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Mueen Nawaz wrote:
> OK. Not how I was interpreting it...
That's how the people in cryptography define it. :-) Basically, you can't
have a random sequence. You can only have a random process. It's impossible
to look at a sequence that has already been generated and decide if it's
random or not.
> I know - just thought I'd point out it could be confusing.
Fair enough.
> Anyway, your original assertion was that a truly random sequence is
> necessarily a normal sequence. That doesn't match up with your
> definition of normal.
I didn't define the term "normal sequence", except by reference to "normal
numbers", via Wikipedia.
> If I have a sequence derived from a Gaussian distribution, then it is
> truly random by the way you defined it. Given the whole sequence, up to
> a point, it doesn't tell me anything about what the next element could
> be (other than what is obvious - that it follows a Gaussian
> distribution).
Correct.
> However, for this sequence "every block of a particular
> length occurs with equal probability" does not hold.
I think there's confusion conflating "random" and "normal" in our
conversation about distributions here. Not every random sequence is normal,
and not all normal sequences are random. Sorry if I confused "the kind of
random you assume idealized monkeys will generate on keyboards" with "any
sort of random distribution".
To have a "normal number", you need linear distribution, basically. I.e.,
all substrings of a given length appear with equal asymptotic probability as
the number of symbols you look at gets large. *Given* that, every sequence
of any given length will appear if you let N be infinity.
In other words, in order to avoid Shakespeare appearing, you would have to
have a non-random distribution *because* the sequence is infinite and not
just unbounded. In exactly the same way that 0*X is zero no matter how big X
gets, until X is actually infinite.
(lim(x->inf) 0*X) =/= (0*inf)
You can't reason about it based on "no matter how big it gets, ..."
--
Darren New, San Diego CA, USA (PST)
There's no CD like OCD, there's no CD I knoooow!
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