The problem is that there are times when the data that we possess regarding the world around us does not have what is necessary in order to be able to guide us in choosing what to assume regarding the unknown. This is the situation when every choice is as good as any other a.k.a. equi-probability. You cannot approximate (i.e. choose the closest relative) in such a situation because every candidate is equally similar to the original.
Paraphrasing what I said in another thread:
Intelligence is the search for the closest relative of some data set d within some set of data sets S.
In effect, the task of intelligence is to approximate.
(Of course, pedants will be quick to say that this is not intelligence but intuition. And not even intuition but induction. And not even induction but something else – something I made up.
My point will be that if you want to understand intelligence then you have to understand intuition. And if you want to understand intuition then you have to understand induction. In fact, you have to understand whatever is fundamental to the process. You need to understand the foundation of intelligence. Any other approach will be horribly superficial.)
When a data set has more than one closest relative then we’re speaking of randomness.
If we have a data set such as {A, A, B, B} that represents “2 occurences of A and 2 occurences of B” and if we want to find out how many occurences of A and how many occurences of B there will be at 5 occurences of either-A-or-B we will have no choice but to conclude either {A, A, B, B, B} or {A, A, B, B, A}. This is because the two data sets are equally similar to the original data set. That’s randomness. The greater the number of closest relatives, the greater the degree of randomness. On the other hand, if what we want to find out is how many A’s and how many B’s there are at, say, 6 occurences of either-A-or-B then we will be able to give a definite answer: 3 A’s and 3 B’s. This is because this data set is more similar to the original data set than all others. That’s order. The lower the number of closest relatives, the greater the degree of order.