Category Theory is newer than Group Theory, and I'm just starting to understand it so can't speak much of it, but it seems to be better and more encompassing than Group Theory. Group Theory and all that can be described with it, covers a lot, an unimaginable universe of design possibilities. Limitations in contemporary computer hardware processing ability necessitate compensation for the lack thereof. Well designed mathematical structures enable vast efficiency compensations. The structures and systems that Group Theory enable are just amazingly efficient. If you can build thinking models, substructures, components, intercommunication networks of objects, decision bots, evolvable reconnaissance agents or whatever you want, described with groups, algebras, related derivatives, operating on graphs, utilizing traditional AI (like a skin) before even coding you have the advantage needed over AGI's that rely heavily on traditional AI conglomerations slapped together with big data reservoirs with lots of hardware and administration thrown at them. You can build, prototype, evolve, without ever coding and start the coding later. This can be done with the usual math constructs, but Group Theory (GT) is more digital, more encompassing, more representative and operational. Yes other math technologies can be described, enhanced, redesigned, but it's like can a NN algorithm be built from scratch with another NN? Maybe, but with GT, esp. if your system had ample of it built in could spit out algorithms and morphisms for the appropriate problem domain. With data representation, the more sophisticated the representation, the less data storage required (compression) alluding to efficiency in modeling real world data objects and systems. With GT, intensely sophisticated constructs (engines?) can describe huge amounts of data (or patterns and morphisms) at a higher order. Basically, many things can be described with a relatively few algorithms and those algorithms can be described with a basic set of math (GT) systems and the more things described means less hardware for storage (RAM, Disk, etc.), and less bandwidth.
John -----Original Message----- From: Benjamin Goertzel [mailto:[EMAIL PROTECTED] Sent: Thursday, April 12, 2007 5:18 PM To: [EMAIL PROTECTED] Subject: Re: [agi] AGI interests > I only know that category theory is some more rarified and > specialized type of group theory. I'd like to hear how it might be > relevant. Category theory isn't really a kind of group theory, it's better thought of an alternative to set theory as a foundation for mathematics... It's relevant to the foundations of functional programming, for example.... Personally I don't think it's all that relevant to AGI engineering, except insofar as an AGI system may use functional programming methods for procedure representation. However, I do think category theory might be a good tool for modeling and interpreting the **emergent structures** that arise within a mind -- reflexive awareness and all that... OTOH, I can see how it might be possible to engineer a reasoning system with category theory at the foundation.... An interesting notion but IMO not necessary. -- Ben ----- 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/?&; ----- 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
