Imagine a chronologically-ordered list of all the n humans who will ever live. I am already assuming that time is linear rather than say a branching structure.

Can the Copernican Principle be defended using Algorithmic Information Theory?

Most humans require a minimal-length computer program of roughly log\_2( n ) bits to specify their position r in the list (using the number n as input). This leads to a uniform conditional probability distribution P( r | n ) = 1 / n and hence the Doomsday argument. If you assume your position can be specified more easily then you are making the unwarranted assumption that your position is special.

Is this correct?

**Background**

The Copernican principle is the assumption that the observer is not special amongst a group of observers.

The Doomsday Argument (DA) is an application of the Copernican Principle that purports to allow us to estimate the total number of humans who will ever be born. A version of the DA goes like this:

Imagine a chronological list of all the n humans who will ever be born (assumes a linear timeline).

If we take an algorithmic information theory view then the majority of humans require a program of length log\_2(n) bits to specify their position r in the list (assuming the program is given the number n as input). This leads to a uniform prior probability density function for their fractional position f = r / n.

By change of variables from f to n we can derive the Doomsday Argument result that the posterior probability density function for n is r / n^2.

But I personally believe that the Doomsday Argument fails because I believe in the Many-Worlds Interpretation of Quantum Mechanics which implies a branching structure to time.