[FRIAM] square land math question

[Steve Smith]

Glen -

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"?

- Steve

> Well, as I tried to point out, I have a tough time understanding nonstandard math. The actuality of infinities seems to have been handled by Cantor and infinitesimals seem to have been fully justified by Conway and Robinson. But I don't understand much about *how* they built up that infrastructure.
>
> Whether the output of division is different from its input or identical to its input doesn't prevent me from applying the function. As I said, it's similar to 1. If I divide X by 1, I get X. So, X is clearly "divisible", even if it has no "parts" ... whatever "part" might mean ... to you or Euclid. >8^D
>
> On 7/23/20 9:48 AM, Steve Smith wrote:
>> Can you unpack that in the light of Euclid's definition of a point, to whose authority I presume Frank was deferring/invoking.
>>
>> I'm curious if this is a matter of dismissing/rejecting Euclid and his definitions in this matter, or an alternative interpretation of his text?
>>
>>     αʹ. Σημεῖόν ἐστιν, οὗ μέρος οὐθέν. 1. A point is that of which there is no part
>>
>> I'm always interested in creative alternative interpretations of intention and meaning, but I'm not getting traction on this one (yet?)
>