"While a point and a vector in R^n might be described by the same tuple, dividing the numeric elements of the tuple does not "partition" the point..."
Good point, Steve. There are infinitely many ways of resolving a vector. E.g. (1, 1) = (1, 0) + (0, 1/2) + (0, 1/4) + (0, 1/4) etc. On Thu, Jul 23, 2020 at 2:09 PM uǝlƃ ↙↙↙ <geprope...@gmail.com> wrote: > Nice challenge! ... Welllll, the original question was basically how Cody > might respond to the kid's suggestion that a point is a square with no > area. My suggestion to Cody would be to answer the kid with a discussion > about the actuality or potentiality of infinity ... or intermediately, > distinguishing between *definitions* of "square". > > And if you define define a square geometrically, then it makes complete > sense that there is no arealess square. But there are OTHER ways to define > a square. And since this kid already pulled out a sophisticated > mathematical argument, it's useful and interesting to see how far that kid > can go. > > You're free to hem and haw about the foundations of math and which > foundation you like better than another. But the point of discussing the > extent of a point was to answer the kid's challenge. Answering a bright kid > with "because Euclid says so" is not all that useful. >8^D > > On 7/23/20 1:00 PM, Steve Smith wrote: > > Can you illuminate us as to what treating the *location* of a point as a > > *quantity* and demonstrating that the quantity can be divided > > arithmetically adds to the meaning of a point? > > > > While a point and a vector in R^n might be described by the same tuple, > > dividing the numeric elements of the tuple does not "partition" the > > point, it merely scales the vector which is quite useful, but I'm not > > sure if in any way doing so has any meaning that could be construed as > > having "divided" the point? > > > > I think Euclid's geometry is pretty "standard math"? > > -- > ↙↙↙ uǝlƃ > > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > 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.471366.n2.nabble.com/FRIAM-COMIC> > http://friam-comic.blogspot.com/ > -- Frank Wimberly 140 Calle Ojo Feliz Santa Fe, NM 87505 505 670-9918
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