As we drift further and further from the OP…
bcullman, you may not believe it, but most of mathematics does. Note that pi has many properties above and beyond being “merely” a real number.
I knew I read about this recently – it was in the last issue of Science, August 3, 2001, p.793. That link will require a registration, I think.
Mathematicians have had surprising difficulty proving that the digits of p are indeed randomly distributed, meaning that you have no information about what any given digit will be even when you know the previous one. Now two mathematicians have taken a large step toward proving p’s randomness, perhaps opening the door to a solution of a centuries-old conundrum.
I believe the article said that there were surprisingly few numbers (mostly cooked up) that they’ve been able to prove actually contain any sequence that you’d dream up.
Why, indeed? I just arbitrarily divided it that way. For that encoding scheme to make any sense we’d need some rules on how to divide up pi when we come to the “0”, “1”, and “2” digits. One sensible way is to make them proportional: when we come to a segment that starts with “1”, 10% of the time we’d consider it an “A” and another letter, and the remaining 90% we’d just consider it one letter. Ditto for numbers in the twenties. For zeroes–uh, I dunno. Looks like this needs some work.
There was a thread in GQ earlier this month addressing this question. Search for “absolutely normal” and you should find it.
I see the concept here. pi is an real number with an infinate number of digits. But does that really mean that we can find any sequence we want in that number? I have a hard time believing that “the catcher in the rye” is hiding somewhere in pi.
It seem more likly that while there are an infinate number of digits to pi, that certain squences never come.
Here’s a site that lets you search for number strings in the first 10 million digits of pi.
Fooling around some more with this pi-code, I see that one famous name can be found in pi:
CECIL ADAMS
3|5|3|9|12 1|4|1|13|19
The string “353912” first occurs at the 1,116,043rd digit, and “1411319” shows up at the 6,494,420th. Neat, eh? But I don’t see how you can practically code anything with this method.
Unfortunately, intuitive notions of what’s “likely” in higher math don’t often turn out to be correct. If by “likely” you mean that the probability of picking a real number with this property is low, you’re right–it’s actually zero. But such numbers are known to exist, and pi might be one of them.
I’ll provide a link for the thread in which this was discussed as soon as I can find it.
Here we go. This thread discusses the normality of pi.
23skidoo, I read the same book (AHA! paradoxes to puzzle and delight). That’s where I heard of this rod, and I thought it was an interesting idea. The rest of the book is great, also.