Warp wrote:
> It only says that the probability for them to appear is larger and larger
> as the amount of time is increased.

Right. And I'm talking about when you actually consider the end result, and 
not the limit.

I don't think you can look at a limit as n -> infinity and say what the 
answer is at infinity by analogy.

>   Since there is an infinite amount of different finite sequences of
> letters, the probability of one specific sequence (in this case the works
> of Shakespeare) to appear is, mathematically speaking, zero.

Err, no. There are an infinite number of sequences that are as long as 
Shakespeare, and only a finite number of *possible* sequences. If all 
sequences are equally likely, they'll all appear an equal number of times.

>   Since the probability for them appearing is zero, does that mean that
> they will never appear?

I think you're mistaken that the probability is zero.

>> Given that truly random sequences are normal, and in a normal sequence every 
>> block of a particular length occurs with equal probability, and we're 
>> talking an infinite sequence, it follows that the bard is in there 
>> somewhere.  If I'm not mistaken about the math of it.
> 
>   There is an infinite amount of sequences *not* containing the works of
> Shakespeare. What stops the RNG from generating *all* of those other
> sequences before generating Shakespeare's works?

Nothing. Nor does doing so keep Shakespeare's works from being generated.

You need to address the theorems about normal numbers. There's actual math 
here not relying on intuition about infinitites.

>   Also, even if the RNG has already produced all the possible letter
> combinations with as many letters as there are in Shakespeare's works,
> that doesn't mean that the works are next. When we pop out the next set
> of letters, there's still a really small probability for them being the
> works of Shakespeare. Even if the RNG would have already produced all the
> possible other combinations a billion times, it still doesn't make the
> probability of Shakespeares' works popping out any more probable. Past
> events do not affect future randomness.

COrrect. I think you're failing to account for infinity.

>   Yes, it's extremely unlikely that popping up all the possible distinct
> combinations of letters (amounting to the total number of letters in the
> works) a billion times will not produce Shakespeare's works, but this
> probability is still larger than zero. There is no guarantee.

A billion? Sure. Infinity? I don't think so. Anything less than infinity? Sure.

-- 
   Darren New, San Diego CA, USA (PST)
   There's no CD like OCD, there's no CD I knoooow!

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