Log24

Friday, May 22, 2015

Mathmagic Land

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

Donald Duck with Pythagorean pentagram on hand

Donald in Mathmagic Land

Manly P. Hall

Friday, July 25, 2014

Magic for Jews

Filed under: Uncategorized — Tags: — m759 @ 8:00 PM

(Continued from April 8, 2013.)

See Two Blocks Short of a Design (May 5, 2011).

Magic in the Moonshine

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

“The yarns of seamen have a direct simplicity, the whole meaning
of which lies within the shell of a cracked nut. But Marlow was not
typical (if his propensity to spin yarns be excepted), and to him the
meaning of an episode was not inside like a kernel but outside,
enveloping the tale which brought it out only as a glow brings out a
haze, in the likeness of one of these misty halos that sometimes
are made visible by the spectral illumination of moonshine.”

— Joseph Conrad in Heart of Darkness

“By groping toward the light we are made to realize
how deep the darkness is around us.”

— Arthur Koestler, The Call Girls: A Tragi-Comedy,
Random House, 1973, page 118

Spectral evidence is a form of evidence
based upon dreams and visions.” —Wikipedia

See also Moonshine (May 15, 2014) and, from the date of the above
New York Times  item, two posts tagged Wunderkammer .

Related material: From the Spectrum program of the Mathematical
Association of America, some non-spectral evidence.

Thursday, July 24, 2014

Death in Mathmagic Land

Filed under: Uncategorized — Tags: , , — m759 @ 11:29 AM

(Continued from May 14, 2014.)

See also consciousness growth and the previous post.

Wednesday, May 14, 2014

Death in Mathmagic Land

Filed under: Uncategorized — 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:

Monday, April 8, 2013

Magic for Jews

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

A commenter on Saturday's "Seize the Dia" has
suggested a look at the work of one Mark Collins.

Here is such a look (click to enlarge):

I find attempts to associate pure mathematics with the words
"magic" or "mystic" rather nauseating. (H. F. Baker's work
on Pascal's mystic hexagram  is no exception; Baker was
stuck with Pascal's obnoxious adjective, but had no truck
with any mystic aspects of the hexagram.)

The remarks above by Clifford Pickover on Collins, Dürer, and
binary representations may interest some non-mathematicians,
who should not  be encouraged to waste their time on this topic.

For the mathematics underlying the binary representation of
Dürer's square, see, for instance, my 1984 article "Binary
Coordinate Systems
."

Those without the background to understand that article
may enjoy, instead of Pickover's abortive attempts above at
mathematical vulgarization, his impressively awful 2009 novel
Jews in Hyperspace .

Pickover's 2002 book on magic squares was, unfortunately,
published by the formerly reputable Princeton University Press.

Related material from today's Daily Princetonian :

See also Nash + Princeton in this journal.

Thursday, May 5, 2011

On Art and Magic

Filed under: Uncategorized — Tags: — m759 @ 10:30 PM

Two Blocks Short of a Design:

A sequel to this morning's post on Douglas Hofstadter

http://www.log24.com/log/pix11A/110505-ThemeAndVariations-Hofstadter.jpg

Photo of Hofstadter by Mike McGrath taken May 13, 2006

Related material — See Lyche's  "Theme and Variations" in this journal
and Hofstadter's "Variations on a Theme as the Essence of Imagination"
Scientific American  October 1982

A quotation from a 1985 book by Hofstadter—

"… we need to entice people with the beauties of clarity, simplicity, precision,
elegance, balance, symmetry, and so on.

Those artistic qualities… are the things that I have tried to explore and even
to celebrate in Metamagical Themas .  (It is not for nothing that the word
'magic' appears inside the title!)"

The artistic qualities Hofstadter lists are best sought in mathematics, not in magic.

An example from Wikipedia —

http://www.log24.com/log/pix11A/110505-BlockDesignTheory.jpg

Mathematics

http://www.log24.com/log/pix11A/110505-WikipediaFanoPlane.jpg

The Fano plane block design

Magic

http://www.log24.com/log/pix11A/110505-DeathlyHallows.jpg

The Deathly Hallows  symbol—
Two blocks short of  a design.

Wednesday, October 18, 2017

Dürer for St. Luke’s Day

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

Structure of the Dürer magic square 

16   3   2  13
 5  10  11   8   decreased by 1 is …
 9   6   7  12
 4  15  14   1

15   2   1  12
 4   9  10   7
 8   5   6  11
 3  14  13   0 .

Base 4 —

33  02  01  30
10  21  22  13
20  11  12  23 
03  32  31  00 .

Two-part decomposition of base-4 array
as two (non-Latin) orthogonal arrays

3 0 0 3     3 2 1 0
1 2 2 1     0 1 2 3
2 1 1 2     0 1 2 3
0 3 3 0     3 2 1 0 .

Base 2 –

1111  0010  0001  1100
0100  1001  1010  0111
1000  0101  0110  1011
0011  1110  1101  0000 .

Four-part decomposition of base-2 array
as four affine hyperplanes over GF(2) —

1001  1001  1100  1010
0110  1001  0011  0101
1001  0110  0011  0101
0110  0110  1100  1010 .

— Steven H. Cullinane,
  October 18, 2017

See also recent related analyses of
noted 3×3 and 5×5 magic squares.

Tuesday, October 17, 2017

Plan 9 Continues

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

See also Holy Field in this journal.

Some related mathematics —

IMAGE- Herbert John Ryser, 'Combinatorial Mathematics' (1963), page 1

Analysis of the Lo Shu structure —

Structure of the 3×3 magic square:

4  9  2
3  5  7    decreased by 1 is
8  1  6

3  8  1
2  4  6
7  0  5

In base 3 —

10  22  01
02  11  20
21  00  12

As orthogonal Latin squares
(a well-known construction) —

1  2  0     0  2  1
0  1  2     2  1  0
2  0  1     1  0  2 .

— Steven H. Cullinane,
     October 17, 2017

Monday, October 16, 2017

Highway 61 Revisited

Filed under: Geometry — Tags: , — m759 @ 10:13 AM

"God said to Abraham …." — Bob Dylan, "Highway 61 Revisited"

Related material — 

See as well Charles Small, Harvard '64, 
"Magic Squares over Fields" —

— and Conway-Norton-Ryba in this  journal.

Some remarks on an order-five  magic square over GF(52):

"Ultra Super Magic Square"

on the numbers 0 to 24:

22   5   18   1  14
  3  11  24   7  15
  9  17   0  13  21
10  23   6  19   2
16   4  12  20   8

Base-5:

42  10  33  01  24 
03  21  44  12  30 
14  32  00  23  41
20  43  11  34  02
31  04  22  40  13 

Regarding the above digits as representing
elements of the vector 2-space over GF(5)
(or the vector 1-space over GF(52)) 

All vector row sums = (0, 0)  (or 0, over GF(52)).
All vector column sums = same.

Above array as two
orthogonal Latin squares:
   
4 1 3 0 2     2 0 3 1 4
0 2 4 1 3     3 1 4 2 0 
1 3 0 2 4     4 2 0 3 1         
2 4 1 3 0     0 3 1 4 2
3 0 2 4 1     1 4 2 0 3

— Steven H. Cullinane,
      October 16, 2017

Monday, February 27, 2017

Tricky Business*

Filed under: Uncategorized — m759 @ 12:45 AM

* For the title, see Sunday morning.

Tuesday, April 5, 2016

Spring Play

Filed under: Uncategorized — 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

Saturday, September 26, 2015

Posthumous Man

Filed under: Uncategorized — m759 @ 3:45 PM

The above book, a tribute by admirers of the late Michael Weinstein
(not, as a campus obituary states, by Weinstein himself),
was reportedly published by Routledge on December 19, 2014.

This journal on that date had a post on an early Greek philosopher who
supposedly was killed because he discovered irrational numbers.

A later approach to academic life —

Emma Stone being directed by Woody Allen in the recent "Irrational Man":

Fans of Allen and Stone may also enjoy Magic in the Moonlight.

Saturday, September 19, 2015

The Observatory Mystery

Filed under: Uncategorized — m759 @ 11:00 AM

Part I:        Magic Moonlight

Part II:    To Walk the Night 

Cover from a 1944 edition of
the 1937 novel by William Sloane


Part III:   Sept. 18, 2015, review by Stephen King
                of the works of William Sloane 

Sunday, August 30, 2015

Lines

Filed under: Uncategorized — Tags: , — m759 @ 11:01 AM

"We tell ourselves stories in order to live." — Joan Didion

A post from St. Augustine's day, 2015, may serve to
illustrate this.

The post started with a look at a painting by Swiss artist
Wolf Barth, "Spielfeld." The painting portrays two
rectangular arrays, of four and of twelve subsquares, 
that sit atop a square array of sixteen subsquares.

To one familiar with Euclid's "bride's chair" proof of the
Pythagorean theorem, "Spielfeld" suggests a right triangle
with squares on its sides of areas 4, 12, and 16.

That image in turn suggests a diagram illustrating the fact
that a triangle suitably inscribed in a half-circle is a right 
triangle… in this case, a right triangle with angles of 30, 60,
and 90 degrees… Thus —

In memory of screenwriter John Gregory Dunne (husband
of Joan Didion and author of, among other things, The Studio
here is a cinematric approach to the above figure.

The half-circle at top suggests the dome of an observatory.
This in turn suggests a scene from the 2014 film "Magic in
the Moonlight."  

As she gazes at the silent universe above
through an opening in the dome, the silent
Emma Stone is perhaps thinking, 
prompted by her work with Spider-Man

"Drop me a line."

As he  gazes at the crack in the dome,
Stone's costar Colin Firth contrasts the vastness 
of the Universe with the smallness of Man, citing 

"the tiny field F2 with two elements."

In conclusion, recall the words of author Norman Mailer
that summarized his Harvard education —

"At times, bullshit can only be countered
with superior bullshit."

Friday, August 28, 2015

Art and Space

Filed under: Uncategorized — Tags: , — m759 @ 10:00 AM

IMAGE- Spielfeld (1982-83), by Wolf Barth
 

            Observatory scene from "Magic in the Moonlight"

"The sixteen nodes… can be parametrized
by the sixteen points in affine four-space
over the tiny field F2 with two elements."

Wolf Barth

Thursday, December 25, 2014

The Savage Tongue

Filed under: Uncategorized — m759 @ 9:00 AM

Tuesday, July 29, 2014

Radio Days

Filed under: Uncategorized — Tags: — m759 @ 11:29 AM

In memoriam :

“Margot Adler, an iconic NPR correspondent and Wiccan priestess,
died on Monday July 28 from endometrial cancer at the age of 68.”

Huffington Post 07/28/2014 5:39 pm EDT

See also Log24 posts tagged NPR Magic.

Friday, July 25, 2014

Actual Talent

Filed under: Uncategorized — m759 @ 8:28 PM

“It’s going to be accomplished in steps,
this establishment of the Talented
in the scheme of things.”

— Anne McCaffrey,  Radcliffe ’47, To Ride Pegasus

From a review of the new film “Magic in the Moonlight”—

“Sophie seems to have some actual talent….
When Sophie meets Aunt Vanessa, she uncovers the spinster’s
long-ago love affair with a member of parliament. It’s eerie.”

Material that is related, if only in story space:

Sunday, July 13, 2014

Useful Princeton

Filed under: Uncategorized — Tags: , — m759 @ 10:30 AM

See…

"Numbers themselves are fictions, abstractions humans invented
to gain more control over the world." — Keith Devlin

Related material:

Friday, July 11, 2014

Thanks for having me on.

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

See also this  journal on April 12, 2014.

Tuesday, June 24, 2008

Tuesday June 24, 2008

Filed under: Uncategorized — Tags: — m759 @ 1:00 PM
Random Walk with
X's and O's

Part I: Random Walk

NY Lottery June 23, 2008: Mid-day 322, Evening 000

Part II: X's

3/22:

Actor contemplating the Chi-rho Page of the Book of Kells

"Shakespeare, Rilke, Joyce,
Beckett and Levi-Strauss are
instances of authors for whom
chiasmus and chiastic thinking
are of central importance,
for whom chiasmus is a
generator of meaning,
tool of discovery and
  philosophical template."
 
— Chiasmus in the
Drama of Life

Part III: O's —

A Cartoon Graveyard
in honor of the late
Gene Persson

Today's Garfield

Garfield cartoon of June 24, 2008

See also
Midsummer Eve's Dream:

"The meeting is closed
with the lord's prayer
and refreshments are served."

Producer of plays and musicals
including Album and
The Ruling Class

Lower case in honor of
Peter O'Toole, star of
the film version of
The Ruling Class.

(This film, together with
O'Toole's My Favorite Year,
may be regarded as epitomizing
Hollywood's Jesus for Jews.)

Those who prefer
less randomness
in their religion
 may consult O'Toole's
more famous film work
involving Islam,
as well as
the following structure
discussed here on
the date of Persson's death:

5x5 ultra super magic square

"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah.
"

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