There's talk about ever-decreasing circles when things get worse on repetition; they made a TV show about it in the Eighties. Does that mean our discourse follows ever-increasing circles when things get better? I've had a few scenarios shadow me through life that I'm clearly supposed to learn from, and right now I'm studying geometry in the context of application to such things as sunflowers.
The Fibonacci sequence, being what you'd call 'irrational', is there in nature at every turn, from shells to pine cones, with the ratio between the numbers of the sequence being known as the Golden Ratio, being represented by the Greek letter Phi, and being everywhere we look.
The Fibonacci sequence, being what you'd call 'irrational', is there in nature at every turn, from shells to pine cones, with the ratio between the numbers of the sequence being known as the Golden Ratio, being represented by the Greek letter Phi, and being everywhere we look.
On the trail of evidence for natural geometry, it came to my attention on looking for examples of irrational numbers that (coincidentally or otherwise) Schroedinger's Wave Equation is also represented by the Greek letter Phi; in Comments to the link attached, you'll find Jonathan noting that It is commonly believed that waves make up the sub-atomic particles which may be the reason why Schroedinger (or someone) chose it to apply to quantum field theory. However, as evidenced by the Wiki entry here on what's called the 'Schroedinger functional', anything that doesn't readily lend itself to renormalisation is still finding it hard to be fashionable.
Schroedinger devoted himself largely to causality and chance (or lack of it) in natural law, and a comprehensive precis of his thought process can be read here. His dwelling on such matters led him to create a wave equation which smoothly evolves through time, just as the Fibonacci sequence smoothly evolves the growth and development of natural things like thistles, roses, and spiral galaxies. The unpopularity of Schroedinger's wave equation in preference to something that can be algebraically calculated in avoidance of those pesky infinities (noting that in Wiki's Fock space definition the author doesn't even mention Schroedinger) says a lot about the mind set still prevalent in quantum mechanical fields, and not a lot about the logic of applying schemes universally adopted by Nature to the quantum paradoxes pondered upon by Man. Men, then. Usually, anyway.
What does this mean for us? That depends on your intuitive relationship with coincidence, or any leaning you have towards synchronicity being circumstantial evidence for powers greater than our own. Fibonacci, Schroedinger and other minds of historical note have been pondering and surmising on the underlying laws of nature for a long time now, and with quantum mechanics at the front of our potentials for New Physics, there's no time like the present for linking the facts as they stand with the fortunes inherent in our own world-line. Time is in reality a far cry from the lineage of onward-marching arrows we mistook for something other than entropy - the wave form we ride may well perpetuate in resonance to the Fibonacci sequence and be dancing merrily to Schroedinger's tune. Would this make sense of life's events coming back to haunt us from time to time? Could it be that what we are given (to experience) and what we learn as a result are in keeping with a pattern at the baseline of creation? For it seems to me that every time we dovetail a piece of life's puzzle with a quantum mechanical principle, we come up with freedoms of infinite probability and an allowance in the small print to accept things as they are, no need to struggle against What Is. Life is hard enough without taking the full weight of its variables on our own shoulders. Some things, they say, are meant to be. Why stop at Some, when the irrationality of All is so evidently preferred by Nature?
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