“Chess problems are the
hymn-tunes of mathematics.”
— G. H. Hardy,
A Mathematician’s Apology
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“The key is the cocktail that begins the proceedings.”
– Brian Harley, Mate in Two Moves
"I named this script ocode and chmod 755'd it to make it executable…"
— Software forum post on the OCR program Tesseract
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From the author of
The Pearly Gates of Cyberspace:
"Like so many other heroes
who have seen the light
of a higher order…."
Yesterday morning's post "First Step" quoted an essay by Michael Spitzer
published online in Aeon on October 18 —
https://aeon.co/essays/
can-music-give-you-an-orgasm-the-short-answer-is-yes .
A look at earlier essays in that publication reveals . . .
Related material — From a search for Wertheim in this journal —
“Space: what you
damn well have to see.”
— James Joyce, Ulysses
“My pursuits are a joke
in that the universe is a joke.
One has to reflect
the universe faithfully.”
— John Frederick Michell
Feb. 9, 1933 –
April 24, 2009
— Robert A. Heinlein,
The Number of the Beast
For Marisa Tomei
(born Dec. 4, 1964) —
on the day that
Bob Seger turns 64 —
A Joke:
Points All Her Own
Points All Her Own,
Part I:
(For the backstory, see
the Log24 entries and links
on Marisa Tomei’s birthday
last year.)
Points All Her Own,
Part II:
(For the backstory, see
Galois Geometry:
The Simplest Examples.)
Points All Her Own,
Part III:
(For the backstory, see
Geometry of the I Ching
and the history of
Chinese philosophy.)
In simpler terms:
Through the
Looking Glass:
A Sort of Eternity
From the new president’s inaugural address:
“… in the words of Scripture, the time has come to set aside childish things.”
The words of Scripture:
“through a glass”—
[di’ esoptrou].
By means of
a mirror [esoptron].
Childish things:
© 2005 The Institute for Figuring
Not-so-childish:
Three planes through
the center of a cube
that split it into
eight subcubes:
Through a glass, darkly:
A group of 8 transformations is
generated by affine reflections
in the above three planes.
Shown below is a pattern on
the faces of the 2x2x2 cube
that is symmetric under one of
these 8 transformations–
a 180-degree rotation:
(Click on image
for further details.)
But then face to face:
A larger group of 1344,
rather than 8, transformations
of the 2x2x2 cube
is generated by a different
sort of affine reflections– not
in the infinite Euclidean 3-space
over the field of real numbers,
but rather in the finite Galois
3-space over the 2-element field.
Galois age fifteen,
drawn by a classmate.
These transformations
in the Galois space with
finitely many points
produce a set of 168 patterns
like the one above.
For each such pattern,
at least one nontrivial
transformation in the group of 8
described above is a symmetry
in the Euclidean space with
infinitely many points.
For some generalizations,
see Galois Geometry.
Related material:
The central aim of Western religion–
"Each of us has something to offer the Creator... the bridging of masculine and feminine, life and death. It's redemption.... nothing else matters." -- Martha Cooley in The Archivist (1998) The central aim of Western philosophy– Dualities of Pythagoras as reconstructed by Aristotle: Limited Unlimited Odd Even Male Female Light Dark Straight Curved ... and so on .... “Of these dualities, the first is the most important; all the others may be seen as different aspects of this fundamental dichotomy. To establish a rational and consistent relationship between the limited [man, etc.] and the unlimited [the cosmos, etc.] is… the central aim of all Western philosophy.” — Jamie James in The Music of the Spheres (1993) “In the garden of Adding — The Midrash Jazz Quartet in City of God, by E. L. Doctorow (2000) A quotation today at art critic Carol Kino’s website, slightly expanded: “Art inherited from the old religion — Octavio Paz,”Seeing and Using: Art and Craftsmanship,” in Convergences: Essays on Art and Literature (New York: Harcourt Brace Jovanovich 1987), 52 From Brian O’Doherty’s 1976 Artforum essays– not on museums, but rather on gallery space: “We have now reached
“Space: what you — James Joyce, Ulysses |
Wikipedia on Rubik's 2×2×2 "Pocket Cube"–
"Any permutation of the 8 corner cubies is possible (8! positions)."
Some pages related to this claim–
Analyzing Rubik's Cube with GAP
Online JavaScript Pocket Cube.
The claim is of course trivially true for the unconnected subcubes of Froebel's Third Gift:
© 2005 The Institute for Figuring
See also:
MoMA Goes to Kindergarten,
Tea Privileges,
and
"Ad Reinhardt and Tony Smith:
A Dialogue,"
an exhibition opening today
at Pace Wildenstein.
For a different sort
of dialogue, click on the
artists' names above.
For a different
approach to S8,
see Symmetries.
"With humor, my dear Zilkov.
Always with a little humor."
-- The Manchurian Candidate
An Indiana Jones Xmas
continues…
Chalice, Grail,
Whatever
Last night on TNT:
The Librarian Part 3:
Curse of the Judas Chalice,
in which The Librarian
encounters the mysterious
Professor Lazlo
Related material:
An Arthur Waite quotation
from the Feast of St. Nicholas:
“It is like the lapis exilis of
the German Graal legend”
as well as
yesterday’s entry
relating Margaret Wertheim’s
“Pearly Gates of Cyberspace:
A History of Space from
Dante to the Internet”
to a different sort of space–
that of the I Ching— and to
Professor Laszlo Lovasz’s
“cube space”
“Click on the Yellow Book.”
Happy birthday, David Carradine.
On a book by Margaret Wertheim:
“She traces the history of space beginning with the cosmology of Dante. Her journey continues through the historical foundations of celestial space, relativistic space, hyperspace, and, finally, cyberspace.” –Joe J. Accardi, Northeastern Illinois Univ. Lib., Chicago, in Library Journal, 1999 (quoted at Amazon.com)
There are also other sorts of space.
© 2005 The Institute for FiguringThis photo may serve as an
introduction to a different
sort of space.
See The Eightfold Cube.
For the religious meaning
of this small space, see
For a related larger space,
see the entry and links of
St. Augustine’s Day, 2006.
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OCODE
"The first credential
— Ezra Pound, "OCR is a field of research in pattern recognition, artificial intelligence and machine vision." — Wikipedia "I named this script ocode and chmod 755'd it to make it executable…" — Software forum post on the OCR program Tesseract
Wednesday, Dec. 3, 2008:
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"Like so many other heroes
who have seen the light
of a higher order…."
For further backstory,
click on the mouse.
— T. S. Eliot,
The Family Reunion
Several voices:
Margaret Wertheim in today’s
Los Angeles Times and at
The Pearly Gates of Cyberspace,
Linda Dalrymple Henderson, and
Madeleine L’Engle and husband.
From Wertheim’s Pearly Gates:
“There is such a thing
as a tesseract.”
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