Ben, No, I wasn't intending any weird chips.
For me, the most important way in which you are a constructivist is that you think AIXI is the ideal that finite intelligence should approach. --Abram On Wed, Oct 29, 2008 at 2:33 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: > > OK ... but are both of these hypothetical computer programs on standard > contemporary chips, or do any of them use weird > supposedly-uncomputability-supporting chips? ;-) > > Of course, a computer program can use any axiom set it wants to analyze its > data ... just as we can now use automated theorem-provers to prove stuff > about uncomputable entities, in a formal sense... > > By the way, I'm not sure the sense in which I'm a "constructivist." I'm not > willing to commit to the statement that the universe is finite, or that only > finite math has "meaning." But, it seems to me that, within the scope of > *science* and *language*, as currently conceived, there is no *need* to > posit anything non-finite. Science and language are not necessarily > comprehensive of the universe.... Potentially (though I doubt it) mind is > uncomputable in a way that makes it impossible for science and math to grasp > it well enough to guide us in building an AGI ;-) ... and, interestingly, in > this case we could still potentially build an AGI via copying a human brain > ... and then randomly tinkering with it!! > > ben > > On Wed, Oct 29, 2008 at 1:45 PM, Abram Demski <[EMAIL PROTECTED]> wrote: >> >> Ben, >> >> The difference can I think be best illustrated with two hypothetical >> AGIs. Both are supposed to be learning that "computers are >> approximately Turing machines". The first, made by you, interprets >> this constructively (let's say relative to PA). The second, made by >> me, interprets this classically (so it will always take the strongest >> set of axioms that it suspects to be consistent). >> >> The first AGI will be checking to see how well the computer's halting >> matches with the positive cases it can prove in PA, and the >> non-halting with the negative cases it can prove in PA. It will be >> ignoring the halting/nonhalting behavior when it can prove nothing. >> >> The second AGI will be checking to see how well the computer's halting >> matches with the positive cases it can prove in the axiom system of >> its choice, and the non-halting with the negative cases it can prove >> in PA, *plus* it will look to see if it is non-halting in the cases >> where it can prove nothing (after significant effort). >> >> Of course, both will conclude nearly the same thing: the computer is >> similar to the formal entity within specific restrictions. The second >> AGI will have slightly more data (extra axioms plus information in >> cases when it can't prove anything), but it will be learning a >> formally different statement too, so a direct comparison isn't quite >> fair. Anyway, I think this clarifies the difference. >> >> --Abram >> >> On Wed, Oct 29, 2008 at 1:13 PM, Ben Goertzel <[EMAIL PROTECTED]> wrote: >> > >> >> >> >> > >> >> > But the question is what does this mean about any actual computer, >> >> > or any actual physical object -- which we can only communicate about >> >> > clearly >> >> > insofar as it can be boiled down to a finite dataset. >> >> >> >> What it means to me is that "Any actual computer will not halt (with a >> >> correct output) for this program". An actual computer will keep >> >> crunching away until some event happens that breaks the metaphor >> >> between it and the abstract machine-- memory overload, power failure, >> >> et cetera. >> > >> > Yes ... this can be concluded **if** you can convince yourself that the >> > formal model corresponds to the physical machine. >> > >> > And to do *this*, you need to use a finite set of finite data points ;-) >> > >> > ben >> > >> > ________________________________ >> > agi | Archives | Modify Your Subscription >> >> >> ------------------------------------------- >> agi >> Archives: https://www.listbox.com/member/archive/303/=now >> RSS Feed: https://www.listbox.com/member/archive/rss/303/ >> Modify Your Subscription: https://www.listbox.com/member/?&; >> Powered by Listbox: http://www.listbox.com > > > > -- > Ben Goertzel, PhD > CEO, Novamente LLC and Biomind LLC > Director of Research, SIAI > [EMAIL PROTECTED] > > "A human being should be able to change a diaper, plan an invasion, butcher > a hog, conn a ship, design a building, write a sonnet, balance accounts, > build a wall, set a bone, comfort the dying, take orders, give orders, > cooperate, act alone, solve equations, analyze a new problem, pitch manure, > program a computer, cook a tasty meal, fight efficiently, die gallantly. > Specialization is for insects." -- Robert Heinlein > > > ________________________________ > agi | Archives | Modify Your Subscription ------------------------------------------- agi Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/ Modify Your Subscription: https://www.listbox.com/member/?member_id=8660244&id_secret=117534816-b15a34 Powered by Listbox: http://www.listbox.com
