On 4/23/07, J. Storrs Hall, PhD. <[EMAIL PROTECTED]> wrote:
We really are pigs in space when it comes to discrete symbol manipulation such as arithmetic or logic. It's actually harder (mentally) to do a multiplication step such as 8*7=56 than to catch a Frisbee -- and I claim
I've learnt multiplication table up to 100 by heart as a kid, I was made to. This is how I would do the multiplication now: 8*7 = 8*(5+2) = 8*5 + 8*2 = 8*(10/2) + 8*2 = (8/2)*10 + 8*2 = 4*10 + 8*2 = 40 + 8*2 = 40 + 10 + 6 = (4+1)*10 + 6 = 50 + 6 = 56 There is much understanding put into it (decimal numbers, laws of arithmetic). Do you know the definition of multiplication? m * 0 = 0 m * S(n) = m + (m * n) (I put m balls into each of n boxes, and I collect the balls one box at a time.) m + 0 = m m + S(n) = S(m + n) (I have two piles of balls and I merge them one ball at a time.) (I could explicitly put balls from one pile to the other: m + S(n) = S(m) + m.) 0 = 0 n = m ==> S(n) = S(m) (Do I have the same number of balls on both piles? Let's take one ball at a time from each pile at once and see if we are left with "empty piles" simultaneously.) AGI could do mining of e.g. CIC for correspondence with the world. The bonus with CIC is that since you understand (e.g. the definition of multiplication on unary numbers), you can compute with it. An AGI working with bigger numbers had better discovered binary numbers. Could an AGI do it? Could it discover rational numbers? (It would initially believe that irrational numbers do not exist, as early Pythagoreans have believed.) After having discovered the basic grounding, it could be taught the more advanced things. Perhaps CIC is simply too impractical. Łukasz ----- 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=231415&user_secret=fabd7936
