I think this pre-cedent to Frank's reply didn't make the list.
-------- Forwarded Message --------
Frank -
Where do you get your understanding of a right triangle
(originally)?
Do you NOT first experience a large number of examples of
imperfect ones, and only then seek out or adopt from others a
mathematical formalism to describe a right triangle in it's
ideal/abstract?
I had split a lot of firewood and cut a lot of pie and
contemplated the similarities and differences among the
resulting bits of them before I saw my first geometry book. I
didn't have any trouble recognizing acute, oblique, right
triangles in the (also not perfect, but closer to) geometry book
and having some embodied understanding of them *long* before I
began learning an axiomatic encoding/manipulation of the
geometry of points, lines, planes, angles, conic sections, etc.
This may be (partly) my intuitive nature dominating, but
Lakoff/Nunez make a pretty strong case in "Where Mathematics
Comes From" for all understanding grounding in our embodied
minds/sensoria. Have you read them? I think they were "the
rage" around 2000ish.
I believe that the realization that "If you measure close
enough, they are not right triangles" and similar awarenesses of
the discrepancy between an idealized (mathematical) description
and the everyday examples that they offer an archetype for, is
entirely post hoc. Is this where Plato and Aristotle
begin to tussle?
If whales are as sentient as many believe, I would bet that
even if they have a geometry that is isomorphic to ours, it
would superficially be somewhat different than our own, probably
grounded in more complex manifolds (to reference another thread
here) than our own preference for the euclidean plane and the
occasional idealized sphere (thus our love of spherical cows).
Sure, they may have an abstract notion of the euclidean plane
(the boundary between ocean and atmosphere or ocean and
seafloor) but probably are hugely more aware/interested in the
3D distributions of density, pressure, salinity, etc. of their
watery embedding than we ever were. Pilots and meteorologists
and scuba divers might have a glimmer of how sea creatures
perceive the basic fundament they live in, and our formalized
geometries might well eventually line up if we've both
elaborated them enough.
My speculation is that cetaceans (and other sentient
ocean-going creatures) probably register their experiences more
in elliptical spaces and perhaps more minkowskian as well since
the scale of the speed of sound (to the extent that is their
dominant sense of distant objects) is close enough to their
physical scale and their mobility. I'm not sure what type of
physical environment would be perceived
Lobachevskiian/Hyperbolic.. It seems like the kind of fiction
Physicist Robert Forward might coin.
- Steve
I personally don't relate tangible, physical
objects to mathematical ones because you get into Hywel(RIP)
territory. "If you measure it carefully enough it's not a
right triangle. There are no right triangles".
So
a shroud is a manifold but not all manifolds are
shrouds?
N
Nicholas
S. Thompson
Emeritus
Professor of Psychology and Biology
Clark
University
http://home.earthlink.net/~nickthompson/naturaldesigns/
From:
Friam [mailto:[hidden email]]
On Behalf Of Frank Wimberly
Sent: Friday, March 08, 2019 8:54 PM
To: The Friday Morning Applied Complexity
Coffee Group <[hidden email]>
Subject: Re: [FRIAM] excess meaning alert?
(was, Re: are we how we behave?)
It's
something you can move around on in a continuous
way?
I
am sure it helps a lot of people; just not
me.
I
need a metaphor.
Nick
Nicholas
S. Thompson
Emeritus
Professor of Psychology and Biology
Clark
University
http://home.earthlink.net/~nickthompson/naturaldesigns/
From:
Friam [mailto:[hidden email]]
On Behalf Of Frank Wimberly
Sent: Friday, March 08, 2019 8:43 PM
To: The Friday Morning Applied
Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] excess meaning
alert? (was, Re: are we how we behave?)
Succinctly, and
I may leave something out, a manifold is a
topological space for which there is a
homeomorphism between every open set and an
open set in Rn for some n. More concretely,
lines and surfaces are manifolds but things
get complicated in higher dimensions. That
probably doesn't help.
Lee,
Just to bend the thread a bit further, is
"excess meaning" a term of art for
you? It seems very close to the term
"surplus meaning" which was used in a
famous article assigned to all Psychology
graduate students in the sixties
on the distinction between hypothetical
constructs and intervening
variables. Wondering if your term has
the same meaning and if it has a
life somewhere.
As to the convex hull I went from there to
the overturned boat in NCIS and
thence to "manifold" which, when the term
is deployed by mathematicians I
always think of a shroud, like a blanket
dropped over some lumpy thing to
contain it, roughly. Which, now that I
mention it, makes me want to explain
wtf you mathematicians mean when you use
the word manifold.
If that's not a thoroughly bent thread I
don't know what is.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and
Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/
-----Original Message-----
From: Friam [mailto:[hidden email]]
On Behalf Of
[hidden email]
Sent: Friday, March 08, 2019 7:04 PM
To: The Friday Morning Applied Complexity
Coffee Group <[hidden email]>
Subject: [FRIAM] excess meaning alert?
(was, Re: are we how we behave?)
Steve writes in relevant part:
> My position is that I favor each and
every one of us taking whatever
> responsibility for understanding our
own "convex hull" of
> capability/knowledge/intuition as we
are capable of and "managing" it
> to the best of our ability.
The quotation marks around the phrase
'convex hull' and the word 'managing'
presumably signal that they are being used
non-literally, and (I guess)
metaphorically. I would particularly like
Steve, if he is willing, to delve
into the intended metaphor in the first
case. On the one hand, lots of my
work uses more or less geometry; on the
other, in lots of my other work I
use metaphor; and I even think and write
about metaphor. So it's likely
that I'm taking the metaphor more
seriously than intended.
With that disclaimer: in the technical
contexts I'm familiar with, to pass
from something X to the convex hull of X
has the effect of (1) 'filling in
holes in X', in a well-defined manner that
is (2) as economical as possible
and (3) (therefore) unique. Which (if any)
of those properties are
reflected, and how, in the case that X is
our
"capability/knowledge/intuition"? ... I
could ramble on a lot more but will
start with that.
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Meets Fridays 9a-11:30 at cafe at St. John's
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Meets Fridays 9a-11:30 at cafe at St. John's College
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Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
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Meets Fridays 9a-11:30 at cafe at St. John's College
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