briand@infmx.UUCP (brian donat) (06/20/89)
Please feel free to hack away at the following: Given that the Human Brain is complex, complex to the point that we regard it now in the terminology of chaos theory, and given that we recognize that the outer expressions of the brain (as a system) are well ordered and that this order implies a system of control functions which successively modify 'lower order' variations into large scale composite outcomes, has anybody... 1. done any significant investigative work regarding the identification of the brain's control apparatus or functions? (this is not to be confused with theoretical rumblings about what intelligence or knowledge, etc. are.) I'm sure something's been done here. But I'm particularly interested in the identity of composite transistion zones which qualify for the term of 'points of bifurcation' in the chaos theory definition and also identify 'contact' with specific control functions. 2. done any mathematical calculations to estimate a probable complexity figure characteristic for the human brain? Is there such an animal as a probable complexity figure? Complexity quotient? 3. done any mathematical calculations to estimate a probable complexity figure characteristic for any chaotic system? 4. identified any of the 'low order' variations which affect outcomes in the human brain? 5. having identified 'low order' variations and having calculated a probable complexity figure for the human brain, has anyone begun to analyze the best possible ways to develope a working model which will duplicate any level of the human brain's functionality while achieving the a similar probable complexity figure? These are just a few thoughts turned into questions. It occurs to me that simple binary logics will not suffice to duplicate the complexity figure for the human brain. Instead, something analog might do better. Also, the brain is filled with minor variations which involve metabolism (cell death, protein synthesis, growth, blood/oxygen variations, etc.). What 'non-living' synthetic model could match the complexity quotient of all these variations and still reflect the order of control necessary to play trivial games such as passing a Turing Machine Test? Really, is there such a thing as a complexity quotient? I assume that this might somehow allow a calculation for the magnitude of changes in the outcomes measured at a larger composite definition for a given system, given that at any one time, a given number of pseudorandom events will be occuring which will affect that outcome. I also assume that the inclusion of control functions at various levels within the organization of the system will mathematically affect the quotient in either a negative or positive direction (system destructive or system non-destructive) and that a series of relative complexity quotients might be calculable between these varying levels. Is a complexity quotient needed to progress with assimilation of artificial intelligence? I would think so. Any thoughts? -- brian /=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-\ | Brian L. Donat Informix Software, Inc. Menlo Park, CA | | ... infmx!briand | | | \=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-/
wlp@calmasd.Prime.COM (Walter Peterson) (06/21/89)
In article <1591@infmx.UUCP>, briand@infmx.UUCP (brian donat) writes: > > Please feel free to hack away at the following: > OK. > > Given that the Human Brain is complex, complex to the point that we regard > it now in the terminology of chaos theory... Complexity alone is not a sufficient condition for chaos. The necessary and sufficient condition for chaotic behavior is that the system be a non-linear dynamic system. > > 2. done any mathematical calculations to estimate a probable > complexity figure characteristic for the human brain? > > Is there such an animal as a probable complexity figure? > Complexity quotient? The term dosn't sound familiar. What do you mean by it ? > What 'non-living' synthetic model could match the complexity quotient of > all these variations and still reflect the order of control necessary to > play trivial games such as passing a Turing Machine Test? I don't really think that the Turing Test, if properly performed, is all that trivial a task for a machine. > Really, is there such a thing as a complexity quotient? I don't believe so. Your basic ideas here are interesting. I for one would like to see some more explaination of what you mean by some of your terms. -- Walt Peterson. Prime - San Diego R&D (Object and Data Management Group) "The opinions expressed here are my own."
briand@infmx.UUCP (brian donat) (06/23/89)
> Walter Peterson >> Brian Donat >> Please feel free to hack away at the following: >OK. Very simply put. Having read your response through once, I thought I'd point that out. >> Given that the Human Brain is complex, complex to the point that we regard >> it now in the terminology of chaos theory... >Complexity alone is not a sufficient condition for chaos. The >necessary and sufficient condition for chaotic behavior is that the >system be a non-linear dynamic system. I have some misgivings that a lot of people really do not know (fully) what Chaos Theory implies. You for example, are certainly correct in saying that complexity alone is not a sufficient condition for chaos. However, what is complexity? The german word for simple is 'einfach' which literally means 'onefold'. Is a twofold system more complex than a onefold system? How complex is a 'manifold' system? Complexity is a relative measure. Now this 'non-linear dynamic' thing is more revealing. However, chaos theory sees 'order from chaos' and therefore there is implied a necessary requirement that linear systems also be inlcuded as part of a study of chaos. The textbook definition is misleading. So what is linearity? This sounds to me like 'order', something regular and repeating, something with a proportional rate of change or an 'x' for 'y' correspondance, so to speak. That chaotic systems speak of dynamic systems, this is true. But what really is a 'static' system? It can be argued that a static system is really dynamic, but balanced. Therefore this definition is also misleading, for 'chaos theory' must consider static systems in this light. Chaos Theory is however, more concerned with the study of such systems when they are exposed to 'change', such that 'prediction' of systematic outcomes are possible or especially, in some systems, noted to be 'not possible' because the relative degree of complexity is too great for observational recording of the variables involved. Consider a standing wave in a river, or less complex, a centrifuge as used in bio-chem. We can predict or extrapolate (either way) the dynamics involved with the centrifuge based on the forces involved (gravity and inertia) and the characteristics of the objects within the system. The centrifuge results in a linear system. This is 'control'. Therefore, chaos theory is inevitably bound up with concepts of Information and Control theory. Consider now, a skin cell (not just any skin cell, but a subcutaneous cell, say on the palm of your hand. What makes this cell different from others is not its DNA compliment, but its actual protein makeup. Cell metabolism is ordered; it has linear components; it is 'controlled' by a host of complex variables. While a cell is 'subcutaneous', it has no need to produce the 'hard' proteins which make up surface skin. However, such cells, when exposed will. Why? Remember that the DNA compliment is the same. RNA? Within a skin cell there are several levels of control. We'll describe most of these as molecular, but all respond to both external and internal influences and the results of their motion, is the dynamic expression of another level of control at the cellular level. Most people make another mistake when relating to chaos theory. They jump off the boat to talk turkey in terms of quantum mechanics. Chaos is concerned with relative complexities and the varying levels of 'order' or control which are seen occuring within the system. Prediction is easy when addressing an ordered system simply because of the 'control' seen at that level. However, small changes below the level of expressed control are said to have large global effects such that prediction is not so easy. What is global? Global is the surface context of a level of control. It's what we note to be the system itself. If there were not control, we wouldn't be able to talk about anything global. >> [Has anyone ...] >> 2. done any mathematical calculations to estimate a probable >> complexity figure characteristic for the human brain? >> >> Is there such an animal as a probable complexity figure? >> Complexity quotient? >The term dosn't sound familiar. What do you mean by it ? What I was after here was a prompter to the community out there to take a look at the current efforts in AI and see if they were applying something to their definition of artificial intelligence such that they do not measure their success merely on the successful imitation of certain human communication concepts, but to the extent that their intelligent system is also subject to the same lack of prediction that the real McCoy is. In a separate response to someone else's article, I pointed out that a truely intelligent system 'defines its own problems'. To me this is something which may well be spontaneous and is not a hardwired iteration through a series of decision processes which give solutions to a pre-defined problem. To achieve this level of intelligence in a machine, one would have to model the machine on concepts which allow the machine the sponteneity to define its own problems (The illusion of freedom). Preliminary to this is the problem of getting the machine to maintain it's own health. However, to measure success in the development of such a machine and, to assist in addressing the theoretical constraints, I propose that some quantitative measure be derived for the complexity (relative of course) required to achieve 'apparent spontaneity' or an equivalent degree of spontaneity as seen in 'non-artifically intelligent' systems. It is my belief that these concepts must be know before the AI community progresses further even with simpler systems. If I can call something threefold or three times more complex, that is in itself a relative measure. However, with what we are working with here, it is too simple. A complexity quotient is however, a relative measure of the complexity of the system such that global outcomes are less predictable given minor changes below the global level, thus giving the allusion of spontaneity in decisions, and allows that global actions are at least partially predictable, at the global level because of the control which exists at that level. Let's not forget that intermediate levels of control exist also. A complexity quotient is thus a milestone by which AI scientists may measure their success in achieving this particular aspect of 'intelligence'. >> What 'non-living' synthetic model could match the complexity quotient of >> all these variations and still reflect the order of control necessary to >> play trivial games such as passing a Turing Machine Test? >I don't really think that the Turing Test, if properly performed, is >all that trivial a task for a machine. Please consider my use of the word trivial to be also a relative usage. Certainly, the effort required to get a machine to behave in a manner which allows passing the Turing Test is no trivial thing. However, a machine that will achieve the true sponateous character of intelligence is by far more displaced from the notion of trivial. -- brian /=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-\ | Brian L. Donat Informix Software, Inc. Menlo Park, CA | | ... infmx!briand | | | \=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-/
vu0112@bingvaxu.cc.binghamton.edu (Cliff Joslyn) (06/23/89)
In article <1600@infmx.UUCP> briand@infmx.UUCP (brian donat) writes: >>> Given that the Human Brain is complex, complex to the point that we regard >>> it now in the terminology of chaos theory... > >>Complexity alone is not a sufficient condition for chaos. The >>necessary and sufficient condition for chaotic behavior is that the >>system be a non-linear dynamic system. > >I have some misgivings that a lot of people really do not know (fully) >what Chaos Theory implies. You for example, are certainly correct in >saying that complexity alone is not a sufficient condition for chaos. This is all very confused. Chaos means (generally) that any two arbitrary trajectories of a system's behavior can become arbitrarily close, so that they cannot be distinguished, and/or that the margins of error increase exponentially in time. Being a dynamical system is not necessary for chaos, rather chaos is only *defined* on dynamical systems. Non-linearity is a necessary, but *not* a sufficient, condition for chaos. While chaos is formally defined, there are many formal and informal meanings of complexity. While many chaotic systems appear complex, complexity and chaos are not mutually necessary. Complexity means to have a lot interacting parts, or to take a long time to construct, or a lot of work. >Now this 'non-linear dynamic' thing is more revealing. However, chaos >theory sees 'order from chaos' and therefore there is implied a necessary >requirement that linear systems also be inlcuded as part of a study of >chaos. The textbook definition is misleading. In a differential system, only three dimensional non-linear systems show chaotic behavior, where linear means that the state variables have only constant coefficients. Chaos is not well defined outside of differential/difference equations. >But what >really is a 'static' system? It can be argued that a static system is >really dynamic, but balanced. A static system is one that does not change in time. No static systems can be chaotic. All static systems appear "balanced", but not all "balances" are static, e.g. dynamic equilibria (steady states), say in a chemical reaction or in population dynamics, where there is continual movement of two opposite kinds which is balanced *on the average* and appears static only *on the large scale*. The answers to the original poster's questions about the state of the art of complexity metrics, complex systems theory, dynamic systems theory, and chaos theory are all readily available in the literature. I'll be happy to post or mail a bibliography. -- O----------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large | Systems Science, SUNY Binghamton, vu0112@bingvaxu.cc.binghamton.edu V All the world is biscuit shaped. . .
cam@edai.ed.ac.uk (Chris Malcolm cam@uk.ac.ed.edai 031 667 1011 x2550) (06/24/89)
In article <1591@infmx.UUCP> briand@infmx.UUCP (brian donat) writes: > >Given that the Human Brain is complex, complex to the point that we regard >it now in the terminology of chaos theory, ... Chaos theory shows that very complex BEHAVIOUR can derive from very SIMPLE SYSTEMS. We also always knew that you could get simple behaviour out of very complex systems, not to mention complex behaviour, without needing chaotic behaviour. Chaos (in the technical mathematical sense) has got nothing to do with how complicated a system is. > 2. done any mathematical calculations to estimate a probable > complexity figure characteristic for the human brain? What do you mean by complexity? What your atomic unit of complexity - the simplest possible thing? And are you concerned with structure, or behaviour, or potential for variation, which are three quite different things? > 4. identified any of the 'low order' variations which affect > outcomes in the human brain? Lots of people are working on this. So far they've identified ethyl alcohol, marihuana, opium, cocaine, tea, coffee, tobacco, mescal, jimson weed ... > 5. having identified 'low order' variations and having > calculated a probable complexity figure for the human brain, > has anyone begun to analyze the best possible ways to > develope a working model which will duplicate any level > of the human brain's functionality while achieving the > a similar probable complexity figure? Why this constraint? Wouldn't it be neat to duplicate functionality with a _simpler_ system? For example, aeroplanes didn't really take off until they stopped trying to flap wings like birds. >play trivial games such as passing a Turing Machine Test? Ah! You have examples of some more complicated games we could try? >Is a complexity quotient needed to progress with assimilation of >artificial intelligence? Give me some simple examples of complexity quotients in operation - I don't understand the idea at all. What is divided by what? -- Chris Malcolm cam@uk.ac.ed.edai 031 667 1011 x2550 Department of Artificial Intelligence, Edinburgh University 5 Forrest Hill, Edinburgh, EH1 2QL, UK