> > Let's consider a program is a network with objects as nodes and paths of > communication as edges... >
"Channels between nodes" are part of an "algorithm", and hence counts towards its "size". Again, I'm looking for *well defined* measurement of "size" and "complexity" where the two aren't the same. Often in science, relations amongst objects are not considered as > significant. > What? This was particularly the case in biology for a long time where a large > number of practitioners thought they could understand biological systems in > their entirety by isolating subsystems and not considering that in reality > these systems exist in an environment Even if this were true once, modern practitioners obviously don't believe this. It's now reasonably well accepted that evolutionary systems seem to thrive on tight coupling and side effects, whereas engineered systems attempt to minimize it. While really fascinating, evolves systems aren't in the scope of what most programming is about. if complexity can be understood in terms of topology and graph theory > But how can complexity be understood in therms of "topology" and "graph theory"? What about the complexity of a sorting algorithm? Are you sure you know what topology is? Cheers, Andrey On Tue, Mar 2, 2010 at 9:25 PM, Wesley Smith <[email protected]> wrote: > On Tue, Mar 2, 2010 at 1:18 PM, Andrey Fedorov <[email protected]> > wrote: > > John Zabroski wrote: > >> > >> the three stumbling blocks are size, complexity and trustworthiness > > > > How are these different? > > A small program is a simple program by definition, assuming it's > expressed > > in an intuitively comprehensible way. > > I disagree that a small program is by definition a simple program. > Let's consider a program os a network with objects as nodes and paths > of communication as edges. If you have a program with N objects and > N-1 edges, it's going to be a simple and pretty linear program. If > however, in the other direction, each object itself has N-1 edges for > N*(N-1) paths of communication you'll quickly end up with a complex > system without growing in size. Complexity is a question of topology > and graph theory, size is a question of quantity. > > Often in science, relations amongst objects are not considered as > significant. This was particularly the case in biology for a long > time where a large number of practitioners thought they could > understand biological systems in their entirety by isolating > subsystems and not considering that in reality these systems exist in > an environment. A powerful case for thinking about relationships was > made by Bertalanaffy in his book General Systems Science. What > particularly struck me about his work is the difference between > informational feedback/openness (e.g. Cybernetics) and structural > feedback/openness particularly of the thermodynamic kind. In > Cybernetics, it's not possible for a system to evolve into a more > complex structure whereas with thermodynamic feedback and input of > negative entropy it is. This may seem like it has nothing to do with > computer science or software, but I think it does. These concepts can > show us how to understand complex systems, especially those that are > capable of changing in structure. > > Incidentally, there's a link between the ideas of Bertalanaffy (and > also the related ideas of Prigogine) to Lambda Calculus via the work > of Walter Fontana and his work on Abstract Chemistry > (http://tuvalu.santafe.edu/~walter/Papers/barrier.pdf<http://tuvalu.santafe.edu/%7Ewalter/Papers/barrier.pdf>, > http://tuvalu.santafe.edu/~walter/Pages/publications.html<http://tuvalu.santafe.edu/%7Ewalter/Pages/publications.html>) > > > > And a simple program is a program I > > can trust to do what I think it does. Conversely, the only reason I > wouldn't > > trust a program (assuming I trust the compilers/interpreters) is because > it > > would be too complicated to understand. That's what I meant when I quoted > > > As for trustworthiness ... if complexity can be understood in terms of > topology and graph theory, then trustworthiness can be understood in > terms of applying graph theoretical techniques to verify or guarantee > behavior of the structures represented by the network. > > All in all, I think there's a pretty clear distinction to be made. > > wes > > _______________________________________________ > fonc mailing list > [email protected] > http://vpri.org/mailman/listinfo/fonc >
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