Tuesday, September 30, 2014

Pythagorean Selfie

Filed under: General — m759 @ 5:01 PM

“Rarely is a TV show as brilliant and as terrible as Selfie .”

Kevin Fallon on a new ABC TV show that starts tonight at 8 PM ET

A recent selfie from Josefine Lyche’s Instagram page:

For some remarks related to Lyche’s pentagram, see
Lyche + Mathmagic* and also yesterday’s Michaelmas Mystery.

In today’s previous post, the late Harvey Cohn posed a question that
he said might have been asked by Pythagoras:

“It is an elementary observation that an integral right triangle
has an even area. Suppose the hypotenuse is prime.

Q.  How do we determine from the prime value of the hypotenuse
when the area is divisible by 4, 8, 16, or any higher power of 2?

A.  We use class fields constructed by means of transcendental
functions, of course!”

— From the preface to Introduction to the Construction of Class Fields ,
by Harvey Cohn (Cambridge University Press, 1985)


For a related song, see Prime Suspect (Dec. 13, 2007).

Footnote of 12:14 AM Oct. 1, 2014 —

* That search yields a link to…

This Lyche webpage’s pentagram  indicates an interest in Disney rather than
in SatanismOther Lyche webpages have been less reassuring.

Related material — Posts tagged Elegantly Packaged.

Pythagoras to Cohn

Filed under: General — m759 @ 1:20 PM

Harvey Cohn on class field theory and a question that might have
been asked by Pythagoras:
IMAGE- Harvey Cohn on class field theory and a question that might have been asked by Pythagoras

See also yesterday’s Michaelmas Mystery and Michaelmas Texts.

Monday, September 29, 2014

Michaelmas Texts

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

This morning’s previous post quoted a sort of
invitation to damnation
from Princeton University Press:

An alternative to damnation:

Michaelmas Mystery

Filed under: General,Geometry — m759 @ 9:30 AM

IMAGE- Pentagram from Arturo Sangalli's novel 'Pythagoras' Revenge'

Some related material in this journal: “Peter J. Cameron” + Magic.

Sunday, September 28, 2014

The Hades Factor

Filed under: General — m759 @ 9:00 PM

Happy birthday to Mira Sorvino.

Related material:

Today’s posts Hitchcockian,  Darkness and Light,
and Requiem for Abse.

Some context for the last of these:

The conclusion of last night’s episode of Intruders .

Requiem for Abse

Filed under: General — m759 @ 7:59 PM

Darkness and Light

Filed under: General — m759 @ 7:01 PM

Click to enlarge.


Filed under: General — m759 @ 12:00 PM

I call it Hitchcockian.

— Helen Mirren on her 2010 film “The Debt

An obituary from BBC News on Sept. 22, 2014:

Israeli Mossad spy Mike Harari dies, aged 87

BBC News did not give a date for the death.

The New York Times  now says that Harari died on Sunday, Sept. 21, 2014.

This journal on that date —

From the BBC America TV series “Intruders,” Season 1, Episode 4,
“Ave Verum Corpus “ (33:34 of 45 min.):

Mira Sorvino pays her respects to a distinguished corpse.


Filed under: General — m759 @ 11:00 AM

Bridge to Alcatraz ('X-Men: The Last Stand')

“… just as God defeats the devil: this bridge exists….” — André Weil

Magneto ('X-Men' series)

The bridge illustration is thanks to Magneto.

Saturday, September 27, 2014

Imaginary Bridge

Filed under: General — m759 @ 5:45 PM

In memory of Nicholas Romanov, who reportedly died on Sept. 15, 2014 (British time).

Frank Rich in a New York Times  book review with online date July 31, 2014:

” The Invisible Bridge  takes its title from a bit of cynical political advice
bestowed on Nixon by Nikita Khrushchev: ‘If the people believe there’s
an imaginary river out there, you don’t tell them there’s no river there.
You build an imaginary bridge over the imaginary river.’ “

The book under review discusses a span of history beginning in 1973.


— Wallace Stevens, Collected Poems

See also Logan and Xavier discussing history at the end of
“X-Men: Days of Future Past.”

Software, Hardware

Filed under: General — m759 @ 12:00 PM

“Pinker’s love for the nuts and bolts of language
(he calls verbs his ‘little friends’)
is equally matched by his appreciation for,
and command of, the way it’s put together,
making him the ideal guide to the subject.”

Laurence Phelan, review of The Stuff of Thought:
Language as a Window into Human Nature ,
by Steven Pinker, in The Independent  on Sunday,
June 22, 2008

“Say hello to my little friend.”

Happy birthday, sweet sixteen.

The Ten

Filed under: General — Tags: — m759 @ 10:20 AM

Ten'll getcha twenty.

Plan B: Books

Filed under: General — m759 @ 9:48 AM

Above: Frank Langella in
Starting Out in the Evening

Right: Johnny Depp in
The Ninth Gate


“One must proceed cautiously, for this road— of truth and falsehood
in the realm of fiction— is riddled with traps and any enticing oasis
is usually a mirage.”

– “Is Fiction the Art of Lying?” by Mario Vargas Llosa,
New York Times  essay of October 7, 1984

For the title plan, see Sisteen in this journal.

Sweet Sixteen

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

Google celebrates its 16th birthday today.

Here are some family values found with its help.

The father-in-law of the late Thomas A. Tombrello
(previous post) was sociologist Robert K. Merton.
See a tribute to Merton by his daughter Stephanie,
Tombrello's widow. See also a Log24 post mentioning
Merton from Oct. 19, 2005. That post leads to a
post from the date of Merton's death, Feb. 23, 2003.

From that 2003 post:

“Her wall is filled with pictures,
She gets ‘em one by one.”

— “Sweet Little Sixteen,” by Chuck Berry
(Chess Records, January 1958)

Diabolically Complex Riddle

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

Steve Chawkins in the Los Angeles Times
Friday, September 26, 2014, 12:09 PM LA time —

"Tom Tombrello, a Caltech physics professor for more than
50 years and an inspiration for freshmen who had to grapple
with diabolically complex riddles to enter his legendary class
on scientific thinking [Physics 11], has died. He was 78.

Tombrello collapsed Tuesday [Sept. 23, 2014] on a bus
between terminals at London's Heathrow airport, his wife,
Stephanie, said. The cause of his death has not yet been determined….

… Tombrello accepted only a handful of students for each year's
session of Physics 11."

How many students is a handful?

Related material from this journal on the day of the professor's death:

Friday, September 26, 2014


Filed under: General — m759 @ 12:00 PM

“You can play things stylishly on the wrong instruments
or unstylishly on the right instruments;
I hope we’ll get it stylish on the right instruments.”

— The late Christopher Hogwood, founder of  the
Academy of Ancient Music

Hogwood reportedly died at his home in Cambridge, England,
on Wednesday, Sept. 24, 2014.

In memoriam—

This journal on Wednesday

The notes of the just intonation major scale:


See also Hogwood on Mozart.


Filed under: General — Tags: — m759 @ 11:30 AM

For T. S. Eliot’s birthday:

“Time present and time past
Are both perhaps present in time future,
And time future contained in time past.
If all time is eternally present
All time is unredeemable.
What might have been is an abstraction
Remaining a perpetual possibility
Only in a world of speculation.
What might have been and what has been
Point to one end, which is always present.”

— Opening passage of  Four Quartets

See also the previous post.

The X-Men Omen

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

Days of Future Past :

Thursday, September 25, 2014

Big Eyes

Filed under: General — m759 @ 7:00 PM

For Amy and Josefine:  Keane .

The 2008 “Perfect Symmetry” album cover illustrated
in the “Keane” search linked to above is by Osang Gwon.


Theology and Art

Filed under: General — m759 @ 12:00 PM

Recommended reading for Josefine Lyche:

See also Ayn Sof (Jan. 7, 2011).


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

"Welcome to America." — Harrison Ford in "The Devil's Own"

America  (current issue):

On readings at Mass on Sunday, Sept. 21, 2014 —

"Isaiah 55:8-9: 'For my thoughts are not your thoughts,
neither are your ways my ways, says the Lord.
For as the heavens are higher than the earth,
so are my ways higher than your ways
and my thoughts than your thoughts.'

The Gospel reading… was a perfect complement to
the passage from Isaiah…."

The America  piece quoting Isaiah was titled "The Mystery of God."

The author "currently works at Xavier College Preparatory
in Palm Desert, CA, where he teaches theology…."

Related material: This  journal that Sunday morning:

See also "The Mystery of God, Part II" —

Other secular stand-ins for "the thing one doesn't know"—
The mysteries of the late Joseph D. McNamara.

Star Wars

Filed under: General — m759 @ 12:16 AM

“Welcome to America.” — Harrison Ford in “The Devil’s Own” (1997)

Wednesday, September 24, 2014

Oslo, 5 A.M.*

Filed under: General — m759 @ 11:00 PM

To thine own selfie be true .

* Title suggested by The Tiffany Puzzle (Dec. 7, 2010).



Filed under: General — m759 @ 8:48 PM

We tell ourselves stories in order to live.
The princess is caged in the consulate.
The man with the candy will lead the children into the sea.
The naked woman on the ledge outside the window
on the sixteenth floor is a victim of accidie, or
the naked woman is an exhibitionist, and it would be
‘interesting’ to know which. We tell ourselves that it makes
some difference whether the naked woman is about to
commit a mortal sin or is about to register a political protest
or is about to be, the Aristophanic view, snatched back to the
human condition by the fireman in priest’s clothing just visible
in the window behind her, the one smiling at the telephoto lens.
We look for the sermon in the suicide, for the social or moral
lesson in the murder of five. We interpret what we see, select
the most workable of the multiple choices. We live entirely,
especially if we are writers, by the imposition of a narrative line
upon disparate images, by the ‘ideas’ with which we have learned
to freeze the shifting phantasmagoria which is our actual

Joan Didion

This evening’s New York Lottery:  659 and 7326.

Variation on a Simple Tune

Filed under: General — Tags: — m759 @ 11:20 AM

The previous post discussed a tune ending in the following
sequence of notes (symbols as in a Wikipedia article):

C#4  B4  A4  E4  G4 .

(This sequence was approximated in that post by integers
representing the relative frequencies of the notes:  5  9  8  6  7 .)

Yesterday’s simple tune may suggest to some a similar refrain:

D4    E4    C4   C3   G3 .

This is, as a helpful page at Ars Nova Software explains,
the theme from “Close Encounters of the Third Kind.”

The notes of the just intonation major scale:

The corresponding ratios from Close Encounters are…

9/8   5/4   1/1   1/2   3/4 , or, in whole numbers, 9  10  8  4  6.

These numbers also correspond, as in yesterday’s post, to the notes

B4  C#5  A4  A3  E4 .

Click the image below to try this on an online keyboard, playing keys

9  10  8  4  6  for Close Encounters.

“And you can tell everybody this is your song…”

Tuesday, September 23, 2014

Simple Tune

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

1  2  3  4  5  9  8  6  7

220 * (1/4) =   55 = A1

220 * (2/4) = 110 = A2

220 * (3/4) = 165 = approximately E3 (164.8)

220 * (4/4) = 220 = A3

220 * (5/4) = 275 = approximately C4/D4 (277.2) 

220 * (6/4) = 330 = approximately E4  (329.6)

220 * (7/4) = 385 = approximately G4  (392.0) 

220 * (8/4) = 440 = A4

220 * (9/4) = 495 = approximately B4  (493.9) 

Exact frequencies (such as 277.2) are from Wikipedia’s Piano key frequencies.

“It may be quite simple, but now that it’s done….

Palm Desert’s Got Talent

Filed under: General — m759 @ 4:59 PM

The film captures the offbeat time warp of the present-day
desert cities around Palm Springs, with the movie being
partly filmed in Palm Desert.”

See also posts on College of the Desert.



Filed under: General — m759 @ 11:00 AM

From AP’s Today in History:

Happy birthday.

“It all adds up.” — Saul Bellow

The Matrix:

Meanwhile, Back at Harvard…

Filed under: General — Tags: — m759 @ 10:18 AM

"William Deresiewicz argued his claim that students of elite universities
are growingly risk-averse, homogeneous, and career-focused with a
panel of faculty members and students on Monday evening.

Hosted by Harvard’s Mahindra Humanities Center, the question-and-
answer-style forum involved a panel…. The panel was moderated by
Homi K. Bhabha, director of the Mahindra Center."

— Alexander H. Patel in today's online Harvard Crimson

See also Con Vocation (Sept. 2, 2014).

Both Hands and an Ass Map

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

Remarks by University Diaries  this morning suggested a search for
Rutgers in this journal. That search yields a post from Dec. 30, 2005,
that is closely related to both this morning's previous post and to recent
Log24 remarks on entities and concrete universals .


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

According to Amazon.com, the first (hardcover) edition of Paranoia ,
by Joseph Finder, the book on which the 2013 film of the same title
was based, was published on January 14, 2004.

Related material — Posts tagged Day 14 in this journal and
the following images from those posts:

Some context — Another 2013 film, Words and Pictures .

Monday, September 22, 2014

The Matrix continues…

Filed under: General — m759 @ 8:15 PM

From the opening credits of the 2013 film “Paranoia,”
a hint that you may have taken the red pill:

(Note the reflection.)

A Holy Cross for Brooklyn

Filed under: General — m759 @ 12:00 PM

Saturday night’s 9  PM post:

“Once again, Harvard defeats Holy Cross.”

That post quoted Joseph Campbell describing a

“… matrix of the cosmic process, whether in the macrocosm
or in a microcosmic field of manifestation.”

Related material —


Microcosmic field of manifestation:


Filed under: General,Geometry — Tags: — m759 @ 11:17 AM

Review of an image from a post of May 6, 2009:

Galois space of six dimensions represented in Euclidean spaces of three and of two dimensions

Sunday, September 21, 2014

Saturday-Morning Concept

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

Why Is Our Sci-Fi So Glum About A.I.?,”
by Jayson Greene, NY Times Sunday Magazine  today —

“You come to pity these advanced beings, bumping against
the dunderheaded constraints that their less-advanced
creators have placed on them. Johansson’s Lucy grows so
powerful as her cerebral capacity multiplies that she is able
to manipulate her cellular structure. And yet, when pursued
by an entire planet’s worth of law enforcement, she settles
on a disguise straight out of Saturday-morning cartoons —
really big sunglasses and a hairdo change.”

See also this  journal on Saturday morning for a definition, and
Geometry of the I Ching for examples, of

changeable, instantiable entities, i.e., concrete universals.

Above the entrance to Plato's Academy: AGEOMETRETOS MEDEIS EISITO


Filed under: General — m759 @ 12:31 PM

Plan 9 continues…

“The number 9… relates traditionally to
the Great Goddess of Many Names (Devi,
Inanna, Ishtar, Astarte, Artemis, Venus, etc.)….”

Joseph Campbell, The Inner Reaches of Outer Space

From the BBC America TV series “Intruders,” Season 1, Episode 4,
Ave Verum Corpus   (33:34 of 45 min.):

Mira Sorvino pays her respects to a distinguished corpse.

(Aired Saturday 10:00 PM Sept. 13, 2014, on BBC America.)

See also Frankie Valli’s hymn  from A Capitol Fourth this year.


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

The previous post discussed the anatomy of the sum 9 + 6.

A different approach:  “A” and “The 6 spreads in A” below —

Uncommon Noncore

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

This post was suggested by Greg Gutfeld’s Sept. 4 remarks on Common Core math.

Problem: What is 9 + 6 ?

Here are two approaches suggested by illustrations of Desargues’s theorem.

Solution 1:

9 + 6 = 10 + 5,
as in Common Core (or, more simply, as in common sense), and
10 + 5 = 5 + 10 = 15 as in Veblen and Young:

Solution 2:

In the figure below,
9 + 6 = no. of  V’s + no. of  A’s + no. of C’s =
no. of nonempty squares = 16 – 1 = 15.
(Illustration from Feb. 10, 2014.)

The silly educationists’ “partner, anchor, decompose” jargon
discussed by Gutfeld was their attempt to explain “9 + 6 = 10 + 5.”

As he said of the jargon, “That’s not math, that’s the plot from ‘Silence of the Lambs.'”

Or from Richard, Frank, and Marcus in last night’s “Intruders”
(BBC America, 10 PM).

Saturday, September 20, 2014


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

Once again, Harvard defeats Holy Cross.

IMAGE- Joseph Campbell, 'The Inner Reaches of Outer Space,' meditation on the number nine, the Goddess, and the Angelus

See also a related remark by Norman Mailer, and Plan 9 in this journal.

Presumably the Holy Cross defeat will please art theorist Rosalind Krauss (below).

(Click to enlarge.)


Filed under: General — m759 @ 8:00 PM

See “Seven is Heaven, Eight is a Gate” in this journal.

For greater detail, see “Seven is Heaven” and “Eight is a Gate” separately.


Filed under: General — m759 @ 7:01 PM

Google News at 7:

* The title refers to Tom Stoppard’s “lying rhyme” .

Plato’s Ghosts

Filed under: General — m759 @ 6:00 PM

The previous post, “Ennead Boo,” refers indirectly to
a passage from Pindar in Plato’s Meno :

See also posts from nine years ago
on the death of director Robert Wise.

Ennead Boo

Filed under: General — m759 @ 12:00 PM

A search in this journal for Yahoo Entities ended with a link to another
Log24 search, Nine Years, which in turn suggested…

A scene from the current TV series “Intruders
(Season 1, Episode 1, at 9:22 of 45 min.)

Symplectic Structure

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


The fictional zero theorem  of Terry Gilliam's current film
by that name should not be confused with the zero system
underlying the diamond theorem.

The Metaphysics of Entities

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

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

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

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

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

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

From pages 182-183 —

13.2 The nature of mathematical entities

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

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

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

Friday, September 19, 2014

Metaphysics for Gilliam

Filed under: General — m759 @ 9:29 PM

See also…

Related remarks: Diederik Aerts at arXiv.org.

See also Aerts (as above) on the metaphysics of entities  (1984):

Song of Praise

Filed under: General — m759 @ 7:45 PM

“Robust and compact, conforming to international standards,
the Altivar 08 is a universal product.”


Filed under: General — m759 @ 12:00 PM

Bill Ayers on Megyn Kelly, and her reply.

Thursday, September 18, 2014

Them Apples

Filed under: General — m759 @ 12:00 PM

John Baez at Google+ has an interesting post on crackpots,
dated September 13, 2014.

Related recent material from this  journal:

Sense (Sept. 13) and Sensibility (Sept. 14 and later).

See also a New York Times  piece from 2009:

Related material:

An Apple for Devlin and

“You don’t need to eat a whole apple to know it’s rotten.”
Warren Siegel

Wednesday, September 17, 2014

Raiders of the Lost Articulation

Tom Hanks as Indiana Langdon in Raiders of the Lost Articulation :

An unarticulated (but colored) cube:

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

A 2x2x2 articulated cube:

IMAGE- Eightfold cube with detail of triskelion structure

A 4x4x4 articulated cube built from subcubes like
the one viewed by Tom Hanks above:

Image-- Solomon's Cube

Solomon’s Cube

A Raid on the Inarticulate

Filed under: General — Tags: , — m759 @ 6:00 PM

                                “… And so each venture
Is a new beginning, a raid on the inarticulate….”

— T. S. Eliot, “East Coker V” in Four Quartets


Filed under: General — Tags: — m759 @ 11:32 AM

The Horse

Filed under: General — Tags: — m759 @ 10:23 AM

A New York Times  piece today on author Donald Antrim:

“The next project is a novel ‘about’ (having loosely to do with)
his father, Harry, a T. S. Eliot scholar who wrote a well-regarded
monograph on the poet.”

— John Jeremiah Sullivan

From Harry T. Antrim’s 1967 thesis on Eliot:

“That words can be made to reach across the void
left by the disappearance of God (and hence of all
Absolutes) and thereby reestablish some basis of
relation with forms existing outside the subjective
and ego-centered self has been one of the chief
concerns of the first half of the twentieth century.”

An epigraph selected by Sullivan for a 2002 Harper’s Magazine
article, “Horseman, Pass By“—

Far back, far back in our dark soul
the horse prances.

— D. H. Lawrence

A related image from pure mathematics
(a source of Absolutes unrelated to theology):

See April 9, 2004, for a post on the “Horseman” article.

Tuesday, September 16, 2014

Plan 9

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

(Continued from St. Augustine's Day, 2012)

"Plan 9 deals with the resurrection of the dead."

Epigraph to "No Great Magic," a story by Fritz Leiber:

 To bring the dead to life
Is no great magic.
Few are wholly dead:
Blow on a dead man’s embers
And a live flame will start.


Outside Space and Time

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

The title phrase appears in today's noon post and also
in a post of October 29, 2007, 'Home from Home.'

Point of Reference

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

A note from the director of the 2014 Scarlett Johansson film Lucy :

Revised version of a post of February 9, 2006, with links repaired:

Space, Time, and Scarlett


From last night’s Grammy awards, lyrics:

“a place where there’s no space or time”
– Leon Russell

Aguilera's version wasn't bad, but …

The image “http://www.log24.com/log/pix06/060209-Blondes.jpg” cannot be displayed, because it contains errors.

“Scarlett Johansson does this ‘old Hollywood glam’ look
much better.”

For a reference to the place described in Russell’s lyrics,
see the riff on the number “265″ linked to in last night’s
Midnight in the Garden of the Soul.”

The "point of reference" outside space and time
in the 2006 Johansson post above is of course "265."

For Plato's remarks at this reference point, see Phaedrus
265d and 265e in this morning's post.

Where the Joints Are

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

An image related to the recent posts Sense and Sensibility:

A quote from yesterday's post The Eight:

A possible source for the above phrase about phenomena "carved at their joints":

See also the carving at the joints of Plato's diamond from the Meno :

Image-- Plato's diamond and a modern version from finite geometry

Related material: Phaedrus on Kant as a diamond cutter
in Zen and the Art of Motorcycle Maintenance .

Monday, September 15, 2014

Lucy Meets Kant

Filed under: General — m759 @ 8:01 PM

“Towards the sticky end of a summer of films based on toys, comic-books
and other films, here, at last, is a film based on the Kantian model of
transcendental idealism.

In his 1781 page-turner, the Critique of Pure Reason , the German
philosopher Immanuel Kant warned that the human brain, in its
pinky-grey feebleness, has to rattle the world into an order
it doesn’t possess purely to make sense of it. Otherwise, as Kant snappily
puts it, ‘all constitution, all relations of objects in space and time, indeed
space and time themselves, would disappear.'”

— Robbie Collin, review of the 2014 film Lucy

IMAGE- Log24 post on Scarlett Johansson, space, time, and jazz

The Eight

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

The image at the end of today’s previous post A Seventh Seal
suggests a review of posts on Katherine Neville’s The Eight .

Update of 1:25 PM ET on Sept. 15, 2014:

Neville’s longtime partner is neurosurgeon and cognitive theorist
Karl H. Pribram. A quote from one of his books:

See also Sense and Sensibility.

A Seventh Seal

Filed under: General,Geometry — m759 @ 10:00 AM

This post was suggested by the two previous posts, Sermon and Structure.

IMAGE- Epigraph to Ch. 7 of Cameron's 'Parallelisms of Complete Designs'- '...fiddle with pentagrams...' from 'Four Quartets'

Vide  below the final paragraph— in Chapter 7— of Cameron’s Parallelisms ,
as well as Baudelaire in the post Correspondences :

Comme de longs échos qui de loin se confondent
Dans une ténébreuse et profonde unité….

— Baudelaire, “Correspondances “

A related image search (click to enlarge):

Sunday, September 14, 2014


Filed under: General — Tags: — m759 @ 6:00 PM

In memory of cartoonist Tony Auth, who reportedly died today

From a Saturday evening post:

“A simple grid structure makes both evolutionary and developmental sense.”

From a post of June 22, 2003:


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

Epigraphs from Parallelisms of Complete Designs
by Peter J. Cameron (Cambridge University Press, 1976)

Through the unknown, remembered gate
When the last of earth left to discover
Is that which was the beginning
(T. S. Eliot: Little Gidding)

I  The existence theorem
Here the impossible union
Of spheres of existence is actual
(T. S. Eliot: The Dry Salvages)

II  The parallelogram property
A condition of complete simplicity
(Costing not less than everything)
(T. S. Eliot: Little Gidding)

III  Steiner points and Veblen points
You say I am repeating
Something I have said before. I shall say it again.
Shall I say it again?
(T. S. Eliot: East Coker)

IV  Edge-colourings of complete graphs
And hollyhocks that aim too high
Red into grey and tumble down
(T. S. Eliot: East Coker)

V  Biplanes and metric regularity
Two and two, necessarye conjunction,
Holding eche other by the hand or the arm
Whiche betokeneth concorde.
(T. S. Eliot: East Coker)

VI  Automorphism groups
At the still point of the turning world. Neither flesh nor fleshless;
Neither from nor towards; at the still point, there the dance is,
But neither arrest nor movement.
(T. S. Eliot: Burnt Norton)

VII  Resolutions and partition systems
… fiddle with pentagrams
Or barbituric acids, or dissect
The recurrent image into pre-conscious terrors .. .
(T. S. Eliot: The Dry Salvages)


Filed under: General,Geometry — Tags: , — m759 @ 9:26 AM

Structured gray matter:

Graphic symmetries of Galois space:
IMAGE - The Diamond Theorem

The reason for these graphic symmetries in affine  Galois space —

symmetries of the underlying projective  Galois space:

Saturday, September 13, 2014


Filed under: General — Tags: — m759 @ 9:09 PM

“A simple grid structure makes both evolutionary and developmental sense.”

— Van Wedeen, MD, of the Martinos Center for Biomedical Imaging at
Massachusetts General Hospital, Science Daily , March 29, 2012

Friday, September 12, 2014

Bee Season

Filed under: General — m759 @ 12:00 PM

Spell the name of the race of intelligent horses in Gulliver’s Travels .

Scarlett Johansson and friend in 'The Horse Whisperer'

Scarlett Johansson and friend in “The Horse Whisperer” (1998)

Some context: “Bee Season” in this journal.

A Poet’s Word

Filed under: General — m759 @ 11:29 AM

The White Goddess link in the previous post led to, among other things,
a discussion of “Yahoo” as a poet’s word.

Another poet’s word: Davos.

Sunnyvale News

Filed under: General — m759 @ 7:11 AM

See a TIME story from yesterday:

IMAGE- Photo of Sunnyvale, California, building dated May 13, 2014

See also a post from the above date:

Friday, May 23, 2014

She  Meets Her

Filed under: Uncategorized — m759 @ 2:01 PM

She :

The White Goddess in this journal.

Her :

“Eventually we see snow particles….”
— Screenplay by Spike Jonze

Thursday, September 11, 2014


Filed under: General — Tags: — m759 @ 10:28 PM

Part I

Image- Josefine Lyche's work (with 1986 figures by Cullinane) in a 2009 exhibition in Oslo

Part II

Part III


Filed under: General — Tags: — m759 @ 5:35 PM

Blackboard Jungle , 1955 —

IMAGE- Richard Kiley in 'Blackboard Jungle,' with grids and broken records

Today's online Harvard Crimson :

Harvard Crimson, 9/11/2014: 'CS50 Logs Record-Breaking Enrollment Numbers,' by Meg P. Bernhard, Crimson Staff Writer

Oh, Moon of Alabama

Filed under: General — Tags: — m759 @ 11:09 AM

The mention of Gauss in today's previous post, along with
recent news, suggested this post.

"How do you  get young people excited about space?"

— Megan Garber in The Atlantic , Aug. 16, 2012

Further details:  Child Buyers (July 16, 2013).

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."

Tuesday, September 9, 2014

In Memoriam

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

For Loren D. Olson, Harvard '64:

"Even 50 years later, I remember his enthusiasm for a very young
and very gifted Harvard professor named Shlomo Sternberg, one
of whose special areas of interest was Lie groups. I still have no real
understanding of what a Lie group is, but not for want of trying on
Loren’s part. Loren was also quite interested in the thinking of the
theologians Paul Tillich and Reinhold Niebuhr, who were then at
Harvard. He attended some of their lectures, read several of their
books, and enjoyed discussing their ideas."

Harvard classmate David Jackson

See also today's previous post.

Smoke and Mirrors

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

This post is continued from a March 12, 2013, post titled
"Smoke and Mirrors" on art in Tromsø, Norway, and from
a June 22, 2014, post on the nineteenth-century 
mathematicians Rosenhain and Göpel.

The latter day was the day of death for 
mathematician Loren D. Olson, Harvard '64.

For some background on that June 22 post, see the tag 
Rosenhain and Göpel in this journal.

Some background on Olson, who taught at the
University of Tromsø, from the American Mathematical
Society yesterday:

Olson died not long after attending the 50th reunion of the
Harvard Class of 1964.

For another connection between that class (also my own) 
and Tromsø, see posts tagged "Elegantly Packaged."
This phrase was taken from today's (print) 
New York Times  review of a new play titled "Smoke."
The phrase refers here  to the following "package" for 
some mathematical objects that were named after 
Rosenhain and Göpel — a 4×4 array —

For the way these objects were packaged within the array
in 1905 by British mathematician R. W. H. T. Hudson, see
a page at finitegometry.org/sc. For the connection to the art 
in Tromsø mentioned above, see the diamond theorem.

Monday, September 8, 2014

The Service

Filed under: General — m759 @ 9:11 AM

The service is described as as a dating app for the elite….”

For examples of dating, see The Date and August 16, 2014.

See also…

A Last Wish

Filed under: General — m759 @ 7:59 AM

“I want Harry Winston to make me a toe tag.” — Joan Rivers

See also this journal on the above date, 24 March 2009: The Child Trap.

Sunday, September 7, 2014

Sunday School

Filed under: General — Tags: — m759 @ 8:28 AM

In memory of Joan Rivers

Heaven's Gate

This post was suggested by the previous post‘s quote

“the subject’s desires are scripted and orchestrated
by an unconscious fundamental fantasy,”

and by one of my favorite musical fantasies:

Melanie – Brand New Key (’71) .

Academics may prefer the following —

Susanne K. Langer,'Philosophy in a New Key'

Saturday, September 6, 2014

Plato Thanks the Academy

Filed under: General — m759 @ 9:00 PM


Plato at Stanford:
Lacan and the Matheme of Fantasy

“… [in] the matheme of fantasy ($ ◊ ),
the diamond-shaped “lozenge” (poinçon )
can be read as a condensation of four symbols:
one, (the logical symbol for conjunction [“and”]);
two, (the logical symbol for disjunction [“or”]);
three, > (the mathematical symbol for “greater than”); and,
four, < (the mathematical symbol for “less than”). As per
Lacan’s matheme, the subject’s desires are scripted and
orchestrated by an unconscious fundamental fantasy
in which the desiring subject ($) is positioned in relation to
its corresponding object-cause of desire ( ).”

— plato.stanford.edu, Stanford Encyclopedia of Philosophy

Plato.stanford.edu on Lacan, and Halle Berry in 'Frankie and Alice'

The Stanford author: 

The author is a professor in Albuquerque.
For other perspectives, see that city in this journal.

For the film  authors, see IMDb.

Roll Credits…

Filed under: General — m759 @ 1:00 PM

for Operation Lightfoot .



YouTube ending credits for 'Exorcist III'

But Seriously…

Filed under: General — Tags: — m759 @ 10:55 AM

The previous post, Infinite Jest, suggests
a midrash on “–1/12” (i.e., minus one-twelfth):


Infinite Jest

Filed under: General,Geometry — Tags: , — m759 @ 9:18 AM

“1 + 2 + 3 + … = –1/12.”

Keith Devlin, Sept. 2, 2014

Robin Williams at Bunker Hill Community College

Robin Williams and the Stages of Math

i)   shock & denial
ii)  anger
iii) bargaining
iv) depression
v)  acceptance

And then…

vi)  checking
vii) Joan Rivers:

Mathematics and Art: Totentanz from Seventh Seal

Friday, September 5, 2014


Filed under: General — Tags: — m759 @ 9:16 AM

The date at the end of yesterday’s noon post was May 25, 2010.
This, together with Keith Devlin’s Twitter page today, suggests
a review of that date.

Res ipsa loquitur.

Thursday, September 4, 2014

Halloween Manifestos, 2013:

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

Here and at Catholics for Classical Education.

See also Tom Wolfe on manifestos —

Wolfe on manifestos in 'From Bauhaus to Our House'

— and part of an interesting Sept. 2, 2014, manifesto by
Common Core supporter Keith Devlin:

“Graduate students of mathematics are introduced to further
assumptions (about handling the infinite, and various other issues),
equally reasonable and useful, and in accord both with our everyday
intuitions (insofar as they are relevant) and with the rest of
mainstream mathematics. And on the basis of those assumptions,
you can prove that

1 + 2 + 3 + … = –1/12.

That’s right, the sum of all the natural numbers equals –1/12.

This result is so much in-your-face, that people whose mathematics
education stopped at the undergraduate level (if they got that far)
typically say it is wrong. It’s not. Just as with the 0.999… example,
where we had to construct a proper meaning for an infinite decimal
expansion before we could determine what its value is, so to we
have to define what that infinite sum means. ….”

For a correction to Devlin’s remarks, see a physics professor’s weblog post —

“From a strictly mathematical point of view,
the equation 1+2+3+4+ … = -1/12 is incorrect,
and involves confusing the Dirichlet series with
the zeta function.”  — Greg Gbur, May 25, 2010

Wednesday, September 3, 2014

Place, Time, Matter

Filed under: General — m759 @ 6:00 PM

Image and Logic, Part Deux

Filed under: General — m759 @ 12:00 PM

The title refers to the previous post.

Click image for some context.
For further context, see some
mathematics from Halloween 1978.

See also May 12, 2014.

Tuesday, September 2, 2014

Image and Logic

Filed under: General — m759 @ 7:59 AM

This morning’s previous post may be regarded as an example of
the Harvard Business School’s “case system.”

A search for this topic yields another example:

Harvard professor Peter Galison discusses the case system’s
origin at Harvard Law School in his book Image and Logic:
A Material Culture of Microphysics

No Image, No Logic

(Click to enlarge.)

Con Vocation

Filed under: General — Tags: , — m759 @ 7:09 AM

Con Vocation

A Case in Point — Discuss:

Monday, September 1, 2014

Mathematics, Not Theology

Filed under: General — Tags: — m759 @ 5:00 PM


“A set having three members is a single thing
wholly constituted by its members but distinct from them.
After this, the theological doctrine of the Trinity as
‘three in one’ should be child’s play.”

— Max Black, Caveats and Critiques: Philosophical Essays
in Language, Logic, and Art
 , Cornell U. Press, 1975

IMAGE- The Trinity of Max Black (a 3-set, with its eight subsets arranged in a Hasse diagram that is also a cube)

“There is  such a thing as a three-set.”
— Saying adapted from a novel by Madeleine L’Engle

Bone-Clock Intruders

Filed under: General — m759 @ 9:00 AM

“For those who like this sort of thing,
this is the sort of thing they like.”

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