[FRIAM] Metaphor [POSSIBLE DISTRACTON FROM]: privacy games

[Steve Smith]

Jon -

This is a nicely crisp and dense description which I found myself
responding to several times (inline) and having to start over, as
multiple readings (and partial responses) did help me unpack it somewhat
better I hope.  If this response makes it through my internal editor, it
is probably still sloppy or incomplete.

> 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.

Can we agree that the term "manifold" is a signifier for a mathematical
object which we have chosen to use as a formalism for describing
something we have (presumably) a more intuitive sense of?   The space we
"move around in" (propriocept?) and "apprehend through
action-at-a-distance" (see, hear, grasp, feel-the-heat-from)?  The
mathematical construct we call a "manifold" is built up from simpler
mathematical concepts of "dimension" and "point" and "set" "curve" and
"surface" (and n-d analogs).   I *think* the distinction between
intrinsic and extrinsic curvature might be the formalism related to what
I am trying to gesture at when I talk about "apprehending" the curvature
of a space directly, and why both "bent" and "curved" space are a little
dubious to me. 

I suppose your terminology of "the metaphor is created when we treat
space *as if it were* a manifold* can work for me, though I might
instead say that the source domain of the metaphorical description of
"bent" or "curved" space IS the formal mathematical construction of "a
manifold"?   To say "bent" (IMO) requires an additional layer of
something like a homogenous substance with plastic (but not elastic?)
deformability?  Colloquially "bent" is a fair standin for "curved" but I
think only intrinsic curvature is really meaningful in this context?

> 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.

Which I think is analogous or at least similar to Guerin's "least action
paths"?  And what I *think* I (imagine that I) experience in my orbital
mechanics dreams (albeit without any direct obvious intuitive grounding,
just one extrapolated from experiences like aerobatics, acrobatics,
high-diving, swimming under-water...

This all reduces to what qualifies for a direct apprehension, a deep
grounded intuition, a (legitimate) gut-feeling?   I'm beginning to
suspect that I might be the only one who has or at least needs that kind
of grounding for formalisms?  

> 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?

/Snowclone/ (new word to me) feels a bit more to me like an "algebra of
cliche's"?   Which is another hazard of "loose" metaphors...  they are
prone to becoming canalized as/into cliche's?

- Steve


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