paradoxes of randomness

[Sarad AV]

hi,

Okay- I need 5 bits to represent 32 coins.I count as
coin 0,coin 1,... coin 31.
If it is a perfectly random fair coin throwing
experiment,then 50 percent of them will be heads.

So I know that 16 of them will be heads.

What we do is i simply place all the 32 coins on the
table in a row or column.
I look at the first coin and determine if it is a head
or a tail. I repeat the same proccess till i count 16
heads. If I count 15 heads at coin 31, then I cant
reduce the entropy. How ever, if i count 16 heads at
coin 30,then I dont have to check that coin 31,I
already know its a tail,so I have less than 5 bits of
entropy.

So if it is a perfectly random experiment,I wouldn't
get 16 heads before i look at coin 31,which is the
last coin and thats what you said-isn't it?

So how did chaitin get to compress the information
from k instances of the turing machine in

http://www.cs.umaine.edu/~chaitin/summer.html 

under the sub-section redundant?

he says-
"Is this K bits of mathematical information? K
instances of the halting problem will give us K bits
of Turing's number. Are these K bits independent
pieces of information? Well, the answer is no, they
never are. Why not? Because you don't really need to
know K yes/no answers, it's not really K full bits of
information. There's a lot less information. It can be
compressed. Why? "




If the input programs are truely random-there is no
redundancy and thats a contradiction to the claim in
the paper.

Thanks.

Regards Sarath.



>It's simple, if I am correct. The redundancy simply
> makes you care
> less about the specific instance you are looking at.
> 
> > To represent 32 coins-i need 5 bits of
> information.
> > Since the experiment is truely random-i know half
> of
> > them will be heads,so in this case using 5 bits of
> > information,i can determine all the coins that are
> > heads and that are tails.
> 
> Same deal, unless you are counting pairs, in which
> case you cannot
> distinguish between the members of a pair. You need
> an extra bit to
> tell a head from a tail.
> 
> > So-the question is what is the minimum number of
> bits
> > or entropy required to determine which all coins
> are
> > heads and which all coins are tails,is it 5 bits
> or 6
> > bits of information?
> 
> With 5 bits, you can count to 31, so you need 6.
> 
> Just my two tails.
> 

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