Outline

Solomonoff’s Lightsaber vs Occam’s Razor (former is more precise and complete, i.e. Technical Simplicity)

Find all the hypotheses that would predict the observation by trying every possible hypothesis through the Universal Turing Machine and keeping the ones that output the observation.

This is incomputable. Both because of the enormous number of possible algorithms and the Halting problem.

In theory, you now have all possible explanatory hypotheses, each a binary sequence.

Assuming randomness (what does that really mean in this context?), each bit has a 50% chance of flipping the way it did. So the the probability of each hypothesis is $(\frac{1}{2})^n$ where $n$ is the number of bits in the hypothesis. This means longer hypotheses are less likely, i.e. they require additional evidence compared to the shorter hypotheses. (these probabilities are not normalized, but still comparable)

This fits with Occam’s Razor

Probability of the observation alone = sum of probabilities of hypotheses that are consistent with the evidence.