"You've got to pick up every stitch . . . ." — Song lyric
Midrash for Philip Van Doren Stern —
Thursday, November 13, 2025
Art Logic: An Unlikely Story
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Thursday, April 27, 2023
Wednesday, February 8, 2023
Local-Global lnduced Actions
See "Two Approaches to Local-Global Symmetry"
(this journal, Jan. 19, 2023), which discusses
local group actions on plane and solid graphic
patterns that induce global group actions.
See also local and global group actions of a different sort in
the July 11, 1986, note "Inner and Outer Group Actions."
This post was suggested by some remarks of Barry Mazur,
quoted in the previous post, on " Wittgenstein's 'language game,' "
Grothendieck, global views, local views and "locales."
Further reading on "locales" — Wikipedia, Pointless topology.
The word "locale" in mathematics was apparently* introduced by Isbell —
ISBELL, JOHN R. “ATOMLESS PARTS OF SPACES.”
Mathematica Scandinavica, vol. 31, no. 1, 1972, pp. 5–32.
JSTOR, http://www.jstor.org/stable/24490585.
* According to page 841 of . . .
Johnstone, P. (2001). "Elements of the History of Locale Theory."
Pp. 835–851 in: Aull, C.E., Lowen, R. (eds) Handbook of the
History of General Topology, Vol 3. Springer, Dordrecht.
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Saturday, January 14, 2023
Châtelet on Weil — A “Space of Gestures”
|
From Gilles Châtelet, Introduction to Figuring Space Metaphysics does have a catalytic effect, which has been described in a very beautiful text by the mathematician André Weil: Nothing is more fertile, all mathematicians know, than these obscure analogies, these murky reflections of one theory in another, these furtive caresses, these inexplicable tiffs; also nothing gives as much pleasure to the researcher. A day comes when the illusion vanishes: presentiment turns into certainty … Luckily for researchers, as the fogs clear at one point, they form again at another.4 André Weil cuts to the quick here: he conjures these 'murky reflections', these 'furtive caresses', the 'theory of Galois that Lagrange touches … with his finger through a screen that he does not manage to pierce.' He is a connoisseur of these metaphysical 'fogs' whose dissipation at one point heralds their reforming at another. It would be better to talk here of a horizon that tilts thereby revealing a new space of gestures which has not as yet been elucidated and cut out as structure. 4 A. Weil, 'De la métaphysique aux mathématiques', (Oeuvres, vol. II, p. 408.) |
For gestures as fogs, see the oeuvre of Guerino Mazzola.
For some clearer remarks, see . . .
Illustrations of object and gestures
from finitegeometry.org/sc/ —
Object
Gestures
An earlier presentation
of the above seven partitions
of the eightfold cube:
|
|
Related material: Galois.space .
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Sunday, October 23, 2022
Mathematical Intelligencer News
For Pekonen in this journal, see
From the Finland Station (25 April 2022).
See as well an obituary from Finland.
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Saturday, October 8, 2022
For Fans of Religious Lunacy … The Firebird Date
("Raiders of the Lost Spell" continues.)
The above flashback to a 2002 post was suggested by a search in
this journal for "Firebird" that yielded, as the only result . . .
http://www.amazon.com/
Witch-Seldom-Firebird-Nancy-Springer/dp/0142302201/.
That URL connects to The Hex Witch of Seldom at Amazon.com.
That book was reportedly published by Firebird on September 16, 2002,
the date of the above Log24 post.
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Thursday, July 21, 2022
Siamese Combinatorial Remarks
Further combinatorial properties* of 24261120 may
be investigated with the aid of a 9×9 square grid, and
perhaps (eventually) also with its triangular counterpart —
.
* Cap sets, gerechte designs, etc.
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Tuesday, October 5, 2021
Halloween 2020
Epilogue to Combinatorics and Finite Geometry ,
first online on Halloween 2020 —
Meanwhile . . .
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Sunday, June 20, 2021
Saturday, June 5, 2021
Bavarian Scholarship
From my search history tonight —
11:11 PM
Number Theory – BSB Catalog opacplus.bsb-muenchen.de
11:13 PM
Klein's paradox, the icosahedron, and ring class fields | SpringerLink
A resulting quotation —
"Our attempt to explain and motivate is not merely a matter of historical whimsy."
— Harvey Cohn. See also Cohn in the previous post's link to 9/11, 2014.
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Sunday, November 8, 2020
Local
“All politics is local.”
— Saying attributed to the late Tip O’Neill
“All time is local.”
— Concept attributed to the late Albert Einstein
Related material —
See also Timequake in this journal.
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Monday, October 19, 2020
“Graffiti in the Library of Babel” Continues.
Click on the Wiktionary image for the Babel story.
Click on the Springer.com link for related posts.
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Sunday, September 27, 2020
Hex Witch
The new Netflix film “Enola Holmes” is from a book by Nancy Springer.
Also by Springer:
See that title in this journal.
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Thursday, September 24, 2020
Ludwig Wittgenstein, P.I. . . .
This post was suggested by a Sept. 24, 2020, article at CrimeReads.com
by Philip K. Zimmerman —
“The Philosopher and the Detectives:
Ludwig Wittgenstein’s Enduring Passion
for Hardboiled Fiction.”
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Thursday, August 27, 2020
The Complete Extended Binary Golay Code
All 4096 vectors in the code are at . . .
http://neilsloane.com/oadir/oa.4096.12.2.7.txt.
Sloane’s list* contains the 12 generating vectors
listed in 2011 by Adlam —
As noted by Conway in Sphere Packings, Lattices and Groups ,
these 4096 vectors, constructed lexicographically, are exactly
the same vectors produced by using the Conway-Sloane version
of the Curtis Miracle Octad Generator (MOG). Conway says this
lexico-MOG equivalence was first discovered by M. J. T. Guy.
(Of course, any permutation of the 24 columns above produces
a version of the code qua code. But because the lexicographic and
the MOG constructions yield the same result, that result is in
some sense canonical.)
See my post of July 13, 2020 —
The lexicographic Golay code
contains, embedded within it,
the Miracle Octad Generator.
For some related results, Google the twelfth generator:
* Sloane’s list is of the codewords as the rows of an orthogonal array —
See also http://neilsloane.com/oadir/.
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Sunday, August 23, 2020
Sprechen Sie Neutsch?
Image added to post on Tuesday, November 4, 2025 —
End of added image. Also on Nov. 4, 2025 . . .
Publication year added to the Coordinates excerpt below.
Related images —
Chess Knight
(in German, Springer)
See also…
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Wednesday, May 13, 2020
Adventures in the Book Trade
Click the Springer “train of thought” advertisement below to enlarge.
A line for Stephen King:
“She gets the locomotive, I get the caboose.”
. . . . . . . 
Cover Design: Will Staehle / Unusual Co.
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Monday, May 4, 2020
May the Fourth
“This is not the Hartshorne you’re looking for.”
“Reality as a Social Process (1953) developed the ideas
that becoming, or process, is fundamental throughout
reality, and that all the things that become are interrelated.”
— From American National Biography
Related material —
The New York Times obituary of Madeline Faith Kripke
and Nietzsche on “becoming, or process.”
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Tuesday, April 28, 2020
Monday, April 20, 2020
Geometry for Poets
From Atomicity and Quanta by James Jeans,
Cambridge University Press, 1926, pp. 55-56 —
| “So far as we can at present conjecture, the investigation of the structure which produces this atomicity appears to be the big problem in the path of the quantum-theory. To conform to the principle of relativity, the new atomicity must admit of expression in terms of the space-time continuum, although we have seen that it cannot be an atomicity of the continuum itself. It may conceivably be an atomicity of its metric properties, such as determine its curvatures. We may perhaps form a very rude picture of it by imagining the curvature of the continuum in the neighbourhood of an atom not to be of the continuous nature imagined by Weyl, but to occur in finite chunks—a straight piece, then a sudden bend, then another straight bit, and so on. A small bit of the continuum viewed through a five-dimensional microscope might look rather like a cubist picture; and, conversely, perhaps a cubist picture looks rather more like a little fragment of the continuum than like anything else.” |
This is, of course, not the “atomicity” of the previous post.
For examples of that atomicity, a concept of pure geometry
rather than of physics, see …
Faure, C. A., and Frölicher, A., “Fundamental Notions of
Lattice Theory,” in Modern Projective Geometry (2000).
(Mathematics and Its Applications, vol 521. Springer, Dordrecht.)
Related art (a “cubist picture”) —
Juan Gris, Fruit Dish and Carafe , 1914
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Sunday, February 9, 2020
Hors d’Oeuvre
From the May Day 2016 link above, in "Sunday Appetizer from 1984" —
The 2015 German edition of Beautiful Mathematics , a 2011 Mathematical Association of America (MAA) book, was retitled Mathematische Appetithäppchen — Mathematical Appetizers . The German edition mentions the author's source, omitted in the original American edition, for his section 5.17, "A Group of Operations" (in German, 5.17, "Eine Gruppe von Operationen")—
That source was a document that has been on the Web since 2002. The document was submitted to the MAA in 1984 but was rejected. The German edition omits the document's title, and describes it as merely a source for "further information on this subject area." |
From the Gap Dance link above, in "Reading for Devil's Night" —
“Das Nichts nichtet.” — Martin Heidegger.
And "Appropriation Appropriates."
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Sunday, January 26, 2020
Harmonic-Analysis Building Blocks
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Saturday, January 11, 2020
Mathematics or Theology?
Hersh wrote a paper with a title containing the phrase
“The Kingdom of Math is Within You.”
In his memory, see Log24 posts from the date of his death
tagged Inner-Space Variations.
Related literature: Hersh's "Death and Mathematics Poems."
See as well this journal on the above publication date.
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Monday, December 30, 2019
Number and Time
(Hat tip for the title to Marie-Louise von Franz.)
Remarks by Metod Saniga from the previous post —
Remarks by Wolfgang Pauli, a friend of von Franz —
"This is to show the world that I can paint like Titian.
[Empty frame with jagged sides]. Only technical details
are missing." — As quoted at Derevianko Group.
Related material (see Oct. 11, 2010) —
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Sunday, December 29, 2019
Springer Link
Related reading —
"I closed my eyes and saw the number 137—
so very close to the reciprocal of alpha—
on the chest of the runner in Van Cortlandt Park.
Should I start the story there? "
— Alpert, Mark. Saint Joan of New York
(Science and Fiction) (p. 103).
Springer International Publishing. Kindle edition.
Cover detail:
See as well St. Joan in this journal.
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Friday, October 25, 2019
Facettenreiche Gestaltung
On the word Gestaltung —
(Here “eidolon” should instead be “eidos .”)
A search for a translation of the book "Facettenreiche Mathematik " —
A paper found in the above search —
A related translation —
See also octad.design.
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Wednesday, October 23, 2019
Tuesday, October 1, 2019
Transylvania Revisited
The previous post suggests . . .
|
Jim Holt reviewing Edward Rothstein's Emblems of Mind: The Inner Life of Music and Mathematics in The New Yorker of June 5, 1995: "The fugues of Bach, the symphonies of Haydn, the sonatas of Mozart: these were explorations of ideal form, unprofaned by extramusical associations. Such 'absolute music,' as it came to be called, had sloughed off its motley cultural trappings. It had got in touch with its essence. Which is why, as Walter Pater famously put it, 'all art constantly aspires towards the condition of music.' The only art that can rival music for sheer etheriality is mathematics. A century or so after the advent of absolute music, mathematics also succeeded in detaching itself from the world. The decisive event was the invention of strange, non-Euclidean geometries, which put paid to the notion that the mathematician was exclusively, or even primarily, concerned with the scientific universe. 'Pure' mathematics came to be seen by those who practiced it as a free invention of the imagination, gloriously indifferent to practical affairs– a quest for beauty as well as truth." [Links added.] |
A line for James McAvoy —
"Pardon me boy, is this the Transylvania Station?"
See as well Worlds Out of Nothing , by Jeremy Gray.
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Thursday, June 13, 2019
Seeing the Seing
The phrase "experimental metaphysics" appeared in Peter Woit's weblog on June 11.
Google reveals that . . .
"… 'experimental metaphysics' is a term coined by Abner Shimony …."
Shimony reportedly died on August 8, 2015. Also on that date —
Update of April 6, 2022 (Click to enlarge) —
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