Darren New wrote:
> Yes. I was phrasing it sloppily there, since we hadn't talked about 
> other distributions at that point in the conversation. To clarify, a 
> "normal sequence" in the way I'm using it means all possible 
> subsequences have the same probability distribution in the asymptote. 

To clarify more, this includes sequences of length 1. So the mathematical 
proof I read a long time ago (and which I don't think I really followed at 
the time) basically said "if you have an equal probability of picking each 
symbol at random, and you string together an infinite number of those 
symbols, then you have an equal probability of picking any particular 
substring of any particular length." Hence, since there are an infinite 
number of substrings of length (size of shakespeare) and *something* in 
there must appear an infinite number of times, shakespeare too must appear 
an infinite number of times.

The heights of people aren't "truly random" even tho they might be 
statistically distributed. It depends on what you ignore when you do the 
measurements.

The difference between arbitrary math (unrelated to the universe) and 
statistics and science (related to the universe) that you described can be 
attributed to what you ignore when you take your measurements. It's actually 
kind of fascinating to think on. Someone once convinced me that subatomic 
particles like electrons aren't just fungible but actually identical, but I 
don't recall what the proof was. It was just logic and relativity and stuff 
like that when you got down to it.

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

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