1. For each entry in your list, cut a straw of length proportional to the value to be sorted
2. Take all your straws in a bundle
3. Bang them gently on a flat table
4. Draw out the straws in order of length, each operation of which can be done in O(1) time
Edit: This is usually the problem with analog algorithms: you can easily tell apart 100 items, but scale it up and you find you need so much energy to differentiate that you'd collapse into a black hole before successfully measuring the differences.
Perhaps by making use of the Oracle of Delphi, you could do away with the array.
Also, the energy requirements... Wouldn't they be proportional to the number of operations required, i.e. the time complexity?
Very good point! Computer-based algorithms need O(log(M) N) storage, I guess.