2. Okay, I know I always ask this question (mostly rhetorically, and never accusatory): what can this be used for? I still see applications with computer graphics and digital interfaces, but that's my bent. I suppose the von Neumann computer model is one avenue where the abstract meets the actual, but I'm blind to other applications. I guess I'll give you a rundown of what I'm thinking since this is the "making connections" portion of the blog: I read a question on Slashdot a few weeks ago that was essentially, "How big is the intersection between philosophy and computer science?" and the general answer was, "Not very." This struck me as odd, because it seems to me that problem definition/specification/nature borders on the philosophical if it isn't outright. In my experience, I see a lot of what I'd call poorly coded applications that imposed arbitrary limitations which I conjecture is because the developer could not or would not prove to his/her satisfaction that certain conditions could not occur without some sweeping restriction. One naive approach to writing anything that models things geometrically might impose arbitrary limits on the types of transformations one could do one things as "tangible" as 3D models or as abstract (conceptually) as graphical user interfaces (which, I think, must exist in spatial dimensions, by definition...?). As a sort of contrived example, I can imagine one ensuring that an entire group of discrete transformations were applied iteratively (since computers do that well) by using a generator and then removing a lot of "logic" code that ensures each transformation was applied with the efficient and elegant approach that, they must have been applied since it's been proven such and such is a generator for the group. Of course, this is the approach Donald Knuth took with his software, in that he said, "Beware of bugs in the above code; I have only proved it correct, not tried it."
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