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What's the length of the hypothesis that F=ma?
How many bits does it take to say "mass times the second derivative of position"? An exact answer would depend on the coding system. But if mass, position, time, multiplication, and differentiation are already defined, then, not many bits. You're defining force as ProductOf(mass,d[d(position)/d(time)]/d(time)).
See the discussion here on the bit complexity of physical laws. One thing missing from that discussion is how to code the rules for interpreting empirical data in terms of a hypothesis. A model is useless if you don't know what empirical phenomena it is supposed to be describing, and that has to be specified somehow too.
I understand all that, I just want a worked example, not only hand-waving. After all, a formalization of Occam's razor is supposed to be useful in order to be considered rational.
Remember, the Kolmogorov complexity depends on your "universal Turing machine", so we should expect to only get estimates. Mitchell makes an estimate of ~50000 bits for the new minimal standard model. I'm not an expert on physics, but the mathematics required to explain what a Lagrangian is would seem to require much more than that. I think you would need Peano arithmetic and a lot of set theory just to construct the real numbers so that you could do calculus (of course people were doing calculus for over one hundred years before real numbers existed, but I have a hard time imagining a rigorous calculus without them...) I admit that 50000 bits is a lot of data, but I'm sceptical that it could rigorously code all that mathematics.
F=ma has the same problem, of course. Does the right hand side really make sense without calculus?
ETA: If you want a fleshed out example, I think a much better problem to start off with would be predicting the digits of pi, or the prime numbers.
My estimate was 27000 bits to "encode the standard model" in Mathematica. To define all the necessary special functions on a UTM might take 50 times that.
I just want something simple but useful. Gotta start small. Once we are clear on F=ma, we can start thinking about formalizing more complicated models, and maybe some day even quantum mechanics and MWI vs collapse.
We can already do MWI vs Collapse without being clear on F=ma. MWI is not even considered because MWI does not output a string that begins with the observed data, i.e. MWI will never be found when doing Solomonoff induction. MWI's code may be a part of correct code, such as Copenhagen interpretation (which includes MWI's code). Or something else may be found (my bet is on something else because general relativity). It is this bloody simple.
The irony is, you can rule MWI out with Solomonoff induction without even choosing the machine or having a halting oracle. Note: you can't rule out existence of many worlds. But MWI simply does not provide the right output.
At this point I am not interested in human logic, I want a calculation of complexity. I want a string (an algorithm) corresponding to F=ma. Then we can build on that.