While the question of human intelligence is interesting please note that my post topic has been restricted to the application of GPT-like / AI-like systems to the automation of proof and computer algebra.
Given the changes I'm seeing and the research I'm doing it is likely that there will be a very rapid change from the legacy version of computer algebra we now use, taking advantage of the growing power of these systems. I've been involved and published in AI-like systems since the 1973, including such "AI-like" areas of machine vision, robotics, expert systems, speech, neural nets, knowledge representation, planning, etc. All of these were considered "intelligent behavior" ... until they weren't. Indeed, in the 1960s computer algebra-like systems were considered "intelligent". Intelligence is a "suitcase word" [0], interesting but irrelevant. The topic at hand is "computational mathematics", meaning the application of recent technology (proof assistants, theorem databases, algorithm proofs, and reasoning assistants) to moving beyond 50-year-old legacy computer algebra. Proving computer algebra algorithms correct and providing useful interfaces is the long-term goal. Tim [0] "Marvin Minsky, in his fascinating book "The Emotion Machine" ... described words such as "emotions," "memory," "thinking" and "intelligence" as suitcase words - words that mean "*nothing by itself, but holds a bunch of things inside * *that you have to unpack*." On Wednesday, January 17, 2024 at 10:03:53 PM UTC-5 elders...@gmail.com wrote: > Good morning Waldek, > > My response will be delving into some areas of philosophical and > metaphysical response. > > On Thu, Jan 18, 2024 at 2:56 AM Waldek Hebisch <de...@fricas.org> wrote: > >> On Thu, Jan 18, 2024 at 01:16:55AM +1100, Hill Strong wrote: >> > On Wed, Jan 17, 2024 at 11:09 PM Tim Daly <axio...@gmail.com> wrote: >> > >> > They can raise the issue all they like. What they are not seeing is that >> > artificial stupidity (AI) systems are limited. As I said above. The only >> > intelligence you will find in these systems is the stuff generated by >> human >> > intelligence. No artificial stupidity (AI) system can ever exceed the >> > limitations of the programming entailed in them. >> >> Well, humans are at least as limited: your claim as true as claim >> that "humans can not ever exceed the limitations of the programming >> entailed in them". In case of humans programming meaning both things >> > > Though we are limited in every sort of way, we are capable of exceeding > any programming that is involved in our development. What is so not obvious > is that there is a category error when comparing humans to any sort of > machine that we build. Though we can build machines stronger, faster and > able to handle tedious tasks far better than we can do, due to our very > distinctive intelligence, we are able to do what no machine can do and that > is solve the problems that arise. > > > hardcoded in genome and chemical machinery of the body and "learned >> stuff". Already at age 1 toys, customized environment and interactions >> > > You speak here about [programming] hard-coded in the genome and chemical > machinery of the human body. But I somehow don't think you realise just how > far beyond us is that machinery. Within a single living cell, the automatic > adaptive capabilities are so far beyond our current levels of technology > that in comparison, we are no more advanced than some caveman when we > compare the entire planetary industrial and planetary capabilities that we > have already made. > > The more we learn about cellular biology with its internal transportation, > control and manufacturing systems the more we should be recognising that we > are not capable of building any computerised system that will ever be > intelligent. > > with other humans make significant difference to learning. At later >> stages there are stories which were perfected for thousends of years, >> school curricula and books. There were myths that people from >> non-western cultures are less "inteligent" than people from western >> culture. More deeper research showed that part of our "inteligence" >> is really "programmed" (learned) and "programming" in differnet >> cultures were different. >> > > Though part of our intelligence is learned there is something that is so > far beyond this, so that, even though this is an active area of research, > we haven't a clue as to what this is. > > >> In slightly different spirit, in fifties there were efforts to >> define inteligence and researcheres from that time postulated >> several abilities that every inteligent being should have. >> Based on that there were "proofs" that artificial inteligence >> is impossible. One of such "proofs" goes as follows: people >> can prove math theorems. But Goedel and Church proved that >> no machine can prove math theorem. So no machine will match >> humans. The fallacy of this argument is classic abuse of >> quantifiers: humans can prove same (easy) math theorems. >> > > Here you are now arguing against the various incompleteness theorems and > in doing so, you are entering the realm of metaphysics and philosophy. > These incompleteness theorems highlight something quite interesting in that > the basis of our logic and mathematics (the fundamental axioms used) cannot > be proved true from within our logic and mathematics. We can argue for them > from metaphysics and philosophy but we are unable to prove them from within > the systems that are based on those fundamental axioms. > > What you have missed here is that any theorems developed within the > systems are provable based on those unprovable axioms and previously proven > theorems. That is how we can build up the various systems of mathematics in > use. However, new mathematical systems require insights not possible to any > computerised system. These new insights are in the realm of human > intelligence which does exceed any programming that individual humans may > be exposed to. > > No machine or human can prove _each_ math theorem. Actually, >> we still do not know how hard is proving, but common belief >> > > All theorems can be proved if they are based on the initial set of axioms > used. How hard it is to prove the theorem is another matter. > > >> is that complexity of proving is exponential in length of the >> proof. What is proven is that that there is no computable >> bound on length of shortest proof. Clearly this difficulty, >> that is large length of proofs affect humans as much as >> computers. >> > > Maybe. The thing of interest here is that it is humans who can find > alternative ways of proving a theorem which is not a part of the exhaustive > processes previously used. > > As you would well know, the Halting problem is not solvable by any Turing > machine or corresponding alternative. But we can see the problem > immediately. We make leaps and find solutions that are not possible within > a logical/mathematical system. > > >> To put is differently, if you put strong requirements on >> inteligence, like ability to prove each math theorem, then >> humans are not inteligent. If you lower your requirements, >> so that humans are deemed inteligent, than appropriately >> programmed computer is likely to qualify. >> > > Your comment above is false. It is false logically, rationally, > metaphysically and philosophically. The ability to prove a mathematics > theorem, if based on previous axioms and theorems, is not a sign of > intelligence. I would agree that we do this as a part of our intelligence, > but this is not a sign of intelligence. The axioms used at the fundamental > level which are designed and specified may well be a sign of intelligence, > but no computerised system does this. I have spent 40 years looking at > these kinds of things and every computerised system is based on the human > intellectual capacity (intelligence) for these systems to even exist. > >> >> One more thing: early in history of AI there was Eliza. >> It was simple pattern matcher clearly having no inteligence, >> yet it was able to fool some humans to belive that they >> communicate with other human (ok, at least for some time). >> > > The ability to fool people does not challenge our intelligence. Every > human is flawed and can be fooled. We see that every day in every society. > This does not lessen what humanity has in terms of being intelligent. We > act irrationally, we act in completely adverse ways. We make decisions that > make no sense. We even choose options that are not actually available to > us. We can see this in the recent Iowa caucus where the winner wasn't even > on the available options. > > Machine programming doesn't allow this. Certainly, we can see all sorts of > errors and when fully studied, we see why those errors occurred. They are > logically defined. > > Some people take this to consider all solved AI problems >> as kind of fake and show that the problem was not about >> inteligence. But IMO there is different possiblity: that >> all our inteligence is "fake" in similar vein. In other >> > > If our intelligence is [fake] then the logical consequence of that > argument is that there is no mathematics, no scientific investigation, no > rationality, no intelligence, no progress in any form. This is a > contradiction. We do do mathematics, we do do scientific investigation, we > do do philosophy and metaphysics, we do do rational things. > > words, we do not solve general problem but use tricks which >> happen to work in real life. Or to put it differently, >> > > Yes we do do tricks and this is one sign of intelligence here. Certainly > we are limited and I have been saying such things for a long time. However, > for all of our limitations, we are in a category that is very different to > all other things, living or otherwise and we often fail to recognise, let > alone understand that category difference. > > I have seen too many people who dismiss philosophy and metaphysics as > being useless. Yet it is by these that we show forth our intelligence and > by which we can justify mathematics and scientific investigation as valid, > rational and proper intellectual pursuits. > > > we may be much more limited than we imagine. Eliza clearly >> shows that we can be easily fooled into assuming that >> something has much more abilities than it really has >> (and "something" may be really "we"). >> >> -- >> Waldek Hebisch >> >> -- >> You received this message because you are subscribed to the Google Groups >> "FriCAS - computer algebra system" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to fricas-devel...@googlegroups.com. >> > To view this discussion on the web visit >> https://groups.google.com/d/msgid/fricas-devel/Zaf4t0bQZRQAsouA%40fricas.org >> . >> > -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To unsubscribe from this group and stop receiving emails from it, send an email to fricas-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/fricas-devel/538038f1-74ca-4a0a-ac07-6ccaf9115356n%40googlegroups.com.
