Write the following statements on a rock: Randomness Does not Exist. The Key To The Unified Field Theory, And God Himself, is Pi.
Buffon's Needle --easily one of the oldest tests of randomness, and problems in the field of geometrical probability-- yields one of the most amazing things this writer has ever seen.
Because from the so-called random output of the test, the same result can consistently --invariably-- be extracted; and that is Pi.
Buffon's Needle involves dropping a needle on a lined sheet of paper and determining the probability of the needle crossing one of the lines on the page.
3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679. It's like it never ends!!
In this case, the length of the needle is one measured unit (we'll call it 'A') and the distance between the lines is also one unit ('B' we'll call it). There are two variables, the angle at which the needle falls (the variable theta, for ease of understanding) and the distance from the center of the needle to the closest line ('D').
Theta can vary from 0 to 180 degrees and is measured against a line parallel to the lines on the paper. The distance from the center to the closest line can never be more that half the distance between the lines (obviously, because that means there's a closer, adjacent line).
Now, from however many needle drops one does, simply take the number of drops and multiply it by two, then divide by the number of hits, or:
(number of hits)
Try it one hundred, ten thousand or one million times, and calculate the result via the formula above.
IT IS ALWAYS WITHIN 2% OF PI.. EVERY TIME.
Using a very handy Java app created by the University of Illinois, I've performed the test 5000 times. Here's my results:
Number of needle drops: 1,000
Number of hits: 630
Drop / Hits: 1.5873016
Length = 1"
Total drops x 2 / hits = 3.17460
2,000 drops - 3.14119
3,000 drops - 3.17331
4,000 drops - 3.16483
5,000 drops - 3.14190
Then, just for sh-ts and giggles, 100,000 drops: 3.14930
So what does this mean? Well, if a seemingly random series of events (the needle drops) yields a predictable result (a formulaic result near Pi) can it really be considered random?
Clearly, randomness can not exist. Or, more importantly, if true randomness does exist, or ever has existed, we can't recreate it.