So in the novel version of Contact by Carl Sagan, Ellie supposedly finds some sort of message, ostensibly from "God", buried deep within the digits of pi (binary, I think). This got me thinking, if pi is truly infinite, shouldn't there be literally infinite hidden messages within its digits? In fact, there should be a representation of War and Peace in there as well as the script from Star Trek V etc., etc. and none of those would indicate any sort of evidence of a higher power. What do you guys think?
It makes sense, but is not actually provable. It could theoretically be possible, for example, for an infinite but non-repeating string of digits to have no zeros in it, if they were not random. (And pi is hardly random.) In the same way, it is theoretically possible for pi not to have certain combinations of digits in it, no matter how far you take it. But that can never be checked. Furthermore, and more importantly a "message" has to convey meaning, and meaning has to be a communication from a sentient being. A string of digits that can be interpreted in a particular way, from a subjective point of view, still doesn't "mean" anything unless they were explicitly put there by someone in order to communicate something. For example, a long enough random string of letters might contain, at some point, the sequence "andriamanitra" without that "meaning" anything. The fact that some people (Madagascans) would "read" that as meaning "God" only means that, in their subjective code (a language is a code), it "means" that to them. But unless someone who knew that code purposely put it there, it doesn't "mean" anything. I'm not a big believer at all in "hidden" messages from God. I think God has made what we need to know clear enough for those who want to know it. (There is plenty that is not clear about God, which is why I state in the other thread that it is my firm belief that no one is completely right in their conception of God, but those are things that are not essential in order to function properly, even with respect to God.)
Okay, here is what the message supposedly entailed (from Wikipedia): In a kind of postscript chapter, Ellie, acting upon a suggestion by the senders of the message, works on a program which computes the digits of pi to record lengths in different bases. Very far from the decimal point (1020) and in base 11, it finds that a special pattern does exist when the numbers stop varying randomly and start producing 1s and 0s in a very long string. The string's length is the product of 11 prime numbers. The 1s and 0s when organized as a square of specific dimensions form a rasterized circle. I guess something like that would be pretty difficult to just happen by chance.
Saw some obscure movie once where some dude stole a prototype CPU to calculate Pi out to umpteen digits or some such. I forget how that worked out, but I do recall thinking it was meant to be a lot more exciting than it turned out.
I think the current assumption is that pi (and also the square root of 2) is some fancy term that means that any given string of digits occurs just as often as any other string of digits of the same length. So, say, 314 should occur just as often as 123 or 000. Or so I remember from an article that I read some years ago. There's also a question of whether this is true in base-2, base-10, or any other base of representation. I think one of the best parts of being a pure mathematician must be that you can always keep busy.
Back in the 1870s, before we young whippersnappers had figured out how to let electrons do the math for us, a man named William Shanks worked out pi to 707 digits by hand. About 70 years later, a man named D. F. Ferguson came along and showed that Shanks had goofed up after the 527th digit. No word on what Shanks's ghost had to say about that. For more stories of Man's eternal struggle with Mathematics, visit your local library and read Journey Through Genius by William Dunham. It's quite enjoyable, and the author makes the actual math involved very clear and understandable.
I forget the term for it, but I read somewhere that Pi, like e and a few other special numbers, which are not only unending, non-repeating decimal numbers in Base 10, but in all base-number systems. Kinda cool! Oh yeah, and ...I want a Pi-shaped pie! Not a Pi-shaped cake!
I see what you did there. So the area of a circle is now 1r^2... uh. Hmm. Ok, the circumference of a circle is now 1r*2... shit. What's 2 in Base-Pi?
[-]-i[/-] No, that would be pi/i. e/i would be something different, probably something with plenty of 1s, 2s, and 3s in it. Probably a few 4s and 5s. Some 6s and 7s too. Lots of 8s and a scattering of 9s. And of course gobs of 0s, because you can hardly take a step without being up to your knees in 0s.
