PROTOPLASMIC OOZE

(Originally written 6/30/18)

For the past several years, I have been reading about that mathematical ratio known as the “Golden Ratio” or “Golden Section.”  It has been variously defined as that “magical” number, or ratio, that often appears in nature and also appears most pleasing to the human eye when manifest in design, usually as a rectangle the sides of which conform to the ratio, known in mathematical circles by the Greek letter ϕ (pronounced “fee,” not “phi”).  My favorite source for this is the eponymous book by Prof. Mario Livio, which is indispensable reading.

The Golden Ratio is geometrically stated simply as any straight line of any fixed length that is divided into two segments, such that the ratio between the two segments is the same as the ratio that the longer segment bears to the whole line.

That ratio is about 0.62, the inverse of which is about1.62, and it is also represented by the numerical sequence known as the “Fibonnaci Series” (named after a famed Italian mathematician), wherein each number in the Series is the sum of the two preceding numbers therein, to-wit: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc.  The difference between each number in the sequence approximates the Golden Ratio after the “5, 8” segment, which is 5/8 (0.625) or 8/5 (1.60).

That, in turn, illustrates another interesting factoid that the difference between the Ratio and its inverse is the whole number “1,” and that brings me to the (tentative) conclusion that the manifestation in nature of the Golden Ratio may well be due to the fact that as an organism grows, it spreads out in all directions until it is stopped by whatever “boundaries” are in place or are generated from within.

As a rectangle, the Ratio often manifests in nature such as with the expansion of the shell of the chambered nautilus, which can be plotted as a logarithmic spiral (inclusive of the Golden Ratio), or even as leaves are radially sprouted from a growing plant stem or branch, whereby the sprouts are spaced relative to their predecessor in accordance with the Golden Ratio!