"I've got a little book with matches three . . ."
— "All My Trials" lyrics, slightly adapted.
Friday, September 12, 2025
Baez Elegy
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Monday, June 20, 2022
John Baez: Grothendieck in Hanoi
Related quotations —
"So we beat on, boats against the current…." — F. Scott Fitzgerald
"There grows a tree in Paradise…." — Joan Baez
Related narrative — River of Death.
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Saturday, December 4, 2021
Baez and the Pink Lotus
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Thursday, February 5, 2026
Friday, November 14, 2025
A Moduli Space
On the Miracle Octad Generator of R. T. Curtis —
|
December 2025 Notices of the American Mathematical Society Jarod Alper, "Evolution of Stacks and Moduli" — "By a moduli space, we mean a geometric space whose points are in 'natural' bijection (more on what we mean by 'natural' in a moment) with isomorphism classes of your favorite mathematical objects, for example, Riemann surfaces or vector bundles on a fixed space. A moduli space is a solution to the classification problem: it packages all of the data of the geometric objects into a single space, a mathematical catalogue where any object can be located by selecting the corresponding point." |
Analogous notions:
Klein Space and Klein Quadric in this journal.
The Source:
Related art from a Log24 post of July 1, 2018 —
Greg Egan’s animated image of the Klein quartic —
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Thursday, February 13, 2025
The Exploitation of Symmetry . . . Continues.
Illustration of a July 1980 title by George Mackey —
Exploitation of Symmetry in 1981 . . .
See also the tetrahedra* in my "square triangles" letter
(1985), as well as "Senechal" in this journal.
"And we both know what memories can bring…" Do we?
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Saturday, September 7, 2024
Sunday, July 21, 2024
For Jack and Jill:
Vinegar and Brown Acid
Vinegar and Brown Acid.
Click to enlarge —
Midrash adapted from T. S. Eliot —
"In his end is his beginning."
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Vinegar and Brown Acid
Vinegar and Brown Acid
Friday, March 29, 2024
Math for Tricksters: Deck Transformation
From the above Baez essay —
"And when the hero arrives, there should be
a little flourish of trumpets, like:
And now we come to a key player:
the group of deck transformations."
This remark and Baez's statement that
"Ideally the tricks I’m suggesting here
will be almost invisible…."
suggest a non-mathematical "deck transformation"
that some will prefer —
In the March 21 Netflix series "3 Body Problem,"
the deck of the ship Judgment Day is transformed
in a spectacular manner by an invisible trick.
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Monday, March 25, 2024
B-B-Biennale 2024: Picture at 11!
The above solar art is . . .
(By John Baez, cousin of Joan)
(The Baez art was also displayed here on Saturday, March 23, 2024 —
the second day of the 2024 Biennale in the Desert Sun article.)
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Saturday, March 23, 2024
For Stephen King: A Mathematical Horror Story
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Sunday, July 9, 2023
This Is Your Brain on Category Theory
Remarks by John Baez today suggest a flashback…
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Tuesday, May 30, 2023
Seal 7 . . .
See John Baez this morning on Galois. Note that Baez's
report of Galois's dies natalis is in error.
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Sunday, May 14, 2023
“The Structure of Space”
The above title. by one Lee E. Mosley, is from
"CreateSpace Independent Publishing Platform;
1st edition (June 4, 2017)."
From the preface —
"So simple . . . ."
"Building blocks"? — See the literature of pop physics.
Natural companions to building blocks, are, of course,
"permutation groups."
See the oeuvre of physics writer John Baez —
For instance, in a Log24 post from the above Mosley
publication date — June 4, 2017 —
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Sunday, March 19, 2023
For Your Consideration
Mank, Baez, Collins — A trip back to Christmas Eve, 2021.
Related art (via Baez) for Josefine Lyche —
See also Lyche in Log24 posts tagged Star Cube.
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Saturday, February 25, 2023
The Al Goldstein Variations
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Tuesday, February 7, 2023
The Graduate School of Design
The above cubic equation may also be written as
x3 – x – 1 = 0.
The equation occurred in my own work in 1985:
An architects' equation that appears also in Galois geometry.
For further details on the plastic number, see an article by
Siobhan Roberts on John Baez in The New York Times —
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Friday, December 2, 2022
Wednesday, October 26, 2022
The Hunt for Galois October
"… Évariste was born on October 25, 1811."
— Eric Temple Bell, Men of Mathematics
Related material —
But seriously . . .
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Friday, July 29, 2022
… From the Stadium
(A sequel to the previous post — "To the Lighthouse")
From that same date . . .
|
Log24 on August 5, 2002 — "To really know a subject you've got to learn a bit of its history." — John Baez, August 4, 2002
"We both know what memories can bring; — Joan Baez, April 1975 "Venn considered three discs R, S, and T as typical subsets of a set U. The intersections of these discs and their complements divide U into 8 nonoverlapping regions." — History of Mathematics at St. Andrews "Who would not be rapt by the thought of such marvels?" — Saint Bonaventure on the Trinity |
"Who would not be rapt?" . . . Cristin Milioti? —
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Saturday, July 9, 2022
Annals of Symbology
See as well Oct. 12, 2018 (and, more generally, Volvo) in this journal.
Related material:
It is not clear whether the above acronym
should be pronounced "psycho" or "sicko."
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Wednesday, June 1, 2022
The Yearning
"… every sufficiently good analogy is yearning to become a functor."
— John Baez, 2004: "Lessons from Topological Quantum Field Theory"
Related images — Quoting scripture at The Master's University
on Jan. 31, 2017 —
… and some images (re)posted here on that same date — Jan. 31, 2017:
A related analogy — Between (1) and (2) below —
-
A right triangle A as the sum of two smaller,
inner, right triangles B and C, each similar to A . -
The square on the longest side of A as the sum
of the squares on the longest sides of B and C.
Exercise for Baez fans: Express the above analogy as a functor.
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Saturday, March 26, 2022
Box Geometry: Space, Group, Art (Work in Progress)
| Name Tag | .Space | .Group | .Art |
|---|---|---|---|
| Box4 |
2×2 square representing the four-point finite affine geometry AG(2,2). (Box4.space) |
S4 = AGL(2,2) (Box4.group) |
(Box4.art) |
| Box6 |
3×2 (3-row, 2-column) rectangular array representing the elements of an arbitrary 6-set. |
S6 | |
| Box8 | 2x2x2 cube or 4×2 (4-row, 2-column) array. | S8 or A8 or AGL(3,2) of order 1344, or GL(3,2) of order 168 | |
| Box9 | The 3×3 square. | AGL(2,3) or GL(2,3) | |
| Box12 | The 12 edges of a cube, or a 4×3 array for picturing the actions of the Mathieu group M12. | Symmetries of the cube or elements of the group M12 | |
| Box13 | The 13 symmetry axes of the cube. | Symmetries of the cube. | |
| Box15 |
The 15 points of PG(3,2), the projective geometry of 3 dimensions over the 2-element Galois field. |
Collineations of PG(3,2) | |
| Box16 |
The 16 points of AG(4,2), the affine geometry of 4 dimensions over the 2-element Galois field. |
AGL(4,2), the affine group of |
|
| Box20 | The configuration representing Desargues's theorem. | ||
| Box21 | The 21 points and 21 lines of PG(2,4). | ||
| Box24 | The 24 points of the Steiner system S(5, 8, 24). | ||
| Box25 | A 5×5 array representing PG(2,5). | ||
| Box27 |
The 3-dimensional Galois affine space over the 3-element Galois field GF(3). |
||
| Box28 | The 28 bitangents of a plane quartic curve. | ||
| Box32 |
Pair of 4×4 arrays representing orthogonal Latin squares. |
Used to represent elements of AGL(4,2) |
|
| Box35 |
A 5-row-by-7-column array representing the 35 lines in the finite projective space PG(3,2) |
PGL(3,2), order 20,160 | |
| Box36 | Eurler's 36-officer problem. | ||
| Box45 | The 45 Pascal points of the Pascal configuration. | ||
| Box48 | The 48 elements of the group AGL(2,3). | AGL(2,3). | |
| Box56 |
The 56 three-sets within an 8-set or |
||
| Box60 | The Klein configuration. | ||
| Box64 | Solomon's cube. |
— Steven H. Cullinane, March 26-27, 2022
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Saturday, January 29, 2022
Friday, October 23, 2020
Temple Bell
The title refers to a man called by John Baez
“The infamous pseudohistorian Eric Temple Bell.”
(See my post The Magpie.)
Today the American Mathematical Society (AMS) has
an obituary for Donald Babbitt (1936-2020), who
reportedly died on October 10.
Babbitt is the co-author of an article on Bell from the
June/July 2013 AMS Notices .
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Monday, August 24, 2020
The Mark of Zaentz
Jung's phrase "'four-square' Heavenly City" in the previous post
suggests a geometric object… the 4×4 square —
The "twelve gates" at the sides of the above figure suggest a song —
The Baez date above suggests in turn a review of
the Jan. 4, 2014, post "Heaven's Gate,"
on the death of film producer Saul Zaentz.
Related material —
The "Heavenly City" is perhaps not Cambridge, Massachusetts.
Recall as well Jean Simmons preaching the Foursquare Gospel
in the 1960 film classic "Elmer Gantry" —
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Sunday, August 9, 2020
Friday, June 26, 2020
Thursday, April 9, 2020
Symmetry: Toro, Torino
For the Toro , see Pierre Cartier in 2001 on the barber of Seville and
“The evolution of concepts of space and symmetry.”
For the Torino , see . . .
“… the ultimate goal of the present essay
which is to illustrate the historic
evolution of the concepts of Space and Symmetry “
— Pp. 157-158 of the above book.
See also Fré et al. , “The role of PSL(2,7) in M-theory”
(2018-2019) at http://arxiv.org/abs/1812.11049v2 ,
esp. Section 4, “Theory of the simple group PSL(2,7)”
on pages 11-27, and remarks on PSL(2,7) in this journal.
Related material —
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Tuesday, July 9, 2019
Schoolgirl Space: 1984 Revisited
Cube Bricks 1984 —
From "Tomorrowland" (2015) —
From John Baez (2018) —
See also this morning's post Perception of Space
and yesterday's Exploring Schoolgirl Space.
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