PHI.........what an amazing number. I have long been fascinated with it. My question is this: Is this number divine or a phenomona? Naturally, anyone who thinks it divine in nature would assume certain intelligent creation principles and/or mystical premises. However, I'm not here to beat that dead horse once again, I am simply interested on peoples thoughts on this amazing mathmatical principle. Aetheist mathmaticians will have to pardon my consideration of it being either divine or a phenomenon, as I do not intend to infer the incalculability of it but rather lend understanding to the magnitude of data that would be prerequisite.
So, what to you all think? Is this proposterous number a divine guidline for the universe? Or is this simply an amusing and useful pattern which has a rational explanation? Whatever you pose, please give some rational behind it. It is my hope that this can be a fun and enlightening discussion. 😉
Originally posted by CliffLandinNo, I do not mean PI. I mean PHI. PHI is an H of a lot cooler than PI (he he......ahem, sorry). Look it up. It's a fascinating phenomona! It is like PI in the sense that it's a proposterous number. Just as PI runs on forever, PHI goes 1.618.....etc.....etc....etc....
I'm not familiar with PHI, do you mean PI. I think phi is a greek letter, but not a number.
EDIT: Where's royalchicken?
Originally posted by XanthosNZYes, yes, personally I am particularly fascinated by how it pops up in nature. Specifically, in animals ( such as humans, or ALSO in humans, whichever you prefer. 😉 ). Truly an interesting pattern of ratio.
Phi, like pi pops up in all sorts of strange places. I've got a whole book about it lying around here somewhere. It's quite good it talks about the ways in which people make phi pop up in places like in the pyramids for example.
For those who are slightly confused by some of the descriptions of 'Phi', it is defined to be:
(1 + sqrt(5))/2
or equivalently,
the unique x > 0 such that 1/x + 1 = x.
http://mathworld.wolfram.com/GoldenRatio.html
Kind of interesting, but I wouldn't say it's mysterious - it's actually a rather well-understood number. As for its frequent occurrence in nature, perhaps some recursion formulae for Phi describe common natural feedback loops.
By contrast, some other well-known and 'special' numbers are still quite poorly understood. For example, it is still not known whether or not pi/e is irrational!
Originally posted by AcolyteNot to hijack but pi is irrational.
For those who are slightly confused by some of the descriptions of 'Phi', it is defined to be:
(1 + sqrt(5))/2
or equivalently,
the unique x > 0 such that 1/x + 1 = x.
http://mathworld.wolfram.com/GoldenRatio.html
Kind of interesting, but I wouldn't say it's mysterious - it's actually a rather well-understood number. As for its frequent occu ...[text shortened]... quite poorly understood. For example, it is still not known whether or not pi/e is irrational!
http://www.mcs.csuhayward.edu/~malek/Mathlinks/Pi.html
So is e.
http://mathforum.org/isaac/problems/eproof.html
Originally posted by AcolyteAdditionally, Phi is the limit of the ratios of consecutive Fibonacci numbers. What is interesting is that if we take the Maclaurin expansion of the reciprocal of the quadratic expression you give, the coefficients will be Fibonacci numbers and the radius of convergence is 1/Phi, the other root of your equation. This is a special case of a more general phenomenon though, and doesn't tell us anything that makes Phi especially interesting.
For those who are slightly confused by some of the descriptions of 'Phi', it is defined to be:
(1 + sqrt(5))/2
or equivalently,
the unique x > 0 such that 1/x + 1 = x.
http://mathworld.wolfram.com/GoldenRatio.html
Kind of interesting, but I wouldn't say it's mysterious - it's actually a rather well-understood number. As for its frequent occu ...[text shortened]... quite poorly understood. For example, it is still not known whether or not pi/e is irrational!
Actually, for what it's worth, in a lecture on linear difference equations, my lecturer, a physicist, referred to the mystique surrounding Phi as a 'complete load of bollocks' [he may have said 'load of complete bollocks'].
Last year in Astronomy Magazine, I came across a "news" blurb from either Nature or JOS or one of the big sci pubs.
The essence was that some bright guy had come up with a formula to explain the distribution of stars in spiral arms of known spiral galaxies to try and explain why the "further out" stars are moving way too fast.
The method was simple right angle triangles kind of analytical geometry stuff as near as I can tell. And that 'ain't too near. Trust me.
After all was said and done, guess what the final ratio of mass to area turned out to be. Good old PHI. Or at least it was used in the final publication of the theory. Don't ask me to explain. I wouldn't have a clue.
They are now doing the same computations on distribution as a function of motion about the center of mass of "Large Galactic Groups".
Any bets that old PHI turns up again?
Whenever I see a "5" in any explanation of the universe, and nature seems to comply with it, I wonder if the five suspected force carrying energies/particles are not at the bottom of it all. But then... until we unite Quantum to Relative, we will never know.
Originally posted by StarValleyWyIf you ever come across the article again, let me know where it is from. This is the kind of tid bit that make me fascinated with PHI. and I love to have my sources handy. Thank you SVW. 🙂
Last year in Astronomy Magazine, I came across a "news" blurb from either Nature or JOS or one of the big sci pubs.
The essence was that some bright guy had come up with a formula to explain the distribution of stars in spiral arms of known spiral galaxies to try and explain why the "further out" stars are moving way too fast.
The method was s ...[text shortened]... not at the bottom of it all. But then... until we unite Quantum to Relative, we will never know.