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Comments (44)
You are wrong because I did specify a probability space.
The probability space I specified was one where the sample space was the set of all outputs of all programs for some universal computer, and the measure was one from the book I mentioned. One could for instance choose the Solomonoff measure, from 4.4.3.
From your writings I conclude that is it quite likely that you are neither quite aware of the concept, nor understanding what I write, while believing you do.
No, you specified the points and not the measure.
OK! Now we've got a space. Of course if you wanted to talk about solomonoff measure, why didn't you just say so 5 comments ago. Pretty much everyone reading less wrong would have immediately known what you were talking about. You still haven't justified calling the solomonoff space "universal".
Now you're just being rude. You don't know me, you certainly don't know what I do or don't know.
It is universal, because every possible sequence is generated.
It is universal, because it is based on universally recursive functions.
It is universal, because it uses an universal computer.
People knowing algorithmic complexity know that it is about probability measures, spaces, universality, etc. You apparently did not, while nitpicking instead.
I'm not nitpicking, you're wrong. "Universal" in this context means, to quote the original poster
What the heck does that have to do with every possible sequence being generated? For that matter what does it have to do with sequences at all? The solomonoff measure is a measure over sequences in a finite alphabet, or to put it simpler, Integers. How do I express an event like "it will rain next tuesday" as a subset of the integers?
Whatever you are using the word "universal" to mean, it is not anything like what the OP had in mind. The Solomonoff measure is an interesting mathematical object for sure, and it may be quite relevant to the topic of real-world Bayesian reasoning, but it's obviously not universal in that sense.
also: what the heck does "universally recursive" mean? Did you just make up that term right now? Because I've never heard it before, it only has 10 google hits, and none of them are relevant to this discussion.