PolySciFi Blog

Update
I offered my co-blogger a gold star if he completed a proof to the Neel hypothesis at the bottom of this article. I thought I would open up this prize to everyone. Should anyone else complete the proof before Thason and feel like driving to Blacksburg, I'll give them the gold star instead.

Original article
I ran across a number of math related articles at about the same time, so I thought I would share (being a dork and all)...

p
Pi is typically the first irrational number a person learns in school and is probably the most frequently encountered irration number. So it's of little wonder that pi works itself into popular culture. For instance pi shows up as the symbol for a shadowy group in The Net and as the title of a movie.

Those with a sci-fi background may be familiar with the sci fi stories where the universe's creator has embedded a message to His creation somewhere way down in the expansion of pi. This is perhaps most famously considered towards the end of Sagan's Contact (BTW, that's a link to the full text of Contact).

While an intriguing concept, it's also poppycock. At least that's the inference I take away from this article in Nature where the authors claim that pi contains all possible sequences of whole numbers and further that all sequences of length N occur with equal frequency.^1. So if there's a message from God in pi, then so is every other possible message from God. So if deep in the expansion of pi you find the message, "Remember, God loves you" just remember, someone else can find "Who left the toilet seat up?"

Of course, if you feel like disproving the authors' claims, one way to go about it is examining the full expansion of pi.^2. So to help those so inclined, here's the first One Miiilion digits of pi. If that's not good enough, then here's the first 50 million digits of Pi. If that's not good enough for you, you can always modify this Fortran code which is supposed to be good for 2^24 digits (about 1/3 of 50 million :().

Riemann Hypothesis
Via Marginal revolution, I saw this article on the Riemann Hypothesis being proven (the proof). In addition to the potential for a $1 Miiiilion prize from the Clay Mathematical Institute for proving the hypothesis, I think the Riemann Hypothesis is cool because it is directly linked to the Prime Number theorem. One version of the prime number theorem states that given an integer n, there are approximately n/ln(n) prime numbers less than n. Mathworld has a good discussion of the Riemann hypothesis and prime numbers.

With all that in mind, I now humbly offer the Neel hypothesis.
Every prime number appears as a subsequence of the the decimal sequential expansion of pi. (like 3, 41, 5, 59 appear in the first in the first six digits of pi - 3.14159).

Based on the material presented in this post, the proof is pretty easy to construct should any one like to attempt it. No prize money, though.

Footnotes
1. This would also make pi an ideal source for a random number table.

2. This is, of course, a fool's errand. There are an infinite number of digits in pi, so it's not possible to compute a full expansion. Further, no matter how many digits of pi I give you, you're really no closer to finishing the expansion.
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