[FRIAM] square land math question

[Frank Wimberly]

"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 ↙↙↙ <gepropella at 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
>
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-- 
Frank Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
505 670-9918
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