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. > __________________________________ Do you Yahoo!? Yahoo! SiteBuilder - Free, easy-to-use web site design software http://sitebuilder.yahoo.com