Log24

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

Friday, July 25, 2014

Magic for Jews

Filed under: General — 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: General — 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: General — 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: 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:

Monday, April 8, 2013

Magic for Jews

Filed under: General,Geometry — 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: General,Geometry — 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: G-Notes,General,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: General,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: G-Notes,General,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

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

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.

Tuesday, July 29, 2014

Radio Days

Filed under: General — 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.

Sunday, July 13, 2014

Useful Princeton

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

See also this  journal on April 12, 2014.

Monday, May 12, 2014

Mass Appeal

Filed under: General — m759 @ 9:00 PM

For those disappointed by the cancellation
of this evening’s Black Mass at Harvard,
here is a somewhat less exciting substitute.

See also Peter J. Cameron + Magic.

Sunday, May 11, 2014

For the Perplexed

Filed under: General — m759 @ 9:48 PM

From a New York Times  obituary by Bruce Weber tonight—

Charles Marowitz, Director and Playwright, Dies at 82

“There are two kinds of bafflement in the theater: the kind that fascinates as it perplexes, and the kind that just perplexes,” he wrote in The Times in 1969 in an essay about Mr. Shepard’s play “La Turista,” which had recently opened in London. “If a play doesn’t make quick sense, but enters into some kind of dialogue with our subconscious, we tend to admit it to that lounge where we entertain interesting-albeit-unfamiliar strangers.

“If it only baffles, there are several courses open to us: we can assume it is ‘above our heads’ or directed ‘to some other kind of person,’ or regretfully conclude that it confuses us because it is itself confused. However, the fear of being proved wrong is so great today that almost every new work which isn’t patently drivel gets the benefit of the doubt.”

 Another play by Sam Shepard mentioned in the obituary suggests a review of…

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.

Friday, May 2, 2014

From the Witch Ball

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

IMAGE- Arcade Fire to headline the 2014 Oslo 'Norwegian Wood' festival at Frognerparken

See also, in this journal, Arcade Fire and Witch Ball.

This post was suggested by remarks today of mathematician
Peter J. Cameron, who seems to enjoy playing the role of
Lord Summerisle (from The Wicker Man , a 1973 horror classic).

Friday, April 25, 2014

Bingo

Filed under: General — m759 @ 10:25 AM

For John Milton at the Cervecería XX —

Related material: Peter J. Cameron on Bertrand Russell
in A Midnight Exorcism.

Sunday, January 26, 2014

A Midnight Exorcism

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

The summoning of the spirit of Bertrand Russell
yesterday by Peter J. Cameron at his weblog
suggests a review of this  weblog’s posts of
Christmas Eve, December 24-25, 2013.

(Recall that Robert D. Carmichael, who, in a book
linked to at midnight last Christmas Eve discusses
some “magic” mathematical structures,
reportedly was trained as a Presbyterian minister.
See also The Presbyterian Exorcist.)

Tuesday, June 24, 2008

Tuesday June 24, 2008

Filed under: General — 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.
"

Wednesday, June 8, 2005

Wednesday June 8, 2005

Filed under: General,Geometry — m759 @ 4:00 PM

Kernel of Eternity

Today is the feast day of Saint Gerard Manley Hopkins, “immortal diamond.”

“At that instant he saw, in one blaze of light, an image of unutterable conviction, the reason why the artist works and lives and has his being–the reward he seeks–the only reward he really cares about, without which there is nothing. It is to snare the spirits of mankind in nets of magic, to make his life prevail through his creation, to wreak the vision of his life, the rude and painful substance of his own experience, into the congruence of blazing and enchanted images that are themselves the core of life, the essential pattern whence all other things proceed, the kernel of eternity.”

— Thomas Wolfe, Of Time and the River

“… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A8 on the octad, the kernel of this action being the translation group of the affine space.)”

Peter J. Cameron,
The Geometry of the Mathieu Groups (pdf)

“… donc Dieu existe, réponse!

— attributed, some say falsely, to Leonhard Euler

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