Ben et al For what it's worth, you might want to reconsider my rudimentary work on tacit knowledge engineering, which deals extensively with association and lower-level functions and its many complications within architectural constraints (as the CAMF). (freely available on researchgate).
For excellent reasons, I never published any white papers on the method after 2008. Still, R&D never stopped. The "missing" work all the way to genetic engineering has been completed. Further, to my mind, the world of "association" and all its complexities has also been conquered, even down to solving the most-relevant riddle of 'priority of priorities'. Based on a useful ontology of natural language, which I see graph theory relies on most similarly, and associative functionality, the struggle to extend the method into operational functionality and how to derive the knowledge contexts from reverse-engineered functionality, was real. I think I spent a year on that aspect before "discovering" a working solution for the method specifically (not for all of science). Still, the work is never done. I'm definitely no mathematician, but if I understood correctly what you're busy talking about, the latest extention to the method - still in theoretical development, as The Pattern of One (Po1) - has opened a doorway to potentially formalizing Riemann functionality, perhaps even to autonomous quantum encryption and messaging, etc. I have my genius, and everyone else has his/her own. It's not a competition, or at least, it should not be. Diversity is a key in itself. Perhaps, it's time to pool diverse genius, with due regard for IP? Point remains, the quantum-based method still hasn't failed after all these years of field testing, and if the hypothesis of seamlessly-scaling concurrent engineering in near-real time proves correct, it shouldn't either. My wild guess is that when quantum computing becomes available, this would be the key constraint developers are going to encounter in their logic. It doesn't have to be this way. My recent "From NGI (Natural General Intelligence) to AGI; troubled thoughts..." article on LinkedIn should give all AGI researchers and developers pause to consider. I was going to publish it on this list, but I decided a broader audence would be more appropriate. Regards Robert Benjamin ________________________________ From: Ben Goertzel <[email protected]> Sent: Tuesday, 09 February 2021 02:39 To: AGI <[email protected]> Subject: Re: [agi] new paper: Logic in Hilbert space I wrestled with similar issues regarding associativity and cognitive operations when writing this paper https://arxiv.org/abs/2004.05269 -- see Section 6.2.1 where I show that if you have a set of mutually associative combinational operators, then you get a very nice subpattern hierarchy ... which is much messier to get without mutual associativity... An interesting question is whether: IF you have a set of mutually associative combinational operators, can you then isomorphically map the functions being combined into Hilbert space vectors to that the (associative) combinations map into vector operations? I have not thought about this before and am not sure if it can be made to work Quantum mechanics uses complex Hilbert spaces, and i did go thru some work to make an approximate isomorphism btw paraconsistent logic truth values and complex amplitudes, https://arxiv.org/abs/2101.07498 but that addresses a different part of the same problem, it seems -- Ben On Sun, Jan 31, 2021 at 2:45 AM YKY (Yan King Yin, ηζ―θ΄€) <[email protected]<mailto:[email protected]>> wrote: On 1/30/21, Ben Goertzel <[email protected]<mailto:[email protected]>> wrote: > Unless I remember wrong (which is possible), function application in a > Scott domain is not associative, e.g. > > (f(g) ) (h) > > is not in general equal to > > f( g(h) ) > > However function composition is associative, and the standard products > on vectors in Hilbert space are associative > > So it seems what you're doing may not be quite right, and you need to > be looking at some sort of fairly general nonassociative algebras over > Hilbert space instead ... or something... > > Or am I misunderstanding something? Damn... you're right π I have no idea how to make one function "apply" to another, except by function composition, so that was what I did. But I forgot about associativity... I don't know if I should pursue along this any further.... it seems computer-implementable but it's very complicated... and I currently don't know how to make non-associative algebras.... Thanks for pointing out my mistake, it's helpful π YKY -- Ben Goertzel, PhD http://goertzel.org βHe not busy being born is busy dying" -- Bob Dylan Artificial General Intelligence List<https://agi.topicbox.com/latest> / AGI / see discussions<https://agi.topicbox.com/groups/agi> + participants<https://agi.topicbox.com/groups/agi/members> + delivery options<https://agi.topicbox.com/groups/agi/subscription> Permalink<https://agi.topicbox.com/groups/agi/T54594b98b5b98f83-M5d4d8e1d1e09d9b49c528cc7> ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T54594b98b5b98f83-Mec971db895f3ba814a9f091d Delivery options: https://agi.topicbox.com/groups/agi/subscription
