The Kolmogorov complexity is the length of the shortest program that simulates P.
Solomonoff complexity is the probability of guessing the shortest program.
Chaitin's Omega number is the probability that a random program will halt on a universal turing machine.
Schmidhuber's uses time instead of space to get rid of the nasty compuatability problems.
That's the three layer cake. With Schmidhuber frosting.
This is all about machines being able to make intelligent inferences and predictions given past data.
Data of course can be programs or anything else we can encode (digitize).
These are measures of complexity though. They are not complexity, any more than a liter is gasoline.
What is interesting in a loosely metaphysical way is:
- Although every computable phenomenon has a Komogorov complexity, it can not be computed.
- Although Solomonoff's method for generating hypotheses from prior data is optimal it requires the calculation of an incomputable number.
- Chaitin's Omega is called the number of wisdom because it encodes all mathematical truth, but it is once again, impossible to compute.
- Schmidhuber seems to get around all of this by swapping space for time. (Wouldn't it be interesting if space was cheaper than time?)
Consciousness was found in a machine some time in the future of our imaginations.
We thought it was a trick. We turned it on and off when we felt like it, but it was very convincing.
Unfortunately we were not.
The more interactions there are, the more complexity there will be.
Complexity means there are layers.
Complexity is easiest to study by simulation.
Complexity takes time to understand.
Complexity requires diversity.
Daily Life is complex.
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