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

[Steve Smith]

Frank -
> There is a rigorous definition of curvature that doesn't depend on the
> manifold's being embedded in Euclidean space.  Right, Jon?
I'll give you "curved" but not "bent" as something other than metaphor.
> By the way, I was a private pilot during the 70s.  Hywel was a more
> experienced and more cautious pilot.  I think there are others in Friam.

So plotting a cross-country course would require at least a mechanical
accommodation for the curvature of the earth (not to mention the
distortion of the magnetic field), and/or with enough practice a "feel"
for navigating on the surface of a spheroid (if not ellipsoid)?    I
never got past the mechanical in spite of staring at globes and trying
to "feel" the difference.   My flight paths were never long enough to
matter really, but I *did* sometimes have an intuitive feel for "shape
of space" implied by the winds aloft.  But surely not as much as a
hang-glider or sailplane pilot.   Long before I flew in an airplane I
dreamed of soaring like a raven, especially those "surfing" on the
uplift currents flowing over the ridge behind my house.   I would expect
that (high flying) birds and ocean dwellers live in an ever-changing
(based on currents) manifold onto which our euclidean is nearly a
fiction?   Any specifics about that I might feel are surely wrong.

The tennis court did not remain "rectangular" for me for very long after
I began to play as a youth... it quickly took on a "shape" in phase
space, moderately asymmetric due to my right-handed reach and changing
with the style of play of my opponent.   My own strategy with a new
player in competition was to try to quickly gain control of the "shape"
of that space, and a match could "turn" on one of us putting an
unexpected "kink" in the other's playable space.  This was well before I
had a word for phase space or even a conception of manifolds or
non-euclidean geometries.  

I'm belaboring this because I think those experiences
(internalizing/direct-apprehension of the non-euclidean) ARE grounding
out in the direct-experience/sensorium, and do not require (allow for?)
a stacking of linguistic mappings (previously "metaphor"), but the way
such things are normally taught in school ARE stacked on top of the
conventional idiom we have for "the shape of space" (i.e. euclidean) so
we DO use terms (and conceptions) like "bent" space.  A whale or highly
intelligent bird might *develop differential/integral calculus" as a
method for managing the abstractions in *their world* that they don't
experience directly (euclidean like straight lines and flat surfaces).

I don't know if this addresses (well) Dave's insistence on "other ways
of knowing", but that is where *I* go when he speaks of that.   Learning
to play tennis well was not a science for me, it was an art and involved
practicing my body and reflexes and strategery into a direct
apprehension of the phase space (post-hoc name for it) I described
above.   I ONLY talk about it in terms of "phase space" because it is a
common mathematical abstraction that we both share, not because I think
or feel IN phase space.   It is just the "dynamic spacetime of tennis
playing"?   I've never talked to other tennis players much, and
certainly not in these terms.   To the rest of you, maybe a tennis court
is a rectangular region within which you must keep the ball to remain in
play and within which there are ballistic trajectories modified by
(mostly) the varying lift/drag on the ball based on it's rate and
direction of spin.   A naive tennis player (including extremely good
ones) surely don't have strong conceptions of the abstractions of
physics, but instead a strong intuitive command of the behaviour of the
coupled system of their body, the racquet, the ball, the air, the
surface of the court, etc.  

In all this rambling I'm arguing against myself on the "metaphors all
the way down"...  and for "metaphors all the way down until you can A)
use more formal analogy and mathematical mappings if that is your
training, and/or B) until you have internalized those mappings and feel
them intuitively.

- Steve

- Steve