We already see that there are purely mathematical reasons for the continuous proportion to appear in the designs of nature independently of causality, be it physical, chemical or biological: in fact the convenience of logarithmic growth is independent even of the form itself, as is the elementary fact of the discrete and asymmetric division of cells.
In this light, it would be an emergent property, just a parallel plane to physical causation and becoming. On the other hand, the idea of parallel planes with a merely circumstantial connection with physical reality looks odd, and in any case very distant from what the diagram of the Pole express so well —that no form or nothing apparent is free from dynamics.
The fact is that the connection between physics and the continuous proportion is very dim, to say the least. However we have important occurrences of this ratio even in the Solar System, where it is almost impossible to avoid celestial mechanics. A better understanding of the presence of the continuous proportion in nature should not ignore the framework defined by fundamental physical theories, nor what these can leave out.
We have three possible approaches with increasing degrees of risk and depth:
The continuous proportion in nature can be studied independently of the underlying physics as a purely mathematical question; this would be the most prudent, but somewhat limited position. The aforementioned A. Stakhov has developed an algorithmic theory of measurement based on this ratio that can be used to analyze in turn other metrological theories of cycles, continuous fractions and fractals as for example the so called Global Scaling.
This proportion can be studied according with views compatible with known mainstream physics; for example, as Richard Merrick has done, in a neopythagorean rereading of the collective harmonic aspects of wave mechanics, such as resonances, and in which phi would be a critical damping factor [7]. These ideas are totally accessible to the experiment, either in acoustics or in optics, so that they can be verified or falsified.
Merrick’s idea of harmonic interference is within everyone’s reach and understanding and it is not without depth. It can be naturally complemented with the holographic concept proposed by David Bohm and his distinction between the implicate and explicate order. Although Bohm’s interpretation is not standard, it is compatible with experimental data. The harmonic interference theory can also be combined with mathematical theories of cycles and scales such as those mentioned.
Or, finally, one can consider other more classical theories that differ from the mainstream but which may provide deeper insights into the subject. Within this category, there are various degrees of disagreement with the standard theories: from just a wider understanding of thermodynamics, to in-depth revisions of classical mechanics, quantum mechanics and calculus. We could say that this third option is not that speculative, but rather divergent in the spirit and the interpretation.
Here we will focus more on the third level, which may also seem the most problematic. One could ask what is the need to question the best established physical theories in order to find a better ground for the occurrence of a constant that maybe does not require them. Furthermore, the first two levels already offer plenty of room for speculation. But this would be a very superficial way of looking at it.
We cannot delve into the presence of the continuous proportion in a symbol of perfect reciprocity ignoring the question of whether our present theories are the best exponent of continuity, homogeneity or reciprocity —and in fact they are far from it.