Golden Ratio in linguistics?

[jess tauber]

Some of you may remember my postings regarding putative parallelisms between language and genome/proteome. If fact such parallelism seems to extend down to the level of the periodic table and possibly lower still.

Now, Golden Ratio patternings have been found at all sorts of levels of material reality, from relative counts of different atoms in coordination compounds and metallic alloys (including the famous quasicrystals which have a relation to Penrose tiling) all the way through many growth regimes and resulting distributions of component parts in plants and animals, up through the orbital resonances of celestial bodies and the distributions of arms in spiral galaxies.

I've found myself robust direct mappings of Fibonacci, Lucas, and other phi-convergent number series to the periodic table, when these numbers are taken as atomic numbers. In addition there are also strong connections to the Pascal Triangle diagonals, which motivate the Fib numbers (which are simply sums of samplings across Pascal diagonals).

Recently I discovered online research by others which show similar Golden Ratio links to genomic structure, on the one hand, and also possibly to linguistic structure, on the other (currently a graduate student at Arizona is pursuing this).  All this seems to feed back onto the increasingly large numbers of parallelisms in structure and function mentioned at the top.

So, I'm starting to wonder whether all complex combinatorial systems make use of such organizational motifs. Bottom-up we would have a quantum-like set of discrete numerals drawn from the phi-convergent series, whose ratios approximate the Golden Ratio. At the other extreme would be a top-down, more continuous system, akin to what we find with relativity, whose effects on electrons distorts atomic structure and behavior from what one would expect based solely on the solutions to the quantum equations. Parallels here would be the rhythmic, prosodic structure of language, which dominates syntax, and similar structures within genomes having to do with repetitions, spacings, timings, and so on. These latter systems would utilize the actual Golden Ratio rather than approximations.

In between we would have a vast landscape of negotiations balancing the opposing extremes, constantly shifting (perhaps in synchronized, multiple cycles at different scales), leading to what we would call 'typology'. There would be constant tension between the extremes, with imposition, selection, etc. going on.

Anyway- I don't expect much commentary here. I know most of you find me good for the occasional belly laugh, and a candidate for the Rodney Dangerfield Prize.

Jess Tauber
phonosemantics at earthlink.net