Posted by
thompnickson2 on
Dec 01, 2020; 8:50pm
URL: http://friam.383.s1.nabble.com/New-ways-of-understanding-the-world-tp7599664p7599727.html
Jon,
Does "encoded a theory" get me off my own hook?
N
Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
[hidden email]
https://wordpress.clarku.edu/nthompson/
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From: Friam <
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Sent: Tuesday, December 1, 2020 10:59 AM
To:
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Subject: Re: [FRIAM] New ways of understanding the world
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,
[hidden email] 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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