[FRIAM] New ways of understanding the world

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That sounds like a fairly standard way of distinguishing between intuitiionist and classical conceptions. For me, the problem boils down to whether or not you allow for *actual* infinities or only possible infinities. If you take a doing like "choose a token, apply unary_1 to it, then apply binary_1 to the original token and the output of unary_1", the result will be a theorem. And there's no, in principle, distinction between the doing and the theorem. But if you then say, "do that forever". Then the result isn't really a theorem because there's really no result. You'd have to add something else ... like a convergence operator. But convergence is persnickety. A better operator would be a similarity/distance operator.

Marcus' "try random stuff, possibly reproduce" allows for options in "reproduce" of strong or weak similarity. (Obviously, for copying a software app, you need pretty strong similarity, but perhaps not when you have complex gen-phen maps.) So it seems reasonable to include similarity operators, but not convergence operators. Then instead of "do that forever", you have "do that until similarity_1 < ε". Even if similarity_1 is NOT monotonic, you can stop when you find a procedure that's close enough to a copy to halt. And that feels like a theorem to me.

Of course, there's no reason those derived theorems have to already be present at the very start of the process. The machine can have a "priming" period where it has to "prove" a bunch of theorems that will *eventually* detect the "order". So Nick's "already possessed" is technically wrong, which is what Marcus points out. But, in some sense, those provable theorems are *already* expressible in the prior language. So Nick is spiritually right.

But re: self discovery as corollary to world discovery -- It seems like Wolpert's paper argues against that: https://arxiv.org/abs/0708.1362 The idea that there can only be a single strong inference device in the world implies an asymmetry between world and self discovery. But I can't really pretend to grok the contents of that paper. Maybe someone else here can?

On 12/1/20 8:09 AM, jon zingale wrote:
> It is a little strange to read "possessed a theory" from Nick because he
> staunchly avoids language like "has consciousness". That said, I read him
> here as saying that discovery of the self is a corollary to discovery of the
> world. From my own perspective, theories are derived from (founded upon?)
> doings, but are not the same thing as doings. Tryings are perhaps more
> subtle, they evoke for me something like proto-theorems or lemmas. -- 2₵

> On 11/30/20 1:24 PM, thompnickson2 at gmail.com wrote:
>> I was arguing  that given, say, a string of numbers, and no information external to that string, that no AI could detect “order” unless it already possessed a theory of what order is.  I found the discussion distressing because I thought the point was trivial but all the smart people in the conversation were arguing against me.


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