Log24

Wednesday, April 26, 2017

Again

Filed under: Uncategorized — Tags: — m759 @ 6:18 PM

See also "Cornerstone" in this journal and

A sidebar from a Google search today —

'The Square of Opposition: A Cornerstone of Thought'

This suggests a review of posts now tagged Obelisk,
which include

Sunday, April 16, 2017

Homily

Filed under: Uncategorized — m759 @ 12:25 PM

See also Plan 9.

Friday, March 24, 2017

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."

Tuesday, March 14, 2017

Backstories

Filed under: Uncategorized — Tags: — m759 @ 12:00 AM

"Backstories do more than amuse guests.
They anchor the hosts.
It's their cornerstone.
The rest of their identity is built around it, layer by layer."

— Elsie Hughes in "Westworld," Season 1, Episode 3,
     "The Stray," at 30:09

See also cornerstone in the Bible.

Dr. Robert Ford (Anthony Hopkins) earlier in that same episode —

Westworld S1E3 23:15- Dr. Ford on fiction

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."

Wednesday, July 4, 2012

Poetic Physics

Filed under: Uncategorized — m759 @ 8:00 AM

IMAGE- July 4th Google search for Heuer + 'The Missing Cornerstone'

    See also Symbology, The Lost Cornerstone, and Now, Here's My Plan.

Thursday, April 5, 2012

Leap Day of Faith

Filed under: Uncategorized — 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.

Thursday, October 13, 2011

Now, Here’s My Plan

Filed under: Uncategorized — m759 @ 4:04 PM

"Plan 9 is an operating system kernel but also a collection of accompanying software."

Webpage pointed out by the late Dennis Ritchie,
     father of the programming language C
     and co-developer of Unix, who reportedly died on October 8.

From Ritchie's own home page

"A brief biography, in first person instead of obituary style."

From that biography—

"Today, as a manager of a small group of researchers, I promote exploration of distributed operating systems, languages, and routing/switching hardware. The recent accomplishments of this group include the Plan 9 operating system…."

Another operating system is that of Alfred Bester.
My laptop now includes his classic The Stars My Destination ,
downloaded this morning…

(Click to enlarge.)

http://www.log24.com/log/pix11C/111013-KindleLibrary-500w.jpg

Not much compared to Widener Library (see this morning's Lost Cornerstone),
but sufficient for present purposes…

"Simple jaunt." — "The Comedian as the Letter C"

See also Plan 9 from Outer Space in this journal.

The Lost Cornerstone

Filed under: Uncategorized — m759 @ 6:29 AM

This post was suggested by this morning's New York Times  story on the missing cornerstone of St. Patrick's Cathedral and by the recent design for an official T-shirt celebrating Harvard's 375th anniversary—

http://www.log24.com/log/pix11C/111011-HtshirtSm.jpg

In Harvard's case, the missing piece beneath the cathedral-like spire* is the VERITAS on the college shield.

Possible sources for a shield image representing VERITAS—

1. "Patrick Blackburn" in this journal, which might be combined with

2. Reflections on Kurt Gödel ** by Hao Wang, Chapter 9, "To Fit All the Parts Together"—

"The metaphor of fitting parts together readily suggests
  the concrete image of solving a picture puzzle…." (p. 243)

Or the image of a Wang tiles puzzle.

A graphic image, colorful but garish, that summarizes these two sources—

http://www.log24.com/log/pix11C/111013-WangShield.bmp

  Shield with matching Wang tiles

* The Lowell House bell tower
** MIT Press, first published in 1987

Tuesday, January 26, 2010

Symbology

Filed under: Uncategorized — Tags: — m759 @ 9:00 PM

From this journal:

Friday December 5, 2008

m759 @ 1:06 PM
 
Mirror-Play of
the Fourfold

For an excellent commentary
 on this concept of Heidegger,

View selected pages
from the book

Dionysus Reborn:

Play and the Aesthetic Dimension
in Modern Philosophical and
Scientific Discourse

(Mihai I. Spariosu,
Cornell U. Press, 1989)

Related material:
the logo for a
web page

Logo for 'Elements of Finite Geometry'

– and Theme and Variations.

Transition to the
Garden of Forking Paths–

(See For Baron Samedi)–

The Found Symbol
Robert Langdon (played by Tom Hanks) and a corner of Solomon's Cube

and Dissemination, by Jacques Derrida,
translated by Barbara Johnson,
London, Athlone Press, 1981–

Pages 354-355
On the mirror-play of the fourfold

Pages 356-357
Shaking up a whole culture

Pages 358-359
Cornerstone and crossroads

Pages 360-361
A deep impression embedded in stone

Pages 362-363
A certain Y, a certain V

Pages 364-365
The world is Zeus's play

Page 366
It was necessary to begin again

 

Sunday, October 8, 2006

Sunday October 8, 2006

Filed under: Uncategorized — m759 @ 12:00 AM
Today’s Birthday:
Matt Damon
 
Enlarge this image

The image “http://www.log24.com/log/pix06A/061008-Departed2.jpg” cannot be displayed, because it contains errors.

“Cubistic”

New York Times review
of Scorsese’s The Departed

Related material:

Log24, May 26, 2006

“The man who lives in contact with what he believes to be a living Church is a man always expecting to meet Plato and Shakespeare to-morrow at breakfast.”

— G. K. Chesterton
 

The image “http://www.log24.com/log/pix06A/060526-JackInTheBox.jpg” cannot be displayed, because it contains errors.
Natasha Wescoat, 2004

Shakespearean
Fool

Not to mention Euclid and Picasso

(Log24, Oct. 6, 2006) —

The image “http://www.log24.com/theory/images/Pythagoras-I47.gif” cannot be displayed, because it contains errors.

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

(Click on pictures for details. Euclid is represented by Alexander Bogomolny, Picasso by Robert Foote.)

See also works by the late Arthur Loeb of Harvard’s Department of Visual and Environmental Studies.

“I don’t want to be a product of my environment.  I want my environment to be a product of me.” — Frank Costello in The Departed

For more on the Harvard environment,
see today’s online 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.

Monday, January 9, 2006

Monday January 9, 2006

Filed under: Uncategorized — m759 @ 5:01 AM
Cornerstone

“In 1782, the Swiss mathematician Leonhard Euler posed a problem whose mathematical content at the time seemed about as much as that of a parlor puzzle. 178 years passed before a complete solution was found; not only did it inspire a wealth of mathematics, it is now a cornerstone of modern design theory.”

— Dean G. Hoffman, Auburn U.,
    July 2001 Rutgers talk

Diagrams from Dieter Betten’s 1983 proof
of the nonexistence of two orthogonal
6×6 Latin squares (i.e., a proof
of Tarry’s 1900 theorem solving
Euler’s 1782 problem of the 36 officers):

The image “http://www.log24.com/log/pix06/060109-TarryProof.gif” cannot be displayed, because it contains errors.

Compare with the partitions into
two 8-sets of the 4×4 Latin squares
discussed in my 1978 note (pdf).

Saturday, May 21, 2005

Saturday May 21, 2005

Filed under: Uncategorized — m759 @ 12:16 AM
Terminator

From a March 10, 2004, entry:

“Language was no more than a collection of meaningless conventional signs, and life could absurdly end at any moment.  [Mallarmé] became aware, in Millan’s* words, ‘of the extremely fine line

separating absence and presence, being and nothingness, life and death, which later … he could place at the very centre of his work and make the cornerstone of his personal philosophy and his mature poetics.’ “

— John Simon, Squaring the Circle

* A Throw of the Dice: The Life of Stéphane Mallarmé, by Gordon Millan

For those who prefer
art that is more lurid:

The image “http://www.log24.com/log/pix05/050520-epi3.jpg” cannot be displayed, because it contains errors.
(Photo in lower half
from Cinetribulations)

Related material:

Pilate, Truth, and
Friday the Thirteenth

and

Nothing Nothings (Again)

Saturday, March 13, 2004

Saturday March 13, 2004

Filed under: Uncategorized — m759 @ 12:00 PM

The Line

From a March 10, 2004, entry:

“Language was no more than a collection of meaningless conventional signs, and life could absurdly end at any moment.  [Mallarmé] became aware, in Millan’s* words, ‘of the extremely fine line

separating absence and presence, being and nothingness, life and death, which later … he could place at the very centre of his work and make the cornerstone of his personal philosophy and his mature poetics.’ “

— John Simon, Squaring the Circle

* A Throw of the Dice: The Life of Stéphane Mallarmé, by Gordon Millan

The illustration of the “fine line” is not by Mallarmé but by myself.  (See Songs for Shakespeare, March 5, where the line separates being from nothingness, and Ridgepole, March 7, where the line represents the “great primal beginning” of Chinese philosophy (or, equivalently, Stevens’s “first idea” or Mallarmé’s line “separating absence and presence, being and nothingness, life and death.”)

By the Associated Press,
Saturday, March 13, 2004:

“Dave Schulthise, known as Dave Blood during his career as a bassist with the 1980’s Philadelphia punk-rock band the Dead Milkmen, died on Wednesday [March 10, 2004] at the home of friends in North Salem, N.Y. He was 47.

‘David chose to end his life,’ Mr. Schulthise’s sister, Kathy, wrote on the band’s Web site.”

I walk the thinnest line
I walk the thinnest line
I walk the thinnest line
Between the light and dark sides of my mind

The Dead Milkmen, Beelzebubba album

Related material: The Word in the Desert.

Wednesday, March 10, 2004

Wednesday March 10, 2004

Filed under: Uncategorized — m759 @ 4:07 AM

Ennui of the First Idea

The ennui of apartments described by Stevens in “Notes Toward a Supreme Fiction” (see previous entry) did not, of course, refer to the “apartments” of incidence geometry.  A more likely connection is with the apartments — the “ever fancier apartments and furnishings” — of Stéphane Mallarmé, described by John Simon as the setting for what might plausibly be called, in Stevens’s words, “an ennui of the first idea”:

“Language was no more than a collection of meaningless conventional signs, and life could absurdly end at any moment. He [Mallarmé] became aware, in Millan’s* words, ‘of the extremely fine line

separating absence and presence, being and nothingness, life and death, which later … he could place at the very centre of his work and make the cornerstone of his personal philosophy and his mature poetics.’ “

— John Simon, Squaring the Circle

* A Throw of the Dice: The Life of Stéphane Mallarmé, by Gordon Millan

The illustration of the “fine line” is not by Mallarmé but by myself.  (See Songs for Shakespeare, March 5, where the line separates being from nothingness, and Ridgepole, March 7, where the line represents the “great primal beginning” of Chinese philosophy (or, equivalently, Stevens’s “first idea” or Mallarmé’s line “separating absence and presence, being and nothingness, life and death.”)

Monday, October 21, 2002

Monday October 21, 2002

Filed under: Uncategorized — Tags: — m759 @ 12:00 AM

Theology for a Small Planet

THE HARVARD DIVINITY BULLETIN for Fall 1989 contained a special section, "Theology for a Small Planet," with a number of short articles by divinity school faculty and others addressing environment and theology.

From The Harvard Divinity Bulletin, XIX, 3 (1989):

" While Angels Weep…"
Doing Theology on a Small Planet

Timothy C. Weiskel
© Copyright, 1989, Timothy C. Weiskel

…We continue to strut and prance about with a sense of supreme self-importance as if all creation were put in place for our benefit….

From where does such arrogance come? How can our beliefs be so far out of touch with our knowledge? How can we maintain such an inflated sense of personal, collective and species self-importance? ….

The answer, in part, is that Western religious traditions have generated and sustained this petty arrogance…. 

Western cultures have come to believe religiously in their own power, importance and capacity to dominate and control nature.

Some religious groups have transcribed and elaborated creation myths which serve to ennoble and authorize this illusion of domination. In these myths a supreme and omnipotent God figure (usually portrayed as male) is said to have created humankind and enjoined this species to be "fruitful and multiply" and "subdue" the earth. Moreover, it is often a feature of these traditions that selected human groups come to feel entitled, empowered or specially ordained by such a God to be his "chosen people." Through their actions and history, it is believed, this God allegedly manifested his intent for the planet as a whole. In short, human groups created God in their own image and generated divine narratives that accorded themselves privileged status in the whole of creation….

…science itself has become the cornerstone of modern mankind's religiously held belief in human control. In our era, this kind of arrogant science, like the self-important religious traditions of the past, must be questioned….

In short, we all stand in need of a theology for a small planet.

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