"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. On Thu, Jul 23, 2020 at 2:47 PM uǝlƃ ↙↙↙ <geprope...@gmail.com> wrote: > Well, we're talking about sub-squares, not just any old reduction. So, > this would be the reductions where both elements of the tuple are reduced > by the same scalar. But, more importantly, 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}? I think most > people would say they're different squares even if they have the same > reductions (area, circumference, etc.). So, by extension, an infinitesimal > closest to zero ("iota"?) is different from one just above, say, 10 even if > they're the same size. > > Along those same lines, I think an alternative answer the kid could've > given was to set the origin of the original square in the middle of the > square, then say that any square with corners at > {{x,x},{-x,x},{-x,-x},{x,-x}} where x less than ½ the length of the > original square would cut into 2 squares. Where the original answer the kid > gave used an alternate definition of "square" than what Cody was using, > this uses yet *another* definition of "square", one that's more agnostic > about the space inside the square's borders. Is a square picture frame a > square? Or just a set of 4 sticks wherein the squareness property is > emergent? [pffft] > > > On 7/23/20 1:20 PM, Frank Wimberly wrote: > > 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. > > > -- > ↙↙↙ 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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