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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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