Did you know that Pi is not a random number? It is exactly Pi and no other number is like that. Yet the digits on down the line have been tested as to be completely random. How do you like that?
I thought about these things before, and you had me think them over again.
I see Pi as a ratio. A conversion factor between straight and curved lengths. The ratio between radians and general numbers. In a way it's no diffrent than conversions between units, such as pounds and grams. You don't expect there to be a nice value, it's a bunch of seemingly arbitrairy digits. Likewise I don't find it very suprising that there is no order to be found in the digits of pi. The only diffrence is that Pi is a purely mathetimatical concept, where as units in science are closer related to reality. (scientific units are less abstract than mathematical units?)
What suprises me isn't that pi's digits are seemingly random. What suprises me is how reoccuring pi is. It comes back in places I'd never expect it, places that have nothing to do with eachother. The gamma function is a continuous variant of the faculty function (!) used in statistics. It's value at 1/2? The square root of pi.
Another thing that suprises me is how there are so few fundamental numbers. Pi, i and e are all I could come up with. Most other numbers either don't seem important or can be expressed in terms of these fundamental ones and regular numbers.
Now I'm not sure whether or not to count i, the imaginary 'unit'. In a way it's not a number, it's a unit. Then again it expresses exactly what I mean. It's the conversion factor between regular and imaginary numbers, just like Pi is the conversion factor between regular numbers and radians.
Just like Pi, e is transcendental number. It occurs naturally, and it occurs frequently in ways that seemingly have no relation to eachother. For example :
d(a^x)/dx = B* a^x.
(df/dx used for derivation). This means that the derivation of a^x is itself times an arbitrairy number B. e is the number 'a' so that d(e^x)/dx = e^x, that is to say the number B becomes 1 and the derivate of e^x is itself. It is this property that makes e (and e^x) so important.
Yet at the same time, this number can be expressed through the simple series :
e= 1 + 1/1 + 1/(1*2) + 1/(1*2*3) + 1/(1*2*3*4) + ... (= aproximately 2.7)
And then there's the way how these fundamentals are connected. Eulers equation is the best example of this.
e^(i*Pi) = -1
Now look at it in terms of digits. How does 2.718^(3.14159*i) = -1. It makes no sense if you look at it this way. It makes sense when you look at the properties of the numbers. Digits don't matter, they're only one representation, something you see on the surface.
I realise I've gone completely offtopic. However, considering the original topic was a complaint about how this forum is hard to find your way around, I guess i've proven OP's point by derailing into maths... For these reasons I hope this paragraph counts as a get-out-of-jail-free-card for derailing.
Edit : somehow, Pi managed to occur in a complaint thread. It does really show up everywhere!
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. I stand by it being cluttery and not wonderful to navigate (could be worse).
