Friday, March 24, 2017

A Large Superset

Filed under: Uncategorized — Tags: — m759 @ 1:06 PM

From a post of Feb. 24

From a search for "Preparation" in this journal (see previous post) —

"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."

"I meant a larger map." — Number Six in "The Prisoner" (1967)

Swimmer in the Ocean of Night

Filed under: Uncategorized — Tags: — m759 @ 3:17 AM

For Scarlett 

From a search for "Preparation" in this journal —

"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)."

From a film in which Scarlett portrays a goddess —

Madness related to several recent posts

Then, with an unheard splash which sent from the silver water to the shore a line of ripples echoed in fear by my heart, a swimming thing emerged beyond the breakers. The figure may have been that of a dog, a human being, or something more strange. It could not have known that I watched—perhaps it did not care—but like a distorted fish it swam across the mirrored stars and dived beneath the surface. After a moment it came up again, and this time, since it was closer, I saw that it was carrying something across its shoulder. I knew, then, that it could be no animal, and that it was a man or something like a man, which came toward the land from a dark ocean. But it swam with a horrible ease.
     As I watched, dread-filled and passive, with the fixed stare of one who awaits death in another yet knows he cannot avert it, the swimmer approached the shore—though too far down the southward beach for me to discern its outlines or features. Obscurely loping, with sparks of moonlit foam scattered by its quick gait, it emerged and was lost among the inland dunes.

— From "The Night Ocean," by H. P. Lovecraft
     and R. H. Barlow

Related news

"When hard-liners seized power in Moscow in August 1991
and imprisoned Mr. Gorbachev in his vacation house on the
Black Sea, Mr. Chernyaev, a guest there and a powerful swimmer,
offered to smuggle out a note by swimming to a beach more than
three miles away. Uncertain where he could take the note, they
dropped the plan. The coup quickly failed in any case."

Saturday, March 11, 2017

Preparation 🞼

Filed under: Uncategorized — m759 @ 9:33 PM

🞼 See the title in this journal.

Monday, February 27, 2017

Best Picture

Filed under: Uncategorized — m759 @ 2:40 PM

'Preparation,' a Log24 post of April 1, 2013

Thursday, July 14, 2016

Meditation from an April 1

Filed under: Uncategorized — m759 @ 9:38 AM

Related material from the same day —

See also

Cube Bricks 1984 —

An Approach to Symmetric Generation of the Simple Group of Order 168

The above bricks appeared in some earlier Log24 posts.

Thursday, January 21, 2016


Filed under: Uncategorized — m759 @ 11:30 AM

Definition of 'ediscovery'

Update of 11:40 AM —

"Share evidence via an online repository. 
Working more effectively means accessing data at night,
at the courthouse, or wherever you are. More importantly,
you need to share evidence with the judge and opposing
parties without delay."

Related material:

“The Old Man’s still an artist with a Thompson.”
— Terry in the Coen brothers film “Miller’s Crossing

See as well Apocalypse Wow and the sequel Chemistry 101.

Thursday, September 11, 2014

A Class by Itself

Filed under: Uncategorized — 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."

Monday, April 1, 2013


Filed under: Uncategorized — m759 @ 7:20 AM

"First published between 1922 and 1925,
the six-volume Principles of Geometry  was
a synthesis of Baker's lecture series on geometry…."

Cambridge University Press

From a different university press, a new logo
can be seen either as six volumes or as
the letter H —

"What is the H for?"

Friday, December 28, 2012

Cube Koan

Filed under: Uncategorized — Tags: , — m759 @ 4:56 AM

From Don DeLillo's novel Point Omega —

I knew what he was, or what he was supposed to be, a defense intellectual, without the usual credentials, and when I used the term it made him tense his jaw with a proud longing for the early weeks and months, before he began to understand that he was occupying an empty seat. "There were times when no map existed to match the reality we were trying to create."

"What reality?"

"This is something we do with every eyeblink. Human perception is a saga of created reality. But we were devising entities beyond the agreed-upon limits of recognition or interpretation. Lying is necessary. The state has to lie. There is no lie in war or in preparation for war that can't be defended. We went beyond this. We tried to create new realities overnight, careful sets of words that resemble advertising slogans in memorability and repeatability. These were words that would yield pictures eventually and then become three-dimensional. The reality stands, it walks, it squats. Except when it doesn't."

He didn't smoke but his voice had a sandlike texture, maybe just raspy with age, sometimes slipping inward, becoming nearly inaudible. We sat for some time. He was slouched in the middle of the sofa, looking off toward some point in a high corner of the room. He had scotch and water in a coffee mug secured to his midsection. Finally he said, "Haiku."

I nodded thoughtfully, idiotically, a slow series of gestures meant to indicate that I understood completely.

"Haiku means nothing beyond what it is. A pond in summer, a leaf in the wind. It's human consciousness located in nature. It's the answer to everything in a set number of lines, a prescribed syllable count. I wanted a haiku war," he said. "I wanted a war in three lines. This was not a matter of force levels or logistics. What I wanted was a set of ideas linked to transient things. This is the soul of haiku. Bare everything to plain sight. See what's there. Things in war are transient. See what's there and then be prepared to watch it disappear."

What's there—

This view of a die's faces 3, 6, and 5, in counter-
clockwise order (see previous post) suggests a way
of labeling the eight corners  of a die (or cube):

123, 135, 142, 154, 246, 263, 365, 456.

Here opposite faces of the die sum to 7, and the
three faces meeting at each corner are listed
in counter-clockwise order. (This corresponds
to a labeling of one of MacMahon's* 30 colored cubes.)
A similar vertex-labeling may be used in describing 
the automorphisms of the order-8 quaternion group.

For a more literary approach to quaternions, see
Pynchon's novel Against the Day .

* From Peter J. Cameron's weblog:

  "The big name associated with this is Major MacMahon,
   an associate of Hardy, Littlewood and Ramanujan,
   of whom Robert Kanigel said,

His expertise lay in combinatorics, a sort of
glorified dice-throwing, and in it he had made
contributions original enough to be named
a Fellow of the Royal Society.

   Glorified dice-throwing, indeed…"

Monday, October 10, 2011

The Aleph

Filed under: Uncategorized — m759 @ 12:00 AM

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—


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

From the same website, another seal.

Monday, August 3, 2009

Monday August 3, 2009

Filed under: Uncategorized — m759 @ 7:11 AM
For Your Consideration

The Police, 'Synchronicity' album, detail of cover

LA Times yesterday:

Steven Miessner, keeper
of the Academy’s Oscars,
died of a heart attack at 48
on Wednesday, July 29, 2009:

LA Times obit for Steven Miessner, 'Keeper of the Oscars,' who died July 29, 2009

Click the above to enlarge.

Steve Miessner, keeper of the Oscars, on Feb. 21, 2009

Steve Miessner, the keeper of the Oscars,
packages the statues for transport

to Kodak Theatre in Los Angeles
in preparation for the 81st
 Academy Awards ceremony held
on Sunday, Feb. 22, 2009
(Chris Carlson/AP).

From the date of
Miessner’s death

Adam and God (Sistine Chapel), with Jungian Self-Symbol and Ojo de Dios (The Diamond Puzzle)

From the following day:

Log24 on Thursday, July 30, 2009

Annals of Aesthetics, continued:

Academy Awards
for Cambridge

“First of all, I’d like
 to thank the Academy.”
Remark attributed to Plato

Arrest of Prof. Henry Louis Gates, Jr., in Cambridge, Mass.

“A poem cannot exhaust reality,
  but it can arrest it.

At War with the Word:
   Literary Theory and
   Liberal Education
   by R. V. Young,
   Chapter One

“Who knows where madness lies?”

— Quoted here July 29, 2009
(the day the keeper of
the Oscars died)

Possible clues:

From Google News at about
7 AM ET Mon., Aug. 3, 2009:

Henry Louis Gates Jr. mulls moving over death threats

Boston Herald – Susan MiltonJessica Van Sack – ‎6 hours ago‎
CHILMARK – Black scholar Henry Louis Gates Jr. has received numerous death threats since he accused a white officer of

Death threats may make Gates move

The Daily Inquirer – ‎4 hours ago‎
Henry Louis Gates Jr. said yesterday that Harvard University suggested he move after receiving numerous death threats since he accused a white officer of

Gates: I’ve received death threats

NECN – ‎9 hours ago‎
Gates spoke at a book signing on Martha’s Vineyard. He also said that he has received death and bomb threats after the incident at his Cambridge home.

Black scholar says he’s able to joke about arrest

The Associated Press – Denise Lavoie – ‎17 hours ago‎
Gates said he received numerous threats after the incident, including an e-mail that read, “You should die, you’re a racist.” Gates has changed his e-mail

Gates grateful for island haven

Cape Cod Times – Susan Milton – ‎4 hours ago‎
As a result of death threats and bomb threats, he hasn’t returned to his Cambridge home, leased from Harvard University. The university has encouraged him

Gates makes public appearance after race debate

Worcester Telegram – Denise Lavoie – ‎20 hours ago‎
Gates, who spoke at a book signing on Martha’s Vineyard Sunday, says there also have been some serious moments. He says he received death and bomb threats

Thursday, August 9, 2007

Thursday August 9, 2007

Filed under: Uncategorized — m759 @ 12:00 PM
“Serious numbers  
will always be heard.”

— Paul Simon

(See St. Luke’s Day, 2005.)  

Bulletin of the American Mathematical Society
Volume 31, Number 1, July 1994, Pages 1-14

Selberg’s Conjectures
and Artin L-Functions

M. Ram Murty


In its comprehensive form, an identity between an automorphic L-function and a “motivic” L-function is called a reciprocity law. The celebrated Artin reciprocity law is perhaps the fundamental example. The conjecture of Shimura-Taniyama that every elliptic curve over Q is “modular” is certainly the most intriguing reciprocity conjecture of our time. The “Himalayan peaks” that hold the secrets of these nonabelian reciprocity laws challenge humanity, and, with the visionary Langlands program, we have mapped out before us one means of ascent to those lofty peaks. The recent work of Wiles suggests that an important case (the semistable case) of the Shimura-Taniyama conjecture is on the horizon and perhaps this is another means of ascent. In either case, a long journey is predicted…. At the 1989 Amalfi meeting, Selberg [S] announced a series of conjectures which looks like another approach to the summit. Alas, neither path seems the easier climb….

[S] A. Selberg, Old and new
      conjectures and results
      about a class of Dirichlet series,
      Collected Papers, Volume II,
      Springer-Verlag, 1991, pp. 47-63.

Zentralblatt MATH Database
on the above Selberg paper:

“These are notes of lectures presented at the Amalfi Conference on Number Theory, 1989…. There are various stimulating conjectures (which are related to several other conjectures like the Sato-Tate conjecture, Langlands conjectures, Riemann conjecture…)…. Concluding remark of the author: ‘A more complete account with proofs is under preparation and will in time appear elsewhere.'”

Related material: Previous entry.

Sunday, July 29, 2007

Sunday July 29, 2007

Filed under: Uncategorized — m759 @ 7:59 AM
Nordic Truth: Jewish Fiction:
Snowball In Hell
From The New York Times in 2005:

Portrait of conductor
Arild Remmereit:

Arild Remmereit

April 24, 2005
Have Baton,
Will Travel

by James R. Oestreich


“HE’S the hottest conductor you’ve never heard of….

In music, as in most other pursuits, one person’s misfortune can be another’s opportunity. Many a podium career has been built on successful substitutions…. typically, the process is cumulative and measured.

In Mr. Remmereit’s case, it seems a sort of spontaneous combustion…. he seems destined for big things, and soon.

Regarding his sudden change in stature, he spoke as if from afar. ‘The snowball has reached such a size that it has started to roll,’ he said matter-of-factly….

‘It’s terrifying when it happens,’ he said, ‘but I can’t tell you how naively happy I am when it goes well. These are such major steps that I wasn’t even hoping for a few weeks ago.’

ARILD REMMEREIT (pronounced AHR-eeld REMM-uh-right, with the r’s heavily rolled) was born in a village in Norway, between Bergen and Trondheim, and has lived in Vienna since 1987. Slim and fresh-faced at 43, he has had a busy but low-level career in Europe….

So here he was, on April 15, conducting the Pittsburgh Symphony… in a vintage… Germanic program…. Wagner’s ‘Siegfried Idyll,’ Schumann’s Fourth Symphony and Brahms’s Second Piano Concerto….”


Württemberg Philharmonic February 2004
Nielsen, Sibelius, Grieg.

Reutlinger Nachrichten.
“Distant closeness, close distance.

Arild Remmereit as a guest conductor: ‘As when the sun rises in the North.’ The Philharmonics and their brilliant guest conductor fetched the mind-blowing, tempting and exciting Scandinavia.

It was like a lucky strike to see the Norwegian conductor on stage with the Philharmonic. When he conducts the Dane Nielsen, the Finn Sibelius and the Norwegian Grieg, one can really feel that this man has the locally marked music floating in his blood.”

From The New York Times today:

Discussion of
a new novel:
Variations on the Beast

Variations on
the Beast
by psychoanalyst
Henry Grinberg

An interview with Henry Grinberg conducted by James R. Oestreich:

“For those who find inspiration and edification in great art, it is always painful to be reminded that artists are not necessarily admirable as people and that art is powerless in the face of great evil. That truth was baldly evident in Nazi Germany and in the way the regime used and abused music and musicians, to say nothing of the way it used and abused human beings of all kinds.

[A new novel touches on] these issues…. In Variations on the Beast (Dragon Press), Henry Grinberg, a psychoanalyst, posits Hermann Kapp-Dortmunder, a powerful maestro, as a fictional rival of Wilhelm Furtwängler (whose qualms about working under the regime he does not share) and Herbert von Karajan (whose vaulting ambition he does).”


“And it soon occurred to me… that, my God, a lot of the famous, the notable, the moving, the magnificent composers in the 18th and 19th centuries and earlier were Germans. And I tried to understand, how did such a nation turn out to be so bestial and cruel, so indifferent to the suffering of others? And I have no explanation for it.

As a practicing psychoanalyst, I can see individual expressions of rage and their causes and their so-called justifications. But for a whole nation to be consumed, to be seduced by an overwhelming idea– well, there are rationalizations, I guess, but not explanations. There’s no forgiveness for this. And I tried to put together a story of a person who was a participant and a causer of these kinds of things….

So I sort of poured my feelings of contempt and rage into the character I was devising. And I have to admit, after having been psychoanalyzed myself in preparation for the training, that something of Hermann Kapp-Dortmunder exists in me. I shudder to think that this may be so, but I have to accept the possibility. Murderous thoughts may have occurred to me, but, thank God, I’ve never killed anyone.”

Sunday, January 9, 2005

Sunday January 9, 2005

Filed under: Uncategorized — m759 @ 3:10 PM

Light at Bologna

“Others say it is a stone that posseses mysterious powers…. often depicted as a dazzling light.  It’s a symbol representing power, a source of immense energy.  It nourishes, heals, wounds, blinds, strikes down…. Some have thought of it as the philosopher’s stone of the alchemists….”

Foucault’s Pendulum
by Umberto Eco,
Professor of Semiotics at
 Europe’s oldest university,
 the University of Bologna.

The Club Dumas

by Arturo Perez-Reverte

(Paperback, pages 346-347):

One by one, he tore the engravings from the book, until he had all nine.  He looked at them closely.  “It’s a pity you can’t follow me where I’m going.  As the fourth engraving states, fate is not the same for all.”

“Where do you believe you’re going?”

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

“To meet someone” was his enigmatic answer. “To search for the stone that the Great Architect rejected, the philosopher’s stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso. From Faust’s black dog to the false angel of light who tried to break down Saint Anthony’s resistance.  But most of all, stupidity bores him, and he hates monotony….”

Eclogues: Eight Stories

by Guy Davenport

Johns Hopkins paperback, 1993, page 127 —

Lo Splendore della Luce a Bologna, VI:

“In 1603, at Monte Paderno, outside Bologna, an alchemist (by day a cobbler) named Vicenzo Cascariolo discovered the Philosopher’s Stone, catalyst in the transformation of base metals into gold, focus of the imagination, talisman for abstruse thought.  Silver in some lights, white in others, it glowed blue in darkness, awesome to behold.”

The Discovery of Luminescence:

The Bolognian Stone

The image “http://www.log24.com/log/pix05/050109-Bologna.jpg” cannot be displayed, because it contains errors.
Bologna, 16th Century

“For the University of Bologna hosting an International Conference on Bioluminescence and Chemiluminescence has a very special significance. Indeed, it is in our fair City that modern scientific research on these phenomena has its earliest roots….

‘After submitting the stone
to much preparation, it was not
the Pluto of Aristophanes
that resulted; instead, it was
the Luciferous Stone’ ”

From one of the best books
of the 20th century:

The Hawkline Monster

by Richard Brautigan

The image “http://www.log24.com/log/pix05/050109-Hawkline.jpg” cannot be displayed, because it contains errors.
“The Chemicals that resided in the jar were a combination of hundreds of things from all over the world.  Some of The Chemicals were ancient and very difficult to obtain.  There were a few drops of something from an Egyptian pyramid dating from the year 3000 B.C.

There were distillates from the jungles of South America and drops of things from plants that grew near the snowline in the Himalayas.

Ancient China, Rome and Greece had contributed things, too, that had found their way into the jar.  Witchcraft and modern science, the latest of discoveries, had also contributed to the contents of the jar.  There was even something that was reputed to have come all the way from Atlantis….

… they did not know that the monster was an illusion created by a mutated light in The Chemicals. a light that had the power to work its will upon mind and matter and change the very nature of reality to fit its mischievous mind.”

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