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Hi as i see it the problem of increasing complexity through exponentially increasing reltions - that might or might not matter - is not the real problem in social simulation. The real problem is that of getting qualitative change into the model, and qualitative change in a fashion that goes beyond the phase transition type of change. This week there is short interview with Frank Schweitzer in c't a german computer magazine. He implicitly argues that one could get from quantitaive changes - the collective state a la pahse transition which emerged form the interactions among agents - via co-evolution to qualitative change, i.e. "second-order emergence" (I am not quite sure whether he really means the same as von Foerster). He concludes - as far as he knows - that nobody has managed to reach self-organisation models of hierarchical social structures. a) Is he right? b) why? And now comes some marketing ;) theres an article of mine in JASSS 4/4/8 from 2001 that touches upon some of the problems. There is also the work of R.A. Watson at Brandeis how is working on a computational implementation. The basic problem is that of emergence and how it is possibly brought about by compartmentalization - that is actually sth that Herber Spencer - despite other misgivings - got right in his trial to identify evolutionary principles in/from biology and sociology. Similarly Margulis theory of increasing complexity in cell-evolution works with fusion and compartmentalization. Szathmary and Maynard Smith also present some mechanisms to overcome this problem in their 1995 article (Nature it was I think). Therefore the way to succes might be to defocus from interaction and get the fusion/compartmentalization into the model since it could deliver the system transition that seems necessary for qualitative change / emergence. This is not necessarily a problem of computing power and computability, but of model / system structure. Comments? Am I right or did i oversee sth? Best, Carl Henning Reschke --- "Bayer, Steffen" <[log in to unmask]> wrote: > Hi, > > as far as I can see Loet's argument about the > enormous increase in the > computational space for social systems is even > stronger than he makes it. > > If we allowed persons to have multiple relations, > there could be many more > than 10^10 configurations of relations between 10 > persons. > > If I am not mistaken there would be (2^9)^10 = 2^90 > configurations if > relations could be uni-directional and (2^9 + 2^8 + > 2^7 + 2^6 + 2^5 + 2^4 + > 2^3 + 2^2 + 2^1 = 2^45) if relations were > bi-directional. > > Steffen > > > Dr Steffen Bayer > Innovation Studies Centre > The Business School > Imperial College London > South Kensington Campus > London, SW7 2AZ, UK > > ph.: +44-(0)20 759 45935 > fax: +44-(0)20 7823 7685 > office: Rm 101, Civil Engineering bldg > http://www.imperial.ac.uk/business/innovation > > > -----Original Message----- > From: Loet Leydesdorff [mailto:[log in to unmask]] > Sent: 08 April 2003 18:37 > To: [log in to unmask] > Subject: Re: computability ... Re: Bit-flipping > model of culture > > Dear Andreas and colleagues, > > I thought that non-computability is particularly > relevant to social > systems because the N of cases is part of the > exponent. The > computational space then rapidly explodes. > > For example, if one throws two dice there are 6^2 > possibilities. If one > throws three dice, there are 6^3 possibilities, etc. > In general: 6^N, > where N is the number of dice. > > Analogously: If we have a group of 10 persons who > can all maintain > relations with each other, this system has 10^10 > possible states if each > configuration of relations is counted as one > possible state. The > specification of mechanisms (hypotheses) selects on > this phase space and > makes the system computable. > > With kind regards, > > > Loet > _____ > > Loet Leydesdorff > Science & Technology Dynamics, University of > Amsterdam > [log in to unmask] ; http://www.leydesdorff.net/ > > > > -----Original Message----- > > From: News and discussion about computer > simulation in the > > social sciences [mailto:[log in to unmask]] On > Behalf Of > > Andreas Schamanek > > Sent: Sunday, April 06, 2003 12:31 AM > > To: [log in to unmask] > > Subject: computability ... Re: Bit-flipping model > of culture > > > > > > Hi SIMSOC, > > > > On Tue, 1 Apr 2003, Alan Penn wrote: > > > > > This brings a question to mind: are there any > qualitative > > properties > > > of systems that are provably _not_ representable > in terms of bits? > > > > > > The theory of computation says that anything > computable can be > > > computed using a finite state machine (if I > understand it > > right) so I > > > suppose such properties - if they exist - must > not be > > computable. If > > > so what are they, and are they socially > interesting? > > > > From a social sciences' point of view (and quite > some more), > > I'd say that I do not like the notion of > 'computability'. Is > > there a property that is not represented in any > way? Is there > > a property that cannot be represented in some way? > Every > > computation is some form of representation (that > we generally > > call model). It depends solely on yourself (and > your > > colleagues) whether a property is computable or > not. > > > > Of course, the notion of 'representation' is also > a > > representation. But, that's a different story. > > > > Another story, since we have already discussed > lots of chaos > > theory, here, goes like this: As most of you know, > one of the > > properties of a deterministic chaotic time series > is the fact > > that values do not repeat. No matter how often you > iterate, > > e.g., the logistic equation > > > > X(n+1) = 4 * X(n) * ( 1- X(n) ) ; X(0) out of [ > 0 ... 1 ] > > > > there will never be a value of X(n) that equals > any other > > X(m) except for m = n. > > > > A computer is only a finite state machine. It can > compute > > everything, but only given enough time and enough > finite > > states :) Our everyday computers are _very_ finite > state > > machines. So, if you compute the logistic equation > with a > > computer (using some computer language, say > FORTRAN or C), > > you will observe that already after only a few > iterations of > > the logistic equation you will get a X(n) that you > have seen > > before. Once you have found this X(n), say after p > > iterations, every X(m+p) will equal X(m) for m = > n, n+1, n+2, > > ... You have found a cycle, a period of length p. > (p, by the > > way, is astonishingly small: often only a few > thousand > > iterations if you declare/define X as a single > precision variable). > > > > So, here is a property that is (generally) not > computable: > > Deterministic chaos. > > > > Besides non-periodicity there is also the Lyapunov > exponent > > which shall be above 1 for chaotic time series. > The Lyapunov > > exponent, by the way, is a measure for how much or > how fast 2 > > time series that describe the same system will > nevertheless > > diverge if computed with slightly different > values. > > > > The strange part of this story is that when you > compute the > > Lyapunov exponent for a time series generated by a > > computation of the logistic equation, i.e, a > periodic time > > series, you still get values above 1. > > > > Does that mean that when we look at computed > non-computable > > properties by means of computation that we see the > world just > > like it is? > > > > > > > === message truncated === __________________________________________________ Do you Yahoo!? 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