Return to the Golden Section: all problems in a new development

In the 19th century the nature of science varies considerably. The problem of structural unity of the Universe, put forward in antiquity, is revived step-by-step in its epistemological status and is provided with all scientific achievements. The idea of the Universe structural unity is confirmed by the evolutionary doctrine in biology (Darvin), by the periodic law in chemistry (Mendeleyev), by the law of energy conservation and conversion (Mayer, Joule, Helmholtz), by the cell theory (. Shwann, Shleiden) and other outstanding scientific discoveries of the 19th century demonstrating availability of intercommunication between all known kinds of matter.

The thesis about the unity of a man and nature conducted sequentially in antiquity is revived again on the outcome of the 19th century and mainly in the first half of the 20th century in the conceptual works of representatives of the "Russian cosmism" (Vernadsky, Fedorov, Ziolkovsky, Florensky, etc.). The search of invariants of the Being, the special stabilities, which found out in the whole classes of different or heterogeneous phenomena becomes the major direction of researches.

This direction of scientific research with inevitability puts forward the problem to find the objective laws of harmony. On the given background the interest in the harmonic proportion, in the golden section and Fibonacci numbers is awaked again.

In the 19th century a special interest in "phyllotaxis" problem is raised again. The special page of our Museum will be dedicated to this problem. Already in the 19th century the "phyllotaxis" is considered as the "puzzle of the alive nature". The famous mathematician Hermann Weil wrote about the "phyllotaxis" the following:

"I am afraid that the modern botanists concern to the "phyllotaxis" doctrine is less seriously than their forerunners".

In the 19th century the known German scientist Zeising attempts to formulate the "Overall Law of Proportionality" and thus once again discovers the "golden section" (we will tell about Zeising's researches at the special page of our Museum).

The "psychological experiments by Fechner", one of the authors of the main psychophysical law, got a wide notoriety in that period. "Fechner's experiments" were directed on revelation of feeling of the beautiful, harmony for the adult people. To evaluate aesthetic feelings the 10 white rectangles with the ratio of sides from 1:1 (the square) up to 2:5 were presented to all participants of "Fechner's experiments" (228 men and 119 women). The "golden" rectangle with the side ratio 21:34 was one of them.

Fechner's rectangles

By means of comparison it was necessary to put in order the compared rectangles by selecting one of the rectangles, which is most preferable since the aesthetical point of view. The experiments appeared by highly favorable for the "golden" rectangle 21:34.

In 1958 the English scientists repeated "Fechner's experiments". These experiments again appeared by rather favorable for the "golden" rectangle. The majority of participants (35%) immediately indicated the "golden" rectangle with the side ratio: 21:34. The rectangles with the ratios 2:3 and 13:23 (adjacent to the "golden" rectangle) also were estimated rather highly (20% - fir the former case and 19 % - for the latter one). All remaining rectangles got no more than 10%.

The same experiments made in children's audience gave other results. It was made from here the conclusion that, apparently, the feeling of the beautiful in its most thin and steep parties is generic only for mature persons.

Thus, the science of the 19th century returned again to search of the answer to those "eternal" problems, which were put forward still by the Ancient Greeks. There was ripened the belief that the "universal law" of a number and rhythm expressing its structural and functional parties prevails in the Universe. In this connection the interest in the "golden section" is awaked again in the science of the 19th century. And we will tell about the brightest examples of the golden section applications at the next pages of our Museum. Follow us!