paradoxes of randomness

[Tim May]

On Monday, August 18, 2003, at 06:37  AM, Sarad AV wrote:

> hi,
>
> Thank you-one more question.
> Will the information obtained from the 2^32 tests have
> a zero compression rate?
> If one of the occurance should yield all heads and one
> occurance yields all tails-there appears to be scope
> for compression.

This outcome is compressible because it has a short description.



>
> If the output is random,then it will have no
> mathametical structure,so I shouldn't be able to
> compress it at all.
>

Our best current description of randomness is that something is random 
when it has no _shorter_ description than itself. (A point of view 
variously credited to Komogoroff, Chaitin, and Solomonoff.)

But, as I said in my last post, before you try to understand 
algorithmic information theory, you need to learn the basics of 
probability. Without understanding things like combinations and 
permutations, binomial and Poisson distributions, the law of large 
numbers, standard deviations, etc., your philosophizing will be 
ungrounded.

You can read articles some of us wrote here about 10-11 years ago by 
using Google on the obvious terms.


--Tim May

"We should not march into Baghdad. To occupy Iraq would
instantly shatter our coalition, turning the whole Arab
world against us and make a broken tyrant into a latter-
day Arab hero. Assigning young soldiers to a fruitless
hunt for a securely entrenched dictator and condemning
them to fight in what would be an unwinable urban guerilla
war, it could only plunge that part of the world into ever
greater instability."
--George H. W. Bush, "A World Transformed", 1998