Hmmm… I’d say that the problem is formulated in a way that allows for some maths, but in the process loses some of its essence.
For example, the ‘proof’ only talks about the length of the hypothesis, because that can be easily quantified. However, that does not rule out very short pseudo-explanations like ‘god did it’ or ‘it’s magic’. To rule out those, in practice one would need to introduce some non-mathematical language about what language is acceptable—but that would make it very hard to reason about it mathematically.
The usual solution to this problem is actually just the opposite: introduce an even more mathematical language, which avoids bringing in pre-cached complex-but-simple-seeming notions like “god” and “magic” so that the message length is more meaningful. Turing machine instructions are a popular choice.
Hmmm… I’d say that the problem is formulated in a way that allows for some maths, but in the process loses some of its essence.
For example, the ‘proof’ only talks about the length of the hypothesis, because that can be easily quantified. However, that does not rule out very short pseudo-explanations like ‘god did it’ or ‘it’s magic’. To rule out those, in practice one would need to introduce some non-mathematical language about what language is acceptable—but that would make it very hard to reason about it mathematically.
The usual solution to this problem is actually just the opposite: introduce an even more mathematical language, which avoids bringing in pre-cached complex-but-simple-seeming notions like “god” and “magic” so that the message length is more meaningful. Turing machine instructions are a popular choice.
More on this here.