Thursday, September 18, 2014

Them Apples

Filed under: Uncategorized — 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

Filed under: Uncategorized — Tags: — m759 @ 6:14 PM

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: Uncategorized — 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: Uncategorized — m759 @ 11:32 AM

The Horse

Filed under: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — m759 @ 5:35 PM

#tbt: 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — m759 @ 8:28 AM

In memory of Joan Rivers

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: Uncategorized — 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: Uncategorized — m759 @ 1:00 PM

for Operation Lightfoot .



YouTube ending credits for 'Exorcist III'

But Seriously…

Filed under: Uncategorized — m759 @ 10:55 AM

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


Infinite Jest

Filed under: Uncategorized — 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: Uncategorized — 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: Uncategorized — 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: Uncategorized — m759 @ 6:00 PM

Image and Logic, Part Deux

Filed under: Uncategorized — 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: Uncategorized — 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: Uncategorized — m759 @ 7:09 AM

A Case in Point — Discuss:

Monday, September 1, 2014

Mathematics, Not Theology

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

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

Sunday, August 31, 2014

Sunday School

Filed under: Uncategorized — m759 @ 9:00 AM

The Folding

Cynthia Zarin in The New Yorker , issue dated April 12, 2004—

“Time, for L’Engle, is accordion-pleated. She elaborated,
‘When you bring a sheet off the line, you can’t handle it
until it’s folded, and in a sense, I think, the universe can’t
exist until it’s folded — or it’s a story without a book.’”

The geometry of the 4×4 square array is that of the
3-dimensional projective Galois space PG(3,2).

This space occurs, notably, in the Miracle Octad Generator (MOG)
of R. T. Curtis (submitted to Math. Proc. Camb. Phil. Soc.  on
15 June 1974).  Curtis did not, however, describe its geometric
properties. For these, see the Cullinane diamond theorem.

Some history: 

Curtis seems to have obtained the 4×4 space by permuting,
then “folding” 1×8 binary sequences into 4×2 binary arrays.
The original 1×8 sequences came from the method of Turyn
(1967) described by van Lint in his book Coding Theory
(Springer Lecture Notes in Mathematics, No. 201 , first edition
published in 1971). Two 4×2 arrays form each 4×4 square array
within the MOG. This construction did not suggest any discussion
of the geometric properties of the square arrays.

[Rewritten for clarity on Sept. 3, 2014.]

Saturday, August 30, 2014

Physics and Theology

Filed under: Uncategorized — m759 @ 7:00 PM

The titles of the previous three posts refer to
Hermann Weyl’s 1918 book Raum, Zeit, Materie
(Space, Time, Matter).

This suggests a look at a poetically parallel 1950 title —
The Lion, the Witch and the Wardrobe —
and at its underlying philosophy:

I am among “those who do not know that this great myth became Fact.”
I do, however, note that some other odd things have become fact.
Those who wish more on this topic may consult:

Friday, August 29, 2014


Filed under: Uncategorized — m759 @ 9:29 AM

(A sequel to Raum  and  Zeit )

See also Christmas Eve, 2012.

“It’s going to be accomplished
in steps, this establishment
of the talented….”

To Ride Pegasus , by
Anne McCaffrey (Radcliffe ’47)


Filed under: Uncategorized — m759 @ 8:25 AM

( A sequel to Raum )

The author reportedly died on August 14, 2014. See a post from that date.


Filed under: Uncategorized — m759 @ 8:00 AM

A possible answer to the 1923 question of Walter Gropius, “Was ist Raum?“—

See also yesterday’s Source of the Finite and the image search
on the Gropius question in last night’s post.

Thursday, August 28, 2014

Brutalism Revisited

Filed under: Uncategorized — m759 @ 11:59 PM

Yesterday’s 11 AM post was a requiem for a brutalist architect.

Today’s LA Times  has a related obituary:

“Architectural historian Alan Hess, who has written several books on
Mid-Century Modern design, said Meyer didn’t have a signature style,
‘which is one reason he is not as well-known as some other architects
of the period. But whatever style he was working in, he brought a real
sense of quality to his buildings.’

A notable example is another bank building, at South Beverly Drive
and Pico Boulevard, with massive concrete columns, a hallmark of
the New Brutalism style. ‘This is a really good example of it,’ Hess said.”

— David Colker, 5:43 PM LA time, Aug. 28, 2014

A related search, suggested by this morning’s post Source of the Finite:

(Click to enlarge.)

Source of the Finite

Filed under: Uncategorized — m759 @ 10:20 AM

“Die Unendlichkeit  ist die uranfängliche Tatsache: es wäre nur
zu erklären, woher das Endliche  stamme….”

— Friedrich Nietzsche, Das Philosophenbuch/Le livre du philosophe
(Paris: Aubier-Flammarion, 1969), fragment 120, p. 118

Cited as above, and translated as “Infinity is the original fact;
what has to be explained is the source of the finite….” in
The Production of Space , by Henri Lefebvre. (Oxford: Blackwell,
1991 (1974)), p.  181.

This quotation was suggested by the Bauhaus-related phrase
“the laws of cubical space” (see yesterday’s Schau der Gestalt )
and by the laws of cubical space discussed in the webpage
Cube Space, 1984-2003.

For a less rigorous approach to space at the Harvard Graduate
School of Design, see earlier references to Lefebvre in this journal.

Wednesday, August 27, 2014

Not Quite

Filed under: Uncategorized — m759 @ 12:00 PM

Click image to enlarge.


Filed under: Uncategorized — m759 @ 11:00 AM

“To every man upon this earth,
Death cometh soon or late.
And how can man die better
Than facing fearful odds,
For the ashes of his fathers,
and the temples of his gods…?”

— Macaulay, quoted in the April 2013 film “Oblivion

“Leave a space.” — Tom Stoppard, “Jumpers”

Related material: The August 16, 2014, sudden death in Scotland
of an architect of the above Cardross seminary, and a Log24 post,
Plato’s Logos, from the date of the above photo: June 26, 2010.

See also…

IMAGE- T. Lux Feininger on 'Gestaltung'

Here “eidolon” should instead be “eidos .”

An example of eidos — Plato’s diamond (from the Meno ) —


Schau der Gestalt

Filed under: Uncategorized — m759 @ 5:01 AM

(Continued from Aug. 19, 2014)

“Christian contemplation is the opposite
of distanced consideration of an image:
as Paul says, it is the metamorphosis of
the beholder into the image he beholds
(2 Cor 3.18), the ‘realisation’ of what the
image expresses (Newman). This is
possible only by giving up one’s own
standards and being assimilated to the
dimensions of the image.”

— Hans Urs von Balthasar,
The Glory of the Lord:
A Theological Aesthetics,

Vol. I: Seeing the Form
[ Schau der Gestalt ],
Ignatius Press, 1982, p. 485

A Bauhaus approach to Schau der Gestalt :

I prefer the I Ching ‘s approach to the laws of cubical space.

Tuesday, August 26, 2014

Le Pianiste

Filed under: Uncategorized — m759 @ 12:00 PM

Bryan Cranston won an Emmy for lead actor in a drama series Monday…”

“Tu es le pianiste….” — Log24 post 641

Lux et Veritas

Filed under: Uncategorized — m759 @ 7:59 AM

Omega by Lux:

Omega by Curtis:

Exotic Sphere

Filed under: Uncategorized — m759 @ 1:00 AM

Two images from posts tagged ‘Objects of Beauty‘ —

“And be these juggling fiends no more believed,
That palter with us in a double sense….”


Filed under: Uncategorized — m759 @ 12:25 AM

Related material:  March 20, 2013.

Monday, August 25, 2014

A Challenging Story:

Filed under: Uncategorized — m759 @ 11:30 PM

Symplectic Macbeth

Lead on, McDuff:

Plato Thanks the Academy

Filed under: Uncategorized — m759 @ 12:00 AM


See Shadowlands in this journal.
The film so titled was directed by Richard Attenborough,
President of the Royal Academy of Dramatic Art,
who reportedly died on Sunday, August 24, 2014.

It’s all in Plato, all in Plato:
bless me, what do  they
teach them at these schools!”
— C. S. Lewis

Sunday, August 24, 2014

Richard Attenborough

Filed under: Uncategorized — m759 @ 11:30 PM

Richard Samuel Attenborough, Baron AttenboroughCBE
… 29 August 1923 – 24 August 2014) was an English actor,
film director, producer and entrepreneur. He was the President of
Royal Academy of Dramatic Art (RADA).” — Wikipedia

Symplectic Structure…

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

In the Miracle Octad Generator (MOG):

The above details from a one-page note of April 26, 1986, refer to the
Miracle Octad Generator of R. T. Curtis, as it was published in 1976:


From R. T. Curtis (1976). A new combinatorial approach to M24,
Mathematical Proceedings of the Cambridge Philosophical Society ,
79, pp 25-42. doi:10.1017/S0305004100052075.

The 1986 note assumed that the reader would be able to supply, from the
MOG itself, the missing top row of each heavy brick.

Note that the interchange of the two squares in the top row of each
heavy brick induces the diamond-theorem correlation.

Note also that the 20 pictured 3-subsets of a 6-set in the 1986 note
occur as paired complements  in two pictures, each showing 10 of the

This pair of pictures corresponds to the 20 Rosenhain tetrads  among
the 35 lines of PG(3,2), while the picture showing the 2-subsets
corresponds to the 15 Göpel tetrads  among the 35 lines.

See Rosenhain and Göpel tetrads in PG(3,2). Some further background:

The Blue Path

Filed under: Uncategorized — m759 @ 2:56 AM

A song for those who prefer the red path: Abracadabra.

IMAGE- Abracadabra 4x6

Saturday, August 23, 2014


Filed under: Uncategorized — m759 @ 8:16 PM



Roman numeral I
as well as capital I

(Not signifying nothing.)

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