Arguing for use of differential equations to model intelligence, is sorta like arguing for use of Lie groups and Feynman diagrams to model biochemistry...
After all, the level underlying biochemistry -- which consist of elementary particles -- is well modeled by Lie groups, Feynman diagrams and associated math... But actually, the math of elementary particle physics is not the simplest tool for modeling biochemistry, even though it's in principle applicable Similarly, the math of differential equations -- though great for physics and useful for lower-level neuroscience and many other areas -- is not necessarily the simplest and most useful tool for modeling cognition... I studied lots of diff eq in grad school, and I would have a great time applying them to cognition, if I saw a good way to do so.... I realize it's different from the direction you're pushing in, but here is a paper of mine that uses continuous math to describe cognitive systems... *HTTP://goertzel*.org/papers/*MindGeometry*_agi_11_v2.pdf It also explicitly relates continuous math to computational math.... It's more inspired by general relativity than by classical physics though -- and more by the geometric aspects than the specific form of equations involved... This is an attempt to use this continuous math to guide the design of an AI component... *HTTP://goertzel*.org/ECAN_v3.pdf But while I see the use of continuous math to model and guide aspects of AGI systems as interesting, I don't see why it's critical... I grew up on diff-eq models of complex dynamical systems, it's great stuff. However, I don't think one needs to take that approach to build a mind.... I believe nonlinear dynamics are important for AGI, but I don't see what you get from continuous-variable diff-eqs that you can't also get from discrete dynamical systems... -- ben g On Tue, Jul 10, 2012 at 6:19 AM, Steve Richfield <[email protected]>wrote: > Derek, > > More good comments... > > On Mon, Jul 9, 2012 at 2:42 PM, Derek Zahn <[email protected]> wrote: > >> >> Steve Richfield wrote: >> >> > Obviously, you haven't grokked this yet. >> >> Yes, this is true. I'm afraid that your subsequent explanations haven't >> really helped much either. You seem to be saying that: >> >> - "Everything" physical works by integrating forces >> - Differential equations mathematically model such forces >> - Therefore... here I'm less clear. Either you're saying that we can >> model minds (which are the product of physical things) with differential >> equations, or that minds themselves are differential equation simulators >> (and therefore AGI programs should most importantly be differential >> equation simulators), or something else... >> > > First, your are asking for my speculations, in which even I have rather > limited faith. > > It is hard to split "modeling" and functionality, except when you do > something (like "weak" AGI) that is clearly NOT being done in minds. Since > I am not proposing anything that is clearly not being done in our own > minds, I am unable to split these possibilities. > >> >> In any case: >> >> >> ... barring some revolutionary new perspective on cognition, >> > >> > Which is exactly what we are looking for here. >> >> >>just to start: what exactly are you thinking the variables in >> differential equations should refer to >> > >> > Whatever works >> >> Surely you can see that this is not very compelling; > > > This is what the neural network folks do - make everything available and > see what gets incorporated. This appears to be the fundamental basis for > self-organization. Do you see any other possibilities to guide > self-organization? > > gotta have a little more development to justify any more time spent on it. >> > > Young bull to old bull: Look up on that hill. I see some cows up there. > I'm going to run up there and get me one. > > Old bull to young bull: You just run along son. I'll take my time and get > the rest of them. > > You appear to be in way too much of a hurry to forge any new trails. > >> >> Instead, you just insist that it must be necessary, but in a fallacious >> way: >> >> > Let me get this right. You expect to build intelligent systems while >> > willfully ignoring the very principles that governs all changes in our >> > environment?!!! >> >> There are so many ways to answer this it's hard to know where to even >> begin... >> - Evolution constructed intelligent systems without thinking carefully >> about differential >> equations (by any reasonable definition of those concepts), so it is >> hardly necessary. >> > > On the contrary. Primitive systems like in the hydra are all about process > control, which is all about diffy-Q. This is where things began. Who knows > how much of this is still inside our heads, but clearly the hypothalamus > must work this way. > > - There are many ways of viewing "the very principles that govern all >> changes in our environment". > > > Some examples would help to make this point. > > >> That describes quantum mechanics. It describes causality. Etc. It's all >> a matter or perspective. >> > > What is needed is the MOST macroscopic way to view things that still > works. quantum mechanics provides little/no macroscopic guidance, whereas > diffy-Q appears to offer a strong possibility. > > Granted that "weak" AGI is more macroscopic than diffy-Q. The **BIG** > question is whether it can be made to work in any sort of useful way. I am > unconvinced, but others (like Ben) are undeterred and are charging on > ahead. Time will tell. > > >> - The map is not the territory. >> > > ... not until integrated circuits came along, whereupon the "print" became > the device - a little like Wilhelm Reich's infamous machines. Have you ever > heard of orgone energy? > > People naturally put more stock in well-developed perspectives or at least >> their own poorly-formed intuitions instead of adopting such from an >> Internet forum. >> > > They SHOULD be considering all the possibilities, applying the scientific > method, and going with whatever works. > >> >> When you have more developments (in particular, more specific answers >> than "whatever works", > > > This is good enough for pretty much everyone who is working the > self-organizing puzzle. What other sort of approach to self-organization > would you suggest? > > >> and something beyond a general call for a revolutionary theory), > > > More than a call, diffy-Q provides some pretty precise guidance. > > >> do post more about it! Without something more, it is hard to justify >> diverting from one's own ideas. >> > > In your case, I think I may agree. > > Steve > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/212726-11ac2389> | > Modify<https://www.listbox.com/member/?&;>Your Subscription > <http://www.listbox.com> > -- Ben Goertzel, PhD http://goertzel.org "My humanity is a constant self-overcoming" -- Friedrich Nietzsche ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-c97d2393 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-2484a968 Powered by Listbox: http://www.listbox.com
