Measuring Disorder: The Entropy of a Tuple of Numbers

[birulami]

Hi,

not sure whether this is a good question.

How would I define the entropy of a tuple of N real numbers, each between zero and some fixed maximum value?

Of course I would expect the entropy to be minimal if they are all identical and maximal if they are all "completely random".

If $v_i$ are the values and $$M$$ is the allowed maximum, then

$-\sum_i \frac{v_i}{M} \log(\frac{v_i}{M})$

would be my candidate. Any comments?

 

[Eynstone]

Does the entropy add when we juxtapose two tuples?

 

[birulami]

Hmm, not sure. I did not think of comparing different arities of tuples. I am just looking for a kind of the measure of the disorder. For example I consider

(1,1,1,1,1,1,1) to be more in order (less entropy) then (1,2,1,1,1,1,1)

but I would not want to compare, say, (1,1,1) with (1,1,1,1).

Harald.