May | 2005 | m759's Xanga Site

Month: May 2005

Subject and Predicates

"A Chu space is a set X of subjects
and a set A of predicates on those subjects. These stand in a
symbiotic relationship in which the nature of each is determined by the
other. Each subject is characterized by the values the predicates take
on it, while each predicate is characterized by its values on
subjects."

-- Vaughan Pratt, Chu Spaces

Click here for Sambin's paper (ps).

It would seem that Pratt and Sambin need to reconcile their similar predicates for the same subject.

For some background on Sambin's approach to the subject, see

Mathematical Modal Logic:
A View of its Evolution (pdf),
by Robert Goldblatt at
Victoria University of Wellington's
Centre for Logic, Language,
and Computation

For some background on Pratt's approach to the subject, see

Information Transfer
Across Chu Spaces (pdf),
by Johan van Benthem
at the University of Amsterdam's
Institute for Logic, Language,
and Computation

For a gloss on Sambin's words

see the Log24 entry of Epiphany, 2005.
Just Say Non

"French opposition to the draft European constitution
is being undermined by an onslaught of state-funded propaganda 'worthy
of Fidel Castro,' according to France's most eurosceptic leader of the
Right, Philippe de Villiers."

de Villiers

-- telegraph.co.uk May 4, 2005

-- telegraph.co.uk May 30, 2005
Immoveable Feast

Today is a holiday of the Roman Catholic Church: the feast of St. Germain, Bishop of Paris. St. Germain is now known for the neighborhood that bears his name, home to what is said to be the oldest church in Paris, and a boulevard...

"... I met Joyce who was walking along the Boulevard St.-Germain after
having been to a matinée alone. He liked to listen to the actors,
although he could not see them. He asked me to have a drink with
him and we went to the Deux-Magots...."

-- Ernest Hemingway, A Moveable Feast

Two writers walk into a bar....
Midnight in the Garden,
continued:

Birth and Death

Today's birthdays:
Kylie Minogue and John Fogerty.

Get well soon, Bad Moon.

And in memory of Eddie Albert,
a talented actor who died
on Thursday, May 26, 2005,

at his home in California
and was born on April 22, 1906,
in Rock Island, Illinois:

Well if you want to ride
you gotta ride it like you find it.

Get your ticket at the station
of the Rock Island Line.

Among his films:

Escape to Witch Mountain.

Drama of the Diagonal,
Part Deux

Wednesday's entry The Turning discussed a work by Roger Cooke. Cooke presents a

"fanciful story (based on Plato's dialogue Meno)."

The History of Mathematics is the title of the Cooke book.

Associated Press thought for today:

"History is not, of course, a cookbook offering pretested recipes. It
teaches by analogy, not by maxims. It can illuminate the consequences
of actions in comparable situations, yet each generation must discover
for itself what situations are in fact comparable."
— Henry Kissinger (whose birthday is today)

For Henry Kissinger on his birthday:
a link to Geometry for Jews.

This link suggests a search for material
on the art of Sol LeWitt, which leads to
an article by Barry Cipra,
The "Sol LeWitt" Puzzle:
A Problem in 16 Squares (ps),
a discussion of a 4x4 array
of square linear designs.
Cipra says that

"If you like, there are three symmetry groups
lurking within the LeWitt puzzle: the rotation/reflection group
of order 8, a toroidal group of order 16, and an 'existential'* group
of order 16. The first group is the most obvious. The
third, once you see it, is also obvious."

* Jean-Paul Sartre,
Being and Nothingness,
Philosophical Library, 1956
[reference by Cipra]

For another famous group lurking near, if not within, a 4x4 array, click on Kissinger's birthday link above.

Kissinger's remark (above) on analogy suggests the following analogy to the previous entry's (Drama of the Diagonal) figure:

The image “http://www.log24.com/log/pix05/021126-diagonH2.jpg” cannot be displayed, because it contains errors.

Logos Alogos II:
Horizon

This figure in turn, together with Cipra's reference to Sartre, suggests the following excerpts (via Amazon.com)--

From Sartre's Being and Nothingness, translated by Hazel E. Barnes, 1993 Washington Square Press reprint edition:

1.	on Page 51:
	"He makes himself known to himself from the other side of the world and he looks from the horizon toward himself to recover his inner being. Man is 'a being of distances.'"
2.	on Page 154:
	"... impossible, for the for-itself attained by the realization of the Possible will make itself be as for-itself--that is, with another horizon of possibilities. Hence the constant disappointment which accompanies repletion, the famous: 'Is it only this?'...."
3.	on Page 155:
	"... end of the desires. But the possible repletion appears as a non-positional correlate of the non-thetic self-consciousness on the horizon of the glass-in-the-midst-of-the-world."
4.	on Page 158:
	"... it is in time that my possibilities appear on the horizon of the world which they make mine. If, then, human reality is itself apprehended as temporal...."
5.	on Page 180:
	"... else time is an illusion and chronology disguises a strictly logical order of deducibility. If the future is pre-outlined on the horizon of the world, this can be only by a being which is its own future; that is, which is to come...."
6.	on Page 186:
	"... It appears on the horizon to announce to me what I am from the standpoint of what I shall be."
7.	on Page 332:
	"... the boat or the yacht to be overtaken, and the entire world (spectators, performance, etc.) which is profiled on the horizon. It is on the common ground of this co-existence that the abrupt revelation of my 'being-unto-death'...."
8.	on Page 359:
	"... eyes as objects which manifest the look. The Other can not even be the object aimed at emptily at the horizon of my being for the Other."
9.	on Page 392:
	"... defending and against which he was leaning as against a wail, suddenly opens fan-wise and becomes the foreground, the welcoming horizon toward which he is fleeing for refuge."
10.	on Page 502:
	"... desires her in so far as this sleep appears on the ground of consciousness. Consciousness therefore remains always at the horizon of the desired body; it makes the meaning and the unity of the body."

11.	on Page 506:
	"... itself body in order to appropriate the Other's body apprehended as an organic totality in situation with consciousness on the horizon-- what then is the meaning of desire?"
12.	on Page 661:
	"I was already outlining an interpretation of his reply; I transported myself already to the four corners of the horizon, ready to return from there to Pierre in order to understand him."
13.	on Page 754:
	"Thus to the extent that I appear to myself as creating objects by the sole relation of appropriation, these objects are myself. The pen and the pipe, the clothing, the desk, the house-- are myself. The totality of my possessions reflects the totality of my being. I am what I have. It is I myself which I touch in this cup, in this trinket. This mountain which I climb is myself to the extent that I conquer it; and when I am at its summit, which I have 'achieved' at the cost of this same effort, when I attain this magnificent view of the valley and the surrounding peaks, then I am the view; the panorama is myself dilated to the horizon, for it exists only through me, only for me."

Illustration of the
last horizon remark:

From CIPRA – Slovenia,
the Institute for the
Protection of the Alps

For more on the horizon, being, and nothingness, see

Drama of the Diagonal

"The beautiful in mathematics
resides in contradiction.
Incommensurability, logoi alogoi, was
the first splendor in mathematics."

-- Simone Weil, Oeuvres Choisies,
éd. Quarto
, Gallimard, 1999, p. 100

Logos Alogos
by S. H. Cullinane

"To a mathematician,
mathematical entities have their own existence, they habitate spaces
created by their intention. They do things, things happen to them,
they relate to one another. We can imagine on their behalf all sorts
of stories, providing they don't contradict what we know of them.
The drama of the diagonal, of the square..."

-- Dennis Guedj, abstract of "The Drama of Mathematics," a talk to be given this July at the Mykonos conference on mathematics and narrative.

For the drama of the diagonal of the square, see
The Changing

The previous entry dealt with a transformation
of the diamond figure
from Plato's Meno
into a visual proof of the Pythagorean theorem:

Here is a transformation of Plato's diamond
into the "gyronny" pattern of heraldry:

Viking Heraldry

For the mathematics dealing with
this sort of transformation, see
The Diamond 16 Puzzle and Diamond Theory.
The Turning

Readers who have an Amazon.com account may view book pages relevant to the previous entry. See page 77
of The Way We Think, by Fauconnier and Turner (Amazon search term = Meno). This page
discusses both the Pythagorean theorem and Plato's diamond figure in
the Meno, but fails to "blend" these two topics. See also page 53
of The History of Mathematics, by Roger Cooke (first edition), where these two topics
are in fact blended (Amazon search term = Pythagorean). The illustration below is drawn from the
Cooke book.
Cooke demonstrates how the Pythagorean theorem might have been derived by "blending" Plato's diamond (left) with the idea of moving the diamond's corners (right).

The previous entry dealt with a conference on mathematics and
narrative. Above is an example I like of mathematics.... Here is
an example I like of narrative:

Kate felt quite dizzy. She didn't know exactly what it was
that had just happened, but she felt pretty damn certain that
it was the sort of experience that her mother would not have
approved of on a first date.
"Is this all part of what we have to do to go to Asgard?"
she said. "Or are you just fooling around?"
"We will go to Asgard...now," he said.
At that moment he raised his hand as if to pluck an apple,
but instead of plucking he made a tiny, sharp turning movement.
The effect was as if he had twisted the entire world through a
billionth part of a billionth part of a degree. Everything
shifted, was for a moment minutely out of focus, and then
snapped back again as a suddenly different world.

-- Douglas Adams, The Long Dark Tea-Time of the Soul

And here is a blend of the concepts "Asgard" and "conference":

"Asgard
    During the Interuniverse
Society conference,
    a bridge was opened to Valhalla...."

Bifrost
   In Norse myth, the rainbow bridge
     that connected Earth to Asgard,
     home of
the gods. It was extended
     to Tellus
Tertius during the
   Interuniverse
Society conference"

-- From A Heinlein Concordance

-- Front page picture from a
local morning newspaper published
today, Wednesday, May 25, 2005

As George Balanchine once asked,
"How much story do you want?"
Midnight in the Garden

continued

"Poetry is a satisfying of
the desire for resemblance....
If
resemblance is described as
a partial similarity between
two dissimilar
things,
it complements and reinforces
that which the two dissimilar
things
have in common.
It makes it brilliant."

-- Wallace Stevens,
"Three Academic Pieces" in
The Necessary Angel (1951)

Two dissimilar things:

1. A talk to be given at a conference on "Mathematics and Narrative" in Mykonos in July:

Mark Turner,
"The Role of Narrative Imagining in Blended Mathematical Concepts" --

Abstract:
"The Way We Think (Gilles Fauconnier and
Mark Turner; Basic Books, 2002) presents a theory of conceptual
integration, or "blending," as a basic mental operation.
See http://blending.stanford.edu.
This talk will explore some ways in which narrative imagining plays
a role in blended mathematical concepts."

2. An application of the "conceptual blending" of Fauconnier and Turner to some journal entries of 2004: Cognitive Blending and the Two Cultures.

Final Arrangements, continued:

Two Poles

From today's New York Times:

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From erraticimpact.com on Paul Ricoeur:

"Ricoeur reserves his greatest admiration for
the
narratologist Algirdas-Julien Greimas.

[See below.]

Ricoeur also explores
the relationship
between the philosophical and religious
domains, attempting to reconcile
the two poles in his thought."

From today's NYT obituary of Sol Stetin:

"Mr. Stetin, who emigrated from Poland at the age of 10 and dropped out
of high school in the ninth grade, was fond of saying he got his
education in the labor movement."

The image “http://www.log24.com/log/pix05/050524-JP2.jpg” cannot be displayed, because it contains errors.

Elementary Art

continued:

From Log24 on May 2, 2005:

"... it is not in isolation that the rhetorical power of such oppositions resides, but
in their articulation in relation to other oppositions.
In Aristotle's Physics the four elements of earth, air, fire and
water were said to be opposed in pairs.
For more than two thousand years oppositional patterns based on these four
elements were widely accepted as the fundamental structure underlying surface reality....

The structuralist semiotician Algirdas Greimas introduced the semiotic square
(which he adapted from the 'logical square' of scholastic philosophy)
as a means of analysing paired concepts more fully...."