Excellent, Jon.
On that basis, in answer to Nick's claim that I have never seen a right
triangle, here's a classic one
{(0, 0), (1,0), (0,1)}
and here's a manifold
{(x,y,z) in R^3: x*x+y*y+z*z = 1} where the open sets are the open sets of
S^2.
Note these are not physical objects.
---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505
505 670-9918
Santa Fe, NM
On Fri, May 29, 2020, 11:17 AM Jon Zingale <jonzing...@gmail.com> wrote:
> Frank, Steve,
>
> My favored approach is to say that *space is like a manifold*.
> For me, space is a *thing* and a manifold is an *object*. The former
> I can experience free from my models of it, I can continue to
> learn facts(?) about space not derived by deduction alone
> (consider Nick's posts on inductive and abductive reasoning).
> I concede here that we talk about an objectified space, but
> I am not intending to. I am using the term space as a place-
> holder for the thing I am physically moving about in. OTOH
> manifolds are fully *objectified*, they exist by virtue of their
> formality. Any meaningful question *about a manifold* itself
> is derived deductively from its construction. Neither in their
> own right are metaphors, the metaphor is created when we
> treat space *as if it were* a manifold. Just my two cents.
>
> At the beginning of MacLane's *Geometrical Mechanics,* (a book
> I have held many times, but never found an inexpensive copy
> to buy) MacLane opens his lecture's with '*The slogan is: Kinetic*
> *energy is a Riemann metric on configuration space*'. What a baller.
>
> Glen,
>
> I love that you mention the <placeholder>, ultimately reducing
> the argument to a *snowclone*. Because the title of the thread
> actually implicates a discussion of metaphor, and because I may
> have missed your point about *xyz,* please allow me this question.
> Do you feel that *snowclones* are necessarily templates for making
> metaphors, or do you feel that a snowclone is somehow different?
>
> Jon
>
> -- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. .
> ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ...
> 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-comic.blogspot.com/
>
-- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ...
... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ...
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-comic.blogspot.com/
