Log24

Monday, May 20, 2013

Church Logic

Filed under: General — m759 @ 6:30 PM

This post is continued from "Church Narrative," a Log24 post of November 17, 2010.

In memory of Ray Manzarek, remarks from a different weblog on that same date:

IMAGE-Quote Investigator post from Nov. 17, 2010- '... and in between are the Doors'

Friday, October 29, 2010

Church Logic

Filed under: General,Geometry — m759 @ 1:23 PM

"The law of excluded middle is the logical principle in
accordance with which every proposition is either true or
false. This principle is used, in particular, whenever a proof
is made by the method of reductio ad absurdum . And it is
this principle, also, which enables us to say that the denial of
the denial of a proposition is equivalent to the assertion of
the proposition."

Alonzo Church, "On the Law of Excluded Middle,"
    Bulletin of the American Mathematical Society ,
    Vol. 34, No. 1 (Jan.–Feb. 1928), pp. 75–78

It seems reasonable to define a Euclidean  geometry as one describing what mathematicians now call a Euclidean  space.

    What sort of geometry
    is the following?

http://www.log24.com/log/pix10B/101029-AffinePlane.bmp

   Four points and six lines,
   with parallel lines indicated
   by being colored alike.

Consider the proposition "The finite geometry with four points and six lines is non-Euclidean."
Consider its negation. Absurd? Of course.

"Non-Euclidean," therefore, does not apply only  to geometries that violate Euclid's parallel postulate.

The problem here is not with geometry, but with writings about  geometry.

A pop-science website

"In the plainest terms, non-Euclidean geometry
 took something that was rather simple and straightforward
 (Euclidean geometry) and made it endlessly more difficult."

Had the Greeks investigated finite  geometry before Euclid came along, the reverse would be true.

Wednesday, May 16, 2018

Church and Temple

Filed under: General — Tags: , , , — m759 @ 10:48 AM

Monday, February 27, 2017

Logic for Jews

Filed under: General — Tags: — m759 @ 9:07 PM

(Continued)

Adam Gopnik in The New Yorker  today reacts to the startling
outcomes of three recent contests: the presidential election,
the Super Bowl, and the Oscar for Best Picture —

"The implicit dread logic is plain."

Related material —

Transformers in this journal and

“Lord Arglay had a suspicion that the Stone would be
purely logical.  Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

See also

The above figure is from Ian Stewart's 1996 revision of a 1941 classic, 
What Is Mathematics? , by Richard Courant and Herbert Robbins.

One wonders how the confused slave boy of Plato's Meno  would react
to Stewart's remark that

"The number of copies required to double an
 object's size depends on its dimension."

Saturday, February 28, 2015

Logical Loop

Filed under: General — Tags: — m759 @ 10:45 PM

In memory of Theodore SturgeonLeonard Nimoy,
and William Thomas McKinley —

From the Boston Modern Orchestra Project today :

"In a good way"

Or not.

Friday, December 19, 2014

Turing’s Church

Filed under: General — Tags: — m759 @ 12:23 PM

This post was suggested by the book Turing's Cathedral  and by
comments 29 and 31 on Scott Aaronson's Dec. 16 post about
"The Imitation Game."

See Church-Turing thesis at Wikipedia and Church Logic here.

Sunday, November 24, 2013

Logic for Jews*

Filed under: General,Geometry — Tags: , — m759 @ 7:20 AM

The search for 1984 at the end of last evening's post
suggests the following Sunday meditation.

My own contribution to this genre—

A triangle-decomposition result from 1984:

American Mathematical Monthly ,  June-July 1984, p. 382

MISCELLANEA, 129

Triangles are square

"Every triangle consists of n  congruent copies of itself"
is true if and only if  is a square. (The proof is trivial.) 
— Steven H. Cullinane

The Orwell slogans are false. My own is not.

* The "for Jews" of the title applies to some readers of Edward Frenkel.

Thursday, December 15, 2011

Logic for Jews

Filed under: General — Tags: — m759 @ 11:02 PM

New York Daily News , 2:55 PM EST today—

Joe Simon, who dreamed up the star-spangled super hero Captain America while riding on a Manhattan bus during the early days of World War II, died Thursday [Dec. 15] after an undisclosed illness. He was 98.

New York Times , about 10 PM EST today—

Joe Simon, a writer, editor and illustrator of comic books who was a co-creator of the superhero Captain America, conceived out of a patriotic impulse as war was roiling Europe, died on Wednesday [Dec. 14] at his home in Manhattan. He was 98.

The discrepancy is perhaps due to initial reports that quoted Simon's family as saying he died "Wednesday night."

Simon was a co-creator of Captain America. For some background on Simon and a photo with his fellow comic artist Jerry Robinson, co-creator of The Joker, see a Washington Post article from this afternoon. Robinson died on either Wednesday, Dec. 7, or Thursday, Dec. 8, 2011.

Los Angeles Times

Jerry Robinson, a pioneer in the early days of Batman comics and a key force in the creation of Robin the Boy Wonder; the Joker;  Bruce Wayne’s butler, Alfred; and Two-Face, died Wednesday afternoon [Dec. 7] in New York City. He was 89.

CNN

Cartoonist Jerry Robinson, who worked on the earliest Batman comics and claimed credit for creating the super-villain The Joker, died Thursday [Dec. 8] at the age of 89, his family confirmed.

A picture by Robinson—

IMAGE- The Joker with calendar page for November 27

The Joker in January 1943
with a Nov. 27 calendar page

A non-joke from a more recent November 27—

Simplex Sigillum Veri

"Oh, what a tangled web we weave…"

Thursday, February 3, 2011

Summa Mythologica, continued…

Filed under: General — Tags: — m759 @ 10:30 AM

Yesterday's New York Lottery— Midday 392, Evening 946.

Catechism of the Catholic Church

392   Scripture speaks of a sin of these angels. This "fall" consists in the free choice of these created spirits, who radically and irrevocably rejected  God and his reign. We find a reflection of that rebellion in the tempter's words to our first parents: "You will be like God." The devil "has sinned from the beginning"; he is "a liar and the father of lies."

946   After confessing "the holy catholic Church," the Apostles' Creed adds "the communion of saints." In a certain sense this article is a further explanation of the preceding: "What is the Church if not the assembly of all the saints?" The communion of saints is the Church.

Some context related to last night's Rite of Change

Glasperlenspiel  Philosophy.

Those who prefer Dan Brown to Hermann Hesse may consult Fast Forward.

Monday, December 27, 2010

Church Diamond

Filed under: General,Geometry — m759 @ 3:09 PM

IMAGE- The diamond property

Also known, roughly speaking, as confluence  or the Church-Rosser property.

From "NYU Lambda Seminar, Week 2" —

[See also the parent page Seminar in Semantics / Philosophy of Language or:
 What Philosophers and Linguists Can Learn From Theoretical Computer Science But Didn't Know To Ask)
]

A computational system is said to be confluent, or to have the Church-Rosser or diamond property, if, whenever there are multiple possible evaluation paths, those that terminate always terminate in the same value. In such a system, the choice of which sub-expressions to evaluate first will only matter if some of them but not others might lead down a non-terminating path.

The untyped lambda calculus is confluent. So long as a computation terminates, it always terminates in the same way. It doesn't matter which order the sub-expressions are evaluated in.

A computational system is said to be strongly normalizing if every permitted evaluation path is guaranteed to terminate. The untyped lambda calculus is not strongly normalizing: ω ω doesn't terminate by any evaluation path; and (\x. y) (ω ω) terminates only by some evaluation paths but not by others.

But the untyped lambda calculus enjoys some compensation for this weakness. It's Turing complete! It can represent any computation we know how to describe. (That's the cash value of being Turing complete, not the rigorous definition. There is a rigorous definition. However, we don't know how to rigorously define "any computation we know how to describe.") And in fact, it's been proven that you can't have both. If a computational system is Turing complete, it cannot be strongly normalizing.

There is no connection, apart from the common reference to an elementary geometric shape, between the use of "diamond" in the above Church-Rosser sense and the use of "diamond" in the mathematics of (Cullinane's) Diamond Theory.

Any attempt to establish such a connection would, it seems, lead quickly into logically dubious territory.

Nevertheless, in the synchronistic spirit of Carl Jung and Arthur Koestler, here are some links to such a territory —

 Link One — "Insane Symmetry"  (Click image for further details)—

http://www.log24.com/log/pix10B/101227-InsaneSymmetry.jpg

See also the quilt symmetry in this  journal on Christmas Day.

Link Two — Divine Symmetry

(George Steiner on the Name in this journal on Dec. 31 last year ("All about Eve")) —

"The links are direct between the tautology out of the Burning Bush, that 'I am' which accords to language the privilege of phrasing the identity of God, on the one hand, and the presumptions of concordance, of equivalence, of translatability, which, though imperfect, empower our dictionaries, our syntax, our rhetoric, on the other. That 'I am' has, as it were, at an overwhelming distance, informed all predication. It has spanned the arc between noun and verb, a leap primary to creation and the exercise of creative consciousness in metaphor. Where that fire in the branches has gone out or has been exposed as an optical illusion, the textuality of the world, the agency of the Logos in logic—be it Mosaic, Heraclitean, or Johannine—becomes 'a dead letter.'"

George Steiner, Grammars of Creation

(See also, from Hanukkah this year,  A Geometric Merkabah and The Dreidel is Cast.)

Link Three – Spanning the Arc —

Part A — Architect Louis Sullivan on "span" (see also Kindergarten at Stonehenge)

Part B — "Span" in category theory at nLab —

http://www.log24.com/log/pix10B/101227-nLabSpanImage.jpg

Also from nLab — Completing Spans to Diamonds

"It is often interesting whether a given span in some partial ordered set can be completed into a diamond. The property of a collection of spans to consist of spans which are expandable into diamonds is very useful in the theory of rewriting systems and producing normal forms in algebra. There are classical results e.g. Newman’s diamond lemma, Širšov-Bergman’s diamond lemma (Širšov is also sometimes spelled as Shirshov), and Church-Rosser theorem (and the corresponding Church-Rosser confluence property)."

The concepts in this last paragraph may or may not have influenced the diamond theory of Rudolf Kaehr (apparently dating from 2007).

They certainly have nothing to do with the Diamond Theory of Steven H. Cullinane (dating from 1976).

For more on what the above San Francisco art curator is pleased to call "insane symmetry," see this journal on Christmas Day.

For related philosophical lucubrations (more in the spirit of Kaehr than of Steiner), see the New York Times  "The Stone" essay "Span: A Remembrance," from December 22—

“To understand ourselves well,” [architect Louis] Sullivan writes, “we must arrive first at a simple basis: then build up from it.”

Around 300 BC, Euclid arrived at this: “A point is that which has no part. A line is breadthless length.”

See also the link from Christmas Day to remarks on Euclid and "architectonic" in Mere Geometry.

Saturday, December 18, 2010

Logic Tale

Filed under: General,Geometry — m759 @ 2:45 PM

Tale (Nov. 23)

Graham Priest (Nov. 28)

A Geometric Merkabah (Dec. 1)

John Baez (Dec. 15, UTC)

Logica Universalis  (journal)

Preface

Universal Logic at Neuchatel

Moretti homepage

Moretti thesis, summary

Moretti thesis (pdf, 5.05 MB)

Church Logic

Church Narrative

Church

Wednesday, November 17, 2010

Church Narrative

Filed under: General,Geometry — m759 @ 2:22 AM

Thanks to David Lavery for the following dialogue on the word "narrative" in politics—

"It's like – does this fit into narrative?
It's like, wait, wait, what about a platform? What about, like, ideas?
What about, you know, these truths we hold to be self-evident?
No, it's the narrative."

"Is narrative a fancy word for spin?"

Related material —

Church Logic (Log24, October 29) —

  What sort of geometry
    is the following?

IMAGE- The four-point, six-line geometry

 

"What about, you know, these truths we hold to be self-evident?"

Some background from Cambridge University Press in 1976 —

http://www.log24.com/log/pix10B/101117-CameronIntro2.jpg

Commentary —

The Church Logic post argues that Cameron's implicit definition of "non-Euclidean" is incorrect.

The four-point, six-line geometry has as lines "all subsets of the point set" which have cardinality 2.

It clearly satisfies Euclid's parallel postulate.  Is it, then, not  non-Euclidean?

That would, according to the principle of the excluded middle (cf. Church), make it Euclidean.

A definition from Wikipedia that is still essentially the same as it was when written on July 14, 2003

"Finite geometry describes any geometric system that has only a finite number of points. Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points…."

This definition would seem to imply that a finite geometry (such as the four-point geometry above) should be called non -Euclidean whether or not  it violates Euclid's parallel postulate. (The definition's author, unlike many at Wikipedia, is not  anonymous.)

See also the rest  of Little Gidding.

Saturday, October 19, 2013

Card

Filed under: General — m759 @ 11:01 AM

This post was suggested by the business card
scene in American Psycho .

See also a post of May 20, Church Logic. The link to that
post was suggested in part by the death on September 23
of the artistic director of a 1960s church theater, and in part
by a Log24 post on September 23, "For Danny Boy."

Tuesday, May 21, 2013

Narratives…

Filed under: General — m759 @ 6:00 AM

from yesterday— Bling Ring and Church Logic.

Related narratives— Get Quotes (source of image below)

as well as Helprin's Doors and Trickster.

Tuesday, November 23, 2010

Back to the Saddle

Filed under: General,Geometry — Tags: — m759 @ 5:30 AM

Recent posts (Church Logic and Church Narrative) have discussed finite  geometry as a type of non-Euclidean geometry.

For those who prefer non-finite geometry, here are some observations.

http://www.log24.com/log/pix10B/101123-CoxeterPilate.jpg

"A characteristic property of hyperbolic geometry
is that the angles of a triangle add to less
than a straight angle (half circle)." — Wikipedia

http://www.log24.com/log/pix10B/101123-Saddle.jpg

From To Ride Pegasus, by Anne McCaffrey, 1973: 

“Mary-Molly luv, it’s going to be accomplished in steps, this establishment of the Talented in the scheme of things. Not society, mind you, for we’re the original nonconformists…. and Society will never permit us to integrate.  That’s okay!”  He consigned Society to insignificance with a flick of his fingers.  “The Talented form their own society and that’s as it should be: birds of a feather.  No, not birds.  Winged horses!  Ha!  Yes, indeed. Pegasus… the poetic winged horse of flights of fancy.  A bloody good symbol for us.  You’d see a lot from the back of a winged horse…”

“Yes, an airplane has blind spots.  Where would you put a saddle?”  Molly had her practical side.

On the practical side:

http://www.log24.com/log/pix10B/101123-CandelaSpire.jpg

The above chapel is from a Princeton Weekly Bulletin  story of October 6th, 2008.

Related material: This journal on that date.

Sunday, October 20, 2019

MSRI (Pronounced “Misery”)

Filed under: General — Tags: — m759 @ 10:29 AM

Friday, October 11, 2019

Dick Date (YouTube, August 7, 2013)

Filed under: General — Tags: — m759 @ 3:47 PM

Down the Rabbit Hole  with Stephen King

Wednesday, October 9, 2019

Philosophical Infanticide

Filed under: General — Tags: — m759 @ 5:51 AM

From Wallace Stevens —

"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."

— “An Ordinary Evening in New Haven” VI

From The Point  magazine yesterday, October 8, 2019
Parricide:  On Irad Kimhi's Thinking and Being .
Book review by Steven Methven.

The conclusion:

"Parricide is nothing that the philosopher need fear . . . .
What sustains can be no threat. Perhaps what the
unique genesis of this extraordinary work suggests is that
the true threat to philosophy is infanticide."

This remark suggests revisiting a post from Monday

Monday, October 7, 2019

Berlekamp Garden vs. Kinder Garten

Filed under: General — m759 @ 11:00 PM

Stevens's Omega and Alpha (see previous post)
suggest a review.

Omega — The Berlekamp Garden. 
                  See Misère Play (April 8, 2019).
Alpha  —  The Kinder Garten. 
                  See Eighfold Cube.

. . . .

Monday, October 7, 2019

Oblivion

Filed under: General — Tags: , — m759 @ 1:09 PM

(A sequel to Simplex Sigillum Veri and 
Rabbit Hole Meets Memory Hole)

" Wittgenstein does not, however, relegate all that is not inside the bounds
of sense to oblivion. He makes a distinction between saying  and showing  
which is made to do additional crucial work. 'What can be shown cannot
be said,' that is, what cannot be formulated in sayable (sensical)
propositions can only be shown. This applies, for example, to the logical
form of the world, the pictorial form, etc., which show themselves in the
form of (contingent) propositions, in the symbolism, and in logical
propositions. Even the unsayable (metaphysical, ethical, aesthetic)
propositions of philosophy belong in this group — which Wittgenstein
finally describes as 'things that cannot be put into words. They make
themselves manifest. They are what is mystical' " (Tractatus  6.522).

Stanford Encyclopedia of Philosophy , "Ludwig Wittgenstein"

From Tractatus Logico-Philosophicus  by Ludwig Wittgenstein.

(First published in Annalen der Naturphilosophie ,1921.
English edition first published 1922 by Kegan Paul, Trench and Trübner. This translation first published 1961 by Routledge & Kegan Paul. Revised edition 1974.)

5.4541

The solutions of the problems of logic must be simple, since they set the standard of simplicity.

Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined — a priori — to form a self-contained system.

A realm subject to the law: Simplex sigillum veri.

Somehow, the old Harvard seal, with its motto "Christo et Ecclesiae ,"
was deleted from a bookplate in an archived Harvard copy of Whitehead's 
The Axioms of Projective Geometry  (Cambridge U. Press, 1906).

In accordance with Wittgenstein's remarks above, here is a new
bookplate seal for Whitehead, based on a simplex

Saturday, October 5, 2019

Midnight Landmarks

Filed under: General — Tags: , , — m759 @ 12:00 AM

Monday, September 23, 2019

Rabbit Hole Meets Memory Hole:

Filed under: General — Tags: , , — m759 @ 9:11 AM

The disappearance of "Christo et Ecclesiae" at Harvard

Rabbit Hole 

Memory Hole

The above Harvard seal in a PDF —

The same page, minus the seal, today at the Internet Archive — 

For a larger image of the seal-less page, click here.

Happy Fall 2019!

Click to enlarge.

Sunday, September 22, 2019

Colorful Tale

Filed under: General — Tags: , — m759 @ 7:59 PM

“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”

— Hermann Weyl, Philosophy of  Mathematics and
    Natural Science 
, Princeton, 1949, p. 237

"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

From page 180, Logicomix — It was a dark and stormy night

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

Monday, March 25, 2019

Espacement

Filed under: General — Tags: , , , , — m759 @ 1:46 PM

(Continued from the previous post.)

In-Between "Spacing" and the "Chôra "
in Derrida: A Pre-Originary Medium?

By Louise Burchill

(Ch. 2 in Henk Oosterling & Ewa Plonowska Ziarek (Eds.),  Intermedialities: Philosophy, Arts, Politics , Lexington Books, October 14, 2010)

"The term 'spacing' ('espacement ') is absolutely central to Derrida's entire corpus, where it is indissociable from those of différance  (characterized, in the text from 1968 bearing this name, as '[at once] spacing [and] temporizing' 1), writing  (of which 'spacing' is said to be 'the fundamental property' 2) and deconstruction (with one of Derrida's last major texts, Le Toucher: Jean-Luc Nancy , specifying 'spacing ' to be 'the first word of any deconstruction' 3)."

1  Jacques Derrida, “La Différance,” in Marges – de la philosophie  (Paris: Minuit, 1972), p. 14. Henceforth cited as  D  .

2  Jacques Derrida, “Freud and the Scene of Writing,” trans. A. Bass, in Writing and  Difference  (Chicago: University of Chicago Press, 1978), p. 217. Henceforth cited as FSW .

3  Jacques Derrida, Le Toucher, Jean-Luc Nancy  (Paris: Galilée, 2000), p. 207.

. . . .

"… a particularly interesting point is made in this respect by the French philosopher, Michel Haar. After remarking that the force Derrida attributes to différance  consists simply of the series of its effects, and is, for this reason, 'an indefinite process of substitutions or permutations,' Haar specifies that, for this process to be something other than a simple 'actualisation' lacking any real power of effectivity, it would need “a soubassement porteur ' – let’s say a 'conducting underlay' or 'conducting medium' which would not, however, be an absolute base, nor an 'origin' or 'cause.' If then, as Haar concludes, différance  and spacing show themselves to belong to 'a pure Apollonism' 'haunted by the groundless ground,' which they lack and deprive themselves of,16 we can better understand both the threat posed by the 'figures' of space and the mother in the Timaeus  and, as a result, Derrida’s insistent attempts to disqualify them. So great, it would seem, is the menace to différance  that Derrida must, in a 'properly' apotropaic  gesture, ward off these 'figures' of an archaic, chthonic, spatial matrix in any and all ways possible…."

16  Michel Haar, “Le jeu de Nietzsche dans Derrida,” Revue philosophique de la France et de l’Etranger  2 (1990): 207-227.

. . . .

… "The conclusion to be drawn from Democritus' conception of rhuthmos , as well as from Plato's conception of the chôra , is not, therefore, as Derrida would have it, that a differential field understood as an originary site of inscription would 'produce' the spatiality of space but, on the contrary, that 'differentiation in general' depends upon a certain 'spatial milieu' – what Haar would name a 'groundless ground' – revealed as such to be an 'in-between' more 'originary' than the play of differences it in-forms. As such, this conclusion obviously extends beyond Derrida's conception of 'spacing,' encompassing contemporary philosophy's continual privileging of temporization in its elaboration of a pre-ontological 'opening' – or, shall we say, 'in-between.'

For permutations and a possible "groundless ground," see
the eightfold cube and group actions both on a set of eight
building blocks arranged in a cube (a "conducting base") and
on the set of seven natural interstices (espacements )  between
the blocks. Such group actions provide an elementary picture of
the isomorphism between the groups PSL(2,7) (acting on the
eight blocks) and GL(3,2) (acting on the seven interstices).

Espacements
 

For the Church of Synchronology

See also, from the reported publication date of the above book
Intermedialities , the Log24 post Synchronicity.

Saturday, September 15, 2018

Axioms

Filed under: G-Notes,General,Geometry — Tags: , — m759 @ 9:50 AM

Tieszen— 'Kurt Godel and Phenomenology' — 1992

Update of 10:18 AM the same day —

See also Logicomix  in this  journal and, at Harvard,

http://www.math.harvard.edu/~mazur/

  • September 6, 2018:  Eric Maskin, Amartya Sen and I
    are giving a course this semester: 'Axiomatic Reasoning'
    (PHIL 273B). Introduction to Axiomatic Reasoning gives a
    general sense of what we intend to cover.

Update of 10:48 AM the same day —

http://www.log24.com/log/pix18/180915-Tieszen_died-March-28-2017.jpg

See Log24 on the date of Tieszen's death.

Monday, August 6, 2018

Summer in Philadelphia

Filed under: General — Tags: — m759 @ 2:59 PM

http://www.log24.com/log/pix18/180806-Old_City_Hall-Philadelphia.jpg

See also this  journal on June 21st, 2013.

Wednesday, May 16, 2018

Review

Filed under: General — Tags: , — m759 @ 5:52 PM

The title of the previous post, "Church and Temple," together
with today's online New York Times  obituaries for singer 
Lara Saint Paul (d. May 8) and playwright Leah Rose Napolin
(d. May 13), suggests a review

See as well a Log24 search for Isaac Singer.

Same Old Story

Filed under: General — Tags: , , — m759 @ 9:00 AM

. . . as time goes by.

Wednesday, September 20, 2017

The Imaginary Professor

Filed under: General — Tags: — m759 @ 8:35 PM
- I was a teacher.
- You're being modest, aren't you?
  You were a professor at Boston University...
  Isn't that right?
- Yes, well, assistant professor.
- And what'd you teach?
- Philosophy. Truth and logic. 
  That sort of thing.

Read more: 
https://www.springfieldspringfield.co.uk/
movie_script.php?movie=gifted

Compare and contrast with a real  Boston University professor,
John Stachel, quoted here on Sept. 5, 2017.

Tuesday, September 5, 2017

Annals of Critical Epistemology

Filed under: General,Geometry — Tags: — m759 @ 5:36 PM

"But unlike many who left the Communist Party, I turned left
rather than right, and returned—or rather turned for the first time—
to a critical examination of Marx's work. I found—and still find—
that his analysis of capitalism, which for me is the heart of his work,
provides the best starting point, the best critical tools, with which—
suitably developed—to understand contemporary capitalism.
I remind you that this year is also the sesquicentennial of the
Communist Manifesto , a document that still haunts the capitalist world."

— From "Autobiographical Reflections," a talk given on June 5, 1998, by
John Stachel at the Max Planck Institute for the History of Science in Berlin
on the occasion of a workshop honoring his 70th birthday, 
"Space-Time, Quantum Entanglement and Critical Epistemology."

From a passage by Stachel quoted in the previous post

From the source for Stachel's remarks on Weyl and coordinatization —

Note that Stachel distorted Weyl's text by replacing Weyl's word 
"symbols" with the word "quantities." —

This replacement makes no sense if the coordinates in question
are drawn from a Galois field — a field not of quantities , but rather
of algebraic symbols .

"You've got to pick up every stitch… Must be the season of the witch."
— Donovan song at the end of Nicole Kidman's "To Die For"

Florence 2001

Filed under: General,Geometry — Tags: — m759 @ 4:44 AM

Or:  Coordinatization for Physicists

This post was suggested by the link on the word "coordinatized"
in the previous post.

I regret that Weyl's term "coordinatization" perhaps has
too many syllables for the readers of recreational mathematics —
for example, of an article on 4×4 magic squares by Conway, Norton,
and Ryba to be published today by Princeton University Press.

Insight into the deeper properties of such squares unfortunately
requires both the ability to learn what a "Galois field" is and the
ability to comprehend seven-syllable words.

Monday, September 4, 2017

Identity Revisited

Filed under: General — Tags: — m759 @ 8:00 PM

From the Log24 post "A Point of Identity" (August 8, 2016) —

A logo that may be interpreted as one-eighth of a 2x2x2 array
of cubes —

The figure in white above may be viewed as a subcube representing,
when the eight-cube array is coordinatized, the identity (i.e., (0, 0, 0)).

Sunday, August 13, 2017

Compare and Contrast

Filed under: General,Geometry — Tags: , , , — m759 @ 1:00 PM

From The Atlantic , September 2017 issue, online —
"How America Lost Its Mind," by former Harvard Lampoon  
writer Kurt Andersen

The Atlantic 's embedded Google ad for "Quantum Space Elements"
is, by the way, completely unrelated to similar-sounding work on 
models of space in finite geometry (cf. tsimtsum . . .

Friday, August 11, 2017

Symmetry’s Lifeboat

Filed under: General,Geometry — Tags: , , — m759 @ 9:16 PM

A post suggested by the word tzimtzum  (see Wednesday)
or tsimtsum  (see this morning) —

Lifeboat from the Tsimtsum  in Life of Pi  —

Another sort of tsimtsum, contracting infinite space to a finite space —

IMAGE- Desargues's theorem in light of Galois geometry

Monday, June 12, 2017

Bubble

Filed under: General,Geometry — m759 @ 1:19 PM

The "bubble" passage in the previous post suggests a review of
a post from December 21, 2006, with the following images —

  

Update of 11:01 PM ET the same day, June 12, 2017 —

Related material for the Church of Synchronology

From a tech-article series that began on Halloween 2006 and
ended on the date of the above Geometry's Tombstones post —

Compare and contrast (from a post of Feb. 27, 2017) —

“Lord Arglay had a suspicion that the Stone would be
purely logical.  Yes, he thought, but what, in that sense,
were the rules of its pure logic?”

Many Dimensions  (1931), by Charles Williams

See also "The Geometry of Logic:
Finite Geometry and the 16 Boolean Connectives
"
by Steven H. Cullinane in 2007.

Tuesday, December 20, 2016

The Project’s Central Problem

Filed under: General — Tags: — m759 @ 10:00 AM

From page 180, Logicomix —

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

Alfred North Whitehead in the first of
the above-named years, 1906 —

"But the project's central problem was always there."

"The deeper we got into our Quest…
The more I doubted its premises."

— Attributed to Bertrand Russell
by Apostolos Doxiadis and Christos
Papadimitriou in Logicomix  (2008-9)

Friday, October 23, 2015

Retro or Not?

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

Happy birthday to the late Michael Crichton (Harvard '64).

See also Diamond Theory Roulette —

Part of the ReCode Project (http://recodeproject.com).
Based on "Diamond Theory" by Steven H. Cullinane,
originally published in "Computer Graphics and Art" 
Vol. 2 No. 1, February 1977.
Copyright (c) 2013 Radames Ajna 
— OSI/MIT license (http://recodeproject/license).

Related remarks on Plato for Harvard's
Graduate School of Design

See also posts from the above publication date, March 31,
2006, among posts now tagged "The Church in Philadelphia."

Saturday, September 26, 2015

Symbols, Local and Global

Filed under: General — Tags: — m759 @ 10:19 PM

Local:

Photo by Jimmy Emerson, DVM

Global

Photo by Brendan Smialowski today

Msgr. Mark Miles, the Pope's translator, at
Independence Hall in Philadelphia today.

What, if anything, the Church means by the symbol
he holds is not clear, but presumably its meaning,
if there is one, is more global than local.

Wednesday, April 8, 2015

The Crosswicks Curse

Filed under: General — Tags: , — m759 @ 8:08 PM

Continues.

It was a dark and stormy night 

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

Saturday, February 28, 2015

Elegy with Stars

Filed under: General — Tags: , — m759 @ 10:00 PM

This evening's New York Times —

"William Thomas McKinley, a prolific American composer
whose music was infused with the jazz he had performed
since childhood, died on Feb. 3 at his home in Reading,
Mass. He was 76.

He died in his sleep, his son Elliott said."

"William Thomas McKinley: Elegy for Strings (2006)

[Elliott McKinley]  

137 views as of 9:45 PM ET Feb. 28, 2015

Published on Feb 11, 2015

Composed as an elegy and tribute for friends and family
that have passed, spurred by the passing of McKinley's
long time friend, drummer Roger Ryan. The performance
heard here is by the Seattle Symphony under the direction
of Gerard Schwarz. 

Photos by Elliott McKinley (Rho Ophiuchi nebula complex…
and the Pleiades…) shot at Cherry Springs State Park."

Related material from the date of McKinley's death —
Expanding the Spielraum.

Recycled Religion

Filed under: General — Tags: , — m759 @ 3:16 PM

The previous post's Kirkridge link leads to
a mention of religious philosopher Parker J. Palmer.

From an Utne Reader  page on Palmer:

See also Theodore Sturgeon's 1949 story "What Dead Men Tell"—

"… He’d read about it in a magazine or somewhere.
He took a strip of scrap film about eighteen
inches long and put the ends together. He turned
one end over and spliced ’em. Now, if you trace
that strip, or mark it with a grease pencil, right up
the center, you find that the doggone thing only
has one side!”
The doctor nodded, and the girl said:
“A Möbius strip.”
“That what they call it?” said Hulon. “Well, I figured
this corridor must be something like that. On that
strip, a single continuous line touched both sides.
All I had to do was figure out an object built so that
a continuous line would cover all three of three sides,
and I’d have it. So I sat down and thought it out…."

— and the following mathematical illustration —

A Kirk for Spock

Filed under: General — Tags: , — m759 @ 2:09 PM

Related material:

What Dead Men Tell*

Filed under: General — Tags: , — m759 @ 1:23 PM

Theodore Sturgeon, 1949 :

"I thought I had an important idea.
It's part of a  call it a philosophy,
if that doesn't sound too high-
falutin'," he said.

"It's a philosophy," she said.
"We can call things by their names."

Leonard Nimoy,  2015 :

"A life is like a garden. 
Perfect moments can be had, 
but not preserved, except in memory."  

* A tale from Astounding Science Fiction
   Vol. 44, No. 3, November 1949

Friday, February 27, 2015

Final Tweet

Filed under: General — Tags: , — m759 @ 1:44 PM

"Final Tweet Will Make You Cry"

Or not.

Monday, December 29, 2014

The Source

Filed under: General — m759 @ 5:55 PM

Bogus religion from a bogus "research lab" —

Journal of Scientific Exploration,
Vol. 18, No. 4 (2004), pp. 547-570
"Sensors, Filters, and the Source of Reality"
Robert G. Jahn and Brenda J. Dunne

Princeton Engineering Anomalies Research
Princeton University 
D-334 Engineering Quadrangle
School of Engineering/Applied Science

"… Consequently, the inferred models of reality are limited to those substances, processes, and sources of information that constitute conventional contemporary science.

In this paper we ally ourselves with the sharply contrary position that there exists a much deeper and more extensive source of reality, which is largely insulated from direct human experience, representation, or even comprehension. It is a domain that has long been posited and contemplated by metaphysicians and theologians, Jungian and Jamesian psychologists, philosophers of science, and a few contemporary progressive theoretical physicists, all struggling to grasp and to represent its essence and its function. A variety of provincial labels have been applied, such as 'Tao,' 'Qi,' 'prana,' 'void,' 'Akashic record,' 'Unus Mundi,' 'unknowable substratum,' 'terra incognita,' 'archetypal field,' 'hidden order,' 'aboriginal sensible muchness,' 'implicate order,' 'zero-point vacuum,' 'ontic (or ontological) level,' 'undivided timeless primordial reality,' among many others, none of which fully captures the sublimely elusive nature of this domain. In earlier papers we called it the 'subliminal seed regime,' (2,3) but for our present purposes we shall henceforth refer to it simply as the 'Source.' "*

References:

2. Jahn, R. G., & Dunne, B. J. (2001). A modular model of mind/matter manifestations (M5). Journal of Scientific Exploration , 15(3), 299–329.
3. Jahn, R. G. (2002). M*: Vector representation of the subliminal seed regime of M5. Journal of Scientific Exploration , 16(3), 341–357.

Note:

* This assortment of contexts, labels, or models should not be regarded as mutually exclusive or hierarchical; nor are they isomorphic to one another. Rather, they represent different perspectives on the same basic search, and hence should be respected as collectively complementary. Where they reinforce one another, or display common features, this may indicate some degree of basic insight. Where they disagree on details, testable hypotheses may present themselves.

This was quoted approvingly in a recent book by
Joseph JaworskiSource  (Berrett-Koehler Publishers
1st ed. Jan. 11, 2012, pp. 2-3).

A book unrelated, despite its title, to Michener's novel 'The Source'

Jaworski, a lawyer-turned-guru,
in 1980 founded a cult for executives
called the American Leadership Forum.

A synchronicity cult I prefer —
the Roman Catholic Church:

Sunday, December 14, 2014

Sermon

Filed under: General,Geometry — Tags: — m759 @ 11:00 AM

"In digital circuit theory, combinational logic 
(sometimes also referred to as time-independent logic)
is a type of digital logic which is implemented by
Boolean circuits, where the output is a pure function of
the present input only."

Wikipedia, quoted in this morning's previous post as
commentary on Nabokov's phrase "combinational delight"

"Time past and time future
Allow but a little consciousness.
To be conscious is not to be in time
But only in time can the moment in the rose-garden,
The moment in the arbour where the rain beat,
The moment in the draughty church at smokefall
Be remembered; involved with past and future.
Only through time time is conquered."

— T. S. Eliot in Four Quartets

"I confess I do not believe in time." 

— Vladimir Nabokov in Speak, Memory

Saturday, September 20, 2014

The Metaphysics of Entities

Filed under: General — Tags: — m759 @ 11:00 AM

Anthony Lane in The New Yorker , issue dated Sept. 22, 2014:

"The hero of 'The Zero Theorem' is a computer genius called Qohen Leth
(Christoph Waltz)…. He is the sole resident of a derelict church, where,
on a crucifix in front of the altar, the head of Christ has been replaced by
a security camera. No prayers are ever said, and none are answered.

In short, the place is deconsecrated, but to claim that it lacks any spark of
sacred yearning would be wrong, because Qohen devotes his days to seeking
the Zero Theorem, which—whatever it may be—lies at the fuzzy limit of
human powers. We crunch entities,” he says, as if that explained anything.
His employer is Mancom, a large corporation that, in Orwellian fashion,
oversees ordinary lives, although it betrays more frantic desperation than
glowering threat."

One approach to the metaphysics of entities was indicated in the previous
post, 'Metaphysics for Gilliam." A different approach:

"Categories, Sets, and the Nature of Mathematical Entities,"
by Jean-Pierre Marquis, Ch. 13, pp. 181-192, in the 2006 book
The Age of Alternative Logics , ed. by van Benthem et al.
(Springer, Netherlands).

From pages 182-183 —

13.2 The nature of mathematical entities

Let us start with the nature of mathematical entities in general and with a
rough and classical distinction that will simply set the stage for the picture we
want to develop. We essentially follow Lowe 1998* for the basic distinctions. We
need to distinguish between abstract and concrete entities, on the one hand, and
universals and particulars on the other hand. For our purpose, it is not necessary
to specify a criterion of demarcation between abstract and concrete entities. We
simply assume that such a distinction can be made, e.g. concrete entities can
change whereas abstract entities cannot. We assume that a universal is an entity
that can be instantiated by entities which themselves are not instantiable, the
latter being of course particulars. Given these distinctions, an entity can be a
concrete particular, a concrete universal, an abstract particular or an abstract
universal.

Our focus here is between the last two possibilities. For we claim that the
current conception of sets makes them abstract particulars whereas for objects
defined within categories, mathematical entities are abstract universals. This,
we claim, is true of category theory as it is.

* Lowe, E.J., 1998, The Possibility of Metaphysics , Oxford: Clarendon Press.

Wednesday, May 21, 2014

Through the Vanishing Point*

Filed under: General,Geometry — Tags: , , — m759 @ 9:48 AM

Marshall McLuhan in "Annie Hall" —

"You know nothing of my work."

Related material — 

"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"

— Paul Simon

It was a dark and stormy night…

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

A photo opportunity for Whitehead
(from Romancing the Cube, April 20, 2011)—

IMAGE- Whitehead on Fano's construction of the 15-point projective Galois space over GF(2)

See also Absolute Ambition (Nov. 19, 2010).

* For the title, see Vanishing Point in this journal.

Wednesday, January 22, 2014

A Riddle for Davos

Filed under: General,Geometry — Tags: , — m759 @ 9:00 PM

Hexagonale Unwesen

Einstein and Thomas Mann, Princeton, 1938


IMAGE- Redefining the cube's symmetry planes: 13 planes, not 9.


See also the life of Diogenes Allen, a professor at Princeton
Theological Seminary, a life that reportedly ended on the date—
January 13, 2013— of the above Log24 post.

January 13 was also the dies natalis  of St. James Joyce.

Some related reflections —

"Praeterit figura huius mundi  " — I Corinthians 7:31 —

Conclusion of of "The Dead," by James Joyce—

The air of the room chilled his shoulders. He stretched himself cautiously along under the sheets and lay down beside his wife. One by one, they were all becoming shades. Better pass boldly into that other world, in the full glory of some passion, than fade and wither dismally with age. He thought of how she who lay beside him had locked in her heart for so many years that image of her lover's eyes when he had told her that he did not wish to live.

Generous tears filled Gabriel's eyes. He had never felt like that himself towards any woman, but he knew that such a feeling must be love. The tears gathered more thickly in his eyes and in the partial darkness he imagined he saw the form of a young man standing under a dripping tree. Other forms were near. His soul had approached that region where dwell the vast hosts of the dead. He was conscious of, but could not apprehend, their wayward and flickering existence. His own identity was fading out into a grey impalpable world: the solid world itself, which these dead had one time reared and lived in, was dissolving and dwindling.

A few light taps upon the pane made him turn to the window. It had begun to snow again. He watched sleepily the flakes, silver and dark, falling obliquely against the lamplight. The time had come for him to set out on his journey westward. Yes, the newspapers were right: snow was general all over Ireland. It was falling on every part of the dark central plain, on the treeless hills, falling softly upon the Bog of Allen and, farther westward, softly falling into the dark mutinous Shannon waves. It was falling, too, upon every part of the lonely churchyard on the hill where Michael Furey lay buried. It lay thickly drifted on the crooked crosses and headstones, on the spears of the little gate, on the barren thorns. His soul swooned slowly as he heard the snow falling faintly through the universe and faintly falling, like the descent of their last end, upon all the living and the dead.

Thursday, October 10, 2013

Nobel Jam

Filed under: General — Tags: — m759 @ 7:00 PM

From this date five years ago in The Guardian

Alice Munro: An Appreciation by Margaret Atwood

"The central Christian tenet is that
two disparate and mutually exclusive elements— 
divinity and humanity— got jammed together
in Christ, neither annihilating the other.
The result was not a demi-god, or a God
in disguise: God became totally a human being
while remaining at the same time totally divine.
To believe either that Christ was only a man or
that he was simply God was declared heretical
by the early Christian church. Christianity thus
depends on a denial of either/or classifying logic
and an acceptance of both-at-once mystery.
Logic says that A cannot be both itself and non-A
at the same time; Christianity says it can. The
formulation 'A but also non-A' is indispensable to it."

Related literary material— "Excluded Middle" and "Couple of Tots."

See also "The Divided Cube" and "Mimsy Were the Borogoves."

Friday, June 8, 2012

Cartoon Graveyard

Filed under: General — Tags: — m759 @ 2:01 AM

Whitehead and Russell, 'Logicomix' page 181

For some background, see "Cartoon Graveyard" and "Many Dimensions."

Monday, November 21, 2011

Random Reference

Filed under: General,Geometry — m759 @ 12:00 PM

IMAGE- NY Evening Lottery Nov. 20, 2011: 245 and 0182

Joseph T. Clark, S. J., Conventional Logic and Modern Logic:
A Prelude to Transition
  (Philosophical Studies of the American
Catholic Philosophical Association, III) Woodstock, Maryland:
Woodstock College Press, 1952—

Alonzo Church, "Logic: formal, symbolic, traditional," Dictionary of Philosophy  (New York: Philosophical Library, 1942), pp. 170-182. The contents of this ambitious Dictionary are most uneven. Random reference to its pages is dangerous. But this contribution is among its best. It is condensed. But not dense. A patient and attentive study will pay big dividends in comprehension. Church knows the field and knows how to depict it. A most valuable reference.

Another book to which random reference is dangerous

http://www.log24.com/log/pix11C/111121-CosmicTrigger-245.jpg

For greater depth, see "Cassirer and Eddington on Structures,
Symmetry and Subjectivity" in Steven French's draft of
"Symmetry, Structure and the Constitution of Objects"

Wednesday, July 13, 2011

The Sinatra Code

Filed under: General — Tags: — m759 @ 2:45 AM
 

From The Da Vinci Code,
by Dan Brown

Chapter 56

Sophie stared at Teabing a long moment and then turned to Langdon.  “The Holy Grail is a person?”

Langdon nodded.  “A woman, in fact.”  From the blank look on Sophie’s face, Langdon could tell they had already lost her.  He recalled having a similar reaction the first time he heard the statement. It was not until he understood the symbology  behind the Grail that the feminine connection became clear.

Teabing apparently had a similar thought.  “Robert, perhaps this is the moment for the symbologist to clarify?”  He went to a nearby end table, found a piece of paper, and laid it in front of Langdon.

Langdon pulled a pen from his pocket.  “Sophie are you familiar with the modern icons for male and female?”  He drew the common male symbol ♂ and female symbol ♀.

“Of course,” she said.

“These,” he said quietly, are not the original symbols for male and female.  Many people incorrectly assume the male symbol is derived from a shield and spear, while the female represents a mirror reflecting beauty.  In fact, the symbols originated as ancient astronomical symbols for the planet-god Mars and the planet-goddess Venus.  The original symbols are far simpler.”  Langdon drew another icon on the paper.

 

 

 

“This symbol is the original icon for male ,” he told her.  “A rudimentary phallus.”

“Quite to the point,” Sophie said.

“As it were,” Teabing added.

Langdon went on.  “This icon is formally known as the blade , and it represents aggression and manhood.  In fact, this exact phallus symbol is still used today on modern military uniforms to denote rank.”

“Indeed.”  Teabing grinned.  “The more penises you have, the higher your rank.  Boys will be boys.”

Langdon winced.  “Moving on, the female symbol, as you might imagine, is the exact opposite.”  He drew another symbol on the page.  “This is called the chalice .”

 

 

Sophie glanced up, looking surprised.

Langdon could see she had made the connection.  “The chalice,” he said, “resembles a cup or vessel, and more important, it resembles the shape of a woman’s womb.  This symbol communicates femininity, womanhood, and fertility.”  Langdon looked directly at her now.  “Sophie, legend tells us the Holy Grail is a chalice—a cup.  But the Grail’s description as a chalice  is actually an allegory to protect the true nature of the Holy Grail.  That is to say, the legend uses the chalice as a metaphor  for something far more important.”

“A woman,” Sophie said.

“Exactly.”  Langdon smiled.  “The Grail is literally the ancient symbol for womankind, and the Holy  Grail represents the sacred feminine and the goddess, which of course has now been lost, virtually eliminated by the Church.  The power of the female and her ability to produce life was once very sacred, but it posed a threat to the rise of the predominantly male Church, and so the sacred feminine was demonized and called unclean.  It was man , not God, who created the concept of ‘original sin,’ whereby Eve tasted of the apple and caused the downfall of the human race.  Woman, once the sacred giver of life, was now the enemy.”

“I should add,” Teabing chimed, “that this concept of woman as life-bringer was the foundation of ancient religion.  Childbirth was mystical and powerful.  Sadly, Christian philosophy decided to embezzle the female’s creative power by ignoring biological truth and making man  the Creator.  Genesis tells us that Eve was created from Adam’s rib.  Woman became an offshoot of man.  And a sinful one at that.  Genesis was the beginning of the end for the goddess.”

“The Grail,” Langdon said, “is symbolic of the lost goddess.  When Christianity came along, the old pagan religions did not die easily.  Legends of chivalric quests for the lost Grail were in fact stories of forbidden quests to find the lost sacred feminine. Knights who claimed to be “searching for the chalice” were speaking in codes as a way to protect themselves from a Church that had subjugated women, banished the Goddess, burned nonbelievers, and forbidden pagan reverence for the sacred feminine.”

http://www.log24.com/log/pix11B/110713-Symbology101.jpg

Happy birthday to Harrison Ford.

One for my baby…

 

 

One more for the road.

 

Wednesday, April 20, 2011

Romancing the Cube

Filed under: General,Geometry — Tags: — m759 @ 1:00 AM

It was a dark and stormy night…

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

“… the class of reflections is larger in some sense over an arbitrary field than over a characteristic zero field.”

– Julia Hartmann and Anne V. Shepler, “Jacobians of Reflection Groups

For some context, see the small cube in “A Simple Reflection Group of Order 168.”

See also the larger cube in “Many Dimensions” + Whitehead in this journal (scroll down to get past the current post).

That search refers to a work by Whitehead published in 1906, the year at the top of the Logicomix  page above—

http://www.log24.com/log/pix11/110420-Whitehead1906Axioms.jpg

A related remark on axiomatics that has metaphysical overtones suitable for a dark and stormy night

“An adequate understanding of mathematical identity requires a missing theory that will account for the relationships between formal systems that describe the same items. At present, such relationships can at best be heuristically described in terms that invoke some notion of an ‘intelligent user standing outside the system.'”

— Gian-Carlo Rota, “Syntax, Semantics, and…” in Indiscrete Thoughts . See also the original 1988 article.

Tuesday, November 23, 2010

Tale

Filed under: General — Tags: , , — m759 @ 8:00 PM

A reviewer says Steve Martin finds in his new novel An Object of Beauty  "a sardonic morality tale."

From this journal on the day The Cube  was published (see today's Art Object ) —

Monday February 20, 2006

m759 @ 12:00 AM

The Past Revisited

From Log24 a year ago on this date, a quote from Many Dimensions  (1931), by Charles Williams:

“Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?”

For the rest of the story, see the downloadable version at Project Gutenberg of Australia.

See also a post on Mathematics and Narrative from Nov. 14, 2009.

That post compares characters in Many Dimensions  to those in Logicomix

Whitehead and Russell, 'Logicomix' page 181

Saturday, November 20, 2010

Search

Filed under: General,Geometry — Tags: — m759 @ 4:00 AM

An Epic Search for Truth

— Subtitle of Logicomix , a work reviewed in the December 2010 Notices of the American Mathematical Society  (see previous post).

Some future historian of mathematics may contrast the lurid cover of the December 2010 Notices

http://www.log24.com/log/pix10B/101119-AMSnoticesThumb.jpg

Excerpts from Logicomix

with the 1979 cover found in a somewhat less epic search —

http://www.log24.com/log/pix10B/101120-79T-A37-500w.jpg

Larger view of Google snippet —

http://www.log24.com/log/pix10B/101120-79T-A37-snippet.jpg

For some purely mathematical background, see Finite Geometry of the Square and Cube.

For some background related to searches for truth, see "Coxeter + Trudeau" in this journal.

Friday, November 19, 2010

Absolute Ambition

Filed under: General — Tags: , — m759 @ 10:30 AM

"It's my absolute ambition that you are touched to the core of your being with the content…."

— Julie Taymor on Spider-Man: Turn Off the Dark  (Playbill video, undated)

Another ambitious comic-book promotion —

"What Logicomix  does that few works in any medium do is to make intellectual passion palpable. That is its greatest strength. And it’s here that its form becomes its substance."

— Judith Roitman, review (pdf, 3.7 MB) of Logicomix: An Epic Search for Truth , in …

http://www.log24.com/log/pix10B/101119-AMSnoticesSm.jpg

 The December 2010 AMS Notices  cover has excerpts from Logicomix.

Related material:

"In the classical grammarians’ sense of the power of form over 'content' and style over 'substance,' he originated the phrase, 'the medium is the message.'"

— Joseph P. Duggan on Marshall McLuhan at The University Bookman

See also, in this  journal, The Medium is the Message, Wechsler, and Blockheads .

Sunday, April 18, 2010

A Generation Lost in Space

Filed under: General — m759 @ 2:29 AM

or, Deja Vu All Over Again

Top two obituaries in this morning's NY Times list–

David Simons, Who Flew High
on Eve of Space Age, Dies at 87

Dr. Simons, a physician turned Air Force officer, had sent animals aloft for several years before his record-breaking flight.

James Aubrey, who Portrayed the Hero
in ‘Lord of the Flies’, Is Dead at 62

Mr. Aubrey portrayed Ralph in the film version of the William Golding novel and had a busy career on stage and television in England.

Simons reportedly died on April 5,
Aubrey on April 6.

This journal on those dates–

April 5 —

Monday, April 5, 2010

Space Cowboys

Filed under: Uncategorized — m759 @ 12:00 PM Edit This

http://www.log24.com/log/pix10/100405-Eastwood.jpg

Google News, 11:32 AM ET today–

http://www.log24.com/log/pix10/100405-SpaceCowboysSm.jpg

Related material:

Yesterday's Easter message,
film notes from March 13,
and Dagger Definitions.

April 6 —

Tuesday, April 6, 2010

Clue

Filed under: Uncategorized — m759 @ 12:00 PM Edit This

Excerpt from 'Cosmic Trigger'
 by Robert Anton Wilson

See also Leary on Cuernavaca,
John O'Hara's fleeting reference
to Cuernavaca in Hope of Heaven,
and Cuernavaca in this journal.

Team Daedalus

Filed under: Uncategorized — m759 @ 9:00 AM Edit This

"Concept (scholastics' verbum mentis)– theological analogy of Son's procession as Verbum Patris, 111-12" –Index to Joyce and Aquinas, by William T. Noon, Society of Jesus, Yale University Press 1957, second printing 1963, page 162

"Back in 1958… [four] Air Force pilots were Team Daedalus, the best of the best." –Summary of the film "Space Cowboys"

"Man is nothing if not labyrinthine." –The Vicar in Trevanian's The Loo Sanction\

 

Commentary by T.S. Eliot

"At the moment which is not of action or inaction
You can receive this: 'on whatever sphere of being
The mind of a man may be intent
At the time of death'—that is the one action
(And the time of death is every moment)
Which shall fructify in the lives of others:
And do not think of the fruit of action.
Fare forward."

 

Tuesday, April 6, 2010

Team Daedalus

Filed under: General — m759 @ 9:00 AM

"Concept (scholastics' verbum mentis)– theological analogy of Son's procession as Verbum Patris, 111-12" –Index to Joyce and Aquinas, by William T. Noon, Society of Jesus, Yale University Press 1957, second printing 1963, page 162

"Back in 1958… [four] Air Force pilots were Team Daedalus, the best of the best." –Summary of the film "Space Cowboys"

"Man is nothing if not labyrinthine." –The Vicar in Trevanian's The Loo Sanction

Sunday, February 7, 2010

Today’s Sermon

Filed under: General — Tags: — m759 @ 11:00 AM

Mathematics and Religion, continued–

Calvin Jongsma, review of an anthology titled Mathematics and the Divine

"Believers of many faiths have found significant points of contact between their religious outlooks and mathematics. Not all of these claims were made in the distant past or by certified crackpots…."

Edward Nelson in "Warning Signs of a Possible Collapse of Contemporary Mathematics"–

"The most impressive feature of Cantor’s theory is that he showed that there are different sizes of infinity, by his famous diagonal argument. But Russell applied this argument to establish his paradox: the set of all sets that are not elements of themselves both is and is not an element of itself."

Jongsma's assertion appears to be true. Nelson's appears to be false. Discuss.

Remarks:

Saying that someone applied some argument– any argument will do here– to establish a paradox– any paradox will do here– casts into doubt the validity of either the argument, the application of the argument, or both. In the Cantor-Russell case, such doubt is unnecessary, since the paradox is clearly independent of the diagonal argument. There is certainly an historical connection between Cantor's argument and Russell's paradox– see, for instance, Wikipedia on the latter. The historical connection is, however, not a logical connection.

For Russell discovering his paradox without the use of Cantor's diagonal argument, see Logicomix

Russell discovers his paradox

Click for some context.

Friday, December 4, 2009

Parallelism

Filed under: General,Geometry — m759 @ 12:00 AM

From Peter J. Cameron's
Parallelisms of Complete Designs (pdf)–

Epigraph by Eliot on Little Gidding in Cameron's 'Parallelisms'

"…the Feast of Nicholas Ferrar
  is kept on the 4th December."

Little Gidding Church

Cameron's is the usual definition
of the term "non-Euclidean."
I prefer a more logical definition.

Saturday, November 14, 2009

Mathematics and Narrative, continued:

Filed under: General,Geometry — Tags: , — m759 @ 10:10 PM

A graphic novel reviewed in the current Washington Post  features Alfred North Whitehead and Bertrand Russell–

Whitehead and Russell, 'Logicomix' page 181

Related material:

Whitehead on Fano’s finite projective three-space:

“This is proved by the consideration of a three dimensional geometry in which there are only fifteen points.”

The Axioms of Projective Geometry , Cambridge University Press, 1906

A related affine six-space:

Grey cube, 4x4x4

Further reading:

See Solomon’s Cube and the link at the end of today’s previous entry, then compare and contrast the above portraits of Whitehead and Russell with Charles Williams’s portraits of Sir Giles Tumulty and Lord Arglay in the novel Many Dimensions .

It was a dark and stormy night….

Monday, March 9, 2009

Monday March 9, 2009

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM

Humorism

'The Manchurian Candidate' campaign button

"Always with a
little humor."
Dr. Yen Lo  

Diamond diagram of the four humors, the four qualities, the four elements, the four seasons, and four colors

From Temperament: A Brief Survey

For other interpretations
of the above shape, see
The Illuminati Diamond.

from Jung's Aion:

"From the circle and quaternity motif is derived the symbol of the geometrically formed crystal and the wonder-working stone. From here analogy formation leads on to the city, castle, church, house, room, and vessel. Another variant is the wheel. The former motif emphasizes the ego’s containment in the greater dimension of the self; the latter emphasizes the rotation which also appears as a ritual circumambulation. Psychologically, it denotes concentration on and preoccupation with a centre…." –Jung, Collected Works, Vol. 9, Part II, paragraph 352

As for rotation, see the ambigrams in Dan Brown's Angels & Demons (to appear as a film May 15) and the following figures:

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison
 
Click on image
for a related puzzle.
For a solution, see
 The Diamond Theorem.

A related note on
"Angels & Demons"
director Ron Howard:

Director Ron Howard with illustration of the fictional discipline 'symbology'
 
Click image for details.

Saturday, October 25, 2008

Saturday October 25, 2008

Filed under: General — Tags: , — m759 @ 11:01 AM
Actual Being

The New York Times Book Review online today has a review by Sam Tanenhaus of a new John Updike book.

The title of the review (not the book) is "Mr. Wizard."

"John Updike is the great genial sorcerer of American letters. His output alone (60 books, almost 40 of them novels or story collections) has been supernatural. More wizardly still is the ingenuity of his prose. He has now written tens of thousands of sentences, many of them tiny miracles of transubstantiation whereby some hitherto overlooked datum of the human or natural world– from the anatomical to the zoological, the socio-economic to the spiritual– emerges, as if for the first time, in the complete­ness of its actual being."

Rolling Stone interview with Sting, February 7, 1991:

"'I was brought up in a very strong Catholic community,' Sting says. 'My parents were Catholic, and in the Fifties and Sixties, Catholicism was very strong. You know, they say, "Once a Catholic, always a Catholic." In a way I'm grateful for that background. There's a very rich imagery in Catholicism: blood, guilt, death, all that stuff.' He laughs."

http://www.log24.com/log/pix08A/081025-Sting.jpg

RS 597, Feb. 7, 1991

Last night's 12:00 AM
Log24 entry:

Midnight Bingo

From this date six years ago:


It All Adds Up.

From this morning's newspaper,
a religious meditation I had not
seen last night:

The image “http://www.log24.com/log/pix08A/081025-WizardOfIdSm.jpg” cannot be displayed, because it contains errors.

Related material:

Juneteenth through
Midsummer Night, 2007

and

Church of the Forbidden Planet

Wednesday, September 19, 2007

Wednesday September 19, 2007

Filed under: General — m759 @ 5:00 AM
Einstein, God, and
the Consolation of Form

“The kind of thing that would make Einstein gag”

Peter Woit, Sept. 18, 2007

    “– …He did some equations that would make God cry for the sheer beauty of them. Take a look at this…. The sonofabitch set out equations that fit the data. Nobody believes they mean anything. Shit, when I back off, neither do I. But now and then, just once in a while…
     — He joined physical and mental events. In a unified mathematical field.
     — Yeah, that’s what I think he did. But the bastards in this department… bunch of goddamned positivists. Proof doesn’t mean a damned thing to them. Logical rigor, beauty, that damned perfection of something that works straight out, upside down, or sideways– they don’t give a damn.”

— “Nothing Succeeds,” in The Southern Reporter: Stories of John William Corrington, LSU Press, 1981

“The search for images of order and the loss of them constitute the meaning of The Southern Reporter.”

Louisiana State University Press

“By equating reality with the metaphysical abstraction ‘contingency’ and explaining his paradigm by reference to simple images of order, Kermode [but see note below] defines the realist novel not as one which attempts to get to grips with society or human nature, but one which, in providing the consolation of form,* makes the occasional concession to contingency….”

Richard Webster on Frank Kermode’s The Sense of an Ending

We are here in the
Church of St. Frank.

Marjorie Garber,
Harvard University

* “The consolations of form” is a phrase Kermode quoted from Iris Murdoch. Webster does not mention Murdoch. Others have quoted Murdoch’s memorable phrase, which comes from her essay “Against Dryness: A Polemical Sketch,” Encounter, No. 88, January 1961, pp. 16-20. The essay was reprinted in a Penguin paperback collection of Murdoch’s work, Existentialists and Mystics. It was also reprinted in The Novel Today, ed. Malcolm Bradbury (Manchester, Manchester U. Press, 1977); in Revisions, ed. S. Hauerwas and A. MacIntyre (Notre Dame, U. of Notre Dame Press, 1981); and in Iris Murdoch, ed. H. Bloom (New York, Chelsea House, 1986).

Wednesday, August 1, 2007

Wednesday August 1, 2007

Filed under: General,Geometry — m759 @ 8:00 AM
August First,
8:00:14 AM:

Cheap Epiphany

SPORTS OF THE TIMES

Restoring the Faith
After Hitting the Bottom

By SELENA ROBERTS
The New York Times
Published: August 1, 2007

What good is a nadir if it's denied or ignored? What's the value of reaching the lowest of the low if it can't buy a cheap epiphany?

 

Pennsylvania Lottery
on the Feast of
St. Ignatius Loyola:
 
PA Lottery July 31, 2007 - Mid-day 215, Evening 298

Restoring the Booze:
A Look at the 50's-

Grace and Bing in the Fifties

Another Epiphany:

Geometry of the I Ching (Box Style)

Box-style I Ching, January 6, 1989

(Click on image for background.)

Detail:

Detail of Box Style I Ching: Hexagram 14.

Related material:
Logos and Logic 
 and Diagon Alley.

"What a swell
  party this is."

— adapted from
     Cole Porter 

Thursday, June 21, 2007

Thursday June 21, 2007

Filed under: General,Geometry — Tags: — m759 @ 12:07 PM
Let No Man
Write My Epigraph

(See entries of June 19th.)

"His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality."

Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007

"At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity."

— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005

"… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)"

— Peter J. Cameron, "The Geometry of the Mathieu Groups" (pdf)

"… donc Dieu existe, réponse!"

— Attributed, some say falsely,
to Leonhard Euler
 
"Only gradually did I discover
what the mandala really is:
'Formation, Transformation,
Eternal Mind's eternal recreation'"

(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)

 

Wolfgang Pauli as Mephistopheles

"Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script."
Physics Today

 

"Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.

'To meet someone' was his enigmatic answer. 'To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'"

The Club Dumas, basis for the Roman Polanski film "The Ninth Gate" (See 12/24/05.)

"Pauli linked this symbolism
with the concept of automorphism."

The Innermost Kernel
 (previous entry)

And from
"Symmetry in Mathematics
and Mathematics of Symmetry
"
(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 14-17, 2007,
we have

The Epigraph–

Weyl on automorphisms
(Here "whatever" should
of course be "whenever.")

Also from the
Cameron paper:

Local or global?

Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:

• exact correspondence of parts;
• remaining unchanged by transformation.

Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them?  A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, "any local symmetry is global."

Some Log24 entries
related to the above politically
(women in mathematics)–

Global and Local:
One Small Step

and mathematically–

Structural Logic continued:
Structure and Logic
(4/30/07):

This entry cites
Alice Devillers of Brussels–

Alice Devillers

"The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
  as many symmetries as possible."

"There is such a thing
as a tesseract."

Madeleine L'Engle 

Sunday, May 20, 2007

Sunday May 20, 2007

Filed under: General,Geometry — m759 @ 8:00 AM
Plato and Shakespeare:
Solid and Central

"I have another far more solid and central ground for submitting to it as a faith, instead of merely picking up hints from it as a scheme. And that is this: that the Christian Church in its practical relation to my soul is a living teacher, not a dead one. It not only certainly taught me yesterday, but will almost certainly teach me to-morrow. Once I saw suddenly the meaning of the shape of the cross; some day I may see suddenly the meaning of the shape of the mitre. One free morning I saw why windows were pointed; some fine morning I may see why priests were shaven. Plato has told you a truth; but Plato is dead. Shakespeare has startled you with an image; but Shakespeare will not startle you with any more. But imagine what it would be to live with such men still living, to know that Plato might break out with an original lecture to-morrow, or that at any moment Shakespeare might shatter everything with a single song. The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast. He is always expecting to see some truth that he has never seen before."

— G. K. Chesterton, Orthodoxy, Ch. IX

From Plato, Pegasus, and the Evening Star (11/11/99):
 

"Nonbeing must in some sense be, otherwise what is it that there is not? This tangled doctrine might be nicknamed Plato's beard; historically it has proved tough, frequently dulling the edge of Occam's razor…. I have dwelt at length on the inconvenience of putting up with it. It is time to think about taking steps."
— Willard Van Orman Quine, 1948, "On What There Is," reprinted in From a Logical Point of View, Harvard University Press, 1980

"The Consul could feel his glance at Hugh becoming a cold look of hatred. Keeping his eyes fixed gimlet-like upon him he saw him as he had appeared that morning, smiling, the razor edge keen in sunlight. But now he was advancing as if to decapitate him."
— Malcolm Lowry, Under the Volcano, 1947, Ch. 10

 

"O God, I could be
bounded in a nutshell
and count myself
a king of infinite space,
were it not that
I have bad dreams."
Hamlet

Coxeter: King of Infinite Space

Coxeter exhuming geometry

From today's newspaper:

Dilbert on space, existence, and the dead

Notes:

For an illustration of
the phrase "solid and central,"
see the previous entry.

For further context, see the
five Log24 entries ending
on September 6, 2006
.

For background on the word
"hollow," see the etymology of
 "hole in the wall" as well as
"The God-Shaped Hole" and
"Is Nothing Sacred?"

For further ado, see
Macbeth, V.v
("signifying nothing")
and The New Yorker,
issue dated tomorrow.

Monday, April 30, 2007

Monday April 30, 2007

Filed under: General,Geometry — Tags: — m759 @ 6:24 PM
Structure and Logic

The phrase “structural logic” in yesterday’s entry was applied to Bach’s cello suites.  It may equally well be applied to geometry.  In particular:

“The aim of this thesis is to classify certain structures which are, from a certain point of view, as homogeneous as possible, that is which have as many symmetries as possible.”

Alice Devillers, “Classification of Some Homogeneous and Ultrahomogeneous Structures,” Ph.D. thesis, Université Libre de Bruxelles, academic year 2001-2002

Related material:

New models of some small finite spaces

In Devillers’s words, the above spaces with 8 and 16 points are among those structures that have “as many symmetries as possible.” For more details on what this means, see Devillers’s thesis and Finite Geometry of the Square and Cube.

The above models for the corresponding projective spaces may be regarded as illustrating the phrase “structural logic.”

For a possible application of the 16-point space’s “many symmetries” to logic proper, see The Geometry of Logic.

Sunday, April 29, 2007

Sunday April 29, 2007

Filed under: General — Tags: — m759 @ 7:00 AM
Rite

Rostropovich at Christ the Savior Cathedral

“The coffin of the cellist and conductor Mstislav Rostropovich seen inside Christ the Savior Cathedral during a farewell ceremony in Moscow, Sunday, April 29, 2007. Hundreds of Russians on Sunday came to bid final farewell to the great cellist and conductor Mstislav Rostropovich who won world fame for his masterly play and his courage in defending human rights. Rostropovich, who fought for the rights of Soviet-era dissidents and later triumphantly played Bach suites below the crumbling Berlin Wall, died Friday at age 80. (AP Photo/Mikhail Metzel)” —AP News

“His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality.” —Allan Kozinn in Friday’s New York Times

Friday, March 16, 2007

Friday March 16, 2007

Filed under: General,Geometry — Tags: — m759 @ 10:48 AM
"Geometry,
 Theology,
 and Politics:

 
Context and Consequences of 

the Hobbes-Wallis Dispute"
(pdf)

 

by Douglas M. Jesseph
Dept. of Philosophy and Religion
North Carolina State University

Excerpt:

"We are left to conclude that there was something significant in Hobbes's philosophy that motivated Wallis to engage in the lengthy and vitriolic denunciation of all things Hobbesian.

In point of fact, Wallis made no great secret of his motivations for attacking Hobbes's geometry, and the presence of theological and political motives is well attested in a 1659 letter to Huygens. He wrote:

But regarding the very harsh diatribe against Hobbes, the necessity of the case, and not my manners, led to it. For you see, as I believe, from other of my writings how peacefully I can differ with others and bear those with whom I differ. But this was provoked by our Leviathan (as can be easily gathered fro his other writings, principally those in English), when he attacks with all his might and destroys our universities (and not only ours, but all, both old and new), and especially the clergy and all institutions and all religion. As if the Christian world knew nothing sound or nothing that was not ridiculous in philosophy or religion; and as if it has not understood religion because it does not understand philosophy, nor philosophy because it does not understand mathematics. And so it seemed necessary that now some mathematician, proceeding in the opposite direction, should show how little he understand this mathematics (from which he takes his courage). Nor should we be deterred from this by his arrogance, which we know will vomit poison and filth against us. (Wallis to Huygens, 11 January, 1659; Huygens 1888-1950,* 2: 296-7)

The threats that Hobbes supposedly posed to the universities, the clergy, and all religion are a consequence of his political and theological doctrines. Hobbes's political theory requires that the power of the civil sovereign be absolute and undivided. As a consequence, such institutions as universities and the clergy must submit to the dictates of the sovereign in all matters. This extends, ironically enough, to geometry, since Hobbes notoriously claimed that the sovereign could ban the teaching of the subject and order 'the burning of all books of Geometry' if he should judge geometric principles 'a thing contrary to [his] right of dominion, or to the interest of men that have dominion' (Leviathan (1651) 1.11, 50; English Works** 3: 91). In the area of church government, Hobbes's doctrines are a decisive rejection of the claims of Presbyterianism, which holds that questions of theological doctrine is [sic] to be decided by the elders of the church– the presbytery– without reference to the claims of the sovereign. As a Presbyterian minister, a doctor of divinity, and professor of geometry at Oxford, Wallis found abundant reason to reject this political theory."

* Huygens, Christiaan. 1888-1950. Les oeuvres complètes de Chrisiaan Huygens. Ed. La Société Hollandaise des Sciences. 22 vols. The Hague: Martinus Nijhoff.

** Hobbes, Thomas. [1839-45] 1966. The English Works of Thomas Hobbes of Malmesbury, now First Collected and Edited by Sir William Molesworth. Edited by William Molesworth. 11 vols. Reprint. Aalen, Germany: Scientia Verlag.

 

Related material:

"But what is it?"
Calvin demanded.
"We know that it's evil,
but what is it?"

"Yyouu hhave ssaidd itt!"
Mrs. Which's voice rang out.
"Itt iss Eevill. Itt iss thee
Ppowers of Ddarrkknesss!"

A Wrinkle in Time

The image “http://www.log24.com/log/pix07/070316-AMScover.jpg” cannot be displayed, because it contains errors.

"After A Wrinkle in Time was finally published, it was pointed out to me that the villain, a naked disembodied brain, was called 'It' because It stands for Intellectual truth as opposed to a truth which involves the whole of us, heart as well as mind.  That acronym had never occurred to me.  I chose the name It intuitively, because an IT does not have a heart or soul.  And I did not understand consciously at the time of writing that the intellect, when it is not informed by the heart, is evil."

 

See also
"Darkness Visible"
in ART WARS.
 

Saturday, March 10, 2007

Saturday March 10, 2007

Filed under: General,Geometry — m759 @ 9:00 AM

The Logic of Dreams

From A Beautiful Mind–

“How could you,” began Mackey, “how could you, a mathematician, a man devoted to reason and logical proof…how could you believe that extraterrestrials are sending you messages? How could you believe that you are being recruited by aliens from outer space to save the world? How could you…?”

Nash looked up at last and fixed Mackey with an unblinking stare as cool and dispassionate as that of any bird or snake. “Because,” Nash said slowly in his soft, reasonable southern drawl, as if talking to himself, “the ideas I had about supernatural beings came to me the same way that my mathematical ideas did. So I took them seriously.”

Ideas:

The image “http://www.log24.com/log/pix07/070309-NYlottery.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix07/070309-PAlottery.jpg” cannot be displayed, because it contains errors.

These numbers may, in the mad way so well portrayed by Sylvia Nasar in the above book, be regarded as telling a story… a story that should, of course, not be taken too seriously.

Friday’s New York numbers (midday 214, evening 711) suggest the dates 2/14 and 7/11.  Clicking on these dates will lead the reader to Log24 entries featuring, among others, T. S. Eliot and Stephen King– two authors not unacquainted with the bizarre logic of dreams.

A link in the 7/11 entry leads to a remark of Noel Gray on Plato’s Meno and “graphic austerity as the tool to bring to the surface, literally and figuratively, the inherent presence of geometry in the mind of the slave.”

Also Friday: an example of graphic austerity– indeed, Gray graphic austerity– in Log24:

Chessboard (Detail)

This illustration refers to chess rather than to geometry, and to the mind of an addict rather than to that of a slave, but chess and geometry, like addiction and slavery, are not unrelated.


Friday’s Pennsylvania numbers, midday 429 and evening 038, suggest that the story includes, appropriately enough in view of the above Beautiful Mind excerpt, Mackey himself.  The midday number suggests the date 4/29, which at Log24 leads to an entry in memory of Mackey.

(Related material: the Harvard Gazette of April 6, 2006, “Mathematician George W. Mackey, 90: Obituary“–  “A memorial service will be held at Harvard’s Memorial Church on April 29 at 2 p.m.“)

Friday’s Pennsylvania evening number 038 tells two other parts of the story involving Mackey…

As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan’s “Mackey Memorial Lecture” (pdf).

More in the spirit of Nash, 38 may also be taken as a reference to Harvard’s old postal address, Cambridge 38, and to the year, 1938, that Mackey entered graduate study at Harvard, having completed his undergraduate studies at what is now Rice University.

Returning to the concept of graphic austerity, we may further simplify the already abstract chessboard figure above to obtain an illustration that has been called both “the field of reason” and “the Garden of Apollo” by an architect, John Outram, discussing his work at Mackey’s undergraduate alma mater:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O’Bedlam:

The image “http://www.log24.com/log/pix05A/050613-Crowe.jpg” cannot be displayed, because it contains errors.

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

Tom O’Bedlam’s Song

Wednesday, January 24, 2007

Wednesday January 24, 2007

Filed under: General — m759 @ 1:00 AM
The Dead Shepherd
starring E. Howard Hunt
and James Jesus Angleton

From this morning’s
New York Times:

The image “http://www.log24.com/log/pix07/070124-Hunt.jpg” cannot be displayed, because it contains errors.

Tim Weiner in today’s New York Times:

“Mr. Hunt was intelligent, erudite, suave and loyal to his friends….

Everette Howard Hunt Jr. was born in Hamburg, N.Y., on Oct. 9, 1918, the son of a lawyer and a classically trained pianist who played church organ. He graduated from Brown University in June 1940 and entered the United States Naval Academy as a midshipman in February 1941.

He worked as a wartime intelligence officer in China, a postwar spokesman for the Marshall Plan in Paris and a screenwriter in Hollywood. Warner Brothers had just bought his fourth novel, ‘Bimini Run,’ a thriller set in the Caribbean, when he joined the fledgling C.I.A. in April 1949.

Mr. Hunt was immediately assigned to train C.I.A. recruits…. He moved to Mexico City, where he became chief of station in 1950. He brought along another rookie C.I.A. officer, William F. Buckley Jr., later a prominent conservative author and publisher, who became godfather and guardian to the four children of Mr. Hunt and his wife, the former Dorothy L. Wetzel.

In 1954, Mr. Hunt helped plan the covert operation that overthrew the elected president of Guatemala….

By the time of the coup, Mr. Hunt had been removed from responsibility. He moved on to uneventful stints in Japan and Uruguay. Not until 1960 was Mr. Hunt involved in an operation that changed history.

The C.I.A. had received orders from both President Dwight D. Eisenhower and his successor, President John F. Kennedy, to alter or abolish the revolutionary government of Fidel in Cuba. Mr. Hunt’s assignment was to create a provisional Cuban government that would be ready to take power once the C.I.A.’s cadre of Cuban shock troops invaded the island…. 

He retired from the C.I.A. in 1970 and secured a job with an agency-connected public relations firm in Washington. Then, a year later, came a call from the White House….

Mr. Hunt’s last book, ‘American Spy: My Secret History in the C.I.A., Watergate and Beyond,’ written with Greg Aunapu, is to be published on March 16 with a foreword by his old friend William F. Buckley Jr.

Late in life, he said he had no regrets, beyond the Bay of Pigs.”

Related Material:

Game Boy,
Philosophy Wars,
and the following:

The image “http://www.log24.com/log/pix07/070124-Solomon.jpg” cannot be displayed, because it contains errors.

Andre Furlani, quoted in
Log24 on January 19:

“In his study of The Cantos,
Davenport defines the Poundian
ideogram as ‘a grammar of images,
emblems, and symbols, rather than
a grammar of logical sequence….
An idea unifies, dominates, and
controls the particulars that make
the ideogram’.”

For such an ideogram,
see Bright Star and the
(clickable) symbol from
Philosophy Wars:

The image “http://www.log24.com/log/pix07/070103-DoubleCross.jpg” cannot be displayed, because it contains errors.

The image “http://www.log24.com/log/pix07/070124-Pound2.jpg” cannot be displayed, because it contains errors.

Photo from Miami University site

Tuesday, January 9, 2007

Tuesday January 9, 2007

Filed under: General — Tags: — m759 @ 12:00 PM
For Balanchine's Birthday

(continued from
January 9, 2003)

George Balanchine

Encyclopædia Britannica Article

born January 22
[January 9, Old Style], 1904,
St. Petersburg, Russia
died April 30, 1983, New York,
New York, U.S.

Photograph:George Balanchine.
George Balanchine.
©1983 Martha Swope

original name 
Georgy Melitonovich Balanchivadze

most influential choreographer of classical ballet in the United States in the 20th century.  His works, characterized by a cool neoclassicism, include The Nutcracker (1954) and Don Quixote (1965), both pieces choreographed for the New York City Ballet, of which he was a founder (1948), the artistic director, and the…


Balanchine,  George… (75 of 1212 words)

"What on earth is
a concrete universal?"
— Robert M. Pirsig

Review:

From Wikipedia's
"Upper Ontology"
and
Epiphany 2007:

"There is no neutral ground
that can serve as
a means of translating between
specialized (lower) ontologies."

There is, however,
"the field of reason"–

the 3×3 grid:

The image “http://www.log24.com/theory/images/grid3x3.gif” cannot be displayed, because it contains errors.

Click on grid
for details.

As Rosalind Krauss
has noted, some artists
regard the grid as

"a staircase to
  the Universal."

Other artists regard
Epiphany itself as an
approach to
the Universal:

"Epiphany signals the traversal
of the finite by the infinite,
of the particular by the universal,
of the mundane by the mystical,
of time by eternity.
"

Richard Kearney, 2005,
in The New Arcadia Review

The image “http://www.log24.com/log/pix07/070109-Kearney2.jpg” cannot be displayed, because it contains errors.

Kearney (right) with
Martin Scorsese (left)
and Gregory Peck
in 1997.

"… one of the things that worried me about traditional metaphysics, at least as I imbibed it in a very Scholastic manner at University College Dublin in the seventies, is that philosophy was realism and realism was truth. What disturbed me about that was that everything was already acquired; truth was always a systematic given and it was there to be learned from Creation onwards; it was spoken by Jesus Christ and then published by St. Thomas Aquinas: the system as perfect synthesis. Hence, my philosophy grew out of a hunger for the 'possible' and it was definitely a reaction to my own philosophical formation. Yet that wasn't my only reaction. I was also reacting to what I considered to be the deep pessimism, and even at times 'nihilism' of the postmodern turn."

— Richard Kearney, interview (pdf) in The Leuven Philosophy Newsletter, Vol. 14, 2005-2006

For more on "the possible," see Kearney's The God Who May Be, Diamonds Are Forever, and the conclusion of Mathematics and Narrative:

 

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

 

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity,
Christ Church College, Oxford
(the home of Lewis Carroll)

Sunday, December 31, 2006

Sunday December 31, 2006

Filed under: General,Geometry — m759 @ 9:00 AM
Aesthetics of Evil
vs. Christ Church

“… the closing number
for Spielberg’s tribute
and the gala itself…
[is] the finale to
the opera ‘Candide,’
  ‘Make Our Garden Grow.'”

Press release from CBS
on this year’s
Kennedy Center Honors

Wallace Stevens,
Esthétique du Mal, XI”
“We are not
At the centre of a diamond.”

The image “http://www.log24.com/log/pix06B/061231-DC.jpg” cannot be displayed, because it contains errors.

The map shows the original
(pre-1846) diamond shape
of the District of Columbia.

For the relevance of the
closing number of “Candide”
to diamonds, see
the previous entry.

For the relevance of the
closing number of the
12/3/06 DC lottery, see
Theme and Variations.

For the relevance of the
earlier mid-day number,
see the conclusion of
Esthétique du Mal” —

“And out of what one sees
   and hears and out
Of what one feels, who could
   have thought to make
So many selves, so many
   sensuous worlds,
As if the air, the mid-day air,
   was swarming
With the metaphysical changes
   that occur,
Merely in living
   as and where we live.”

The image “http://www.log24.com/log/pix06B/061203-DCday.jpg” cannot be displayed, because it contains errors.

A search on the mid-day number
in the context of metaphysics
yields the following:

The image “http://www.log24.com/log/pix06B/061231-Herm536.jpg” cannot be displayed, because it contains errors.

Related material:

“In ‘Esthétique du Mal,’ one of his later poems, Wallace Stevens considers existence from a variety of critical and philosophical perspectives, among them various moral, aesthetic, political, theological, and philosophic ‘epistemes’ that condition how humanity perceives and experiences the world. These epistemological ‘modes’ dictate how we live and perceive the world about us, providing preconceptions that shroud understanding and obfuscate ontological explanation. What Stevens accomplishes in ‘Esthétique du Mal‘ is to create a dialogue with various historical and philosophical ‘schools,’ systematically confronting and rejecting their perspectives, and creating a movement toward Martin Heidegger’s ‘aletheia’ to uncover the ontological substructure that exists beneath the individual’s experience in the world. This movement of ‘uncovering’ and exposing the nature of what it means ‘to be in the world’ is a journey to an ontological substructure that allows Stevens to arrive at a dynamic, ontological proof: that existence is full of ‘reverberating’ possibilities, not solitary and ‘univocal’ statements.”

Conversations with the Dead:
The Ontological Substructure of
Wallace Stevens’s “Esthétique du Mal

a 1999 Master’s thesis

For further remarks on
ontological substructure,
see A First Class Degree
(on a notable graduate of
Christ Church, Oxford).

Friday, December 29, 2006

Friday December 29, 2006

Filed under: General — Tags: — m759 @ 11:01 AM
Tools
of Christ Church

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon

Cover of Thomas, by Shelley Mydans: Sword and its shadow, a cross

Click on picture for details.

Today is the feast
of St. Thomas Becket.

In his honor, a meditation
on tools and causation:

"Lewis Wolpert, an eminent developmental biologist at University College London, has just published Six Impossible Things Before Breakfast, a pleasant, though rambling, look at the biological basis of belief. While the book focuses on our ability to form causal beliefs about everyday matters (the wind moved the trees, for example), it spends considerable time on the origins of religious and moral beliefs. Wolpert defends the unusual idea that causal thinking is an adaptation required for tool-making. Religious beliefs can thus be seen as an odd extension of causal thinking about technology to more mysterious matters. Only a species that can reason causally could assert that 'this storm was sent by God because we sinned.' While Wolpert's attitude toward religion is tolerant, he's an atheist who seems to find religion more puzzling than absorbing."

Review by H. Allen Orr in
The New York Review of Books,
Vol. 54, No. 1, January 11, 2007    


"An odd extension"–

Wolpert's title is, of course,
from Lewis Carroll.

Related material:

"It's a poor sort of memory
that only works backwards."
Through the Looking-Glass

An event at the Kennedy Center
broadcast on
December 26, 2006
(St. Steven's Day):

"Conductor John Williams, a 2004 Honoree, says, 'Steven, sharing our 34-year collaboration has been a great privilege for me. It's been an inspiration to watch you dream your dreams, nurture them and make them grow. And, in the process, entertain and edify billions of people around the world. Tonight we'd like to salute you, musically, with a piece that expresses that spirit beautifully … It was written by Leonard Bernstein, a 1980 Kennedy Center Honoree who was, incidentally, the first composer to be performed in this hall.' Backed by The United States Army Chorus and The Choral Arts Society, soprano Harolyn Blackwell and tenor Gregory Turay sing the closing number for Spielberg's tribute and the gala itself. It's the finale to the opera 'Candide,' 'Make Our Garden Grow,' and Williams conducts."

CBS press release

See also the following,
from the conclusion to

"Mathematics and Narrative"

(Log24, Aug. 22, 2005):

Diamond on cover of Narrative Form, by Suzanne Keen

"At times, bullshit can
only be countered
   with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to at least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

"Il faut cultiver notre jardin."
— Voltaire

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

Diamond in a square

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
 Regius Professor of Divinity,
  Christ Church College, Oxford
(the home of Lewis Carroll)

For further details,
click on the
Christ Church diamond.

Tuesday, April 25, 2006

Tuesday April 25, 2006

Filed under: General,Geometry — m759 @ 3:09 PM

“There is a pleasantly discursive treatment
of Pontius Pilate’s unanswered question
‘What is truth?'”

— H. S. M. Coxeter, 1987, introduction to
Richard J. Trudeau’s remarks on
the “Story Theory” of truth
as opposed to
the “Diamond Theory” of truth
in The Non-Euclidean Revolution

A Serious Position

“‘Teitelbaum,’ in German,
is ‘date palm.'”
Generations, Jan. 2003   

“In Hasidism, a mystical brand
of Orthodox Judaism, the grand rabbi
is revered as a kinglike link to God….”

Today’s New York Times obituary
of Rabbi Moses Teitelbaum,
who died on April 24, 2006
(Easter Monday in the
Orthodox Church
)

From Nextbook.org, “a gateway to Jewish literature, culture, and ideas”:

NEW BOOKS: 02.16.05
Proofs and Paradoxes
Alfred Teitelbaum changed his name to Tarski in the early 20s, the same time he changed religions, but when the Germans invaded his native Poland, the mathematician was in California, where he remained. His “great achievement was his audacious assault on the notion of truth,” says Martin Davis, focusing on the semantics and syntax of scientific language. Alfred Tarski: Life and Logic, co-written by a former student, Solomon Feferman, offers “remarkably intimate information,” such as abusive teaching and “extensive amorous involvements.”

From Wikipedia, an unsigned story:

“In 1923 Alfred Teitelbaum and his brother Wacław changed their surnames to Tarski, a name they invented because it sounded very Polish, was simple to spell and pronounce, and was unused. (Years later, he met another Alfred Tarski in northern California.) The Tarski brothers also converted to Roman Catholicism, the national religion of the Poles. Alfred did so, even though he was an avowed atheist, because he was about to finish his Ph.D. and correctly anticipated that it would be difficult for a Jew to obtain a serious position in the new Polish university system.”

The image “http://www.log24.com/log/pix06/060425-Tarski.jpg” cannot be displayed, because it contains errors.

Alfred Tarski

The image “http://www.log24.com/log/pix06/060424-Crimson2.jpg” cannot be displayed, because it contains errors.

See also
 
The Crimson Passion.

Friday, March 31, 2006

Friday March 31, 2006

Filed under: General — Tags: — m759 @ 9:00 PM
Reason and Rhyme

"Philosophers ponder the idea of identity: what it is to give something a name on Monday and have it respond to that name on Friday…."

— Bernard Holland in
   The New York Times
  
Monday, May 20, 1996

Related material:
 
Philadelphia Stories

The image “http://www.log24.com/log/pix05B/051016-Mont.jpg” cannot be displayed, because it contains errors.

and, from Monday,
March 27, 2006–

 A Living Church,

Today's Pennsylvania lottery:

Mid-Day: 888

See today's noon entry
and Eight is a Gate.

Evening: 557

See
 Dogma in the State of Grace,
Is Nothing Sacred?,
 
and, from page 557 of
Webster's
New World Dictionary
,
College Edition, 1960:

"flower"

The image “http://www.log24.com/log/pix06/BirdsBeastsAndFlowers.jpg” cannot be displayed, because it contains errors.

Birds, Beasts & Flowers

As performed by
Princess Grace of Monaco

Presented at
St James's Palace, London,

on 22nd November 1978
in the presence of Her Majesty,
Queen Elizabeth
The Queen Mother

Friday March 31, 2006

Filed under: General,Geometry — Tags: , — m759 @ 12:00 PM

Women's History Month continues…
 
Ontology Alignment

"He had with him a small red book of Mao's poems, and as he talked he squared it on the table, aligned it with the table edge first vertically and then horizontally.  To understand who Michael Laski is you must have a feeling for that kind of compulsion."

— Joan Didion in the
Saturday Evening Post,
Nov. 18, 1967 (reprinted in
Slouching Towards Bethlehem)

"Or were you," I said.
He said nothing.
"Raised a Catholic," I said.
He aligned a square crystal paperweight with the edge of his desk blotter.

— Joan Didion in
The Last Thing He Wanted,
Knopf, 1996

"It was Plato who best expressed– who veritably embodied– the tension between the narrative arts and mathematics….

Plato clearly loved them both, both mathematics and poetry.  But he approved of mathematics, and heartily, if conflictedly, disapproved of poetry.  Engraved above the entrance to his Academy, the first European university, was the admonition: Oudeis ageometretos eiseto.  Let none ignorant of geometry enter.  This is an expression of high approval indeed, and the symbolism could not have been more perfect, since mathematics was, for Plato, the very gateway for all future knowledge.  Mathematics ushers one into the realm of abstraction and universality, grasped only through pure reason.  Mathematics is the threshold we cross to pass into the ideal, the truly real."

— Rebecca Goldstein,
Mathematics and
the Character of Tragedy

Monday, August 22, 2005

Monday August 22, 2005

Filed under: General — Tags: — m759 @ 4:07 PM
The Hole

Part I: Mathematics and Narrative

The image “http://www.log24.com/log/pix05B/050822-Narr.jpg” cannot be displayed, because it contains errors.

Apostolos Doxiadis on last month's conference on "mathematics and narrative"–

Doxiadis is describing how talks by two noted mathematicians were related to

    "… a sense of a 'general theory bubbling up' at the meeting… a general theory of the deeper relationship of mathematics to narrative…. "

Doxiadis says both talks had "a big hole in the middle."  

    "Both began by saying something like: 'I believe there is an important connection between story and mathematical thinking. So, my talk has two parts.  [In one part] I’ll tell you a few things about proofs.  [And in the other part] I’ll tell you about stories.' …. And in both talks it was in fact implied by a variation of the post hoc propter hoc, the principle of consecutiveness implying causality, that the two parts of the lectures were intimately related, the one somehow led directly to the other."
  "And the hole?"
  "This was exactly at the point of the link… [connecting math and narrative]… There is this very well-known Sidney Harris cartoon… where two huge arrays of formulas on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’ And one of the two mathematicians standing before it points at this and tells the other: ‘I think you should be more explicit here at step two.’ Both… talks were one half fascinating expositions of lay narratology– in fact, I was exhilarated to hear the two most purely narratological talks at the meeting coming from number theorists!– and one half a discussion of a purely mathematical kind, the two parts separated by a conjunction roughly synonymous to ‘this is very similar to this.’  But the similarity was not clearly explained: the hole, you see, the ‘miracle.’  Of course, both [speakers]… are brilliant men, and honest too, and so they were very clear about the location of the hole, they did not try to fool us by saying that there was no hole where there was one."
 

Part II: Possible Worlds

"At times, bullshit can only be countered with superior bullshit."
Norman Mailer

Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:

    "The concept of possible worlds dates back to a least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds.  Voltaire satirized this view in his picaresque novel Candide….
    Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."

 

Background:

Modal Logic in Wikipedia

Possible Worlds in Wikipedia

Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)

The God-Shaped Hole
 

Part III: Modal Theology

  "'What is this Stone?' Chloe asked….
  '…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"

  — Many Dimensions, by Charles Williams, 1931 (Eerdmans paperback, April 1979, pp. 43-44)


"The lapis was thought of as a unity and therefore often stands for the prima materia in general."

  — Aion, by C. G. Jung, 1951 (Princeton paperback, 1979, p. 236)

"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."

 
  — The Stars My Destination, by Alfred Bester, 1956 (Vintage hardcover, July 1996, p. 216)
 
"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Sunday, August 7, 2005

Sunday August 7, 2005

Filed under: General — m759 @ 7:20 AM
Presbyterian Justice

News from today’s New York Times:

The Rev. Dr. Theodore Alexander Gill Sr., a Presbyterian theologian, a philosophy teacher, and an influential provost emeritus of John Jay College of Criminal Justice in Manhattan, died at 85 on June 10 in Princeton.  In retirement from John Jay, The Rev. Dr. Gill was theologian in residence at Nassau Presbyterian Church in Princeton.

In memory of The Rev. Dr. Gill:

Religious Symbolism at Princeton
    (on Nassau Presbyterian Church),
Pro-Semitism
    (on number theory at Princeton),
For the Mad Musicians of Princeton,
     (on Schroeder and Bernstein),
Movie Date and its preceding entries
   (on Princeton’s St. John von Neumann),
Why Me?
   (for Princeton theologian Elaine Pagels),
Notes on Literary and Philosophical Puzzles
   (Princeton’s John Nash as Ya Ya Fontana), and
Go Tigers!
   (for the Princeton Evangelical Fellowship).

For a more conventional memorial, see

The image “http://www.log24.com/log/pix05B/050807-SFTS-Logo.gif” cannot be displayed, because it contains errors.

the obituary from

San Francisco Theological Seminary.

Thursday, March 3, 2005

Thursday March 3, 2005

Filed under: General — Tags: — m759 @ 3:26 PM
Necessity, Possibility, Symmetry

The image “http://www.log24.com/log/pix05/050303-Symmetry.gif” cannot be displayed, because it contains errors.


Matrix group actions,
March 26, 1985

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Sunday, February 20, 2005

Sunday February 20, 2005

Filed under: General,Geometry — Tags: , — m759 @ 2:20 PM

Relativity Blues

Today, February 20, is the 19th anniversary of my note The Relativity Problem in Finite Geometry.  Here is some related material.

In 1931, the Christian writer Charles Williams grappled with the theology of time, space, free will, and the many-worlds interpretation of quantum mechanics (anticipating by many years the discussion of this topic by physicists beginning in the 1950's).

(Some pure mathematics — untainted by physics or theology — that is nevertheless related, if only by poetic analogy, to Williams's 1931 novel, Many Dimensions, is discussed in the above-mentioned note and in a generalization, Solomon's Cube.)

On the back cover of Williams's 1931 novel, the current publisher, William B. Eerdmans Publishing Company of Grand Rapids, Michigan, makes the following statement:

"Replete with rich religious imagery, Many Dimensions explores the relation between predestination and free will as it depicts different human responses to redemptive transcendence."

One possible response to such statements was recently provided in some detail by a Princeton philosophy professor.  See On Bullshit, by Harry G. Frankfurt, Princeton University Press, 2005.

A more thoughtful response would take into account the following:

1. The arguments presented in favor of philosopher John Calvin, who discussed predestination, in The Death of Adam: Essays on Modern Thought, by Marilynne Robinson

2. The physics underlying Einstein's remarks on free will, God, and dice
 
3. The physics underlying Rebecca Goldstein's novel Properties of Light and Paul Preuss's novels  Secret Passages and Broken Symmetries

4. The physics underlying the recent so-called "free will theorem" of John Conway and Simon Kochen of Princeton University

5. The recent novel Gilead, by Marilynne Robinson, which deals not with philosophy, but with lives influenced by philosophy — indirectly, by the philosophy of the aforementioned John Calvin.

From a review of Gilead by Jane Vandenburgh:  

"In The Death of Adam, Robinson shows Jean Cauvin to be the foremost prophet of humanism whose Protestant teachings against the hierarchies of the Roman church set in motion the intellectual movements that promoted widespread literacy among the middle and lower classes, led to both the American and French revolutions, and not only freed African slaves in the United States but brought about suffrage for women. It's odd then that through our culture's reverse historicism, the term 'Calvinism' has come to mean 'moralistic repression.'"

For more on what the Calvinist publishing firm Eerdmans calls "redemptive transcendence," see various July 2003 Log24.net entries.  If these entries include a fair amount of what Princeton philosophers call bullshit, let the Princeton philosophers meditate on the summary of Harvard philosophy quoted here on November 5 of last year, as well as the remarks of November 5, 2003,  and those of November 5, 2002.

From Many Dimensions (Eerdmans paperback, 1963, page 53):

"Lord Arglay had a suspicion that the Stone would be purely logical.  Yes, he thought, but what, in that sense, were the rules of its pure logic?"

A recent answer:

Modal Theology

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

Thursday, February 17, 2005

Thursday February 17, 2005

Filed under: General,Geometry — Tags: — m759 @ 1:00 PM
Modal Theology

"We symbolize logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

On the Lapis Philosophorum,
the Philosophers' Stone –

"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"
Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)

"The lapis was thought of as a unity
and therefore often stands for
the prima materia in general."
Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)

"Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe."
The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)

"The possibilia that exist,
and out of which
the Universe arose,
are located in
     a necessary being…."

Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)

See also
The Diamond Archetype.

For more on modal theology, see

Kurt Gödel's Ontological Argument
and

 The Ontological Argument
 from Anselm to Gödel.

Thursday, February 5, 2004

Thursday February 5, 2004

Filed under: General — m759 @ 12:00 PM

Affirmation of Place and Time:
East Coker and Grand Rapids

This morning’s meditation:

“Let us talk together with the courage, humor, and ardor of Socrates.

In that long conversation, we may find ourselves considering something Plato’s follower Plotinus said long ago about ‘a principle which transcends being,’ in whose domain one can ‘assert identity without the affirmation of being.’  There, ‘everything has taken its stand forever, an identity well pleased, we might say, to be as it is…. Its entire content is simultaneously present in that identity: this is pure being in eternal actuality; nowhere is there any future, for every then is a now; nor is there any past, for nothing there has ever ceased to be.’  Individuality and existence in space and time may be masks that our sensibilities impose on the far different face of quantum reality.”

— Peter Pesic, Seeing Double: Shared Identities in Physics, Philosophy, and Literature, MIT Press paperback, 2003, p. 145

A search for more on Plotinus led to sites on the Trinity, which in turn led to the excellent archives at Calvin College in Grand Rapids.

A search for the theological underpinnings of Calvin College led to the Christian Reformed church:

“Our emblem is
the cross in a triangle.”

The triangle, as a symbol of “the delta factor,” also plays an important role in the semiotic theory of Walker Percy.  A search for current material on Percy led back to one of my favorite websites, that of Percy expert Karey Perkins, and thus to the following paper:

The “East Coker” Dance
in T. S. Eliot’s Four Quartets:
An Affirmation of Place and Time

by Karey Perkins

For a rather different, but excellent, literary affirmation of place and time — in Grand Rapids, rather than East Coker — see, for instance, Michigan Roll, a novel by Tom Kakonis.

We may, for the purposes of this trinitarian meditation, regard Percy and Kakonis as speaking for the Son and Karey Perkins as a spokesperson for the Holy Spirit.  As often in my meditations, I choose to regard the poet Wallace Stevens as speaking perceptively about (if not for, or as) the Father.  A search for related material leads to a 1948 comment by Thomas McGreevy, who

“… wrote of Stevens’ ‘Credences of Summer’ (Collected Poems 376),

On every page I find things that content me, as ‘The trumpet of the morning blows in the clouds and through / The sky.’

A devout Roman Catholic, he added, ‘And I think my delight in it is of the Holy Spirit.’ (26 May 1948).”

An ensuing search for material on “Credences of Summer” led back, surprisingly, to an essay — not very scholarly, but interesting — on Stevens, Plotinus, and neoplatonism.

Thus the circle closed.

As previous entries have indicated, I have little respect for Christianity as a religion, since Christians are, in my experience, for the most part, damned liars.  The Trinity as philosophical poetry, is, however, another matter.  I respect Pesic’s speculations on identity, but wish he had a firmer grasp of his subject’s roots in trinitarian thought.  For Stevens, Percy, and Perkins, I have more than respect.

Wednesday, July 2, 2003

Wednesday July 2, 2003

Filed under: General — m759 @ 7:00 PM

Three Days Late
and a Dollar Short

THE BOOK AGAINST GOD
By James Wood.
257 pp. New York:
Farrar, Straus & Giroux. $24. 

This is a book that attempts to recreate the myth of Saint Peter.

See the New York Times review of this book from today, July 2, 2003, three days late.  The Feast of St. Peter was on June 29.

The price, $24, also falls short of the theological glory reflected in the number 25, the common denominator of Christmas (12/25) and AntiChristmas (6/25), as well as the number of the heart of the Catholic church, the Bingo card

For all these issues, see my entries and links in memory of St. Peter, from June 29

The real “book against God,” a novel by Robert Stone, is cited there.  The legend of St. Peter is best described by Stone, not Wood.

Tuesday, December 10, 2002

Tuesday December 10, 2002

Filed under: General — Tags: — m759 @ 1:06 AM

Three Coins in the Fountain

Mars

Victory

Sol Invictus

The reverse of three bronze coins
minted during Constantine’s early years

"Constantine like many of his predecessors had worshipped the Greek and Roman gods, particularly Apollo, Mars and Victory. This fact is evident in the portrayal of these gods on the earliest of Constantine’s coins. Yet surprisingly, even after his dream experience, and subsequent victory over Maxentius, it is recorded that he continued to worship these gods. Although the images of Apollo, Mars and Victory quickly disappeared from his coinage, later coins minted under Constantine shows that he likely continued to worship the sol invicta [sic] or ‘Unconquered Sun’ for 10 years or more after his dream experience. Yet, over a period of years, the experience of the sign, and the victory at the Milvian bridge, eventually led Constantine to favour and later to convert to the Christian faith."

— Ross Nightingale, "The 'Sign' that Changed the Course of History," in Ancient Coin Forum

"Three coins in the fountain,
Each one seeking happiness.
Thrown by three hopeful lovers,
Which one will the fountain bless?

Three hearts in the fountain,
Each heart longing for its home.
There they lie in the fountain
Somewhere in the heart of Rome."

Sinatra's version of the 1954 song
(Lyrics by Sammy Cahn,
 music by Jule Styne)

Which one will the fountain bless?

In order to answer this theological conundrum, we need to know more about the unfamiliar god Sol Invictus.

A quick web search reveals that some fanatical Protestants believe that the Roman deities Sol Invictus and Mithra were virtually the same.  Of course, it is unwise to take the paranoid ravings of Protestants too seriously, but in this case they may be on to something.

The Catholic Church itself seems to identify Sol Invictus with Mithra:

"Sunday was kept holy in honour of Mithra…. The 25 December was observed as his birthday, the natalis invicti, the rebirth of the winter-sun, unconquered by the rigours of the season. A Mithraic community was not merely a religious congregation…"

The Catholic Encyclopedia, 1911 edition.

Nihil Obstat, October 1, 1911. Remy Lafort, S.T.D., Censor
Imprimatur. +John Cardinal Farley, Archbishop of New York

It would seem, therefore, that as December 25 approaches we are preparing to celebrate the festival of Sol Invictus. This perhaps answers the theological riddle posed by Sammy Cahn.

From "Things Change," starring Don Ameche:
"A big man knows the value of a small coin."

Today's site music celebrates
Cahn, Styne, Sinatra, and the spirit of the 1950's.
Many thanks to
Loyd's Piano Music Page
for this excellent rendition of a Styne classic
.

Friday, November 8, 2002

Friday November 8, 2002

Filed under: General,Geometry — m759 @ 3:33 AM

Religious Symbolism
at Princeton

In memory of Steve McQueen (“The Great Escape” and “The Thomas Crown Affair”… see preceding entry) and of Rudolf Augstein (publisher of Der Spiegel), both of whom died on November 7 (in 1980 and 2002, respectively), in memory of the following residents of

The Princeton Cemetery
of the Nassau Presbyterian Church
Established 1757

SYLVIA BEACH (1887-1962), whose father was pastor of the First Presbyterian Church, founded Shakespeare & Company, a Paris bookshop which became a focus for struggling expatriate writers. In 1922 she published James Joyce’s Ulysses when others considered it obscene, and she defiantly closed her shop in 1941 in protest against the Nazi occupation.

KURT GÖDEL (1906-1978), a world-class mathematician famous for a vast array of major contributions to logic, was a longtime professor at the Institute for Advanced Study, founded in 1930. He was a corecipient of the Einstein Award in 1951.

JOHN (HENRY) O’HARA (1905-1970) was a voluminous and much-honored writer. His novels, Appointment in Samarra (1934) and Ten North Frederick (1955), and his collection of short stories, Pal Joey (1940), are among his best-known works.

and of the long and powerful association of Princeton University with the Presbyterian Church, as well as the theological perspective of Carl Jung in Man and His Symbols, I offer the following “windmill,” taken from the Presbyterian Creedal Standards website, as a memorial:

The background music Les Moulins de Mon Coeur, selected yesterday morning in memory of Steve McQueen, continues to be appropriate.

“A is for Anna.”
— James Joyce

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