> > > ... what criteria should apply [to complexity] and why one ranks higher > than another. >
Ack, please forgive the copy/paste fumble. I found the source of Dijkstra's observation, and it seems I had added quite a bit of my own conclusions. His was: For us scientists it is very tempting to blame the lack of education of the > average engineer, the short-sightedness of the managers and the malice of > the entrepreneurs for this sorry state of affairs, but that won't do. You > see, while we all know that unmastered complexity is at the root of the > misery, we do not know what degree of simplicity can be obtained, nor to > what extent the intrinsic complexity of the whole design has to show up in > the interfaces. We simply do not know yet the limits of disentanglement. We > do not know yet whether intrinsic intricacy can be distinguished from > accidental intricacy. We do not know yet whether trade-offs will be > possible. We do not know yet whether we can invent for intricacy a > meaningful concept about which we can prove theorems that help. To put it > bluntly, we simply do not know yet what we should be talking about, but that > should not worry us, for it just illustrates what was meant by "intangible > goals and uncertain rewards". (November 19th, 2000 - > EWD1304<http://www.cs.utexas.edu/users/EWD/transcriptions/EWD13xx/EWD1304.html> > ) I think he's a little too doom-and-gloom here. I think it's fair to say that a given solutions to a problem has some intrinsic complexity - that dependent on which cognitive models we decide use to consider the problem. Exploring the intrinsic complexity of problems and solutions is the domain of mathematics. Then there is the related complexity of designing a machine to derive the solution for a given instance of the problem (or as is more common nowadays, designing an algorithm to run on modern hardware). The latter complexity is "extrinsic" to the problem itself, and also, in some sense, "extrinsic" to our cognitive reasoning about it. EWD seems most pessimistic about the meta-properties of our models - measuring the complexities in relation to the problem and to each other. But while modeling our cognitive models is a much younger domain, there's certainly people asking these questions under the guise of "foundations of mathematics" or "cogsci of mathematics" or "cognitive science" in general. Personally, I find Lakoff and Núñez's "Where Mathematics Comes From" rather convincing in its broad strokes, even if lacking in testable hypotheses. Cheers, Andrey
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