Log24

Monday, November 10, 2014

Meanwhile, Back in 1962…

Filed under: General — Tags: — m759 @ 11:59 pm

Remember him to Herald Square.

Thursday, September 27, 2012

April 9, 1962

Filed under: General — Tags: — m759 @ 1:01 am

IMAGE- Andy Williams sings 'Moon River' from 'Breakfast at Tiffany's' at the Academy Awards on April 9, 1962.

The "1961" Oscars ceremony shown above was for the films of 1961.
The ceremony itself was held on April 9, 1962.

For a different Tiffany, see Tuesday's Another Day.

Thursday, December 21, 2023

Mutternacht

Filed under: General — Tags: , — m759 @ 1:31 am
 
"Ich bin ein Teil des Teils, der anfangs alles war
Ein Teil der Finsternis, die sich das Licht gebar
Das stolze Licht, das nun der Mutter Nacht
Den alten Rang, den Raum ihr streitig macht,
Und doch gelingt’s ihm nicht, da es, so viel es strebt,
Verhaftet an den Körpern klebt.
Von Körpern strömt’s, die Körper macht es schön,
Ein Körper hemmt’s auf seinem Gange;
So, hoff ich, dauert es nicht lange,
Und mit den Körpern wird’s zugrunde gehn."
 
Goethe, Faust
 

"The title of the book … is taken from a speech by Mephistopheles in Goethe’s Faust. As translated by Carlyle F. MacIntyre (New Directions, 1941), the speech is this:

I am a part of the part that at first was all, part of the darkness that gave birth to light, that supercilious light which now disputes with Mother Night her ancient rank and space, and yet can not succeed; no matter how it struggles, it sticks to matter and can’t get free. Light flows from substance, makes it beautiful; solids can check its path, so I hope it won’t be long till light and the world’s stuff are destroyed together."

— Vonnegut, Kurt. Mother Night: A Novel 
     (Gold Medal Books, 1962).

Mutternacht , as opposed to Mutter Nacht , is tonight,
the night of December 20-21, Winter Solstice Eve.

Saturday, October 7, 2023

Dance

Filed under: General — Tags: , — m759 @ 3:23 pm

Comment # 200 — "Tubular. (Valspeak, 1962.)"

Saturday, August 19, 2023

Speak, Memory: The Jewel in Ray Houchins’s Lotus

Filed under: General — m759 @ 5:21 pm

"Does the name 'Coulter' mean anything to you?"

See as well this  journal on 07/19/2021, the Lotus-page date above. 

Thursday, August 17, 2023

Gathering Moss

Filed under: General — Tags: — m759 @ 6:28 am

"Formed in 1962, Alpert and Moss’ A&M (named after their initials)
label’s quarter-plus century run included some major blockbuster
albums, including Carole King’s Tapestry, Peter Frampton’s Frampton
Comes Alive!
, and Alpert’s own Whipped Cream & Other Delights."

— BY ALTHEA LEGASPI  August 16, 2023 

See as well "Report from Clouded Mountain" (Log24, June 8, 2023).

Monday, June 19, 2023

The Original Portable Door

Filed under: General — Tags: , , — m759 @ 3:26 pm

"… a cardboard tube, more or less the same length as
the inner core of a toilet roll, but thicker. He frowned,
took the roll out, laid it on the desk and poked up it
with the butt end of a pencil. Something slid out.
It looked like a rolled-up black plastic dustbin liner;
but when he unfolded it, he recognised it as the funny
sheet thing he’d found in the strongroom and briefly
described as an Acme Portable Door, before losing
his nerve and changing it to something less facetious." 

— Holt, Tom. The Portable Door . Orbit. Kindle Edition. 

According to goodreads.com, the Holt book was
"first published March 6, 2003."

Compare and contrast the "portable door" as a literary device
with the "tesseract" in A Wrinkle in Time  (1962).

See also this  journal on March 6, 2003.

Saturday, April 15, 2023

Arrival

Filed under: General — Tags: , — m759 @ 12:58 pm

See as well this  journal on June 1, 2012 — Matrix Problem Reloaded.

Saturday, March 11, 2023

Law Play

Filed under: General — Tags: , , — m759 @ 8:43 am
 

   Nietzsche, 'law in becoming' and 'play in necessity'   Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Simplified version —

'Law Play' by Cullinane, 11 March 2023

Monday, August 1, 2022

Interality Again: The Art of the Gefüge

Filed under: General — Tags: , , — m759 @ 2:52 pm

"Schufreider shows that a network of linguistic relations
is set up between Gestalt, Ge-stell,  and Gefüge, on the
one hand, and Streit, Riß,  and Fuge, on the other . . . ."

— From p. 14 of French Interpretations of Heidegger ,
edited by David Pettigrew and François Raffoul.
State U. of New York Press, Albany, 2008. (Links added.)

One such "network of linguistic relations" might arise from
a non-mathematician's attempt to describe the diamond theorem.

(The phrase "network of linguistic relations" appears also in 
Derrida's remarks on Husserl's Origin of Geometry .)

For more about "a system of slots," see interality in this journal.

The source of the above prefatory remarks by editors Pettigrew and Raffoul —

"If there is a specific network that is set up in 'The Origin of the Work of Art,'
a set of structural relations framed in linguistic terms, it is between
Gestalt, Ge-stell and Gefüge, on the one hand, and Streit, Riß and Fuge
on the other; between (as we might try to translate it)  
configuration, frame-work and structure (system), on the one hand, and
strife, split (slit) and slot, on the other. On our view, these two sets go
hand in hand; which means, to connect them to one another, we will
have to think of the configuration of the rift (Gestalt/Riß) as taking place
in a frame-work of strife (Ge-stell/Streit) that is composed through a system
of slots (Gefüge/Fuge) or structured openings." 

— Quotation from page 197 of Schufreider, Gregory (2008):
"Sticking Heidegger with a Stela: Lacoue-Labarthe, art and politics."
Pp. 187-214 in David Pettigrew & François Raffoul (eds.), 
French Interpretations of Heidegger: An Exceptional Reception.
State University of New York Press, 2008.

Update at 5:14 AM ET Wednesday, August 3, 2022 —

See also "six-set" in this journal.

"There is  such a thing as a six-set."
— Saying adapted from a 1962 young-adult novel.

Wednesday, June 8, 2022

Meta Four

Filed under: General — Tags: , — m759 @ 12:42 pm

Tonight is Replacement Eve —

"The metaphor for metamorphosis no keys unlock" — Cullinane, 1986

Related remarks —

From a Log24 search for "Notation+Levi-Strauss" —

"There is  such a thing as a four-set."

— Motto adapted from a 1962 young-adult novel.

Thursday, February 17, 2022

Four Dots, Six Lines

Filed under: General — Tags: — m759 @ 1:46 am

"There is  such a thing  as  a tesseract." 

— Mrs. Whatsit in  A Wrinkle in Time  (1962)

"Simplify, simplify." — Henry David Thoreau in Walden  (1854)

Von Franz representation of the I Ching's Hexagram 2, The Receptive
 

A Jungian on this six-line figure:

“They are the same six lines that exist in the I Ching…. Now observe the square more closely: four of the lines are of equal length, the other two are longer…. For this reason symmetry cannot be statically produced and a dance results.”
 
— Marie-Louise von Franz,
   Number and Time  (1970)

Monday, February 7, 2022

Morphart Meets Morph Art

Filed under: General — Tags: , — m759 @ 1:51 pm

Warren (PA) Public Library's Instagram
on January 21, 2022 —

Morphart

Morph Art — from Raiders of the Lost Coordinates

"There is  such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.

Sunday, February 6, 2022

Ringing the Changes

Filed under: General — Tags: , — m759 @ 11:23 pm

In memory of Hale Trotter, a mathematician who reportedly
died at Princeton, N.J., on Jan. 17, 2022.

Other perspectives —

“The carnival is an incredibly close-knit, hermetic society.” 

— Guillermo del Toro, director and co-writer of
the new remake of "Nightmare Alley"

Dialogue from that remake  —

STAN — How do you ever get a guy to geek?
CLEM — Oh- I ain’t going to crap you up. It ain’t easy.

"There is  such a thing as a four-set." 
— Saying adapted from a 1962 young-adult novel

Thursday, January 13, 2022

(Belated) Meditation for New Year’s Day, 2022

Filed under: General — Tags: — m759 @ 5:37 pm

Hexagram 51:

"I woke last night to the sound of thunder,
How far off, I sat and wondered.
Started humming a song from 1962.
Ain't it funny how the night moves?"

See also . . .

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Thursday, December 30, 2021

Antidote to Chaos?

Filed under: General — Tags: , , , , — m759 @ 3:57 pm

Some formal symmetry —

"… each 2×4 "brick" in the 1974 Miracle Octad Generator
of R. T. Curtis may be constructed by folding  a 1×8 array
from Turyn's 1967 construction of the Golay code.

Folding a 2×4 Curtis array yet again  yields
the 2x2x2 eightfold cube ."

— Steven H. Cullinane on April 19, 2016 — The Folding.

Related art-historical remarks:

The Shape of Time  (Kubler, Yale U.P., 1962).

See yesterday's post The Thing 

Wednesday, August 4, 2021

“Old men ought to be explorers” — T. S. Eliot

Filed under: General — Tags: — m759 @ 2:38 am

My own lucubrations from April 12, 2012 include . . .

From the target of the above link —

Image of MOMA Chess Set cover.

"Here's to efficient packing.

Sunday, August 1, 2021

Freudenthal vs. Weyl

Filed under: General — Tags: — m759 @ 2:10 am

Hans Freudenthal in 1962 on the axiomatic approach to geometry
of Fano and Hilbert —

"The bond with reality is cut."

Some philosophical background —

For Weyl's "few isolated relational concepts," see (for instance)
Projective Geometries over Finite Fields , by
J. W. P. Hirschfeld (first published by Oxford University Press in 1979).

Weyl in 1932 —

Mathematics is the science of the infinite , its goal the symbolic comprehension of the infinite with human, that is finite, means. It is the great achievement of the Greeks to have made the contrast between the finite and the infinite fruitful for the cognition of reality. The intuitive feeling for, the quiet unquestioning acceptance of the infinite, is peculiar to the Orient; but it remains merely an abstract consciousness, which is indifferent to the concrete manifold of reality and leaves it unformed, unpenetrated. Coming from the Orient, the religious intuition of the infinite, the apeiron , takes hold of the Greek soul in the Dionysiac-Orphic epoch which precedes the Persian wars. Also in this respect the Persian wars mark the separation of the Occident from the Orient. This tension between the finite and the infinite and its conciliation now become the driving motive of Greek investigation; but every synthesis, when it has hardly been accomplished, causes the old contrast to break through anew and in a deepened sense. In this way it determines the history of theoretical cognition to our day. 

— "The Open World: Three Lectures on the Metaphysical Implications of Science," 1932

Monday, June 14, 2021

Diagon Alley

Filed under: General — Tags: — m759 @ 10:49 am

Schoolboy Problem

Sir Laurence Olivier, in "Term of Trial" (1962), dangles
a participle in front of schoolboy Terence Stamp:

"Walking to school today
my arithmetic book
fell into the gutter"

Saturday, April 10, 2021

Possibility

Filed under: General — Tags: , — m759 @ 2:31 pm

The previous post, on a Joyce symposium in
Utrecht on June 15-20, 2014, suggests a review
of this  journal in June 2014.  From June 21
of that year —

"Without the possibility that
an origin can be lost, forgotten,
or alienated into what springs
forth from it, an origin could
not be an origin. The possibility
of inscription is thus a necessary
possibility, one that must always
be possible."

— Page 157 of The Tain of the Mirror:
Derrida and the Philosophy of Reflection ,
by Rodolphe Gasché, Harvard U. Press, 1986

Related art suggested by the above modal logic

Nietzsche, 'law in becoming' and 'play in necessity'

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Wednesday, February 17, 2021

Raiders of the Lost Coordinates . . .

Continues.

From other posts tagged Tetrahedron vs. Square —

"There is  such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.

Illustration (central detail  a  from the above tetrahedral figure) —

A Harvard Variation
from Timothy Leary —

The topics of Harvard and Leary suggest some other cultural
history, from The Coasters"Poison Ivy" and "Yakety Yak."

Wednesday, February 3, 2021

Art of the Possible

Filed under: General — Tags: , , , — m759 @ 3:40 pm

Nietzsche, 'law in becoming' and 'play in necessity'

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Related philosophy — Wittgenstein's Diamond.

Sunday, January 10, 2021

From Fly-Bottle

Filed under: General — Tags: — m759 @ 5:48 pm

Illustrations from posts now tagged Ved Mehta in this  journal —

Epigraph to Fly and the Fly-Bottle: Encounters with British Intellectuals ,
by Ved Mehta , remarks first published in  The New Yorker  in 1961 and 1962 —

See as well the Wallace Stevens phrase “The Ruler of Reality.”

Tuesday, December 29, 2020

Memorial by Kinbote for Cardin: WWW

Filed under: General — m759 @ 12:13 pm

A Harvard student* attempts to summarize Nabokov’s aesthetics —

“Take ‘Pale Fire,’ his 1962 poem-as-novel
bursting with butterfly as theme:

‘I can do what only a true artist can do —
pounce upon the forgotten butterfly of revelation …
see the web of the world,
and the warp and the weft of that web.’ “

“True artist” here refers to Kinbote, not Nabokov.

* Tessa K.J. Haining, Harvard Crimson  Contributing Opinion Writer.
Tessa K.J. Haining ’23 lives in Adams House. Her column appears on
alternate Fridays. December 11, 2020.

Saturday, October 17, 2020

Modernist Cuts

Filed under: General — Tags: , , — m759 @ 10:05 pm

"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

Related screenshot of a book review
from the November AMS Notices

Thursday, August 20, 2020

“One More Reality Show”

Filed under: General — Tags: — m759 @ 9:27 am

“The bond with reality is cut.”

— Hans Freudenthal, 1962

Indeed it is.

Monday, July 13, 2020

Unpoetic License

Filed under: General — Tags: , — m759 @ 6:21 am

The above novel uses extensively the term “inscape.”
The term’s originator, a 19th-century Jesuit poet,
is credited . . . sort of.  For other uses of the term,
search for Inscape in this journal. From that search —

A quote from a 1962 novel

“There’s something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz.”

Addendum for the Church of Synchronology

The Joe Hill novel above was published (in hardcover)
on Walpurgisnacht —April 30, 2013.  See also this journal
on that date.

Thursday, June 11, 2020

Software Engineering I Prefer

Filed under: General — m759 @ 6:09 pm

(to that of the previous post) —

Click the image for
      the source.

Related literature —

Tuesday, May 12, 2020

Mehta Physics

Filed under: General — Tags: — m759 @ 1:16 pm

Epigraph to Fly and the Fly-Bottle:
Encounters with British Intellectuals ,
by Ved Mehta , remarks first published
in  The New Yorker  in 1961 and 1962 —

See as well the Wallace Stevens phrase “The Ruler of Reality.”

Monday, February 24, 2020

Hidden Figure

Filed under: General — m759 @ 2:55 pm

“There is  such a thing as  ▦  .”

— Saying adapted from a 1962 young-adult novel.

Saturday, January 18, 2020

Interplay

Filed under: General — Tags: , — m759 @ 1:40 pm

"This interplay of necessity and contingency
produces our anxious— and highly pleasurable—
speculation about the future path of the story."

— Michel Chaouli in "How Interactive Can Fiction Be?"
(Critical Inquiry  31, Spring 2005, page 613.)

See also . . .

Nietzsche, 'law in becoming' and 'play in necessity'

Continuing previous Modal Diamond Box posts:

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Saturday, November 30, 2019

X Marks the Spot

Filed under: General — m759 @ 12:00 pm

From 'Models and Metaphors' by Max Black, Cornell U. Press 1962

Thursday, November 7, 2019

For Connoisseurs of Insane Fantasy

Filed under: General — Tags: — m759 @ 11:23 am

From a 1962 young-adult novel —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical —

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Google News 'For you' comic book news item

Friday, October 18, 2019

A Song for St. Luke’s Day

Filed under: General — m759 @ 1:19 am

From a 1962 young-adult novel —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical —

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Tuesday, October 15, 2019

Inside the Fire Temple

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

(The title refers to Log24 posts now tagged Fire Temple.)

In memory of a  New Yorker  cartoonist who
reportedly died at 97 on October 3, 2019  …

"Read something that means something." 
New Yorker  advertising slogan

From posts tagged Tetrahedron vs. Square

This  journal on October 3

"There is  such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.

Illustration (central detail   from the above tetrahedral figure) —

Thursday, October 3, 2019

The Overbye Metaphors

Filed under: General — Tags: — m759 @ 12:00 pm

(For Harlan Kane)

"Once Mr. Overbye identifies a story, he said, the work is
in putting it in terms people can understand. 'Metaphors
are very important to the way I write,' he said. The results
are vivid descriptions that surpass mere translation."

— Raillan Brooks in The New York Times  on a Times
science writer, October 17, 2017.  Also on that date —

"There is  such a thing as a 4-set."
— Saying adapted from a 1962 young-adult novel.

See as well The Black List (Log24, September 27).

Friday, September 27, 2019

The Black List

Filed under: General — Tags: , , — m759 @ 11:46 am

"… Max Black, the Cornell philosopher, and others have pointed out
how 'perhaps every science must start with metaphor and end with
algebra, and perhaps without the metaphor there would never have
been any algebra' …."

— Max Black, Models and Metaphors, Cornell U. Press, 1962,
page 242, as quoted in Dramas, Fields, and Metaphors, by 
Victor Witter Turner, Cornell U. Press, paperback, 1975, page 25
 

Metaphor —

Algebra —

The 16 Dirac matrices form six anticommuting sets of five matrices each (Arfken 1985, p. 214):

1. alpha_1alpha_2alpha_3alpha_4alpha_5,

2. y_1y_2y_3y_4y_5,

3. delta_1delta_2delta_3rho_1rho_2,

4. alpha_1y_1delta_1sigma_2sigma_3,

5. alpha_2y_2delta_2sigma_1sigma_3,

6. alpha_3y_3delta_3sigma_1sigma_2.

SEE ALSO:  Pauli Matrices

REFERENCES:

Arfken, G. Mathematical Methods for Physicists, 3rd ed.  Orlando, FL: Academic Press, pp. 211-217, 1985.

Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. "Algebra of Dirac Matrices." §22 in Quantum Electrodynamics, 2nd ed.  Oxford, England: Pergamon Press, pp. 80-84, 1982.

Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms.  New York: Plenum, pp. 47-48, 1977.

Bjorken, J. D. and Drell, S. D. Relativistic Quantum Mechanics.  New York: McGraw-Hill, 1964.

Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed.  Oxford, England: Oxford University Press, 1982.

Goldstein, H. Classical Mechanics, 2nd ed.  Reading, MA: Addison-Wesley, p. 580, 1980.

Good, R. H. Jr. "Properties of Dirac Matrices." Rev. Mod. Phys. 27, 187-211, 1955.

Referenced on Wolfram|Alpha:  Dirac Matrices

CITE THIS AS:

Weisstein, Eric W.  "Dirac Matrices."

From MathWorld— A Wolfram Web Resource. 
http://mathworld.wolfram.com/DiracMatrices.html

Desiring the exhilarations of changes:
The motive for metaphor, shrinking from
The weight of primary noon,
The A B C of being,

The ruddy temper, the hammer
Of red and blue, the hard sound—
Steel against intimation—the sharp flash,
The vital, arrogant, fatal, dominant X.

— Wallace Stevens, "The Motive for Metaphor"

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

Wednesday, September 18, 2019

The Perpetual Identity Crisis

Filed under: General — Tags: — m759 @ 8:56 am

"There is  such a thing as a 4-set." — Saying adapted
from a 1962 young-adult novel.

Midrash — An image posted here on August 6

Sunday, August 25, 2019

Design Theory

Filed under: General — Tags: , , — m759 @ 7:58 pm

"Mein Führer Steiner"

See Hitler Plans and Quadruple System.

"There is  such a thing as a quadruple system."

— Saying adapted from a 1962 young-adult novel

Tuesday, August 6, 2019

Mathematics and Narrative:  The Crosswicks Curse Continues.

Filed under: General — m759 @ 7:03 pm

"There is  such a thing as a desktop."

— Saying adapted from a 1962 young-adult novel.

Monday, July 15, 2019

Possibility and Necessity: Kierkegaard Meets Nietzsche

Filed under: General — Tags: — m759 @ 7:29 am

The previous post’s search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity.
Further details —

See also . . .

Nietzsche, 'law in becoming' and 'play in necessity'

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Saturday, July 13, 2019

Which Roof?

Filed under: General — Tags: , , , — m759 @ 10:15 am

Related material — Tetrahedron vs. Square and Cézanne's Greetings

Compare and contrast:

A figure from St. Patrick's Day 2004 that might represent a domed  roof

Inscribed Carpenter's Square:

In Latin, NORMA

and a cinematic "Fire Temple" from 2019

Monday, May 20, 2019

The Bond with Reality

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


"The bond with reality is cut."

— Hans Freudenthal, 1962

Indeed it is.

Tuesday, April 9, 2019

Zero Dark Nine:

Filed under: General — Tags: , — m759 @ 12:09 am

The Crosswicks Curse Continues . . .

"There is  such a thing as geometry."

— Saying adapted from a 1962 young-adult novel.

Sunday, March 10, 2019

Review

Filed under: General — Tags: , — m759 @ 12:08 pm

Related material —

Nietzsche, 'law in becoming' and 'play in necessity'

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

Friday, February 15, 2019

The Gifts Reserved for Age

Filed under: General — m759 @ 3:30 pm

"But, as the passage now presents no hindrance
     To the spirit unappeased and peregrine
     Between two worlds become much like each other…."

T. S. Eliot, Four Quartets

Related obituary:

https://www.nytimes.com/2019/02/15/obituaries/tom-cade-dead.html

Related date:

"as of Feb. 6, 2019" (from a post at 12 AM ET Feb. 7) —

"There is  such a thing as a four-dimensional finite affine space."
— Saying adapted from a 1962 young-adult novel by Madeleine L'Engle

Wednesday, December 12, 2018

An Inscape for Douthat

Some images, and a definition, suggested by my remarks here last night
on Apollo and Ross Douthat's remarks today on "The Return of Paganism" —

Detail of Feb. 20, 1986, note by Steven H. Cullinane on Weyl's 'relativity problem'

Kibler's 2008 'Variations on a theme' illustrated.

In finite geometry and combinatorics,
an inscape  is a 4×4 array of square figures,
each figure picturing a subset of the overall 4×4 array:


 

Related material — the phrase
"Quantum Tesseract Theorem" and  

A.  An image from the recent
      film "A Wrinkle in Time" — 

B.  A quote from the 1962 book —

"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."

Tuesday, November 13, 2018

Blackboard Jungle Continues.

Filed under: G-Notes,General,Geometry — Tags: , , — m759 @ 6:19 pm

From the 1955 film "Blackboard Jungle" —

From a trailer for the recent film version of A Wrinkle in Time

Detail of the phrase "quantum tesseract theorem":

From the 1962 book —

"There's something phoney
in the whole setup, Meg thought.
There is definitely something rotten
in the state of Camazotz."

Related mathematics from Koen Thas that some might call a
"quantum tesseract theorem" —

Some background —

Koen Thas, 'Unextendible Mututally Unbiased Bases' (2016)

See also posts tagged Dirac and Geometry. For more
background on finite  geometry, see a web page
at Thas's institution, Ghent University.

Tuesday, August 28, 2018

See Becomes Saw

Filed under: General — Tags: — m759 @ 2:46 pm

http://www.log24.com/log/pix18/180828-Two_for_the_Seesaw-1962-intro-500w.jpg

http://www.log24.com/log/pix18/180828-NYT-Condescending-Appiah.jpg

Tuesday, August 7, 2018

The Search for Harmonic Analysis

Filed under: General — m759 @ 11:45 am

See Harmonic Analysis in this journal.

See also Loop.

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

"Here we go loop de lie."

Tuesday, June 19, 2018

Death on Father’s Day

Filed under: General — m759 @ 8:45 pm

From the University of Notre Dame in an obituary dated June 17

Timothy O’Meara, provost emeritus, Kenna Professor of Mathematics Emeritus and Trustee Emeritus at the University of Notre Dame, died June 17. He was 90.

A member of the Notre Dame faculty since 1962, O’Meara twice served as chairman of the University’s mathematics department and served as its first lay provost from 1978 to 1996.
. . . .         

He was graduated from the University of Cape Town in 1947 and earned a master’s degree in mathematics there the following year.  Earning his doctoral degree from Princeton University in 1953, he taught at the University of Otago in New Zealand from 1954 to 1956 before returning to Princeton where he served on the mathematics faculty and as a member of the Institute for Advanced Study for the next six years.  
. . . .

In addition to his mathematical teaching and scholarship, he published magisterial works, including “Introduction to Quadratic Forms,” “Lectures on Linear Groups,” “Symplectic Groups” and “The Classical Groups and K-Theory,” co-authored with Alexander J. Hahn, professor of mathematics emeritus at Notre Dame and a former O’Meara doctoral student.
. . . .

Related material (update of 9:20 PM ET on June 19) —

Saturday, March 31, 2018

Cube Theory

Filed under: General — m759 @ 9:00 pm

For Greta Gerwig and Saoirse Ronan —

See also a Log24 post from the above Cube Theory date —
April 12, 2016 — Lyrics for a Cartoon Graveyard — as well as . . .

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Notes for the Harrowing of Hell

Filed under: General — Tags: — m759 @ 12:18 pm

From a post of April 15, 2006

From elsewhere

Sunday, February 4, 2018

Logos for Sunday, February 4

Filed under: General,Geometry — Tags: — m759 @ 10:00 am

"The walls in the back of the room show geometric shapes
that remind us of the logos on a space shuttle. "

Web page on an Oslo art installation by Josefine Lyche.

See also Subway Art posts.

The translation above was obtained via Google.

The Norwegian original —

"På veggene bakerst i rommer vises geometriske former
som kan minne om logoene på en romferge."

Related logos — Modal Diamond Box in this journal:

Nietzsche, 'law in becoming' and 'play in necessity'

Logos for Philosophers
(Suggested by Modal Logic) —

Nietzsche, 'law in becoming' and 'play in necessity'

Thursday, January 25, 2018

Beware of Analogical Extension

Filed under: General,Geometry — Tags: — m759 @ 11:29 am

"By an archetype  I mean a systematic repertoire
of ideas by means of which a given thinker describes,
by analogical extension , some domain to which
those ideas do not immediately and literally apply."

— Max Black in Models and Metaphors 
    (Cornell, 1962, p. 241)

"Others … spoke of 'ultimate frames of reference' …."
Ibid.

A "frame of reference" for the concept  four quartets

A less reputable analogical extension  of the same
frame of reference

Madeleine L'Engle in A Swiftly Tilting Planet :

"… deep in concentration, bent over the model
they were building of a tesseract:
the square squared, and squared again…."

See also the phrase Galois tesseract .

Thursday, December 21, 2017

Wrinkles

Filed under: General — Tags: — m759 @ 1:00 pm

TIME magazine, issue of December 25th, 2017 —

" In 2003, Hand worked with Disney to produce a made-for-TV movie.
Thanks to budget constraints, among other issues, the adaptation
turned out bland and uninspiring. It disappointed audiences,
L’Engle and Hand. 'This is not the dream,' Hand recalls telling herself.
'I’m sure there were people at Disney that wished I would go away.' "

Not the dream?  It was, however, the nightmare, presenting very well
the encounter in Camazotz of Charles Wallace with the Tempter.

From a trailer for the latest version —

Detail:

From the 1962 book —

"There's something phoney in the whole setup, Meg thought.
There is definitely something rotten in the state of Camazotz."

Song adapted from a 1960 musical —

"In short, there's simply not
A more congenial spot
For happy-ever-aftering
Than here in Camazotz!"

Friday, December 8, 2017

Logos (Continued)

Filed under: General — Tags: — m759 @ 3:00 pm

Nietzsche, 'law in becoming' and 'play in necessity'

"Denn die Welt braucht ewig die Wahrheit,
also braucht sie ewig Heraklit:
obschon er ihrer nicht bedarf.
Was geht ihn sein Ruhm an?
Der Ruhm bei »immer fortfließenden Sterblichen!«,
wie er höhnisch ausruft.
Sein Ruhm geht die Menschen etwas an, nicht ihn,
die Unsterblichkeit der Menschheit braucht ihn,
nicht er die Unsterblichkeit des Menschen Heraklit.
Das, was er schaute, die Lehre vom Gesetz im Werden
und vom
Spiel in der Notwendigkeit 
, muß von jetzt
ab ewig geschaut werden: er hat von diesem größten
Schauspiel den Vorhang aufgezogen."

Logos for Philosophers
(Suggested by Modal Logic) —

Nietzsche, 'law in becoming' and 'play in necessity'

Monday, September 4, 2017

Labor Date

Filed under: General — m759 @ 2:00 pm

(A sequel to the previous post, Up to Date

"Dr. Sekler lectured around the world, but one trip proved life-changing.
In 1962, the year he married, Dr. Sekler made his first trip to Nepal.
'It was the way it had been for centuries — a beautiful valley filled with
happy, peaceful people. It seemed like Shangri-La,' he told the Harvard
Gazette 
in 2004."

Bryan Marquard in The Boston Globe  today

See also "Eight is a gate" in this  journal.

Saturday, September 2, 2017

Try to Remember the Kind of September

Filed under: General — m759 @ 3:07 pm

(A prequel to an Ursula K. Le Guin story
in Fantastic  magazine, September 1962)

Cover art by Lloyd Birmingham for "Plane Jane"

Knight Moves

Filed under: General — Tags: — m759 @ 12:42 pm

Ursula K. Le Guin, in Amazing Stories , Sept. 1992, published
"The Rock That Changed Things" (pp. 9-13) and her story from
thirty years earlier, "April in Paris" (Fantastic Stories , Sept. 1962.)
The latter (pp. 14-19) was followed by some brief remarks (p. 19)
comparing the two stories.

For "The Rock," see Le Guin + Rock in this journal.

"April in Paris" is about time travel by means of an alchemist's
pentagram. The following figure from 1962 is in lieu of a pentagram —

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

See as well a search for 1962 in this journal.

Tuesday, May 23, 2017

In Memoriam

Filed under: General — m759 @ 11:26 am

"From 1962 to 1969 Mr. Moore was Simon Templar . . . ."

The New York Times  online today

A related post — "Intruders for Mira" (Sept. 28, 2015).

Saturday, May 6, 2017

Talk Amongst Yourselves

Filed under: General — m759 @ 1:45 pm

A search for recent activity by the Liesl Schillinger of
the previous post yields

Talk amongst yourselves.

Midrash for elitists —

The novel 2666  by Roberto Bolaño (see Bolaño in this journal
and Adam Kirsch in the above) and

Matt Helm in Donald Hamilton's 1962 novel The Silencers

"I cleaned up a little, went downstairs, and, rather than
get the pickup out of hock, paid sixty cents to have a taxi
take me to the international bridge. Two cents let me walk
across the Rio Grande into Mexico. The river bed was
almost dry. The usual skinny dark kids were playing their
usual incomprehensible games around the pools below
the bridge. Stepping off the south end of the span, I was
in a foreign country. Mexicans will tell you defensively that
Juarez isn't Mexico-that no border town is-but it certainly
isn't the United States of America, even though Avenida
Juarez, the street just south of the bridge, does bear a
certain resemblance to Coney Island. I brushed off a
purveyor of dirty pictures and shills for a couple of dirty
movie houses." 

Midrash for populists —

The photo in the New York Times  obituary
above is from the 1966 film based, very
loosely, on Donald Hamilton's The Silencers.

Saturday, March 25, 2017

Security Complex

Filed under: General — m759 @ 9:36 pm

"All on a Saturday night" — Johnny Thunder, 1962

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Wednesday, March 22, 2017

Pulp Fiction Incarnate

Filed under: General — m759 @ 2:20 pm

From Log24 earlier —

More recently, an image from the above March 18 VUDU date —

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Saturday, March 18, 2017

Back to the Past

Filed under: General — Tags: — m759 @ 7:35 pm

"Old men ought to be explorers" — T. S. Eliot

"All on a Saturday night" — Johnny Thunder, 1962

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Update of 8:25 PM ET on March 18 —

"Analysis." — Dr. Robert Ford in "Westworld"

"Master theorist and conceptual genius."

— Jon Pareles, front page, online New York Times   tonight

Saturday, February 4, 2017

Time Loop

Filed under: General — m759 @ 10:09 pm

"On a Saturday night" — Johnny Thunder, 1962

"Only a peculiar can enter a time loop." — Tim Burton film, 2016

Highly qualified —

Saturday, January 14, 2017

1984: A Space Odyssey

Filed under: General,Geometry — m759 @ 2:40 pm

See Eightfold 1984 in this journal.

Related material —

"… the object sets up a kind of
 frame or space or field
 within which there can be epiphany."

"… Instead of an epiphany of being,
we have something like
an epiphany of interspaces."

— Charles Taylor, "Epiphanies of Modernism,"
Chapter 24 of Sources of the Self ,
Cambridge University Press, 1989

"Perhaps every science must start with metaphor
and end with algebra; and perhaps without the metaphor
there would never have been any algebra."

— Max Black, Models and Metaphors ,
Cornell University Press, Ithaca, NY, 1962

Epiphany 2017 —

Click to enlarge:

Tuesday, January 10, 2017

Analogical Extension Meets Analytic Continuation

Filed under: General — m759 @ 7:35 pm

From Models and Metaphors , by Max Black,
Cornell University Press, 1962 —

I do not recommend the work of Lewin, nor that of a later
science groupie, Keith Devlin

In September 2014, Devlin wrote an ignorant column about
a sort of bad mathematical joke based on a divergent infinite series.

He has now returned to the topic, this time writing more about
its proper mathematical background: analytic continuation .

Lewin is to Devlin as Lévi-Strauss is to Chomsky.
None of these four should be taken very seriously.

Max Black, however, should .

Monday, January 9, 2017

Diamond Song

Filed under: General — m759 @ 8:40 pm

From "Night Moves," by Bob Seger

And oh, the wonder
Felt the lightning
Yeah, and we waited on the thunder
Waited on the thunder

I woke last night to the sound of thunder
How far-off, I sat and wondered
Started humming a song from 1962
Ain't it funny* how the night moves?

See as well Johnny Thunder on Diamond Records in 1962 —

'Loop De Loop,' Diamond Records, 1962

* Funny peculiar, not funny ha-ha.

Analogical Extension at Cornell

Filed under: General,Geometry — Tags: — m759 @ 1:30 pm

Click to enlarge the following (from Cornell U. Press in 1962) —

For a more recent analogical extension at Cornell, see the
Epiphany 2017 post on the eightfold cube and yesterday
evening's post "A Theory of Everything."

Friday, December 30, 2016

For the Accountant*

Filed under: General — Tags: — m759 @ 2:17 pm

From "The Man Who Tried to Redeem the World with Logic" —

"To store the programs as data, the computer would need
something newa memory. That’s where Pitts’ loops 
came into play.  'An element which stimulates itself
will hold a stimulus indefinitely,' von Neumann wrote
in his report . . . ."

Amanda Gefter, Nautilus , Feb. 5, 2015

Related material —

"Here we go loop de loop" — Johnny Thunder, 1962

* I.e., Ben Affleck in his new film.

Thursday, December 29, 2016

Quick Now, Here, Now, Always

Filed under: General — Tags: — m759 @ 11:25 am

'Only a peculiar can enter a time loop' — Nov. 21, 2016

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Tuesday, December 27, 2016

The Dark Side

Filed under: General — m759 @ 10:04 pm

"The record, released on the Diamond label,
became a big hit, rising to no. 4 on the
Billboard  Hot 100 in early 1963." — Wikipedia

'Loop De Loop,' Johnny Thunder, Diamond Records, 1962

Saturday, December 3, 2016

SIAM Publication

Filed under: General — m759 @ 10:01 am

For "the Trojan family" —

Related material on the late Solomon W. Golomb —

"While at JPL, Sol had also been teaching some classes
at the nearby universities: Caltech, USC and UCLA. In
the fall of 1962, following some changes at JPL—and
perhaps because he wanted to spend more time with
his young children— he decided to become a full-time
professor. He got offers from all three schools. He
wanted to go somewhere where he could 'make
a difference'. He was told that at Caltech 'no one has
any influence if they don’t at least have a Nobel Prize',
while at UCLA 'the UC bureaucracy is such that no one
ever has any ability to affect anything'. The result was
that—despite its much-inferior reputation at the time—
Sol chose USC. He went there in the spring of 1963 as
a Professor of Electrical Engineering—and ended up
staying for 53 years." — Stephen Wolfram, 5/25/16

See also Priority (Nov. 25) and "What's in a Name" (Dec. 1).

Thursday, June 2, 2016

Bullshit Studies

Filed under: General,Geometry — Tags: , — m759 @ 11:30 am

(Continued)

"The allusion to 'the most precious square of sense' shows
Shakespeare doing an almost scholastic demonstration of
the need for a ratio and interplay among the senses as
the very constitution of rationality."

— Marshall McLuhan, The Gutenberg Galaxy ,
University of Toronto Press, 1962, page 13

"What Shakespeare refers to in Lear  as the 'precious
square of sense' probably has reference to the traditional
'square of opposition' in logic and to that four-part analogy
of proportionality which is the interplay of sense and reason."     

— McLuhan, ibid. , page 241

This is of course nonsense, and, in view of McLuhan's pose
as a defender of the Catholic faith, damned  nonsense.

Epigraph by McLuhan —

"The Gutenberg Galaxy  develops a mosaic or field
approach to its problems."

I prefer a different "mosaic or field" related to the movable
blocks  of Fröbel, not the movable type  of Gutenberg.

Wednesday, April 13, 2016

Black List

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

A search for "Max Black" in this journal yields some images
from a post of August 30, 2006 . . .

A circular I Ching

The image “http://www.log24.com/log/pix06A/060830-SeventhSymbol.jpg” cannot be displayed, because it contains errors.

"Jackson has identified the seventh symbol."
— Stargate

The "Jackson" above is played by the young James Spader,
who in an older version currently stars in "The Blacklist."

"… the memorable models of science are 'speculative instruments,'
to borrow I. A. Richards' happy title. They, too, bring about a wedding
of disparate subjects, by a distinctive operation of transfer of the
implications  of relatively well-organized cognitive fields. And as with
other weddings, their outcomes are unpredictable."

Max Black in Models and Metaphors , Cornell U. Press, 1962

A Motive for Metaphor

Filed under: General — m759 @ 12:00 pm

From 'Models and Metaphors' by Max Black, Cornell U. Press 1962

Saturday, March 26, 2016

Story Idea

Filed under: General — m759 @ 3:24 am

From last evening's online New York Times

"Mr. Hamner moved to California in 1962
and got his first break when 'The Twilight Zone'
accepted two of his story ideas. His eight scripts
for the series included 'The Hunt,' about a man
who is dead but does not realize it until his hunting
dog prevents him from wandering into hell . . . ."

— William Grimes

Hamner reportedly died on Thursday, March 24.
See this journal on that date.

Wednesday, February 24, 2016

The Media Message

Filed under: General — m759 @ 10:26 pm

See a link referencing The Gutenberg Galaxy  (a Catholic's 1962 view of literacy)
in a Log24 post yesterday suggested by a New York Times  obituary.

A different obituary this evening in that newspaper describes a Jew's 1979 view
of literacy.  See "Elizabeth Eisenstein, Historian of Movable Type, Dies at 92."

Related material — McLuhan in Eisenstein's The Printing Press as an Agent
of Change
, Cambridge University Press, 1979.

Eisenstein reportedly died on January 31, 2016. Synchronologists may
consult some media-related material reposted here on that date —

Fittingly, the Times  concludes Eisenstein's obituary as follows —

"This article will be set in 8.7 point Imperial and printed on
one of several presses, including the Goss Colorliner."

For a perhaps more interesting printing press related to change,
see Despedida  in this journal.

The image “http://www.log24.com/log/pix06B/061122-Flywheel.gif” cannot be displayed, because it contains errors.

Sunday, November 22, 2015

Overlook Video

Filed under: General — Tags: — m759 @ 7:26 am

CALIFORNIA, UNITED STATES – OCTOBER 1962:
People watching President John F. Kennedy’s
TV announcement of Cuban blockade during the
missile crisis in a department store.  (Photo by
Ralph Crane/Life Magazine/The LIFE Picture
Collection/Getty Images) 

A Sunday opinion column from 2011,
"The Enduring Cult of Kennedy" —

"In this landscape, the death of J.F.K. looms up
like the Overlook Hotel." — Ross Douthat
on November 27, 2011

From this journal on that date

http://www.log24.com/log/pix11C/111127-Ong-PresenceOfTheWord.jpg

Sunday, August 16, 2015

Sunday School

Filed under: General — m759 @ 9:00 am

The title of the previous post, "For Quantum Mystics,"
suggests a search in this journal for Quantum + Mystic.

That search in turn suggests, in particular, a review of
a post of October 16, 2007 — a discussion of the 
P.T. Barnum-like phrase "deep beauty" used to describe
a topic under discussion at Princeton by physicists.

Princeton, by the way, serves to illustrate the "gutter"
mentioned by Sir Laurence Olivier in a memorable
classroom scene from 1962

Saturday, August 15, 2015

Schoolboy Problem

Filed under: General,Geometry — Tags: — m759 @ 10:07 am

Sir Laurence Olivier, in "Term of Trial" (1962), dangles
a participle in front of schoolboy Terence Stamp:

"Walking to school today
my arithmetic book
fell into the gutter"

Were Stamp a Galois, the reply might be "Try this one, sir."

Friday, August 14, 2015

Schoolgirl Problem

Filed under: General,Geometry — m759 @ 6:00 pm

But first, a word from our sponsa* 

Sir Laurence Olivier in "Term of Trial" (1962),
a film starring Sarah Miles as a schoolgirl —

* Bride  in Latin. See also "bride's chair,"
  a phrase from mathematical pedagogy.

Sunday, July 26, 2015

Sunday School

Filed under: General — m759 @ 9:00 am

Hexagram 51:

"I woke last night to the sound of thunder,
How far off, I sat and wondered.
Started humming a song from 1962.
Ain't it funny how the night moves?"

Wednesday, December 17, 2014

Launched from Cuber

Filed under: General — Tags: , — m759 @ 5:55 pm

Continued from Nobel Note (Jan. 29, 2014).

IMAGE- 'Launched from Cuber' scene in 'X-Men: First Class'

From Tradition in Action , "The Missal Crisis of '62,"
remarks on the revision of the Catholic missal in that year—

"Neither can the claim that none of these changes
is heretical in content be used as an argument
in favor of its use, for neither is the employment of
hula girls, fireworks, and mariachis strictly speaking
heretical in itself, but they belong to that class of novel
and profane things that do not belong in the Mass."

— Fr. Patrick Perez, posted Sept. 11, 2007 

See also this  journal on November 22, 2014

Say Bingo to my little friend

    … and on Bruce Springsteen's birthday this year —

Tuesday, September 23, 2014

Matrix

Filed under: Uncategorized — m759 @ 11:00 AM 

From AP’s Today in History:

Happy birthday.

“It all adds up.” — Saul Bellow

The Matrix:

 

 

 

 

 

 

Thursday, September 11, 2014

A Class by Itself

Filed under: General — Tags: , — m759 @ 9:48 am

The American Mathematical Society yesterday:

Harvey Cohn (1923-2014)
Wednesday September 10th 2014

Cohn, an AMS Fellow and a Putnam Fellow (1942), died May 16 at the age of 90. He served in the Navy in World War II and following the war received his PhD from Harvard University in 1948 under the direction of Lars Ahlfors. He was a member of the faculty at Wayne State University, Stanford University, Washington University in St. Louis, the University of Arizona, and at City College of New York, where he was a distinguished professor. After retiring from teaching, he also worked for the NSA. Cohn was an AMS member since 1942.

Paid death notice from The New York Times , July 27, 2014:

COHN–Harvey. Fellow of the American Mathematical Society and member of the Society since 1942, died on May 16 at the age of 90. He was a brilliant Mathematician, an adoring husband, father and grandfather, and faithful friend and mentor to his colleagues and students. Born in New York City in 1923, Cohn received his B.S. degree (Mathematics and Physics) from CCNY in 1942. He received his M.S. degree from NYU (1943), and his Ph.D. from Harvard (1948) after service in the Navy (Electronic Technicians Mate, 1944-46). He was a member of Phi Beta Kappa (Sigma Chi), won the William Lowell Putnam Prize in 1942, and was awarded the Townsend Harris Medal in 1972. A pioneer in the intensive use of computers in an innovative way in a large number of classical mathematical problems, Harvey Cohn held faculty positions at Wayne State University, Stanford, Washington University Saint Louis (first Director of the Computing Center 1956-58), University of Arizona (Chairman 1958-1967), University of Copenhagen, and CCNY (Distinguished Professor of Mathematics). After his retirement from teaching, he worked in a variety of capacities for the National Security Agency and its research arm, IDA Center for Computing Sciences. He is survived by his wife of 63 years, Bernice, of Laguna Woods, California and Ft. Lauderdale, FL, his son Anthony, daughter Susan Cohn Boros, three grandchildren and one great-granddaughter.

— Published in The New York Times  on July 27, 2014

See also an autobiographical essay found on the web.

None of the above sources mention the following book, which is apparently by this same Harvey Cohn. (It is dedicated to "Tony and Susan.")

From Google Books:

Advanced Number Theory, by Harvey Cohn
Courier Dover Publications, 1980 – 276 pages
(First published by Wiley in 1962 as A Second Course in Number Theory )

Publisher's description:

" 'A very stimulating book … in a class by itself.'— American Mathematical Monthly

Advanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.

The book is divided into three parts. Part I is concerned with background material — a synopsis of elementary number theory (including quadratic congruences and the Jacobi symbol), characters of residue class groups via the structure theorem for finite abelian groups, first notions of integral domains, modules and lattices, and such basis theorems as Kronecker's Basis Theorem for Abelian Groups.

Part II discusses ideal theory in quadratic fields, with chapters on unique factorization and units, unique factorization into ideals, norms and ideal classes (in particular, Minkowski's theorem), and class structure in quadratic fields. Applications of this material are made in Part III to class number formulas and primes in arithmetic progression, quadratic reciprocity in the rational domain and the relationship between quadratic forms and ideals, including the theory of composition, orders and genera. In a final concluding survey of more recent developments, Dr. Cohn takes up Cyclotomic Fields and Gaussian Sums, Class Fields and Global and Local Viewpoints.

In addition to numerous helpful diagrams and tables throughout the text, appendices, and an annotated bibliography, Advanced Number Theory  also includes over 200 problems specially designed to stimulate the spirit of experimentation which has traditionally ruled number theory."

User Review –

"In a nutshell, the book serves as an introduction to Gauss' theory of quadratic forms and their composition laws (the cornerstone of his Disquisitiones Arithmeticae) from the modern point of view (ideals in quadratic number fields). I strongly recommend it as a gentle introduction to algebraic number theory (with exclusive emphasis on quadratic number fields and binary quadratic forms). As a bonus, the book includes material on Dirichlet L-functions as well as proofs of Dirichlet's class number formula and Dirichlet's theorem in primes in arithmetic progressions (of course this material requires the reader to have the background of a one-semester course in real analysis; on the other hand, this material is largely independent of the subsequent algebraic developments).

Better titles for this book would be 'A Second Course in Number Theory' or 'Introduction to quadratic forms and quadratic fields'. It is not a very advanced book in the sense that required background is only a one-semester course in number theory. It does not assume prior familiarity with abstract algebra. While exercises are included, they are not particularly interesting or challenging (if probably adequate to keep the reader engaged).

While the exposition is *slightly* dated, it feels fresh enough and is particularly suitable for self-study (I'd be less likely to recommend the book as a formal textbook). Students with a background in abstract algebra might find the pace a bit slow, with a bit too much time spent on algebraic preliminaries (the entire Part I—about 90 pages); however, these preliminaries are essential to paving the road towards Parts II (ideal theory in quadratic fields) and III (applications of ideal theory).

It is almost inevitable to compare this book to Borevich-Shafarevich 'Number Theory'. The latter is a fantastic book which covers a large superset of the material in Cohn's book. Borevich-Shafarevich is, however, a much more demanding read and it is out of print. For gentle self-study (and perhaps as a preparation to later read Borevich-Shafarevich), Cohn's book is a fine read."

Sunday, July 6, 2014

Game News

Filed under: General — m759 @ 3:00 pm

An essay linked to here on the date of Kuhn’s
death discussed the film “Good Will Hunting”:

“You can be sure that when an experienced movie director
like Gus Van Sant selects an establishing shot for the lead
character, he does so with considerable care, on the advice
of an expert.”

Establishing shots —

1. From a post of January 29, 2014:

2. From a post of April 12, 2011:

http://www.log24.com/log/pix11/110412-HuntingCreditsSm.jpg

Parting shot —

From another post of January 29, 2014:

Note Watson‘s title advice.

Thursday, June 26, 2014

Study This Example, Part II

Filed under: General,Geometry — Tags: — m759 @ 11:06 am

(Continued from 10:09 AM today)

The quotation below is from a webpage on media magnate
Walter Annenberg.

Annenberg Hall at Harvard, originally constructed to honor
the Civil War dead, was renamed in 1996 for his son Roger,
Harvard Class of ’62.

www.broadcastpioneers.com/
walterannenberg.html

“It was said that Roger was ‘moody and sullen’
spending large parts of his time reading poetry
and playing classical music piano. It had been
reported that Roger attempted suicide at the
age of eleven by slitting his wrists. He recovered
and was graduated Magna Cum Laude from
Episcopal Academy in our area. For awhile,
Roger attended Harvard, but he was removed
from the school’s rolls after Roger stopped doing
his school work and spent almost all his time
reading poetry in his room. He then was sent to
an exclusive and expensive treatment center
in Bucks County, Pennsylvania. At that facility,
Roger became more remote. It was said that he
often didn’t recognize or acknowledge his father.
On August 7, 1962, Roger Annenberg died from
an overdose of sleeping pills.”

A more appropriate Annenberg memorial, an article
in The Atlantic  magazine on June 25, notes that…

“Among those who ended up losing their battles
with mental illness through suicide are
Virginia Woolf, Ernest Hemingway, Vincent van Gogh,
John Berryman, Hart Crane, Mark Rothko, Diane Arbus,
Anne Sexton, and Arshile Gorky.”

Monday, May 26, 2014

Springtime for Vishnu

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

Continues.

A post by Margaret Soltan this morning:

Links (in blue) from the above post:
Cane and Mondo Cane.

Bagger Vance — “Time for you to see the field.”

From Pictures for Kurosawa (Sept. 6, 2003) —

“As these flowing rivers that go towards the ocean,
when they have reached the ocean, sink into it,
their name and form are broken, and people speak of
the ocean only, exactly thus these sixteen parts
of the spectator that go towards the person (purusha),
when they have reached the person, sink into him,
their name and form are broken, and people speak of
the person only, and he becomes without parts and
immortal. On this there is this verse:

‘That person who is to be known, he in whom these parts
rest, like spokes in the nave of a wheel, you know him,
lest death should hurt you.’ “

— Prasna Upanishad

Related material — Heaven’s Gate  images from Xmas 2012:

“This could be heaven or this could be hell.” — Hotel California

Those who prefer mathematics to narrative may consult Root Circle.

Thursday, January 30, 2014

Test

Filed under: General — Tags: — m759 @ 12:00 am

From Fritz Leiber's 1959 sci-fi classic "Damnation Morning" —

She drew from her handbag a pale grey
gleaming implement that looked by quick turns
to me like a knife, a gun, a slim sceptre, and a
delicate branding iron— especially when its tip
sprouted an eight-limbed star of silver wire.

“The test?” I faltered, staring at the thing.

“Yes, to determine whether you can live in the
fourth dimension or only die in it.”

Related 1962 drama  from the Twilight Zone —

"He's a physicist, maybe he can help us out."

See also Step.

Wednesday, August 14, 2013

The Gift

Filed under: General — m759 @ 9:45 am

"Give 'em hell." — Ben Bernanke at Princeton's Baccalaureate, 2013

Some background — Janet Leigh and the Museum of Modern Art

"The Varnedoe Debacle," by Hilton Kramer (Dec. 1991)

Hell… Hell. — Sinatra in The Manchuran Candidate

Wednesday, July 10, 2013

Diagon Alley

Filed under: General — m759 @ 9:29 pm

You say goodbye, I say

A YouTube video uploaded on March 2, 2012—

This  journal on the date of the above video's uploading— March 2, 2012:

"…des carreaux mi-partis de deux couleurs par une ligne diagonale…."

See also Josefine Lyche in Vril Chick and Bowling in Diagon Alley.

Saturday, March 16, 2013

The Crosswicks Curse

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

Continues.

From the prologue to the new Joyce Carol Oates
novel Accursed

"This journey I undertake with such anticipation
is not one of geographical space but one of Time—
for it is the year 1905 that is my destination.

1905!—the very year of the Curse."

Today's previous post supplied a fanciful link
between the Crosswicks Curse of Oates and
the Crosswicks tesseract  of Madeleine L'Engle.

The Crosswicks Curse according to L'Engle
in her classic 1962 novel A Wrinkle in Time —

"There is  such a thing as a tesseract."

A tesseract is a 4-dimensional hypercube that
(as pointed out by Coxeter in 1950) may also 
be viewed as a 4×4 array (with opposite edges
identified).

Meanwhile, back in 1905

For more details, see how the Rosenhain and Göpel tetrads occur naturally
in the diamond theorem model of the 35 lines of the 15-point projective
Galois space PG(3,2).

See also Conwell in this journal and George Macfeely Conwell in the
honors list of the Princeton Class of 1905.

Friday, January 18, 2013

Solomon’s Rep-tiles

Filed under: General,Geometry — Tags: — m759 @ 1:04 pm

"Rep-tiles Revisited," by Viorel Nitica, in MASS Selecta: Teaching and Learning Advanced Undergraduate Mathematics ,  American Mathematical Society, 2003—

"The goal of this note is to take a new look at some of the most amazing objects discovered in recreational mathematics. These objects, having the curious property of making larger copies of themselves, were introduced in 1962 by Solomon W. Golomb [2], and soon afterwards were popularized by Martin Gardner [3] in Scientific American…."

2.  S. W. Golomb: "Replicating Figures in the Plane," Mathematical Gazette  48, 1964, 403-412

3.  M. Gardner: "On 'Rep-tiles,' Polygons That Can Make Larger and Smaller Copies of Themselves," Scientific American  208, 1963, 154-157

Two such "amazing objects"—

Triangle

Square

For a different approach to the replicating properties of these objects, see the square-triangle theorem.

For related earlier material citing Golomb, see Not Quite Obvious (July 8, 2012; scroll down to see the update of July 15.).

Golomb's 1964 Gazette  article may now be purchased at JSTOR for $14.

Saturday, December 1, 2012

Star Wars

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

IMAGE- Rudolf Koch's version of the 'double cross' symbol

  Source: Rudolf KochThe Book of Signs

The American Mathematical Society
(AMS) yesterday:

Lars Hörmander (1931-2012)
Friday November 30th 2012

Hörmander, who received a Fields Medal in 1962,
died November 25 at the age of 81. …

more »

Some related material:

See also posts on Damnation Morning and, from the
date of Hörmander's death,

Sunday, November 18, 2012

Sermon

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

Happy birthday to

IMAGE- Margaret Atwood, Kim Wilde, Peta Wilson

Today's sermon, by Marie-Louise von Franz

Number and Time, by Marie-Louise von Franz

For more on the modern physicist analyzed by von Franz,
see The Innermost Kernel , by Suzanne Gieser.

Another modern physicist, Niels Bohr, died
on this date in 1962

Diamond Theory version of 'The Square Inch Space' with yin-yang symbol for comparison

The circle above is marked with a version
of the classic Chinese symbol
adopted as a personal emblem
by Danish physicist Niels Bohr,
leader of the Copenhagen School.

For the square, see the diamond theorem.

"Two things of opposite natures seem to depend
On one another, as a man depends
On a woman, day on night, the imagined
On the real. This is the origin of change.
Winter and spring, cold copulars, embrace
And forth the particulars of rapture come."

— Wallace Stevens,
  "Notes Toward a Supreme Fiction,"
  Canto IV of "It Must Change"

Wednesday, July 18, 2012

Incommensurables

Filed under: General — Tags: — m759 @ 9:48 am

(Continued from Midsummer Eve)

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

— Norman Mailer, March 3, 1992, PBS transcript

"Just because it is a transition between incommensurables, the transition between competing paradigms cannot be made a step at a time, forced by logic and neutral experience. Like the gestalt switch, it must occur all at once (though not necessarily in an instant) or not at all."

Thomas Kuhn, The Structure of Scientific Revolutions , 1962, as quoted in The Enneagram of Paradigm Shifting

"In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry." 

The Enneagram as Mandala

I have little respect for Enneagram enthusiasts, but they do at times illustrate Mailer's maxim.

My own interests are in the purely mathematical properties of the number nine, as well as those of the next square, sixteen.

Those who prefer bullshit may investigate non-mathematical properties of sixteen by doing a Google image search on MBTI.

For bullshit involving nine, see (for instance) Einsatz  in this journal.

For non-bullshit involving nine, sixteen, and "asymmetry that resides at the very heart of symmetry," see Monday's Mapping Problem continued. (The nine occurs there as the symmetric  figures in the lower right nine-sixteenths of the triangular analogs  diagram.)

For non-bullshit involving psychological and philosophical terminology, see James Hillman's Re-Visioning Psychology .

In particular, see Hillman's "An Excursion on Differences Between Soul and Spirit."

Tuesday, June 12, 2012

Meet Max Black (continued)

Filed under: General,Geometry — Tags: , — m759 @ 11:59 pm

Background— August 30, 2006—

The Seventh Symbol:

The image “http://www.log24.com/log/pix06A/060830-Algebra.jpg” cannot be displayed, because it contains errors.

In the 2006 post, the above seventh symbol  110000 was
interpreted as the I Ching hexagram with topmost and
next-to-top lines solid, not broken— Hexagram 20, View .

In a different interpretation, 110000 is the binary for the decimal
number 48— representing the I Ching's Hexagram 48, The Well .

“… Max Black, the Cornell philosopher, and 
others have pointed out how ‘perhaps every science
must start with metaphor and end with algebra, and
perhaps without the metaphor there would never
have been any algebra’ ….”

– Max Black, Models and Metaphors,
Cornell U. Press, 1962, page 242, as quoted
in Dramas, Fields, and Metaphors,
by Victor Witter Turner, Cornell U. Press,
paperback, 1975, page 25

The algebra is certainly clearer than either I Ching
metaphor, but is in some respects less interesting.

For a post that combines both the above I Ching
metaphors, View  and Well  , see Dec. 14, 2007.

In memory of scholar Elinor Ostrom,
who died today—

"Time for you to see the field."
Bagger Vance

Thursday, April 26, 2012

Rainbow People

Filed under: General — m759 @ 6:29 pm

(Mythopoetic continued)

Voice of America  today—

Thousands of Norwegians Defy Confessed Killer Breivik in Song

"The demonstrators waved roses and flags
Thursday as they and Norwegian folk singer
Lillebjoern Nilsen sang an adaptation
of the children's song, 'My Rainbow Race,' 
which Breivik in court last week called
an example of Marxist brainwashing."

[See also PETE SEEGER AND LILLEBJØRN NILSEN.
Click on the image below for Seeger's original version.]

Liberia Reacts to Taylor Conviction With Mixed Emotions

"As the verdict was read out, a rainbow was seen
in the sky, encircling the sun.  For many Liberians,
superstition is a part of life.  The rainbow heralded
a new era, they said, beginning with the verdict of Taylor."

["You're not the only one… with mixed emotions."]

Thursday, April 5, 2012

Leap Day of Faith

Filed under: General — m759 @ 9:48 am

Presidential candidate Mitt Romney on Monday, April 2, 2012—

"I think there is in this country a war on religion.
 I think there is a desire to establish a religion
 in America known as secularism."

Nancy Haught of The Oregonian  on Leap Day, Feb. 29, 2012

IMAGE- Theologian William Hamilton at the University of St. Andrews, Scotland, February 10, 1950

William Hamilton, the retired theologian who declared in the 1960s that God was dead, died Tuesday [Feb. 28, 2012] in his downtown Portland apartment at 87. Hamilton said he'd been haunted by questions about God since he was a teenager. Years later, when his conclusion was published in the April 8, 1966, edition of Time Magazine, he found himself in a hornet's nest.

Time christened the new movement "radical theology" and Hamilton, one of its key figures, received death threats and inspired angry letters to the editor in newspapers that carried the story. He encountered hostility at Colgate Rochester Crozer Divinity School, where he had been teaching theology,  and lost his endowed chair in 1967.

Hamilton moved on to teach religion at New College in Sarasota, Fla.

(See also this  journal on Leap Day.)

From New College: The Honors College of Florida

History Highlights

Oct. 11, 1960: New College is founded as a private college

1961: Trustees obtain options to purchase the former Charles Ringling estate on Sarasota Bay and 12 acres of airport land facing U.S. 41 held by private interests. The two pieces form the heart of the campus

Nov. 18, 1962: the campus is dedicated. Earth from Harvard is mixed with soil from New College as a symbol of the shared lofty ideals of the two institutions.

See also, in this journal, "Greatest Show on Earth" and The Harvard Crimson

The Harvard Crimson,
Online Edition
Sunday,
Oct. 8, 2006

POMP AND
CIRCUS-STANCE


CRIMSON/ MEGHAN T. PURDY

Friday, Oct. 6:

 

The Ringling Bros. Barnum & Bailey Circus has come to town, and yesterday the animals were disembarked near MIT and paraded to their temporary home at the Banknorth Garden.

OPINION

At Last, a
Guiding Philosophy

The General Education report is a strong cornerstone, though further scrutiny is required.

After four long years, the Curricular Review has finally found its heart.

The Trouble
With the Germans

The College is a little under-educated these days.

By SAHIL K. MAHTANI
Harvard College– in the best formulation I’ve heard– promulgates a Japanese-style education, where the professoriate pretend to teach, the students pretend to learn, and everyone is happy.

Sunday, December 4, 2011

Code Wars

Filed under: General — m759 @ 2:00 pm

Steve Buscemi last night on Saturday Night Live
describing Christmas tree ornaments with his mate Sheila—

"This one's a little computer."

http://www.log24.com/log/pix11C/111203-SnakeApple.jpg

"Beep Boop Beep"

http://www.log24.com/log/pix11C/111204-ElectricDreams.jpg

"This one's a little pinecone. … Beep Boop Beep"

Meanwhile…

http://www.log24.com/log/pix11C/111204-NewWorldDisorder.jpg

In related news…

http://www.log24.com/log/pix11C/111204-RosettaStone-Sheila.jpg

"Her name drives me insane."

— Rosetta Stone, 1978 cover of "Sheila," Tommy Roe's 1962 classic

http://www.log24.com/log/pix11C/111204-SNLcard.jpg

Click image for sketch.

Saturday, November 26, 2011

Innermost Kernel (continued*)

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

A search on the word "innermost" in a PDF copy of a book
by Suzanne Gieser on Jung and Pauli yields no definite meaning
for the book's title, The Innermost Kernel  (Springer, 2005).

The author does, however, devote a section (pp. 36-41) to the
influence of Schopenhauer on Jung and Pauli, and that section at least
suggests that the historical  origin of her title is in Schopenhauer's
reformulation of Kant's "Ding an sich."

The Innermost Kernel , p. 37—

"… an expression of an underlying invisible world,
the one that forms the innermost essence of reality,
the thing-in-itself. This is the will, a blind existence
that forms an omnipresent entity beyond time, space
and individuality." *

* Arthur Schopenhauer, "Über die Vierfache Wurzel
  des Satzes vom zureichenden Grunde" (1813),
  Kleinere Schriften, SämtlicheWerke III 
  (Stuttgart, 1962), 805–806.

* See also Mann on Schopenhauer and an "innermost kernel."

Monday, October 10, 2011

The Aleph

Filed under: General — m759 @ 12:00 am

COLLEGE OF THE DESERT
Minutes — Organization Meeting
11:00 a.m., Saturday, July 1, 1961—

15. Preparation of College Seal:

By unanimous consent preparation of a College
Seal to contain the following features was
authorized: A likeness of the Library building
set in a matrix of date palms, backed by
a mountain skyline and rising sun; before
the Library an open book, the Greek symbol
Alpha on one page and Omega on the other;
the Latin Lux et Veritas, College of the
Desert, and 1958 to be imprinted within or
around the periphery of the seal.

From the website http://geofhagopian.net/ of
Geoff Hagopian, Professor of Mathematics,
College of the Desert—

http://www.log24.com/log/pix11C/111010-CollegeOfTheDesert-Seal.gif

Note that this version of the seal contains
an Aleph  and Omega instead of Alpha and Omega.

From another Hagopian website, another seal.

Thursday, April 28, 2011

Hard Bargain

Filed under: General — m759 @ 1:31 am

Continued from Good Friday

Emmylou Harris and Rivka Galchen in the May 2, 2011 New Yorker

The New Yorker , in the above excerpt, says of David Deutsch that
"his books have titles of colossal confidence
('The Fabric of Reality,' 'The Beginning of Infinity')."

The Fabric of Reality — A post from Good Friday

Friday, April 22, 2011

Hard Bargain

m759 @ 11:01 PM

In memory of Hazel Dickens, two links —
Unique Figure and Hello Stranger .

Weepin' like a willow, mournin' like a dove
Weepin' like a willow, mournin' like a dove
There's a girl of the country
That I really love

The Beginning of Infinity — Another Good Friday death—

Sidney Michaels, adapter of the 1962 play "Tchin-Tchin."

"At play's end they are Chaplinesque waifs living in the charmed circle
of innocents that includes saints, children, drunkards and madmen.
Subliminally, Tchin-Tchin is a Christian existential fable." — TIME

Saturday, October 30, 2010

Keanu vs. the Devil

Filed under: General — Tags: — m759 @ 4:04 am

(Continued from Little Buddha  (1994), The Matrix  (1999), and Constantine  (2005))

This post was suggested by yesterday's post on Habermas and by his 1962 book The Structural Transformation of the Public Sphere  (English translation, 1989).

The "public sphere" of Habermas has come to pass; it is, of course, the World-Wide Web.

For October 30, the day leading up to Devil's Night, a more private sphere—though in a public setting— seems appropriate…

http://www.log24.com/log/pix10B/101030-CentralParkSphere.jpg

The Day the Earth Stood Still  (2008)

A Keanu Reeves scene related to this image—

"The low point of the movie’s persuasiveness is the single scene with Professor Barnhardt (John Cleese) — in the original an Einstein-like scientist who impresses Klaatu with his highly evolved thinking, here a caricature of professorial enlightenment. Helen decides to bring Klaatu to Professor Barnhardt when Klaatu professes his disappointment with earth’s leaders. 'Those aren’t our leaders!' she protests earnestly. 'Let me take you to one of our leaders!'"

A perhaps more persuasive scene, from today's New York Times

Prize in Hand, He Keeps His Eye on Teaching

http://www.log24.com/log/pix10B/101030-VargasLlosa.jpg

Nobel winner Mario Vargas Llosa teaches
a seminar on Borges at Princeton

(Photo by James Leynse for The New York Times )

Wednesday, August 25, 2010

That X

Filed under: General — m759 @ 5:01 am

Martin Heidegger, Being and Time,  translated by
John Macquarrie and Edward Robinson, Harper hardcover, 1962, p. 262—

"…the ultimate business of philosophy is to preserve
the force of the most elemental words…."

Heidegger was quoted, in a different translation, by Richard Rorty in 1998
in a review of Ein Meister aus Deutschland.

Related material: an August 18 death and this journal on that date

"… it is impossible that there should be time if there is no soul,
  except that there could be that X which time is…."
  — Aristotle, Physics, IV.14, translated by Edward Hussey

See also Berlinerblau in this journal on August 10.

Monday, February 1, 2010

Frame by Frame

Filed under: General,Geometry — m759 @ 7:26 pm

From "Time's Breakdown," September 17, 2003

“… even if we can break down time into component Walsh functions, what would it achieve?”

– The Professor, in “Passing in Silence,” by Oliver Humpage

“Being is not a steady state but an occulting one: we are all of us a succession of stillness blurring into motion on the wheel of action, and it is in those spaces of black between the pictures that we find the heart of mystery in which we are never allowed to rest. The flickering of a film interrupts the intolerable continuity of apparent world; subliminally it gives us those in-between spaces of black that we crave.”

Gösta Kraken, Perception Perceived: an Unfinished Memoir (p. 9 in Fremder, a novel by Russell Hoban)

This flashback was suggested by

  1. A review in next Sunday's New York Times Book Review of a new novel, Point Omega, by Don DeLillo. The review's title (for which the reviewer, Geoff Dyer, should not be blamed) is "A Wrinkle in Time." The review and the book are indeed concerned with time, but the only apparent connection to the 1962 novel of Madeleine L'Engle also titled A Wrinkle in Time is rather indirect– via the Walsh functions mentioned above.
  2. A phrase in the Times's review, "frame by frame," also appeared in this jounal on Saturday. It formed part of the title of a current exhibition at Harvard's Carpenter Center for the Visual Arts.
  3. The Carpenter Center exhibition will have an opening reception on February 4.
  4. February 4 is also the birthday of the above Russell Hoban, who will turn 85. See a British web page devoted to that event.

DeLillo is a major novelist, but the work of Hoban seems more relevant to the phrase "frame by frame."

Sunday, December 20, 2009

The Test

Filed under: General,Geometry — m759 @ 11:00 am

Dies Natalis of
Emil Artin

From the September 1953 Bulletin of the American Mathematical Society

Emil Artin, in a review of Éléments de mathématique, by N. Bourbaki, Book II, Algebra, Chaps. I-VII–

"We all believe that mathematics is an art. The author of a book, the lecturer in a classroom tries to convey the structural beauty of mathematics to his readers, to his listeners. In this attempt he must always fail. Mathematics is logical to be sure; each conclusion is drawn from previously derived statements. Yet the whole of it, the real piece of art, is not linear; worse than that its perception should be instantaneous. We all have experienced on some rare occasions the feeling of elation in realizing that we have enabled our listeners to see at a moment's glance the whole architecture and all its ramifications. How can this be achieved? Clinging stubbornly to the logical sequence inhibits the visualization of the whole, and yet this logical structure must predominate or chaos would result."

Art Versus Chaos

http://www.log24.com/log/pix09A/091220-ForakisHypercube.jpg
From an exhibit,
"Reimagining Space
"

The above tesseract (4-D hypercube)
sculpted in 1967 by Peter Forakis
provides an example of what Artin
called "the visualization of the whole."

For related mathematical details see
Diamond Theory in 1937.

"'The test?' I faltered, staring at the thing.
'Yes, to determine whether you can live
in the fourth dimension or only die in it.'"
Fritz Leiber, 1959

See also the Log24 entry for
Nov. 26,  2009, the date that
Forakis died.

"There is such a thing
as a tesseract."
Madeleine L'Engle, 1962

Tuesday, December 15, 2009

A Christmas Carol

Filed under: General — m759 @ 2:56 pm

“There are two silences.
One when no word is spoken.
The other when perhaps a torrent
of language is being employed.”

Harold Pinter, 1962

Stille Nacht…

Pinter died on December 24, 2008:

Top center front page, online NY Times, Christmas 2008-- Pinter dead at 78

Heilige Nacht…

Also on Christmas Eve, 2008

(“24/12/08  3:23 pm”):

http://www.log24.com/log/pix09A/091215-KaehrCitationsSm.jpg

Click to enlarge.

 

Wednesday, March 4, 2009

Wednesday March 4, 2009

Filed under: General — m759 @ 9:00 am
Markoff Process

“So fearsome was Dr. Schwartz’s early reputation as a mathematician that when John Forbes Nash Jr., the Nobel Prize winning mathematician and economist, learned that he was attempting to solve an extremely challenging mathematical problem…. he became agitated, apparently fearing Dr. Schwartz might beat him to a solution, said Sylvia Nasar, author of ‘A Beautiful Mind,’ a biography of Nash.”

New York Times obituary of Jacob T. Schwartz dated Tuesday, March 3, 2009

 Author of the obituary:
John Markoff.

New York Lottery
March 3, 2009:

NY Lottery March 3, 2009-- Midday 491, Evening 116

“His background in mathematical algorithms led Dr. Schwartz to develop an early programming language…. The language would later influence the designer of the Python programming language, widely used by programmers today.” —NY Times

“Treatment of Autistic Schizophrenic Children with LSD-25 and UML-491“–

“Autistic schizophrenic children present challenging and baffling problems in treatment…. Many of the children have been followed subsequently into later childhood, adolescence, and adulthood…. Meanwhile, a new group of young autistic children are always available for new treatment endeavors as the new modes become available.”*

Monty Python - Bright Side of Life

Dr. Schwartz died on Monday,
birthday of Tom Wolfe —
who wrote
The Painted Word.

1/16: “It’s all there, hiding behind the realistic side.” –Andrew Wyeth

Related material: The previous five entries.

* by Lauretta Bender, M.D., Lothar Goldschmidt, M.D., and D.V. Siva Sankar, Ph.D., in Recent Advances in Biological Psychiatry, 1962, 4, 170-177
.

Friday, June 20, 2008

Friday June 20, 2008

Filed under: General — Tags: — m759 @ 9:00 am
Drunkard's Walk
In memory of Episcopal priest and Jungian analyst Brewster Yale Beach,
who died on Tuesday, June 17, 2008
"A man walks down the street…" — Paul Simon, Graceland album

NY Times obituaries, Tuesday, June 17, 2008-- Tony Schwartz, Walter Netsch, Tim Russert

Related material:

In the above screenshot of New York Times obituaries on the date of Brewster Beach's death, Tim Russert seems to be looking at the obituary of Air Force Academy chapel architect Walter Netsch. This suggests another chapel, more closely related to my own experience, in Cuernavaca, Mexico. Some background… Walter Netsch in Oral History (pdf, 467 pp.):

"I also had a book that inspired me– this is 1947– called Communitas by Percival and Paul Goodman. Percival Goodman was the architect, and Paul Goodman was the writer and leftist. And this came out of the University of Chicago– part of the leftist bit of the University of Chicago…. I had sort of in the back of my mind, Communitas appeared from my subconscious of the new town out of town, and there were other people who knew of it…."

Center of Town, Cuernavaca, from Paul Goodman's Communitas
Log24, Feb. 24, 2008:

Candela's 'Capilla Abierta' chapel, Cuernavaca, Mexico

Chapel, Cuernavaca, Mexico

"God As Trauma" by Brewster Yale Beach:

"The problem of crucifixion is the beginning of individuation."

"Si me de veras quieres, deja me en paz."

Lucero Hernandez, Cuernavaca, 1962

A more impersonal approach to my own drunkard's walk (Cuernavaca, 1962,
after reading the above words): Cognitive Blending and the Two Cultures
An approach from the culture (more precisely, the alternate religion) of Scientism–
The Drunkard's Walk: How Randomness Rules Our Lives— is sketched
in Today's Sermon: The Holy Trinity vs. The New York Times (Sunday, June 8, 2008).
The Times illustrated its review of The Drunkard's Walk with facetious drawings
by Jessica Hagy, who uses Venn diagrams to make cynical jokes.

A less cynical use of a Venn diagram:

  "No se puede vivir sin amar."  

  — Malcolm Lowry, Under the Volcano  

 

Photo by Gerry Gantt

(March 3, 2004)

Saturday, July 14, 2007

Saturday July 14, 2007

Filed under: General — m759 @ 4:07 am
A Note from the
Catholic University
of America


The August 2007 issue of Notices of the American Mathematical Society contains tributes to the admirable personal qualities and mathematical work of the late Harvard professor George Mackey.  For my own tributes, see Log24 on March 17, 2006April 29, 2006, and March 10, 2007.  For an entry critical of Mackey’s reductionism– a philosophical, not mathematical, error– see Log24 on May 23, 2007 (“Devil in the Details”).

Here is another attack on reductionism, from a discussion of the work of another first-rate mathematician, the late Gian-Carlo Rota of MIT:

“Another theme developed by Rota is that of ‘Fundierung.’ He shows that throughout our experience we encounter things that exist only as founded upon other things: a checkmate is founded upon moving certain pieces of chess, which in turn are founded upon certain pieces of wood or plastic. An insult is founded upon certain words being spoken, an act of generosity is founded upon something’s being handed over. In perception, for example, the evidence that occurs to us goes beyond the physical impact on our sensory organs even though it is founded upon it; what we see is far more than meets the eye. Rota gives striking examples to bring out this relationship of founding, which he takes as a logical relationship, containing all the force of logical necessity. His point is strongly antireductionist. Reductionism is the inclination to see as ‘real’ only the foundation, the substrate of things (the piece of wood in chess, the physical exchange in a social phenomenon, and especially the brain as founding the mind) and to deny the true existence of that which is founded. Rota’s arguments against reductionism, along with his colorful examples, are a marvelous philosophical therapy for the debilitating illness of reductionism that so pervades our culture and our educational systems, leading us to deny things we all know to be true, such as the reality of choice, of intelligence, of emotive insight, and spiritual understanding. He shows that ontological reductionism and the prejudice for axiomatic systems are both escapes from reality, attempts to substitute something automatic, manageable, and packaged, something coercive, in place of the human situation, which we all acknowledge by the way we live, even as we deny it in our theories.”

Robert Sokolowski, foreword to Rota’s Indiscrete Thoughts

Father Robert Sokolowski

Father Robert Sokolowski

Fr. Robert Sokolowski, Ph.D., is Professor of Philosophy at The Catholic University of America in Washington, D.C. Ordained a Roman Catholic priest in 1962, he is internationally recognized and honored for his work in philosophy, particularly phenomenology. In 1994, Catholic University sponsored a conference on his work and published several papers and other essays under the title, The Truthful and the Good, Essays In Honor of Robert Sokolowski.

Thomas Aquinas College newsletter

The tributes to Mackey are contained in the first of two feature articles in the August 2007 AMS Notices.  The second feature article is a review of a new book by Douglas Hofstadter.  For some remarks related to that article, see Thursday’s Log24 entry “Not Mathematics but Theology.”

Monday, May 14, 2007

Monday May 14, 2007

Filed under: General — Tags: — m759 @ 3:09 am

Crossing Point

From Log24's
"Footprints for Baudrillard"–

"Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?

— Madeleine L'Engle, A Wind in the Door,
Farrar, Straus and Giroux, 1973,
conclusion of Chapter Three,
"The Man in the Night"

"Oh, Euclid, I suppose."

— Madeleine L'Engle, A Wrinkle in Time,
Farrar, Straus and Giroux, 1962,
conclusion of Chapter Five,

"The Tesseract"

From Log24's
Xanga footprints,
3:00 AM today:

 

Texas /431103703/item.html 5/14/2007 3:00 AM

The link leads to a Jan. 23, 2006 entry
on what one philosopher has claimed is
"exactly that crossing point
of constraint and freedom
which is the very essence
of man's nature."

Wednesday, March 7, 2007

Wednesday March 7, 2007

Filed under: General,Geometry — Tags: , — m759 @ 8:35 am
Footprints for
Baudrillard

The image “http://www.log24.com/log/pix07/070307-Baudrillard.jpg” cannot be displayed, because it contains errors.

"Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?

 

— Madeleine L'Engle, A Wind in the Door,
Farrar, Straus and Giroux, 1973,
conclusion of Chapter Three,
"The Man in the Night"

 

"Oh, Euclid, I suppose."

— Madeleine L'Engle, A Wrinkle in Time,
Farrar, Straus and Giroux, 1962,
conclusion of Chapter Five,
"The Tesseract"

In memory of the French philosopher Jean Baudrillard, who died yesterday, Tuesday, March 6, 2007. 

The following Xanga footprints may be regarded as illustrating Log24 remarks of Dec. 10, 2006 on the Library of Congress, geometry, and bullshit, as well as remarks of Aug. 28, 2006 on the temporal, the eternal, and St. Augustine.

From the District of Columbia–
Xanga footprints in reverse
chronological order from
the noon hour on Tuesday,
March 6, 2007, the date
of Baudrillard's death:

District of Columbia
/499111929/item.html
Beijing String
3/6/2007
12:04 PM
District of Columbia
/497993036/item.html
Spellbound
3/6/2007
12:03 PM
District of Columbia
/443606342/item.html
About God, Life, Death
3/6/2007
12:03 PM
District of Columbia
/494421586/item.html
A Library of Congress Reading
3/6/2007
12:03 PM
District of Columbia
/500434851/item.html
Binary Geometry
3/6/2007
12:03 PM
District of Columbia
/404038913/item.html
Prequel on St. Cecelia's Day
3/6/2007
12:03 PM

Thursday, March 1, 2007

Thursday March 1, 2007

Filed under: General,Geometry — Tags: — m759 @ 6:29 am

Senior Honors

Notes in Memory of
a Father, a Son, and a Holy Ghost

From the obituary in today's New York Times of historian Arthur M. Schlesinger Jr.–

"Mr. Schlesinger, partly through his appreciation of history, fully realized his good fortune. 'I have lived through interesting times and had the luck of knowing some interesting people,' he wrote.

A huge part of his luck was his father, who guided much of his early research, and even suggested the topic for his [Harvard] senior honors: Orestes A. Brownson, a 19th-century journalist, novelist and theologian. It was published by Little, Brown in 1938 as 'Orestes A. Brownson: A Pilgrim's Progress.'"

Douglas Martin

From The Catholic Encyclopedia:

"It is sufficient for true knowledge that it affirm as real that which is truly real."

Article on Ontologism

From The Diamond Theory of Truth:

"Was there really a cherubim waiting at the star-watching rock…?
Was he real?
What is real?

— Madeleine L'Engle, A Wind in the Door, Farrar, Straus and Giroux, 1973, conclusion of Chapter Three, "The Man in the Night"

"Oh, Euclid, I suppose."

— Madeleine L'Engle, A Wrinkle in Time, Farrar, Straus and Giroux, 1962, conclusion of Chapter Five, "The Tesseract"

Related material: Yesterday's first annual "Tell Your Story Day" at Harvard and yesterday's entry on Euclid.

Wednesday, January 31, 2007

Wednesday January 31, 2007

Filed under: General — Tags: — m759 @ 3:09 pm
Ontotheology

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

“It may be that universal history is the
history of the different intonations
given a handful of metaphors.”
— Jorge Luis Borges (1951),
“The Fearful Sphere of Pascal,”
in Labyrinths, New Directions, 1962

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.'”

— Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf)

Goguen does not give a source for this alleged “thoughts of God” statement.

A Web search for the source leads only to A Mathematical Journey, by Stanley Gudder, who apparently also attributes the saying to Euclid.

Neither Goguen nor Gudder seems to have had any interest in the accuracy of the Euclid attribution.

Talk of “nature” and “God” seems unlikely from Euclid, a pre-Christian Greek whose pure mathematics has (as G. H. Hardy might be happy to point out) little to do with either.

Loose talk about God’s thoughts has also been attributed to Kepler and Einstein… and we all know about Stephen Hawking.

Gudder may have been misquoting some other author’s blather about Kepler.  Another possible source of the “thoughts of God” phrase is Hans Christian Oersted. The following is from Oersted’s The Soul in Nature

“Sophia. Nothing of importance; though indeed I had one question on my lips when the conversion took the last turn. When you alluded to the idea, that the Reason manifested in Nature is infallible, while ours is fallible, should you not rather have said, that our Reason accords with that of Nature, as that in the voice of Nature with ours?

Alfred. Each of these interpretations may be justified by the idea to which it applies, whether we start from ourselves or external nature. There are yet other ways of expressing it; for instance, the laws of Nature are the thoughts of  Nature.

Sophia. Then these thoughts of Nature are also thoughts of God.

Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God; I therefore beg you will not proceed to [sic] fast.”

Oersted also allegedly said that “The Universe is a manifestation of an Infinite Reason and the laws of Nature are the thoughts of God.” This remark was found (via Google book search) in an obscure journal that does not give a precise source for the words it attributes to Oersted.

The image “http://www.log24.com/log/pix07/070131-OerstedGudder.jpg” cannot be displayed, because it contains errors.

Sunday, November 12, 2006

Sunday November 12, 2006

Filed under: General — Tags: — m759 @ 12:25 am

Instance

Log24, Feb. 25, 2004:

From a review by Adam White Scoville of Iain Pears's novel titled An Instance of the Fingerpost:

"Perhaps we are meant to see the story as a cubist retelling of the crucifixion, as Pilate, Barabbas, Caiaphas, and Mary Magdalene might have told it. If so, it is sublimely done so that the realization gradually and unexpectedly dawns upon the reader. The title, taken from Sir Francis Bacon, suggests that at certain times, 'understanding stands suspended' and in that moment of clarity (somewhat like Wordsworth's 'spots of time,' I think), the answer will become apparent as if a fingerpost were pointing at the way."

Another instance:

The film "Barabbas" (1962) shown on Turner Classic Movies at 8 PM Friday, Nov. 10.

Compare and contrast–

  • Barabbas emerging from prison as if from Plato's cave, and Barabbas's vision of Christ in blinding sunlight: "Flung into the sunlight, he stands blinking at a young man in white robes; is it merely the unaccustomed light that dazzles his eyes, or does he really see a radiance streaming from the young man's face?" —TIME Magazine, 1962
  • 1 Peter 2 on Christ as the "living stone"
  • The cover of the novel Stone 588 shown in Friday's 11:20 PM entry

The film is based on the novel by Par Lagerkvist, winner of the Nobel Prize in Literature.

The Lagerkvist novel may be of more enduring interest than Stone 588, but, as Friday's lottery numbers indicate, even lesser stories have their place.

Thursday, September 7, 2006

Thursday September 7, 2006

Filed under: General — m759 @ 4:04 am
A Game of Chess

for Isak Dinesen,
who died in 1962
on this date

The image “http://www.log24.com/log/pix06A/060907-SeventhSeal.jpg” cannot be displayed, because it contains errors.

 Meanwhile…

 

Click on pictures for details.

Thursday, August 31, 2006

Thursday August 31, 2006

Filed under: General — Tags: , — m759 @ 11:09 pm
Wag the Dogma
(continued from 2001)
Ingrid Thulin and
Glenn Ford in
“The 4 Horsemen
of the Apocalypse”:

The 4 Horsemen, Ingrid Thulin, Glenn Ford

A sneering review from TIME Magazine, March 23, 1962:

“Hero Ford, a playboy from Argentina, falls pampassionately in love with Heroine Thulin, a Parisienne married to a patriotic editor. When the editor joins the Resistance, the hero realizes his duty and secretly does the same. Unaware of his decision, the heroine decides that he is merely a lightweight, and goes back to her husband. At the fade, while the violins soar among the bomb bursts, the poor misunderstood playboy dies heroically in an attempt to weaken the Wehrmacht’s defenses in Normandy.

The tale is trite, the script clumsy, and the camera work grossly faked. Though the lovers wander all over Paris, the Cathedral of Notre Dame turns up in the background practically everywhere they go, almost as if it were following them around like a little dog.”

TIME Magazine is still wearing the Ivy League sneer it displayed so impressively in 1962.

A less dismissive summary from Answers.com:

“The World War I setting of the original Blasco-Ibanez novel has been updated to World War II, but the basic plot remains the same. A well-to-do Argentinian family, rent asunder by the death of patriarch Lee J. Cobb, scatters to different European countries in the late 1930s. Before expiring, Cobb had warned his nephew Carl Boehm that the latter’s allegiance to the Nazis would bring down the wrath of the titular Four Horsemen: War, Conquest, Famine and Death. Ford, Cobb’s grandson, has promised to honor his grandfather’s memory by thwarting the plans of Boehm. At the cost of his own life, Ford leads allied bombers to Boehm’s Normandy headquarters.”

In memory of Glenn Ford, a talented character actor who died at 90 yesterday, the opening paragraphs of an obituary in The Scotsman:

The image “http://www.log24.com/log/pix06A/060831-ScotsmanLogo3.gif” cannot be displayed, because it contains errors.

Screen icon Glenn Ford
dies at 90

RHIANNON EDWARD

GLENN Ford, one of the most enduring stars of the silver screen, has died at the age of 90.

Ford, who appeared in more than 200 films in a career spanning five decades, died at his home in Beverly Hills.

The actor’s health had been in decline for a number of years after he suffered a series of strokes.

Although he never achieved the superstardom he craved, Ford was widely acclaimed as one of the best character actors in the business.

The business of narrative:

From a narrative suggested by the name of The Scotsman‘s reporter and related, if only by association with Normandy, to Ford’s “Four Horsemen” film:

“The Vandaleurs are a family of Norman nobles with a heritable version of the mages’ Gift. They have been using magic covertly for what appears to have been a very long time…. Another branch of the family is known to hold a fief in Normandy, but it is not yet known if they are covert magicians as well.”

The Vandaleur narrative may be of interest to fans of The Da Vinci Code. (Ford is said to have been a Freemason, a charter member of Riviera Lodge No. 780, Pacific Palisades, California.)

For Catholics and others who prefer more traditional narratives:

The image “http://www.log24.com/log/pix06A/060831-4Horsemen.jpg” cannot be displayed, because it contains errors.

 Illuminated parchment,
1047 A.D.,
The Four Horsemen
of the Apocalypse

Related material:

Yesterday’s entries, and
an entry from April 7. 2003,
that they link to:

Mathematics and The Seventh Seal

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