The Eternal Melody of Pi Base 12

[Angleae]

[snappyturtle]

1. Lovely. Have no idea what's going on here BUT I enjoyed the listen. Thanks. nt

[EOTE]

2. How interesting. Reminds me of Carl Sagan's book "Contact".

In it, the protagonist Dr. Arroway creates a program that calculates pi in different bases upon the suggestion she received in an alien signal. When she calculates pi in base 11, after a ridiculous amount of digits (10^20 I believe), she starts to see a repeating pattern of 1s and 0s. The ones and zeroes form a circle of sorts when arranged in a particular square. When the aliens are presented with this information, they state that even they aren't sure of the significance of that, but they believe it to be a signature incorporated into the universe itself. It's always been one of my favorite books and I've had a fascination with pi ever since.

[hunter]

3. The Bailey–Borwein–Plouffe formula, discovered in 1995, seems to make pi less mysterious.

To me, anyways.

http://en.wikipedia.org/wiki/BBP_formula

Many of the "mysteries" we've attributed to the digits of pi become artifacts of the number base we are counting in.

In a counting system based on powers of two, finding any digit of pi is not complicated. You don't need to know all the preceding digits.

What the The Bailey–Borwein–Plouffe formula says to me is that the familiar base 10 representation of pi, 3.1415926... expresses a "mystery" of 5 (since 10 equals 2 times 5.)

In the base 12 representation of this music, any "mystery" we experience is a mystery of 3 (since 12 equals 2 times 2 times 3.)

A base 11 representation of pi, as in Sagan's book, if it really did produce such a result, I'd consider a mystery of 11, not of pi.

[EOTE]

4. In the book, it was suggested it was more a "mystery" or "signature" of the universe, rather than a

particular number. It was part of what led Dr. Arroway to reconsider her position as an atheist (along with her having to try to convince a governmental panel of her experiences based on faith rather than any scientific basis).

As far as I know, there have really been no patterns noticed in pi calculated under any base, though there have been quite a few repeating numbers such as 9 consecutive 6s, 7s and 8s at ridiculous lengths when calculated in decimal. As for the mystery of the base rather than of the ratio itself, I guess I'd have to consider that a chicken or the egg scenario as pi in base-11 would be utterly meaningless if it weren't for it expressing the ratio of diameter to circumference.

[hunter]

5. The way I look at it...

... the The Bailey–Borwein–Plouffe formula describes a "pattern" in the digits of pi.

In number bases other than powers of base 2 (binary, quaternary, octal, hexadecimal...) this pattern is obscured.

[eppur_se_muova]

6. Thanks for that ref, it led me off into some interesting directions. nt