The Theory of the Million Monkeys states that any infinite, non-repeating string will eventually contain any finite string you can define. But are not pi, e, and other such irrational numbers precisely such infinite, non-repeating strings? Would it not thus follow that pi, in fact, contains the Bible, the collected works of Shakespear, and the screenplay to "City Slickers"? Would it not also follow that if you could but determine exactly what block of digits in pi or some other irrational contain the information you desire to convey, you could simply convey the location of that block, and the proper decryption sequence? Effectively, my question is whether, assuming unlimited processing power, data storage and transmission as we know them might not, theoretically speaking, be rendered obsolete, to be replaced by constant computation and analysis of pi?
This thought struck me when I reached the end of the book "Contact". Sagan seemed to think that it would be a great and mystical find if someone were to discover that at some point in a binary representation of pi, all the ones and zeros when lined up just so, would form a circle. This would seem to be a rather obvious thing, as all possible permutations are present somewhere in pi.
Thoughts?
Posted by Aethelwer (Member # 36) on :
This would require computing pi to an infinite number of decimal places, which isn't that easy to do. In addition, you'd need a perfect method of computing pi (none exists), or you'd have to compute an arbitrary standardised value and then store the whole thing...which would be equivalent to storing all the data in the universe, if you want this to work.
Posted by Omega (Member # 91) on :
Well you wouldn't need to compute pi to an INFINITE number of decimal places. Just some rediculous number that's probably millions of digits long. But heck, our supercomputers can do that now, can't they? What makes you think that desktop compys in the next century couldn't?
Posted by Aethelwer (Member # 36) on :
Due to the randomness of it all, your name, for example, might be at decimal 10^99999999999999999 ("millions of digits long" would be only a multiple of 10^6), and you'd have to compute pi all the way out to that decimal place. If we're talking about computers that can do things like that instantly (and accurately!), you wouldn't need this method anyway. Besides, let's say the word "nifty" is at a random decimal place in the millions...you'd have to transmit that as decimal 31245683, or something like that. Hardly a savings, and only so much data fits in the first million decimal places.
Posted by PsyLiam (Member # 73) on :
Yes. If we have all the information we need in this ridiculously long computation of pi, would it not be more efficient to simply store the information as needed? Is it really going to be simplier to say to a computer "the binary code for Hamlet is from decimal point 9zingquikmillion blah blah blah to 13 scubadoobyillion blah blah blah", rather than simply sending it the binary info? It's very inefficient. Rather than storing, say, a megabytes worth of information, you'd need to store a number many many times that to get the same information.
Besides, do you know how much binary data is needed to store even simple things? If we took the most advanced supercomputer in the world, and got it to calculate pi to as long as it possibly could, I doubt it'd even be long enough to store Microsoft Office, let alone all the knowledge in the world. Considering that pi's pretty much random, for it to accuratly contain all the information you suggest, it would be so mind bogginly long that the mind would boggle. Not millions of digits. Not billions. But super duper mega really rather large quadzinqzorakplutillions.
As a side note, does anyone know how many digits of pi they can now count up to? And exactly how big would that be converted into bytes?
And if you're assuming that computers could do it on the fly, well, do they now? Do they leave computers running, and they spit out a new number every 5 minutes? Do they check it thoroughly? How often do they get a new decimal number anyway?
Beware the devil, by the way. He speaks to you when you get to that page.
Posted by Jeff Raven (Member # 20) on :
Don't forget, in Contact, they mention computing pi NOT just in base 10, but in another bases as well..
Posted by TSN (Member # 31) on :
But the point is that, since the number carries on infinitely, the string of ones and zeroes that create the circle will show up, no matter what. In an infinite series of random numbers, you can find any string you look for.
Posted by Gurgeh (Member # 318) on :
Although it's a fascinating idea, an important point has been overlooked. The thing is, we can't really say that the digits in pi are random, which is an important part of the million monkey theorem. Pi is calculated the same every time you do it. We can't infer that it has any known string just because it is infinite. However, it may be possible to decode the numbers in such a way as to get some strings out of it.
Besides, let's say the word "nifty" is at a random decimal place in the millions...you'd have to transmit that as decimal 31245683, or something like that. Hardly a savings, and only so much data fits in the first million decimal places.