There really does not need to be a difference, Coordinate free geometry is much like vector analysis. You have the equivalent of axioms and I suppose if you so desire you can bring in formal proofs and all the other concepts you like. But what it does for me is give a unified view of linear algebra, odes and geometry as just different instantiations of the same objects and their methods.
Ed _______________________ Ed Angel Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab) Professor Emeritus of Computer Science, University of New Mexico 1017 Sierra Pinon Santa Fe, NM 87501 505-984-0136 (home) an...@cs.unm.edu <mailto:an...@cs.unm.edu> 505-453-4944 (cell) http://www.cs.unm.edu/~angel <http://www.cs.unm.edu/~angel> > On Jul 23, 2020, at 3:46 PM, Frank Wimberly <wimber...@gmail.com> wrote: > > OK. As long as you grok the difference between the mathematical concept and > the OO concept. > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > On Thu, Jul 23, 2020, 3:41 PM uǝlƃ ↙↙↙ <geprope...@gmail.com > <mailto:geprope...@gmail.com>> wrote: > We used to have this argument all the time about the apt use of relational > vs. OO databases. As in Ed's conception, the same square can be associated > with multiple locations. Then to update all the renderings of that 1 square, > say, change its color from red to blue, all you need do is change the object > and all its renderings change as a result. That's pretty handy. > > But what if you really did want multiple squares so that changing the color > of this square over here didn't change the color of that square over there? > You might want "square" to be a class but have color be an instance property > so you could change each square to a different color. Or you might even have > a concept of *scope* so that all the squares in a neighborhood changed, but > no those far away ... or only the squares that are also rotated 90° > (invisibly) would change color, but those that haven't been rotated stay > whatever color they are. > > To my mind, computationalists tend to think like the latter (collections of > instances) whereas analysts tend to think like the former ("normalized" or > "unified"). I'm agnostic and like both teams. But when I see one team > winning, I tend to traitoriously jump from one side to the other. > > On 7/23/20 2:26 PM, Frank Wimberly wrote: > > What? > > > > On Thu, Jul 23, 2020, 2:56 PM uǝlƃ ↙↙↙ <geprope...@gmail.com > > <mailto:geprope...@gmail.com> <mailto:geprope...@gmail.com > > <mailto:geprope...@gmail.com>>> wrote: > > > > Ha! No way. If that were true, then to mow my lawn, I'd only have to > > mow the little part in the corner and voilá all the other patches would > > also be mowed. > > > > On 7/23/20 1:52 PM, Frank Wimberly wrote: > > > "is the same sized square, e.g. at {0.5,0.5}, the same square as the > > one at {10.5-10,10.5-10}" > > > > > > If you agree that 10.5 - 10 = 0.5 then same square, different name. > > -- > ↙↙↙ uǝlƃ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > <http://bit.ly/virtualfriam> > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > <http://redfish.com/mailman/listinfo/friam_redfish.com> > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC <http://friam.471366.n2.nabble.com/FRIAM-COMIC> > http://friam-comic.blogspot.com/ <http://friam-comic.blogspot.com/> > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/
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