[FRIAM] square land math question

[Edward Angel]

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)		 	angel at cs.unm.edu <mailto:angel at 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 <wimberly3 at 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 ↙↙↙ <gepropella at gmail.com <mailto:gepropella at 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 ↙↙↙ <gepropella at gmail.com <mailto:gepropella at gmail.com> <mailto:gepropella at gmail.com <mailto:gepropella at 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
> 
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