ABOUT THE NUMBER TO ANSWER EVERYTHING
Autor: Renato | Publicado: 2012-10-20T06:36:00-07:00

Some people came across Pi and seeing its properties as an irrational number, wondered if it would contain the answer to all the possible questions encoded on its digits. Well, it turns out being an infite non-repeating string of digits doesn't mean anything of that.
Talking a little about irrational numbers, we don't know what is the content of irrational numbers. That is, it has been proven that, in decimal notation, they can only be written as an neverending sequence of non-repeating digits (I don't know yet how, but I think textbooks in Real Analysis must explain it). We don't know yet &nbsp;if there's a pattern behind it (we couldn't find one until now), but that's only because we can't prove yet that isn't. Mathematicians don't actually believe (at least I think) there's a pattern that can make the digits of Pi predictable. Or maybe there's a pattern that doesn't make the digits predictable (can that actually be??).
Long story short: nothing we know allows us to say that a string of digits of any length is encoded in Pi. We now that 1, 4, 5, 9 are there and probably many of the short strings like 99, 11, 14, 15, 999, 123, 368, 9999, but we can't guarantee "any phrase" is encoded in ASCII or any other encoding within the digits of Pi.
All of the above facts regarding Pi extend to any other irrational number.

Now let's talk about a random number. Call it R. R is a number (can we call it irrational? I really have my doubts about it...) that can be constructed by randomly assing digits to it (before or after zero of both, it doesn't matter). Let's say we have the following hypothetical part of R: "2385872932". The digit following that portion has an equal 10% chance of being anything from 0 to 9. Nobody can really say what it will be, so that each time you build R it will be built differently (but will it be a different number?). Note that Pi is nothing like that. If you are "building" Pi, you know that you have a 100% chance to guess correctly the following digit. You just don't know how it relates to the previous or the following ones, whereas on R you know that theres absolutely no relation whatsoever.

Onto a short digression [you can safely skip this paragraph]: If you're not familiarized with this discussion, think about the examples of the "typing monkeys". If you have monkeys typing on typewriters forever (and if we assume they type randomly, what biologists, ethologists and veterinarians know is not true), then maybe, after an indefinitely long interval time, they come up with one of Shakespeare's work. Merely because the chance that they type each character in that work in the correct order is not null, so that this occurrence would only demand a finite (no one bothered to calculate it) amount of time (a HUGE one, for sure). Pretty neat, huh? (But hey, since monkeys most surely don't type randomly, that event wouldn't probably occur, right? What can we find to substitute the monkeys that can actually generate ramdonly typed characters? Is there even such a thing that produces true ramdonness?)

Now, since R is completely random, you can think of any string of digits that there will be a finite probability that it will be contained in R. In particular, that probability will be 1/10 to the power of N if you let N be the length of that string you chose. So it doesn't really matter that you build R different ways, does it? Since the probability that one entire R is contained in another R is 1 (this isn't even a conjecture, even less of a theorem, but would someone else care to prove it?), all R's are the same (except for the ones with different constrainsts, like "this R has no digits to the right of zero", "this one has no integer part" etc).
Therefore, if we encode "the answer to every question" and "every question" in a single string of digits in ASCII or Morse, there's certainly a finite probability that it will be found there!

How amazing! But now to some questions...
Can we obtain that number from a fact of reality (like the way we obtain the square root of 2 or Pi)? I personally don't believe so...
Can we find that number given only the clues in this text? I also don't believe so, since it's totally random.
But if we think of any R, there certainly "is" that number!! The number with all the informations we want is certainly there! The only thing is that you can't arrive at it by simply constructing a totally random number. And by that I mean this: even if we build an R, what we certainly can, how are we to interpret it? How are we to read it? How to recognize the questions and answers we most want? In other words, any R that we build in the current stage is useless, since we are not attaching any information into the process in the first place. That's way different from the way we discover Pi. In the process of generating Pi we had to give some information, namely that we had a circumference and the diameter of it. Perhaps the "fastest" way to build the useful R would be to already know every answer and every question and only then build it! But that defeats the purpose, doesn't it?
Also, how are we supposed to interpret that number, given it's infinitely long? This one is a killer...
[Another digression: what if in Douglas Adams' novel, the computer built to give the answer to everything was trying to generate a random number and reading it on the run to find something like: "The answer to everything is: forty-two", but then they would have to find a different string that would me be more complicated to search for, the one that gives the fundamental question?]

So, the answer to everything is already encoded in a number (i.e. something we created!), but only to find it is the same thing as to find all the answers we are looking for in the way we are currently looking... So it doesn't make a difference.
If only we could find something that ramdonly types the digits 0 to 9... But I personally don't believe randomness exists... I don't think we'll ever achieve that, so let's keep looking the old-fashioned way, no short-cuts!