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Originally Posted by Rekna
One more oddity I just found out Phi (1.61803399) has a multiplicative inverse known as phi(.61803399). The strange thing is these are the only 2 numbers whose multiplicative inverses vary by exactly one.
Phi/phi are irrational numbers, that is they cannot be written as a fraction and their decimals go one forever without repeating. The fact that Phi's multiplicative inverse is exactly 1 less is amazing.
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No, it is a necessary consequence of the way Phi is defined:
http://www.mcs.surrey.ac.uk/Personal...html#simpledef
One definition of Phi (the golden section number) is that to square it you just add 1, or, in mathematics: Phi^2 = Phi + 1
Phi is also defined geometrically, but this definition is mathematically equivalent to the above:
http://www.dace.co.uk/proportion_child.htm
Phi is defined as the proportion that results when a line is divided into two unequal parts, such that the ratio between the whole and the larger part is equal to the ratio between the larger and the smaller part.
Visually, this definition can be represented thus:
A---------B-----C
Where the line AB is 1 unit, and where where AC/AB = AB/BC, and both ratios equal Phi:
Phi = AC/AB = AB/BC
Since AB is 1, and BC is AC-AB, we can rewrite this as
Phi = AC/1 = 1/(AC-1)
and then since Phi = AC/1 we can substitute Phi for AC and get
Phi = 1/(Phi-1)
Multiplying everything by (Phi-1) and rearranging terms quickly gives
Phi^2 = Phi + 1
Which says exactly that "Phi is the number which, when squared, equals itself plus one." The long and the short of it is that there is absolutely nothing even remotely amazing or surprising about the fact that Phi squared is Phi +1, or that 1/Phi is Phi-1; that's what Phi
means.
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Originally Posted by Rekna
I havn't seen pi, but pi and Phi are completely unreleated.
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Judging by your interest in Phi, you would love the movie pi - you just have to understand that the people who made it are idiots, and have no idea that what they are actually talking about throughout the entire film is Phi, not pi. The characters are always making Fib. spirals out of Go beads and whatnot, so while you're watching it, every time someone says "pi," just translate it into "Phi."
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Originally Posted by Rekna
So my question is how can something occur so frequently and so perfectly and not be caused by something? To me this is the single greatest fact pointing to a higher being, some sort of creator of the universe. I’d love to see someone explain Phi without acknowledging the very likely existence of a divine creator.
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I do think God probably exists, but your argument is spurious, Rekna. That constants such as Phi or
e do exist in nature doesn't necessarily mean that God put them there. It is interesting to speculate as to why they are there, but just because we have no definitive naturalistic explanation doesn't mean there
is no naturalistic explanation. This line of argument...
"X is unexplained. Therefore, X must be caused by God"
...is relatively easy to refute - there were many unexplained things in the past which have now been explained, such as the appearance of bacteria in sealed containers or the existence of live on earth, and their explanations do not invoke God. If God didn't cause
previously unexplained things, why should we think that God caused
presently unexplained things?
That stated, there are mathematical arguments out there which do suggest the existence of a God, and I worked out one of them myself at this page:
http://www.childrenofmillennium.org/philosophy.htm --> Math & God
That seems like the kind of argument you would enjoy, Rekna.
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Originally Posted by CoachAlan
I think that the commonality of phi is more than just coincidence, but not neccessarily indicitave of the existence of a Creator. There are many things about nature we do not understand, and mathematics is only in its infancy where it relates to modeling the real world. The more knowledgable we become, I think we will begin to understand better why we see phi so often.
Some people, after all, say that the architecture of the pyramids indicates a precise knowledge of pi. Others, however, say that the architecture of the pyramids indicates that they used a wheel to measure out their dimensions. Pi was simply a byproduct of that process.
As an agnostic, the jury's still out on the existence of God, but I'm not putting phi in to the evidence pile just yet.
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Ahhhh. Agnostics see things so clearly.
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Originally Posted by rukkyg
Because everything is quantum, it would stand to reason that there be a certain ratio that will come up more than others between adjacent or used quantum states.
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No - there could just as easily be dozens of set ratios that come up more often than others (and, in fact, there are).
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--Mark