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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