Log24

Wednesday, January 24, 2018

The Pentagram Papers

Filed under: General,Geometry — Tags: — m759 @ 12:40 PM

(Continued)

From a Log24 post of March 4, 2008 —

SINGER, ISAAC:
"Are Children the Ultimate Literary Critics?"
— Top of the News 29 (Nov. 1972): 32-36.

"Sets forth his own aims in writing for children and laments
'slice of life' and chaos in children's literature. Maintains that
children like good plots, logic, and clarity, and that they
have a concern for 'so-called eternal questions.'"

— An Annotated Listing of Criticism
by Linnea Hendrickson

"She returned the smile, then looked across the room to
her youngest brother, Charles Wallace, and to their father,
who were deep in concentration, bent over the model
they were building of a tesseract: the square squared,
and squared again: a construction of the dimension of time."

— A Swiftly Tilting Planet,
by Madeleine L'Engle

Cover of 'A Swiftly Tilting Planet' and picture of tesseract

For "the dimension of time," see A Fold in TimeTime Fold,
and Diamond Theory in 1937

A Swiftly Tilting Planet  is a fantasy for children 
set partly in Vespugia, a fictional country bordered by
Chile and Argentina.

Ibid.

The pen's point:

Wm. F. Buckley as Archimedes, moving the world with a giant pen as lever. The pen's point is applied to southern South America.
John Trever, Albuquerque Journal, 2/29/08

Note the figure on the cover of National Review  above —

A related figure from Pentagram Design

See, more generally,  Isaac Singer  in this  journal.

Friday, January 19, 2018

The Pentagram Papers

Filed under: General — Tags: — m759 @ 11:45 AM

(Continued)

Jodie Foster in  a Dec. 15, 2017, sketch  with Stephen Colbert —

"People invest in and take ownership of brands,
and they wonder why the brand didn’t
ask their permission to change."

— Michael Bierut of Pentagram Design
in  a Design Week  article  of Jan. 17, 2018

Tuesday, January 16, 2018

The Pentagram Papers

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

Other intersection-points-counting material —

The Finkelstein Talisman:

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

See also Hanks + Cube in this journal —

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

Friday, September 16, 2016

Wittgenstein’s Pentagram

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

Related material —

See the story of a British man who reportedly had a doctorate in
physics and mathematics and became a witchcraft enthusiast.
He is said to have died at 85 on September 11, 2016.

As Wittgenstein noted, it is not always clear whether the pentagram
expresses a mathematical or an experiential proposition.

For some mathematical propositions related to the pentagram,
see (for instance) John Baez's slides for his 2008 Glasgow
lecture on the number 5.

For som experiential propositions, see Pentagram in this journal.

Thursday, November 8, 2018

Geometry Lesson

Filed under: G-Notes,General,Geometry — Tags: — m759 @ 12:00 AM

From "The Trials of Device" (April 24, 2017) —

Wittgenstein's pentagram and 4x4 'counting-pattern'

Pentagon with pentagram    

See also Wittgenstein in a search for "Ein Kampf " in this journal.

Saturday, February 24, 2018

The Ugly Duck

Filed under: General,Geometry — m759 @ 7:11 PM

"What of the night
That lights and dims the stars?
Do you know, Hans Christian,
Now that you see the night?"

— The concluding lines of
"Sonatina to Hans Christian,"
by Wallace Stevens
(in Harmonium  (second edition, 1931))

From "Mathmagic Land" (May 22, 2015)

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

From "The Trials of Device" (April 24, 2017)

Wittgenstein's pentagram and 4x4 'counting-pattern'

Pentagon with pentagram    

Friday, January 19, 2018

Details

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

Wednesday, January 17, 2018

At Heaven’s Gate

Filed under: General — Tags: — m759 @ 7:30 AM

(Continued from September 12, 2005)

The previous post contrasted the number-triple 11-7-8 below
with number triples 12-9-5 and 12-5-9.

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

A perhaps more logical counterpart of the triple 11-7-8, based
on opposite  locations of star-points or cube-edges, is
the triple 9-12-5. For a theological interpretation, see 9/12/05.

Tuesday, January 16, 2018

An Orison for Ha-Why

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

'Cloud Atlas' book cover illustrating the film

Lines from characters played in the film by Tom Hanks and Halle Berry —

— Cloud Atlas , by David Mitchell (2004).

An orison of sorts from a post on Martin Scorsese's
birthday, Sunday, Nov. 18, 2007 —

BlackBerry with pictures from Log24

Displayed on the BlackBerry are parts
of Log24 posts from October 25, 2007,
and October 24, 2007.

Related pattern geometry 

From a Log24 search for Angleton + Brotherhood:
A photo of Angleton in a post from 12/9/5

The image “http://www.log24.com/log/pix05B/051209-Angleton.jpg” cannot be displayed, because it contains errors.

From a post of 11/7/8

http://www.log24.com/log/pix08A/081107-Tilespuzzle.jpg

A cryptic note for Dan Brown:

The above dates 11/7/8 and 12/9/5 correspond to the corner-labels
(read clockwise and counter-clockwise) of the two large triangles
in the Finkelstein Talisman

Magic cube and corresponding hexagram, or Star of David, with faces mapped to lines and edges mapped to points

Above: More symbology for Tom Hanks from
this morning's post The Pentagram Papers.

The above symbology is perhaps better suited to Hanks in his
role as Forrest Gump than in his current role as Ben Bradlee.

The image “http://www.log24.com/log/pix05B/051211-gump.jpg” cannot be displayed, because it contains errors.

For Hanks as Dan Brown's Harvard symbologist 
Robert Langdon, see the interpretation 12/5/9, rather
than 12/9/5, of the above triangle/cube-corner label.

Saturday, September 2, 2017

Knight Moves

Filed under: General — m759 @ 12:42 PM

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

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

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

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

See as well a search for 1962 in this journal.

Wednesday, April 26, 2017

A Tale Unfolded

Filed under: General,Geometry — Tags: , , — m759 @ 2:00 AM

A sketch, adapted tonight from Girl Scouts of Palo Alto

From the April 14 noon post High Concept

From the April 14 3 AM post Hudson and Finite Geometry

IMAGE- Geometry of the Six-Set, Steven H. Cullinane, April 23, 2013

From the April 24 evening post The Trials of Device

Pentagon with pentagram    

Note that Hudson's 1905 "unfolding" of even and odd puts even on top of
the square array, but my own 2013 unfolding above puts even at its left.

Monday, April 24, 2017

The Trials of Device

Filed under: General,Geometry — Tags: , , — m759 @ 3:28 PM

"A blank underlies the trials of device"
— Wallace Stevens, "An Ordinary Evening in New Haven" (1950)

A possible meaning for the phrase "the trials of device" —

See also Log24 posts mentioning a particular device, the pentagram .

For instance —

Wittgenstein's pentagram and 4x4 'counting-pattern'

Related figures

Pentagon with pentagram    

Tuesday, April 4, 2017

Test

Filed under: General — m759 @ 1:01 PM

See also, in this  journal, St. Cyprian's Day last year.

Thursday, October 27, 2016

“Space Is the Place!”

Filed under: General,Geometry — m759 @ 4:44 PM

Or:  Pentagram Meets Counting-Pattern, Continued

Arts & Letters Daily  today links to a Chronicle of Higher Education
piece on philosophy with an illustration by the late Paul Laffoley 

This suggests a review of Laffoley's work. In particular —

For a larger view of the above Laffoley pentagram, click here.
Contrast with Wittgenstein's "counting-pattern" above, which
is, in fact, a hyperspace.

Monday, October 17, 2016

Memorial Encounter:

Filed under: General — Tags: — m759 @ 5:40 PM

Pentagram Meets Counting-Pattern

Illustrations by Wittgenstein:

    

See posts from September 16, 2016, the date of death
for Professor Whitman A. Richards.

See also MIT News today

Monday, October 3, 2016

Hudson’s Inscape

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

Yesterday evening's post Some Old Philosophy from Rome
(a reference, of course, to a Wallace Stevens poem)
had a link to posts now tagged Wittgenstein's Pentagram.

For a sequel to those posts, see posts with the term Inscape ,
a mathematical concept related to a pentagram-like shape.

The inscape concept is also, as shown by R. W. H. T. Hudson
in 1904, related to the square array of points I use to picture
PG(3,2), the projective 3-space over the 2-element field.

Sunday, October 2, 2016

Some Old Philosophy from Rome

Filed under: General — m759 @ 6:45 PM

See also Log24 posts from the above reported date of death —
posts now tagged Wittgenstein's Pentagram.

Monday, September 19, 2016

Squaring the Pentagon

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

The "points" and "lines" of finite  geometry are abstract
entities satisfying only whatever incidence requirements
yield non-contradictory and interesting results. In finite
geometry, neither the points nor the lines are required to
lie within any Euclidean (or, for that matter, non-Euclidean)
space.

Models  of finite geometries may, however, embed the
points and lines within non -finite geometries in order
to aid visualization.

For instance, the 15 points and 35 lines of PG(3,2) may
be represented by subsets of a 4×4 array of dots, or squares,
located in the Euclidean plane. These "lines" are usually finite
subsets of dots or squares and not*  lines of the Euclidean plane.

Example — See "4×4" in this journal.

Some impose on configurations from finite geometry
the rather artificial requirement that both  points and lines
must be representable as those of a Euclidean plane.

Example:  A Cremona-Richmond pentagon —

Pentagon with pentagram

A square version of these 15 "points" —

A 1905 square version of these 15 "points" 
with digits instead of letters —

See Parametrizing the 4×4 Array
(Log24 post of Sept. 13, 2016).

Update of 8 AM ET Sunday, Sept. 25, 2016 —
For more illustrations, do a Google image search
on "the 2-subsets of a 6-set." (See one such search.)

* But in some models are subsets of the grid lines 
   that separate squares within an array.

Friday, September 16, 2016

For Albee’s Walk of Fame

Filed under: General — Tags: — m759 @ 10:00 PM

Every picture tells a story.

A Counting-Pattern

Filed under: General,Geometry — Tags: , — m759 @ 10:48 AM

Wittgenstein, 1939

Dolgachev and Keum, 2002

IMAGE- Dolgachev and Keum, coordinatization of the 4x4 array in 'Birational Automorphisms of Quartic Hessian Surfaces,' AMS Transactions, 2002

For some related material, see posts tagged Priority.

Tuesday, April 5, 2016

Spring Play

Filed under: General — Tags: , , — m759 @ 4:24 PM

The spring play this March at Princeton's McCarter Theatre Center
was Agatha Christie's "The Mousetrap."

In related news —

See as well, in this  journal, a post from the date pictured above,
that of the Disneyland Diamond Celebration on May 22, 2015 —

Donald Duck with pentagram

Friday, May 22, 2015

Mathmagic Land

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

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

Manly P. Hall

You Can’t Make This Stuff Up

Filed under: General — Tags: — m759 @ 2:45 AM

Continued .

A tale for pentagram enthusiasts

Synchronicity check on the date of the above Salon  story:

Two posts from Log24 on Jan. 5, 2014 —
 

Hits

Filed under: Uncategorized — m759 @ 7:59 AM 

Wikipedia on a Springsteen album released on
this date in 1973—

"… when Columbia Records president Clive Davis 
heard the album, he felt that it lacked a hit single.
As such, Springsteen wrote and recorded
'Blinded by the Light' and 'Spirit in the Night.' "

The upload dates from the above links are also dates
of some posts in this journal— Thursday, June 26, 2008,
and Sunday, July 6, 2008.

Little Mornings…

Filed under: Uncategorized — m759 @ 6:29 AM 

 que cantaba el rey David.

Update of 7 AM Jan. 5— See also Endor's Game.

Wednesday, October 1, 2014

Good Question

Filed under: General — m759 @ 11:00 AM

Related material:

Here “Lucifer’s temple” refers to Josefine Lyche’s Lynx 760 gallery in Oslo.

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)

Illustration:

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.

Monday, September 29, 2014

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.

Monday, September 15, 2014

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

Sermon

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

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

Introduction
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)

Wednesday, May 14, 2014

Death in Mathmagic Land

Filed under: General — Tags: , — m759 @ 3:28 PM

"It was our old friend Pythagoras who discovered
that the pentagram was full of mathematics."

— Narrator, "Donald in Mathmagic Land," Disney, 1959

… and it was Peter J. Cameron who discovered that
mathematics was full of pentagrams.

From Log24 on May 3:  Gray Space —

Robert J. Stewart (left) and a pentagram photo posted May 2
by Oslo artist Josefine Lyche. See also Lyche in this journal.

From Log24 on May 13:  An Artist's Memorial —

The death mentioned in the above May 13 post occurred on
May 12, the date of a scheduled Black Mass at Harvard.

Related material:

Two -Year College

Filed under: General — m759 @ 9:45 AM

See last night’s pentagram photo and a post from May 13, 2012.

That post links to a little-known video of a 1972 film.
A speech from the film was used by Oslo artist Josefine Lyche as a
voice-over in her  2011 golden-ratio video (with pentagrams) that she
exhibited along with a large, wall-filling copy of some of my own work.
The speech (see video below) is clearly nonsense.

The patterns* Lyche copied are not.

“Who are you, anyway?” 

— Question at 00:41 of 15:00, Rainbow Bridge (Part 5 of 9)
at YouTube, addressed to Baron Bingen as “Mr. Rabbit”

* Patterns exhibited again later, apparently without the Lyche pentagram video.
It turns out, by the way, that Lyche created that video by superimposing
audio from the above “Rainbow Bridge” film onto a section of Disney’s 1959
Donald in Mathmagic Land” (see 7:17 to 8:57 of the 27:33 Disney video).

Saturday, May 3, 2014

Gray Space

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

Or: Three Shades of Gray

(Continued from previous Gray Space posts.)

Cube subdivided into 8 subcubes by planes through the center

Click the above image for some related mathematics.

Those who prefer “magic” approaches to mathematics*
may consult the works of Robert J. Stewart and his
mentor William G. Gray.

Robert J. Stewart (left) and a pentagram photo posted yesterday evening
by Oslo artist Josefine Lyche. See also Lyche in this journal.

* See the April 2014 banners displayed at the websites
of the American Mathematical Society and of  the
Mathematical Association of America, as well as
a mathematician’s remarks linked to here last evening.

Saturday, February 18, 2012

Logo

Filed under: General,Geometry — Tags: — m759 @ 8:48 AM

Pentagram design agency on the new Windows 8 logo

"… the logo re-imagines the familiar four-color symbol
as a modern geometric shape"—

http://www.log24.com/log/pix12/120218-Windows8Logo.jpg

Sam Moreau, Principal Director of User Experience for Windows,
yesterday—

On Redesigning the Windows Logo

"To see what is in front of one's nose
needs a constant struggle."
George Orwell

That is the feeling we had when Paula Scher
(from the renowned Pentagram design agency)
showed us her sketches for the new Windows logo.

Related material:

http://www.log24.com/log/pix12/120218-SmallSpaces-256w.gif

Wednesday, May 16, 2007

Wednesday May 16, 2007

Filed under: General — m759 @ 4:01 AM
Star Wars

From this morning's New York Times:

"In April, Wiccans won an important victory when the Department of Veterans Affairs settled a lawsuit and agreed to add the Wiccan pentacle to a list of approved religious symbols that it will engrave on veterans' headstones….

Many Wiccans practice some form of magic or witchcraft, which they say is a way of affecting one's destiny, but which many outsiders see as evil. The Wiccan pentacle, a five-pointed star inside a circle, is often confused with symbols of Satanism."

A version of the pentacle or pentagram symbol

"Don't underestimate the Force."

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