see, I secretly exist in a metaphysical stasis of AllThatIs, a zero-sum infinity in which all things happen at all times everywhere, wherein my hobby, if you will, is discerning the initial conditions and patterning considerations upon which particular semblances of order mainfest in sensitive dependence, the primary of which in this local universe appears to be described by the Fibonacci Sequence.

So: had I gotten started, I would no doubt have said (written) something like what just got written, and I'm not so sure that anyone really wants to hear it.

Anyway, the problem with that kind of thing is, the instant you start describing it, it's already gone and a new manifestation emerges to fascinate.

Besides, the next thing you know, I'd be tempted to explain how F.Sequence resolves Fermat's Theorem ( xn + yn = zn ~n!>2 ). And I have NEVER heard anyone ask for that!

Besides, I'm not a mathematician: who'd listen?!!

Next question?