a professor of philosophy at Idaho State University, that he and a
colleague, Jim Hardy, have devised another geometric approach to logic:
a system of arrow diagrams that illustrate classical propositional
logic. The diagrams resemble those used to illustrate Euclidean
vector spaces, and Westphal and Hardy call their approach "a vector
system," although it does not involve what a mathematician would regard
as a vector space.
Month: September 2007
-
ART WARS continued:
Vector LogicI learned yesterday from Jonathan Westphal,See "Logic as a Vector System,"Journal of Logic and Computation15(5) (October, 2005), pp. 751-765.Related material:(1) Quilt Geometry,(2) the quilt patternbelow (click forthe source) --and(3) yesterday's entry"Christ! What arepatterns for?"-- Amy Lowell -
Jomini Meets Rommel:
Battlefield Geometry"The general, who wrote the Army's book on
counterinsurgency, said he and his staff were 'trying to do the
battlefield geometry right now' as he prepared his troop-level
recommendations."
-- Steven R. Hurst, The Associated Press, Wednesday, Aug. 15, 2007"'... we are in the process of doing the battlefield geometry to determine the way ahead.'"
-- Charles M. Sennott, Boston Globe, Friday, Sept. 7, 2007"Based on these considerations, and having worked the battlefield
geometry ... I have
recommended a drawdown of the surge forces from Iraq."
-- United States Army, Monday, Sept. 10, 2007
Related material:Log24 entries of
June 11 and 12, 2005:
"In the desert you can
remember your name
'Cause there ain't no one
for to give you no pain." -
Beauty Bare: A Poem
The Story Theory
of Truth --"I'm a gun for hire,
I'm a saint, I'm a liar,
because there are no facts,there is no truth,
just data to be manipulated."
Data
The data in more poetic form:
Commentary:
23: See
The Prime Cut Gospel.
16: See
Happy Birthday, Benedict XVI.Related material:
The remarks yesterday
of Harvard president
Drew G. Faust
to incoming freshmen.Faust "encouraged
the incoming class
to explore Harvard’s
many opportunities.'Think of it as
a treasure room
of hidden objects
Harry discovers
at Hogwarts,'
Faust said."For a less Faustian approach,
see the Harvard-educated
philosopher Charles Hartshorne
at The Harvard Square Library
and the words of another
Harvard-educated Hartshorne:"Whenever one
approaches a subject
from
two different directions,
there is bound to be
an
interesting theorem
expressing their relation."
-- Robin
Hartshorne -
Saturday Evening:
May 25, 2007:
"Let's give 'em somethin' to talk about,
A little mystery to figure out"-- Scarlett Johansson singing on
Saturday Night Live, April 21, 2007Related material:
Today's previous entry
and the following:
-
Requiem for a Storyteller:
The Intensest Rendezvous "There is one story and one story onlyThat will prove worth your telling....
Dwell on her graciousness, dwell on her smiling,
Do not forget what flowers
The great boar trampled down in ivy time.
Her brow was creamy as the crested wave,
Her sea-blue eyes were wild
But nothing promised that is not performed. "
-- Robert Graves,
To Juan at the Winter Solstice
The Devil and Wallace Stevens:"In a letter to Harriet Monroe, written December 23, 1926, Stevens
refers to the Sapphic fragment that invokes the genius of evening:
'Evening star that bringest back all that lightsome Dawn hath scattered
afar, thou bringest the sheep, thou bringest the goat, thou bringest
the child home to the mother.' Christmas, writes Stevens, 'is like
Sappho's evening: it brings us all home to the fold.' (Letters of Wallace Stevens, 248)"-- "The Archangel of Evening," Chapter 5 of Wallace Stevens: The Intensest Rendezvous, by Barbara M. Fisher, The University Press of Virginia, 1990, pages 72-73
"Evening. Evening of this day. Evening of the century. Evening of my own life....At Christmastime my parents held open house on Sunday evenings, and a
dozen or more people gathered around the piano, and the apartment was
full of music, and theology was sung into my heart."-- Madeleine L'Engle, Bright Evening Star: Mystery of the Incarnation
From the date of
L'Engle's death:
Some enchanted evening...
-
A Place Reserved:
This place was reserved at 9:29 PM Sept. 7, 2007.
The place now seems suitable to note a memorial to Burt Hasen, an artist who died on Sept. 7, 2007. For the memorial itself, see Sept. 13, 2007, 2:02 AM.
-
Philosophy Wars, continued:
The New York Times online,
Friday, Sept. 7, 2007:
Madeleine L’Engle,
Children’s Writer,
Is Dead"Madeleine L’Engle, who in
writing more than 60 books, including childhood fables, religious
meditations and science fiction, weaved emotional tapestries
transcending genre and generation, died Thursday [Sept. 6, 2007] in Connecticut. She
was 88.Her death, of natural causes, was announced today by her publisher, Farrar, Straus and Giroux."
Related material:
Log24 entries of
August 31--"That is how we travel."
-- A Wrinkle in Time,
Chapter 5,
"The Tesseract"-- and of
September 2
(with update of
September 5)--"There is such a thing
as a tesseract."
-- A Wrinkle in Time -
Annals of Quantum Geometry
Comment at the
n-Category CafeRe: This Week’s Finds in Mathematical Physics (Week 251)
On Spekkens’ toy system and finite
geometryBackground–
- In “Week 251” (May 5, 2007),
John wrote:“Since Spekkens’ toy system resembles a qubit, he calls it a “toy
bit”. He goes on to study systems of several toy bits - and the
charming combinatorial geometry I just described gets even more
interesting. Alas, I don’t really understand it well: I feel
there must be some mathematically elegant way to describe it all,
but I don’t know what it is…. All this is fascinating. It would
be nice to find the mathematical structure that underlies this
toy theory, much as the category of Hilbert spaces underlies
honest quantum mechanics.” - In the n-Category Cafe (
May 12, 2007, 12:26 AM, ) Matt Leifer wrote:
“It’s crucial to Spekkens’ constructions, and
particularly to the analog of superposition, that the state-space
is discrete. Finding a good mathematical formalism for his theory
(I suspect finite fields may be the way to go) and placing it
within a comprehensive framework for generalized theories would
be very interesting.” - In the n-category Cafe (
May 12, 2007, 6:25 AM) John Baez wrote:“Spekkens and I spent an afternoon trying to think about his
theory as quantum mechanics over some finite field, but failed
— we almost came close to proving it couldnt’
work.”
On finite geometry:
- In “Week 234” (June 12, 2006),
John wrote:
“For a pretty explanation of M24… try this:… Steven H. Cullinane, Geometry of the 4 × 4
square,
http://finitegeometry.org/sc/16/geometry.html”
The actions of permutations on a 4 × 4
square in Spekkens’ paper (quant-ph/0401052),
and Leifer’s suggestion of the need for a “generalized
framework,” suggest that finite geometry might supply such a
framework. The geometry in the webpage John
cited is that of the affine 4-space
over the two-element field.Related material:
Update of
Sept. 5, 2007See also arXiv:0707.0074v1 [quant-ph], June 30, 2007:
A fully epistemic model for a local hidden variable emulation of quantum dynamics,
by Michael Skotiniotis, Aidan Roy, and Barry C. Sanders, Institute for
Quantum Information Science, University of Calgary. Abstract: "In this article we consider an augmentation of
Spekkens’ toy model for the epistemic view of quantum states [1]...."Skotiniotis et al. note that the group actions on the 4x4
square described in Spekkens' paper [1] may be viewed (as in Geometry of the 4x4 Square and Geometry of Logic) in the context of a hypercube, or tesseract, a structure in which adjacency is isomorphic to adjacency in the 4 × 4
square (on a torus).Hypercube from the Skotiniotis paper:
Reference:
[1] Robert W. Spekkens, Phys. Rev. A 75, 032110 (2007),
Evidence for the epistemic view of quantum states: A toy theory,Perimeter Institute for Theoretical Physics, 31 Caroline Street North,
Waterloo, Ontario, Canada N2L 2Y5 (Received 11 October 2005; revised 2
November 2006; published 19 March 2007.) - In “Week 251” (May 5, 2007),
Recent Comments