Continuing with some threads that have interested me, and to which I bring my understanding of Wittgenstein, here's a new Wikipedia page: http://en.wikipedia.org/wiki/Quadray_coordinates This is not new material, actually had an article published in an old FoxPro Advisor, though I didn't cite that as this mag is no longer in print I don't think, hard to find even on the web. I should dig up the date though -- added assignment to inbox. This was a collaborative effort, as I make clear in the docs (the Wikipedia entry is deliberately short and sweet, almost more literary than mathematical, like about some gizmo in Uru (a computer game, by Cyan in Spokane, WA **). Why this relates to Wittgenstein is it's clearly a little language game that's easy enough to grasp, yet runs counter to so many standard assumptions and therefore comes across as disruptive, breaking gestalts. But to "break a gestalt" is, in a more positive light, fighting the bewitchment of our intelligence by means of language. Going back to earlier posts, I've been discussing a model of 3rd powering based on the tetrahedron instead of the cube, and a consistent way of evaluating the volumes of other shapes based on this standard. There's a change in nomenclature, some ripple effects, yet the underlying mathematics is indifferent to these ripples in the sense that its seamless logic is undisturbed. There's no broken glass at the end of the day. We're free to go back to our other games and keep playing them too, perhaps with some new perspective that'll even help us play better? I think that's what "philosophy leaves everything as it is" sort of means. Wittgenstein is sometimes portrayed as an iconoclast. I prefer to see him as a defender of ordinary language that's doing work in the world, trying to keep it from falling into various traps that may have ensnared some philosopher types, rendering them fascinated and transfixed by some deep grammatical problems. There's the therapy aspect, but also preventive health. The PI supplies memetic (mnemonic) antibodies at some level. One might suggest students read it, web-publish about it, even if studying some apparently unrelated science? OK, back to my studies. Comments welcome as always though I know this is arcane material. If you follow links to Quadray Papers you might end up in my blog, something about Quaker Geometry. Talk about esoteric! Kirby ** http://cyanworlds.com/company/index.php ========================================== Need Something? Check here: http://ludwig.squarespace.com/wittrslinks/