On Sat, Oct 13, 2007 at 03:28:51PM +0100, Mike Tintner wrote: > > "I felt sad" - is a grounded statement - grounded in your internal > kinaesthetic experience of your emotions.
OK.. > Would you like to rephrase your question in the light of this - the common > sense nature of grounding, which I think obvious and beyond dispute? ? Sorry, I don't get it. What is "grounding"? Its not obvious to me ... > the developmental history of human understanding altogether. > [...] Yes, of course, children learn to reason from concrete to more abstract levels, and lawyers, engineers and mathematicians working at a particularly abstract level. The concrete levels are indeed grounded in sensory input. However, once one has actually learned how to think abstractly, its not obvious to me that sensory grounding is needed; and indeed, trying to touch back to the grounding can prevent one from making the next leap of abstraction. > Ben a mathematician looked at the immense complexity of the numbers and maths > he deals with and failed to appreciate that they are composite affairs - > which can only be mastered, psychologically, stage by stage, building from > very directly grounded numbers like ten's, to very complexly and indirectly > grounded numbers like trillions, "very large numbers", irrational numbers > etc. For maths this is actually rather obvious WHEN you look at things > developmentally. ? I don't quite get it. Sure, kids are taught math by starting with integers and moving to base-ten stuff. Two remakrs, though: -- It is painfully obvious to me that math education in primary schol (kindergarten-5th grade) is painfully broken. It pains me to watch my kids homework -- we got rid of troy ounces and furlongs long ago, yet the equivalent lives on in math education. Its time to get rid of 90% of the crap that passes as math in primary school, and replace it with the real stuff (e.g. modulo-3 counting in 1st grade, set theory in second grade, etc) -- I don't quite understand what grounding, math and AGI have to do with each other. Yes, if you wanted to create an AGI that would independently rediscover math, it may well need to start with a sensory input such as "one apple plus one apple is two apples". The redeiscovry of math would proceed as a rediscovery of physics (physics is "grounded math"). But there are alternatives. As I mentioned, I think Ramanujan was able to train a set of neurons to do long division, and was thus able to rattle off seemingly magical relationships at will. .. even as he could not provide rigorous proofs for them. Now that we have computers (which easily do long division), we have many people who can also make astounding statements, which are anchored in the "intuition" of the computer, even as they lack formal proof. Take, for example, work on hypergeometric series, which, these days, seems to be the creation of algorithms that spew out magical, astounding relationships. The point here is that Ramanujan's "grounding" was not visual or auditory or sensory, even; it was access to a part of his brain that could natively manipulate polynomials. Linas. ----- This list is sponsored by AGIRI: http://www.agiri.org/email To unsubscribe or change your options, please go to: http://v2.listbox.com/member/?member_id=8660244&id_secret=53761124-840d0c
