Well, I think Dave gets at something important, here, that SteveS misses by jumping to reflection (model of self modeling the world), though I agree SteveS' response to Q1 is correctly oriented. But first, we can't ignore Wolpert's run-up to that 1st question. It seems to me he is treating proto-computational cognition with the respect it deserves. (E.g. baby ontogeny & society ontogeny.) The very asking of the question indicates that respect.
I.e. Why is it that learning those proto-computational techniques (including culture) gives us the ability to come up with science and mathematics (SAM)? In the transition from question 4 to 5, he explicitly mentions the "unreasonable effectiveness" of math, and agrees with Dave (generally) that such things are woefully impoverished compared to full models of reality. Math, as we've developed it, is inherently incapable of representing things like baby ontogeny. And perhaps that limitation is an example of "what we cannot even imagine". Where I agree with SteveS' orientation is toward this self-referencing loopiness. Wolpert relies on his assertion that "All statements in mathematics consist of finite sequences of elements from a finite set." This is right after his discussion of how category theory may seem so beautiful to us *because* we're LIMITED in our ability to represent the world with math. It's counter-intuitive. But in general, it seems to me that it lines up well with Dave's intuition of the limitation. While math can represent circular definitions (what Robert Rosen complained about), there are deep problems in the foundations of math ... things like the iterative conception of sets ... that are attempts to do what Wolpert asks for in the later questions. And it's unclear to me that commutative categories reduce to "finite sequences of elements from a finite set", prolly 'cause I'm just ignorant. But diagrammatic loops in graphs don't look to me like finite sequences. In any case, the question is a can kicked down the road. Even if our math is growing more powerful, what *can* we understand about where it might go if, say, we meet some advanced intelligent aliens or whatever? On 9/11/22 10:35, Prof David West wrote:
Wolpert's questions are fantastic. Thanks glen for prompting this discussion. Re: question one about the "chasm with minimal cognitive capabilities necessary ..." I have two major problems with the assumptions behind this question. First, the assumption that Godel, Einstein, and Beethoven exemplify 'greater' (in some sense of that word) cognitive abilities. This is analogous the the AI notions advanced by Newel and Simon that they had succeeded in creating a thinking machine because the thinking reproduced was that of university professors. They thought that the way they thought was the apex of human thinking. A much greater challenge— still avoided, even by the most sophisticated ML approaches — is how a baby is able to learn and extract meaning from a chaotic cacophony of inputs. Second, that the cognitive capabilities of pre-Holocene humans were "minimal." The most pernicious myth with regard our long ago ancestors derive from either Rousseau or Hobbes—both of whom conjectured, with no evidence, that our ancestors existed in a primitive state—Edenic for Rousseau, and brutish for Hobbes, but simplistically primitive. Quite the opposite was true. The world was far more complex and challenging, with everything from social relations to 'food chemistry' (e.g. brewing beer) to explanations of why everything in the world was as it was being highly variable across population groups and constantly in flux. A bit analogous to the baby making sense of the world. Humans today are able to "survive" primarily because of tens of thousands of years accumulation of "culture." Because we have that resource, we do not have to figure out if that nice striped quadruped over there will eat me; or, if that red berry will kill me but the other red berry is essential for a great BLT. It might be possible to make an argument: Godel, et. al., were able to do what they did because 'culture' reduced the daily (hourly, millisecond-ly) cognitive load such that it was possible to put the 'surplus' to work on issues of math and music; but, not that there was any kind of qualitative or quantitative difference in cognitive abilities of humans then and now. to be continued ... davew
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