I find it hard to believe that the measure of a program/book/movie/experience is proportional to the number it is executed/read/seen/lived, independently of everything else.

I have an alternative proposition:

Measure is a function of how accessible a particular program/book/movie/experience is from a given observer moment.

More formally we can say that the measure of observer-moment B with respect observer-moment A is the probability that observer moment B occurs following observer moment A. Measure is simply a conditional probability.

Thus, it is the probability of transition to the program/book/movie that defines the measure. The actual number of copies is meaningless.

This definition of measure has the advantage of  conforming with everyday experience. In addition, it is a relative quantity because it requires the specification of an observer moment from which the transition can be accomplished.

For example the measure of the book Digital Fortress is much higher for someone who has read The Da Vinci Code than for someone who hasn't, independently of how many copies of Digital Fortress has actually been printed, or read and not understood, or read and understood. (These books have the same author).

If one insists in using the context of program to define measure, than one could define measure as the probability that program B be called as a subroutine from another given program A, or more generally,  from a set of program A{}. The actual number of copies of the subroutine B is meaningless. It is the number of calls to B from A{}that matters.

George Levy


Hal Finney wrote:
David Barrett-Lennard writes:
  
Why is it assumed that a multiple "runs" makes any difference to the
measure?  
    

One reason I like this assumption is that it provides a natural reason
for simpler universes to have greater measure than more complex ones.

Imagine a Turing machine with an infinite program tape.  But suppose the
actual program we are running is finite size, say 100 bits.  The program
head will move back and forth over the tape but never go beyond the
first 100 bits.

Now consider all possible program tapes being run at the same time,
perhaps on an infinite ensemble of (virtual? abstract?) machines.
Of those, a fraction of 1 in 2^100 of those tapes will start with that
100 bit sequence for the program in question.  And since the TM never
goes beyond those 100 bits, all such tapes will run the same program.
Therefore, 1/2^100 of all the executions of all possible program tapes
will be of that program.

Now consider another program that is larger, 120 bits.  By the same
reasoning, 1 in 2^120 of all possible program tapes will start with that
particular 120-bit sequence.  And so 1/2^120 of all the executions will
be of that program.

Therefore runs of the first program will be 2^20 times more numerous
than runs of the second.

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