Bruce Reynolds, chief architect of
the Great Train Robbery, who reportedly
died today:
"We all have our benchmarks….
it’s the same madness, I suppose,
that drives people to bivouac on
the north face of the Eiger."
For the Eiger in this journal, see "Parts of a World."
(A sequel to yesterday's post Publication )
Meanwhile, in this journal …
Les Miserables at the Academy Awards
"I’ve had the privilege recently of being a Harvard University
professor, and there I learned one of the greatest of Harvard
jokes. A group of rabbis are on the road to Golgotha and
Jesus is coming by under the cross. The young rabbi bursts
into tears and says, 'Oh, God, the pity of it!' The old rabbi says,
'What is the pity of it?' The young rabbi says, 'Master, Master,
what a teacher he was.'
'Didn’t publish!'
That cold tenure- joke at Harvard contains a deep truth.
Indeed, Jesus and Socrates did not publish."
— George Steiner, 2002 talk at York University
See also Steiner on Galois.
Les Miserables at the Academy Awards
"Hans Castorp is a searcher after the Holy Grail.
You would never have thought it when you read
his story—if I did myself, it was both more and
less than thinking. Perhaps you will read the
book again from this point of view. And perhaps
you will find out what the Grail is: the knowledge
and the wisdom, the consecration, the highest
reward, for which not only the foolish hero but
the book itself is seeking. You will find it in the
chapter called 'Snow'…."
— Thomas Mann, "The Making of
The Magic Mountain "
In related entertainment news…
Click image for some backstory.
Mann's tale is set in Davos, Switzerland.
See also Mayer at Davos.
The previous post suggests two sayings:
"There is such a thing as a Galois space."
— Adapted from Madeleine L'Engle
"For every kind of vampire, there is a kind of cross."
Illustrations—
Yesterday's post Permanence dealt with the cube
as a symmetric model of the finite projective plane
PG(2,3), which has 13 points and 13 lines. The points
and lines of the finite geometry occur in the cube as
the 13 axes of symmetry and the 13 planes through
the center perpendicular to those axes. If the three
axes lying in a plane that cuts the cube in a hexagon
are supplemented by the axis perpendicular to that
plane, each plane is associated with four axes and,
dually, each axis is associated with four planes.
My web page on this topic, Cubist Geometries, was
written on February 27, 2010, and first saved to the
Internet Archive on Oct. 4, 2010.
For a more recent treatment of this topic that makes
exactly the same points as the 2010 page, see p. 218
of Configurations from a Graphical Viewpoint , by
Tomaž Pisanski and Brigitte Servatius, published by
Springer on Sept. 23, 2012 (date from both Google
Books and Amazon.com):
For a similar 1998 treatment of the topic, see Burkard Polster's
A Geometrical Picture Book (Springer, 1998), pp. 103-104.
The Pisanski-Servatius book reinforces my argument of Jan. 13, 2013,
that the 13 planes through the cube's center that are perpendicular
to the 13 axes of symmetry of the cube should be called the cube's
symmetry planes , contradicting the usual use of of that term.
That argument concerns the interplay between Euclidean and
Galois geometry. Pisanski and Servatius (and, in 1998, Polster)
emphasize the Euclidean square and cube as guides* to
describing the structure of a Galois space. My Jan. 13 argument
uses Galois structures as a guide to re-describing those of Euclid .
(For a similar strategy at a much more sophisticated level,
see a recent Harvard Math Table.)
Related material: Remarks on configurations in this journal
during the month that saw publication of the Pisanski-Servatius book.
* Earlier guides: the diamond theorem (1978), similar theorems for
2x2x2 (1984) and 4x4x4 cubes (1983), and Visualizing GL(2,p)
(1985). See also Spaces as Hypercubes (2012).
Inscribed hexagon (1984)
The well-known fact that a regular hexagon
may be inscribed in a cube was the basis
in 1984 for two ways of coloring the faces
of a cube that serve to illustrate some graphic
aspects of embodied Galois geometry—
Inscribed hexagon (2013)
A redefinition of the term "symmetry plane"
also uses the well-known inscription
of a regular hexagon in the cube—
Related material
"Here is another way to present the deep question 1984 raises…."
— "The Quest for Permanent Novelty," by Michael W. Clune,
The Chronicle of Higher Education , Feb. 11, 2013
“What we do may be small, but it has a certain character of permanence.”
— G. H. Hardy, A Mathematician’s Apology
"Forget about your rainbow schemes,
Spin a little web of dreams."
Related material:
See "Mind of Winter" in this journal.
"And we may see the meadow in December…."
"Currently in post-production": The Zero Theorem.
Raiders of the Lost Tesseract continues…
SOCRATES: Is he not better off in knowing his ignorance?
MENO: I think that he is.
SOCRATES: If we have made him doubt, and given him the 'torpedo's shock,' have we done him any harm?
MENO: I think not.
Part I: The Midnight Ending Lincoln's Birthday, 2013
Part II: The Death of Barnaby Conrad on that day
Part III: The Second Life of John Wilkes Booth
Whether Conrad now enjoys a second life, I do not know.
Part I: Professor Marvin W. Meyer (this journal yesterday)
Part II: Producer/writer Richard Collins (Los Angeles Times today)
(Continued from August 23, 2012)
“Good is a noun. That was it.
That was what Phaedrus had been looking for.
That was the homer over the fence
that ended the ballgame.”
But perhaps not a proper noun.
See the link to Good's Singularity
at the end of today's previous post.
Yesterday's link to Aaronson and Turing suggests a review
of events on August 16, 2012 in the light of Log24 on that date.
Exhibit A: New Institute for Quantum Studies at Chapman University—
Exhibit B: The Aug. 16, 2012, death of Chapman University's Indiana Jones—
Whether this Indiana Jones successfully transgressed
the boundaries of space and time, I do not know.
Exhibit C: Related quantum hype—
Chapman Professor Lands Discover Cover Story,
Chapman University Happenings, March 18, 2010
See also Good's Singularity.
Story, Structure, and the Galois Tesseract
Recent Log24 posts have referred to the
"Penrose diamond" and Minkowski space.
The Penrose diamond has nothing whatever
to do with my 1976 monograph "Diamond Theory,"
except for the diamond shape and the connection
of the Penrose diamond to the Klein quadric—
The Klein quadric occurs in the five-dimensional projective space
over a field. If the field is the two-element Galois field GF(2), the
quadric helps explain certain remarkable symmetry properties
of the R. T. Curtis Miracle Octad Generator (MOG), hence of
the large Mathieu group M24. These properties are also
relevant to the 1976 "Diamond Theory" monograph.
For some background on the quadric, see (for instance)…
See also The Klein Correspondence,
Penrose Space-Time, and a Finite Model.
Related material:
|
"… one might crudely distinguish between philosophical – J. M. E. Hyland. "Proof Theory in the Abstract." (pdf) |
Those who prefer story to structure may consult
The title refers not to the 1996 Sokal hoax (which has
Boundaries , plural, in the title), but to the boundary
discussed in Monday's Penrose diamond post—
"Science is a differential equation.
Religion is a boundary condition."
— Alan Turing in the epigraph to the
first chapter of a book by Terence Tao
From the Tao book, page 170—
"Typically the transformed solution extends to the
boundary of the Penrose diamond and beyond…."
Transgressing the boundary between science
and religion is the topic of a 1991 paper available
at JSTOR for $29.
For the Pope on Ash Wednesday:
"Think you might have access
to this content via your library?" —JSTOR
See also Durkheim at Harvard.
(Continued, to mark Tuesday's birthdays of Lincoln and Darwin.)
A British reporter who died at 97 on Tuesday is said to have
"covered the space race in its entirety." In his honor, here
in review are posts containing the phrase Space Race
and, more generally, the two words Galois + Space.
Related material:
See also remarks on Penrose linked to in Sacerdotal Jargon.
(For a connection of these remarks to
the Penrose diamond, see April 1, 2012.)
In memory of Rabbi David Hartman, who died yesterday.
The architecture is by Lou Gelehrter.
I do not know the logo designer's name.
Click image for some background.
Context:
and the following post from last October:
* Who is Kearney? See, for instance, this book.
Suggested by a recent review of a
book by Richard Kearney:
The World, the Flesh, and the Devil.
Talk amongst yourselves.
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