What about the Lamin A /C protein in progeria. I think that progeria is an angular miscode with elephants. Can the Fibonacci be sequenced, to determine age. Comparing the chromosomal filaments of the nucleus. Can the golden ratio itself bring about the differentials this desease causes? Are they elephants in humans or humans as elephants? This is a protein filament structure yet I find no one sequencing the golden ration.. Could we be missing out on a true human structure sequencing map of human / animal of plants and thing- differences.? (Liber Abaci) . Within filament and fibers, everything spirals intelligently designed, structured, mathematic is the true language. I know of the ratio found in cells, bone, so why not in the nucleus filaments. 🫶

Take any rational approximation of Phi, for instance 13/8 and you know that 8/13 + 1 is not 13/8 again but 21/13

All good points about the uniqueness of the golden ratio that makes it suitable for phyllotaxis.

I think though that you misunderstood the point of the discussion on the statement, “Nothing can be the Golden Ratio because it is irrational.” There are certain writers on the golden ratio who try to say that NOTHING in the material world can “be” the golden ratio for the simple reason that the golden ratio has an infinite number of digits and nothing in the material world could be that accurate. So by their logic, the golden ratio cannot appear in phyllotaxis because any angle that one claimed to be a golden angle would be off by some small amount and thus not really be a golden angle.

To me this is a rather pointless argument. As you noted, the golden ratio and golden angle DO appear in phyllotaxis. The small differences make no difference in the application or in our understanding of the principles involved. By their logic, we might as well say that we can’t have circular wheels because the circle will never perfectly accurate. We can’t even drill a 1″ hole because that too will not be perfectly 1″. It’s just the nature of the material world, and has no meaningful impact on our application of the concepts.

Specifically, the reason that nature chose the Golden Angle for the phyllotaxis, is that it is the most irrational number turn of a circle that solves the engineering problem of distributing points around a circle in such a way that seeds, leaves or petals are less likely to interfere with each other.

Obviously, a rational number cannot be used for this purpose because it would create ‘spokes’ at each partial turn that corresponds to the common divisor of the angle chosen, for example, 1/3 or 2/3 of a turn would create three spokes at 0, 120°, 240°.

Other irrational numbers are usually not suited, because in general, they usually have pronounced spokes at places early in the sequence, that eventually slowly spiral around the circle.. (This can be verified with the Wolfram applet linked in the blog post)

The Golden Angle wins out over other irrational numbers, In that it produces the most even distribution with low numbers of iterations of the phyllotaxis process. I’m not sure how to succinctly prove this mathematically, but consider the continued fraction representation of the Golden Ratio: 1+(1/(1+1/(1+1/…))) which implies a uniform smoothness to its irrationality..

This can also be used to explain why we see Fibonacci and Lucas Numbers in the count of spirals originating from the origin point of a phyllotaxis process, because the ratio of adjacent members of these sequences rapidly converge to the Golden Ratio, these spirals serve as the ‘spokes’ that approximate it.

planetary rotation
optimal planetary arrangement
planet distance from the Sun → link to Newton’s Law of Universal Gravitation
planet type
hypothetical planet

https://liberabaci.net/