n digit binary rational numbers

There are 8 binary fractions with 3 digits:

{.000,.001,.010,...,0.111}

If we were to chose such a fraction at random them the probability would be 1/8 or in binary 0.001

This is a 3 digit binary fraction!

So we can say that there is a 1/8 chance of picking the 3 digit fraction which represents the probability that it was picked.

OR we can say that .001 is that binary number that represents the probability that itself gets picked.

Scenario 1) If we have a lucky dip (with replacement) with these numbers buried in the wood chips then on average every 8 tries we will pick out .001. We have only one go.

Scenario 2) If we have another bucket of these numbers and we go seeking the answer to the question above about the probability of picking .001 we don't get one go we need a few goes to get the answer. In this case we are "seeking" the answer and only one asnwer will do.

Let us assume that numbers are things with "selves". We are lying in the bucket waiting to get picked. When we are picked we say what we are. In scenario 1 we are waiting and when we eventually get picked (in one of the trials) we say that we are the probability that we were actually picked. We might think that we were special here because we are saying something about ourself.

In the second scenario however we need to answer that we are the probability that we get picked in random trials - which this isn't.

I have someone talking at length in the library which is distracting me from this quite involved thought - I could ask them to hold the discussion outside but I guess they have their reasons - oh good they stopped...

The original thought was this...
.001 is just one amongst the 8 numbers. It has a property that it will be picked 1 in 8 times in random trials, and it is true that it represents that property. ".010" has the same propertybut it just "happens" that it doesn't represent that property. There is no causal link between the number and it bearing that property. It is effectively chance that it has that property altho the chance can't be easily worked out.

Let Self-Knowing be the name of the property of having the value that represents the probability of that number in binary being picked at random from numbers of equal digits.

The SK(x) function returns true for x=0.001. Then what is the property of Not(Self-Knowing) i.e. SK(x)

The probability of not picking ".001" is 0.111 and the probability of not picking ".111" is 0.111. ".111" represents the probability that it itself is not picked. Interesting if that could be folded into the question of finding the probability in the first place so that it could be proven never to be known!

2bcompleted...