Log24

Saturday, February 7, 2026

Lowell Space

Filed under: General — Tags: , , — m759 @ 4:29 am


 

 The Pride of Lowell —

IMAGE- Scenes from 'The Fighter'- Amy Adams, Christian Bale

Sunday, May 18, 2025

Language Models History:  Points in a Space, 1966

Filed under: General — Tags: , , — m759 @ 3:31 pm

Update from 10 minutes later:  

Summary of the 1966 Landin paper in a Google AI Overview

In his 1966 paper "The Next 700 Programming Languages," Peter Landin explored the potential for a large and diverse family of programming languages, arguing for a principled approach to language design focusing on well-defined frameworks and a "well-mapped space" of possible languages. He introduced ISWIM (If You See What I Mean), an abstract language that served as a foundational concept for functional programming. [1, 2]
 
Here's a more detailed explanation:
  • Landin's Vision: Landin's work challenged the idea that programming languages should be designed individually and instead advocated for a more systematic approach. He envisioned a vast, interconnected space of languages, each tailored to specific needs and functionalities. [1, 1, 2]
  • ISWIM: ISWIM, described in his paper, was an abstract, functional language that aimed to provide a flexible framework for building various programming languages. It was not intended to be a concrete language, but rather a blueprint for how languages could be designed based on principles of functional programming and dataflow programming. [2, 2, 3, 4]
  • Influence on Functional Programming: ISWIM's concepts profoundly influenced the development of functional programming languages like SASL, Miranda, ML, Haskell, and their successors, as well as dataflow languages like Lucid, according to Wikipedia. [2, 2]
  • Principle-Based Design: Landin's paper highlighted the importance of principled design in programming languages, emphasizing the need for clear rules and conventions regarding user-defined names, functional relationships, and the use of abstract notation. [1, 1, 5, 5]
  • "Well-Mapped Space": The idea of a "well-mapped space" suggests that rather than designing languages from scratch, they can be derived from a larger framework, making the process more organized and efficient. [1, 1]
  • Focus on Expressions: ISWIM prioritized expressions over statements, aiming to enable a wider range of user needs to be met through concise, functional expressions. [6, 6]
  • Abstract Nature: Landin's ISWIM was an abstract language, meaning it didn't prescribe a specific physical form or syntax, allowing for flexibility in implementation. [2, 7, 7]
In essence, Landin's "Next 700 Programming Languages" paper was a seminal work that envisioned a future where programming languages would be designed more systematically and in a more principled manner, paving the way for the development of various functional and dataflow programming paradigms. [1, 2, 6]
 
AI responses may include mistakes.

Two links from the homepage of the Crary of the cmu.edu link above —

A Man For All Seasons
The Gods of the Copybook Headings .

Other material related to the name Crary —

http://m759.net/wordpress/?tag=crary-art .

Saturday, April 12, 2025

Lily_Collins – Klein_Space – Tartan_Day

Filed under: General — Tags: , — m759 @ 8:43 pm

From the post "Well Plaid" of February 8, 2024 —

and from "Moss on the Wall," a post of September 10, 2013 —

Thursday, August 1, 2024

For Coppola’s Megalopolis:
Brick Space in the Big Apple

Filed under: General — Tags: — m759 @ 12:00 am

See also Big Apple and Brick Space.

Saturday, June 15, 2024

Screwing Up a Space

Filed under: General — Tags: — m759 @ 11:39 am

Flashback to April 12, 2011

National Gallery of Art

In the landscape of minimalism, John McCracken cuts a unique figure. He is often grouped with the “light and space” artists who formed the West Coast branch of the movement. Indeed, he shares interests in vivid color, new materials, and polished surfaces with fellow Californians enamored of the Kustom Kar culture. On the other hand, his signature works, the “planks” that he invented in 1966 and still makes today, have the tough simplicity and aggressive presence of New York minimalism….

“They kind of screw up a space because they lean,” McCracken has said of the planks. Their tilting, reflective surfaces activate the room, leaving the viewer uncertain of traditional boundaries. He notes that the planks bridge sculpture (identified with the floor) and painting (identified with the wall)….

His ultimate goal, as with all mystics, is unity— not just of painting and sculpture, but of substance and illusion, of matter and spirit, of art and life. Such ideas recall the utopian aspirations of early modernists like Piet Mondrian and Wassily Kandinsky.

Related Art —

http://www.log24.com/log/pix11/110412-32x192plusmargin6.bmp

Unity

Roman numeral I
as well as capital I

For a related figure, see a  film review by A. O. Scott at The New York Times  (September 21, 2010)—

“You Will Meet a Tall Dark Stranger” begins with an unseen narrator— Zak Orth, sounding a lot like Woody Allen— paraphrasing Shakespeare. You may remember the quotation from high school English, about how life is a tale told by an idiot, full of sound and fury, signifying nothing. The observation is attributed to the playwright himself (“Shakespeare once said”), rather than to Macbeth, whose grim experience led him to such nihilism, but never mind. In context, it amounts to a perfectly superfluous statement of the obvious.

If life signifies nothing, perhaps the tall dark figure above signifies something . Discuss.

Related (if only phonetically) drama . . . Detective Cruz at Planck's Café.

Monday, November 28, 2022

Groups, Spaces, and Ripoffs

Filed under: General — Tags: , — m759 @ 8:21 pm

"Rubik's Cube, and the simpler [2x2x2] Super Cube, represent
one form of mathematical and physical reality."

— Solomon W. Golomb, "Rubik's Cube and Quarks:
Twists on the eight corner cells of Rubik's Cube
provide a model for many aspects of quark behavior
,"
American Scientist , Vol. 70, No. 3 (May-June 1982), pp. 257-259 

From the last (Nov. 14, 2022) of the Log24 posts now tagged Groups and Spaces

From the first (June 21, 2010) of the Log24 posts now tagged Groups and Spaces

Thursday, May 19, 2022

Schoolgirl.space

Filed under: General — Tags: , — m759 @ 5:46 am

See also a Log24 post from 2010, "Class of 64."

Sunday, February 20, 2022

Ceremonial Space

Filed under: General — Tags: — m759 @ 1:23 pm

From posts now tagged iching.space (also a URL) —

IMAGE- Concepts of Space

 

Monday, March 25, 2019

Espacement

(Continued from the previous post.)

In-Between "Spacing" and the "Chôra "
in Derrida: A Pre-Originary Medium?

By Louise Burchill

(Ch. 2 in Henk Oosterling & Ewa Plonowska Ziarek (Eds.),  Intermedialities: Philosophy, Arts, Politics , Lexington Books, October 14, 2010)

"The term 'spacing' ('espacement ') is absolutely central to Derrida's entire corpus, where it is indissociable from those of différance  (characterized, in the text from 1968 bearing this name, as '[at once] spacing [and] temporizing' 1), writing  (of which 'spacing' is said to be 'the fundamental property' 2) and deconstruction (with one of Derrida's last major texts, Le Toucher: Jean-Luc Nancy , specifying 'spacing ' to be 'the first word of any deconstruction' 3)."

1  Jacques Derrida, “La Différance,” in Marges – de la philosophie  (Paris: Minuit, 1972), p. 14. Henceforth cited as  D  .

2  Jacques Derrida, “Freud and the Scene of Writing,” trans. A. Bass, in Writing and  Difference  (Chicago: University of Chicago Press, 1978), p. 217. Henceforth cited as FSW .

3  Jacques Derrida, Le Toucher, Jean-Luc Nancy  (Paris: Galilée, 2000), p. 207.

. . . .

"… a particularly interesting point is made in this respect by the French philosopher, Michel Haar. After remarking that the force Derrida attributes to différance  consists simply of the series of its effects, and is, for this reason, 'an indefinite process of substitutions or permutations,' Haar specifies that, for this process to be something other than a simple 'actualisation' lacking any real power of effectivity, it would need “a soubassement porteur ' – let’s say a 'conducting underlay' or 'conducting medium' which would not, however, be an absolute base, nor an 'origin' or 'cause.' If then, as Haar concludes, différance  and spacing show themselves to belong to 'a pure Apollonism' 'haunted by the groundless ground,' which they lack and deprive themselves of,16 we can better understand both the threat posed by the 'figures' of space and the mother in the Timaeus  and, as a result, Derrida’s insistent attempts to disqualify them. So great, it would seem, is the menace to différance  that Derrida must, in a 'properly' apotropaic  gesture, ward off these 'figures' of an archaic, chthonic, spatial matrix in any and all ways possible…."

16  Michel Haar, “Le jeu de Nietzsche dans Derrida,” Revue philosophique de la France et de l’Etranger  2 (1990): 207-227.

. . . .

… "The conclusion to be drawn from Democritus' conception of rhuthmos , as well as from Plato's conception of the chôra , is not, therefore, as Derrida would have it, that a differential field understood as an originary site of inscription would 'produce' the spatiality of space but, on the contrary, that 'differentiation in general' depends upon a certain 'spatial milieu' – what Haar would name a 'groundless ground' – revealed as such to be an 'in-between' more 'originary' than the play of differences it in-forms. As such, this conclusion obviously extends beyond Derrida's conception of 'spacing,' encompassing contemporary philosophy's continual privileging of temporization in its elaboration of a pre-ontological 'opening' – or, shall we say, 'in-between.'

For permutations and a possible "groundless ground," see
the eightfold cube and group actions both on a set of eight
building blocks arranged in a cube (a "conducting base") and
on the set of seven natural interstices (espacements )  between
the blocks. Such group actions provide an elementary picture of
the isomorphism between the groups PSL(2,7) (acting on the
eight blocks) and GL(3,2) (acting on the seven interstices).

Espacements
 

For the Church of Synchronology

See also, from the reported publication date of the above book
Intermedialities , the Log24 post Synchronicity.

Sunday, December 9, 2018

Quaternions in a Small Space

Filed under: G-Notes,General,Geometry — Tags: , , , — m759 @ 2:00 pm

The previous post, on the 3×3 square in ancient China,
suggests a review of group actions on that square
that include the quaternion group.

Click to enlarge

Three links from the above finitegeometry.org webpage on the
quaternion group —

Related material —

Iain Aitchison on the 'symmetric generation' of R. T. Curtis

See as well the two Log24 posts of December 1st, 2018 —

Character and In Memoriam.

Tuesday, June 13, 2017

Annals of Embedded Space

Filed under: General — Tags: , , — m759 @ 12:55 am

Max Maxfield: 'What's Happening in Embedded Space,' April 13, 2017

This  journal on the above date —

Thursday, April 13, 2017

Space

Tags:  — m759 @ 7:00 PM 

See "Smallest Perfect" in this journal.

 

Making Space

— m759 @ 6:00 PM 

The New York Times  online today:

At MoMA, Women at Play in the Fields of Abstraction

In Zoe's fall, we sinnèd all.

Monday, January 30, 2017

Devotional Space

Filed under: General — Tags: — m759 @ 4:16 pm

Quotations by and for an artist who reportedly died
on Sunday, January 15, 2017 —

"What drives my vision is a need to locate
a 'genetically felt' devotional space
in which a simultaneous multiplicity
of disparate realities coexists."

— The late Ciel Bergman, in her webpage
     "Artist's Statement"

"Once a registered nurse who worked in a hospital
psychiatric ward, Ms. Bergman was a struggling
single mom of two when she couldn’t resist the pull
of her art. In 1969, she entered a painting in the
Jack London Invitational, an art contest in Oakland,
and won first prize. This compelled her to enroll at
the San Francisco Art Institute, where she earned
her master of fine arts with honors in painting."

Sam Whiting in the San Francisco Chronicle

See also Oakland in this journal and
"Only a peculiar can enter a time loop."

"The peculiar kind of 'identity' that is attributed to
apparently altogether heterogeneous figures
in virtue of their being transformable into one another
by means of certain operations defining a group,
is thus seen to exist also in the domain of perception."

— Ernst Cassirer, quoted here on
     Midsummer Eve (St. John's Eve), 2010

Monday, October 12, 2015

Space, Time, Matter (continued)

Filed under: General — m759 @ 5:08 pm

Cool Mystery:

http://www.log24.com/log/pix11C/111005-PlancksCafe-CruzEnters.jpg

Detective Cruz enters Planck's Constant Café in "The Big Bang."

The above images are from a Log24 post of October 5, 2011.

Related material for fans of recreational math and Manil Suri

A book that Amazon.com says was published on that same date —
October 5, 2011 —

Space, Time and Matter 

by Ashay Dharwadker (Author), Vinay Dharwadker  (Author)

Product Details

  • Paperback: 98 pages
  • Publisher: CreateSpace Independent Publishing
                       Platform (October 5, 2011)
  • Language: English
  • Amazon Best Sellers Rank: #7,605,448 in Books 

See as well

Con Vocation  (Log24, Sept. 2, 2014).

Monday, August 4, 2014

A Wrinkle in Space

Filed under: General,Geometry — Tags: , , — m759 @ 10:30 am

"There is  such a thing as a tesseract." — Madeleine L'Engle

An approach via the Omega Matrix:

http://www.log24.com/log/pix10A/100619-TesseractAnd4x4.gif

See, too, Rosenhain and Göpel as The Shadow Guests .

Friday, August 23, 2013

Vacant Space

Filed under: General — Tags: — m759 @ 9:00 pm

A passage from Wallace Stevens

The spirit and space,
The empty spirit 
In vacant space.

A frame from the film American Psycho  (2000), starring Christian Bale—

IMAGE- 'espace' sign from the film 'American Psycho'

The rest of the film is not recommended.

Related material—

"24 Hour Psycho" at the Museum of Modern Art in the novel Point Omega .

Illustration from a New York Times  review

IMAGE- NY Times headline 'A Wrinkle in Time' with 24 Hour Psycho and Point Omega scene

Sunday, November 20, 2011

Occupy Space

Filed under: General — Tags: , — m759 @ 11:35 am

A chess set previously mentioned in this journal—

http://www.log24.com/log/pix11C/111120-ChessSet-419x1180.jpg

These chessmen appeared in the weblog Minimalissimo 
on Sept. 20, 2010. In Log24 on that date, the issue was
not so much the chessmen as the underlying board.
See "The Unfolding." See also the following from
the Occupy Space  gallery in Limerick today—

C A V E S – Anthony Murphy Solo Exhibition
 
Opening 7 pm Thursday 1st Dec
Exhibition 2nd – 22nd Dec 2011

Plato's allegory of the cave describes prisoners, inhabiting the cave since childhood, immobile, facing an interior wall. A large fire burns behind the prisoners, and as people pass this fire their shadows are cast upon the cave's wall, and these shadows of the activity being played out behind the prisoner become the only version of reality that the prisoner knows.

C A V E S  is an exhibition of three large scale works, each designed to immerse the viewer, and then to confront the audience with a question regarding how far they, as privileged viewers of the shadows and reflections being played out upon the walls, are willing to allow themselves to believe what they know to be a false reality.

The works are based on explorations of simple 2D shapes; regular polygons are exploded to create fractured pattern, or layered upon one another until intricate forms emerge, upon which the projections can begin to draw out a third dimension.

Sunday, April 18, 2010

A Generation Lost in Space

Filed under: General — m759 @ 2:29 am

or, Deja Vu All Over Again

Top two obituaries in this morning's NY Times list–

David Simons, Who Flew High
on Eve of Space Age, Dies at 87

Dr. Simons, a physician turned Air Force officer, had sent animals aloft for several years before his record-breaking flight.

James Aubrey, who Portrayed the Hero
in ‘Lord of the Flies’, Is Dead at 62

Mr. Aubrey portrayed Ralph in the film version of the William Golding novel and had a busy career on stage and television in England.

Simons reportedly died on April 5,
Aubrey on April 6.

This journal on those dates–

April 5 —

Monday, April 5, 2010

Space Cowboys

Filed under: Uncategorized — m759 @ 12:00 PM Edit This

http://www.log24.com/log/pix10/100405-Eastwood.jpg

Google News, 11:32 AM ET today–

http://www.log24.com/log/pix10/100405-SpaceCowboysSm.jpg

Related material:

Yesterday's Easter message,
film notes from March 13,
and Dagger Definitions.

April 6 —

Tuesday, April 6, 2010

Clue

Filed under: Uncategorized — m759 @ 12:00 PM Edit This

Excerpt from 'Cosmic Trigger'
 by Robert Anton Wilson

See also Leary on Cuernavaca,
John O'Hara's fleeting reference
to Cuernavaca in Hope of Heaven,
and Cuernavaca in this journal.

Team Daedalus

Filed under: Uncategorized — m759 @ 9:00 AM Edit This

"Concept (scholastics' verbum mentis)– theological analogy of Son's procession as Verbum Patris, 111-12" –Index to Joyce and Aquinas, by William T. Noon, Society of Jesus, Yale University Press 1957, second printing 1963, page 162

"Back in 1958… [four] Air Force pilots were Team Daedalus, the best of the best." –Summary of the film "Space Cowboys"

"Man is nothing if not labyrinthine." –The Vicar in Trevanian's The Loo Sanction\

 

Commentary by T.S. Eliot

"At the moment which is not of action or inaction
You can receive this: 'on whatever sphere of being
The mind of a man may be intent
At the time of death'—that is the one action
(And the time of death is every moment)
Which shall fructify in the lives of others:
And do not think of the fruit of action.
Fare forward."

 

Friday, March 5, 2010

Space Case

Filed under: General — Tags: , , — m759 @ 9:48 am

Large ad, front page top, for Tom Brokaw's 'Boomers' in NY Times of March 4th, 2010

"And there we were all in one place,
A generation lost in space…"
— Don McLean, "American Pie

    Cybill Shepherd (born 1950) and Jeff Bridges (born 1949) in 'The Last Picture Show'

Today's NY Times says Robert T. McCall, space artist, died at 90 on Feb. 26.

"His most famous image may be the gargantuan mural, showing events from the creation of the universe to men walking on the Moon, on the south lobby wall of the National Air and Space Museum on the National Mall in Washington. More than 10 million people a year pass it.

Or it might be his painting showing a space vehicle darting from the bay of a wheel-shaped space station, which was used in a poster for Stanley Kubrick’s landmark 1968 film, '2001: A Space Odyssey.'"

Space station image by Robert T. McCall for '2001'

Cover art by McCall, with autograph dated
8/19/05, from a personal web page

Hal in "2010"– "Will I dream?"

Log24 on the day that McCall died

"Which Dreamed It?"
– Title of final chapter,Through the Looking Glass

"Go ask Alice… I think she'll know."
– Grace Slick, 1967  

Related material: James Joyce in this journal–

"Space: what you damn well have to see."

Monday, December 30, 2024

100 Years of “The Smallest Perfect Universe”

Filed under: General — Tags: — m759 @ 11:04 am

The phrase "smallest perfect universe" is by Burkard Polster.
It refers to the smallest finite projective space of three dimensions.
As a sort of memorial to mathematics during the first 100 years
since the 1910 publication of Conwell's classic study of that space,
see a Log24 search for Space 2010 .

Friday, April 25, 2025

Imago Review: “The Thing and I” Continues.

Filed under: General — Tags: , — m759 @ 12:26 pm

Tuesday, June 15, 2010

Imago, Imago, Imago
 

Tags: , , , , — m759 @ 11:07 am

Recommended— an online book—

Flight from Eden: The Origins of Modern Literary Criticism and Theory,
by Steven Cassedy, U. of California Press, 1990.

See in particular

Valéry and the Discourse On His Method.

Pages 156-157—

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. “Every act of understanding is based on a group,” he says (C, 1:331). “My specialty—reducing everything to the study of a system closed on itself and finite” (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one “group” undergoes a “transformation” and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: “The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind’s momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. “Mathematical science . . . reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind” (O, 1:36). “Psychology is a theory of transformations, we just need to isolate the invariants and the groups” (C, 1:915). “Man is a system that transforms itself” (C, 2:896).

Notes:

  Paul Valéry, Oeuvres (Paris: Pléiade, 1957-60)

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

Compare Jung’s image in Aion  of the Self as a four-diamond figure:

http://www.log24.com/log/pix10A/100615-JungImago.gif

and Cullinane’s purely geometric four-diamond figure:

http://www.log24.com/log/pix10A/100615-FourD.gif

For a natural group of 322,560 transformations acting on the latter figure, see the diamond theorem.

What remains fixed (globally, not pointwise) under these transformations is the system  of points and hyperplanes from the diamond theorem.

Friday, February 7, 2025

Apple Entertainment

Filed under: General — Tags: , — m759 @ 12:49 pm

The Miracle Octad Generator (MOG) of R. T. Curtis

Monday, January 29, 2024

Self as Imago Dei:  Hofstadter vs. Valéry

Filed under: General — Tags: , , , — m759 @ 9:41 am
 

Google search result:

Imago Dei  in Thomas Aquinas

Saint Anselm College

https://www.anselm.edu › Documents › Brown

PDF

by M Brown · 2014 · Cited by 14 — Thomas insists that the image of God exists most perfectly in the acts of the soul, for the soul is that which is most perfect in us and so best images God, and …

11 pages

For a Douglas Hofstadter version of the Imago Dei , see the
"Gödel, Escher, Bach" illustration in the Jan. 15 screenshot below —

Tuesday, June 15, 2010

Imago, Imago, Imago
 

Filed under: General,Geometry — Tags: , , , , — m759 @ 11:07 am

Recommended— an online book—

Flight from Eden: The Origins of Modern Literary Criticism and Theory,
by Steven Cassedy, U. of California Press, 1990.

See in particular

Valéry and the Discourse On His Method.

Pages 156-157—

Valéry saw the mind as essentially a relational system whose operation he attempted to describe in the language of group mathematics. “Every act of understanding is based on a group,” he says (C, 1:331). “My specialty—reducing everything to the study of a system closed on itself and finite” (C, 19: 645). The transformation model came into play, too. At each moment of mental life the mind is like a group, or relational system, but since mental life is continuous over time, one “group” undergoes a “transformation” and becomes a different group in the next moment. If the mind is constantly being transformed, how do we account for the continuity of the self? Simple; by invoking the notion of the invariant. And so we find passages like this one: “The S[elf] is invariant, origin, locus or field, it’s a functional property of consciousness” (C, 15:170 [2: 315]). Just as in transformational geometry, something remains fixed in all the projective transformations of the mind’s momentary systems, and that something is the Self (le Moi, or just M, as Valéry notates it so that it will look like an algebraic variable). Transformation theory is all over the place. “Mathematical science . . . reduced to algebra, that is, to the analysis of the transformations of a purely differential being made up of homogeneous elements, is the most faithful document of the properties of grouping, disjunction, and variation in the mind” (O, 1:36). “Psychology is a theory of transformations, we just need to isolate the invariants and the groups” (C, 1:915). “Man is a system that transforms itself” (C, 2:896).

Notes:

  Paul Valéry, Oeuvres (Paris: Pléiade, 1957-60)

C   Valéry, Cahiers, 29 vols. (Paris: Centre National de le Recherche Scientifique, 1957-61)

Compare Jung’s image in Aion  of the Self as a four-diamond figure:

http://www.log24.com/log/pix10A/100615-JungImago.gif

and Cullinane’s purely geometric four-diamond figure:

http://www.log24.com/log/pix10A/100615-FourD.gif

For a natural group of 322,560 transformations acting on the latter figure, see the diamond theorem.

What remains fixed (globally, not pointwise) under these transformations is the system  of points and hyperplanes from the diamond theorem.

Tuesday, December 5, 2023

The Annenberg Knell

Filed under: General — Tags: , — m759 @ 11:38 pm

From a Log24 search for the above phrase . . .

"For many of us, the geometry course sounded the death knell
for our progress — and interest — in mathematics."

— "Shape and Space in Geometry"

© 1997-2003 Annenberg/CPB. All rights reserved.

See also Annenberg Hall.

Sunday, June 4, 2023

The Galois Core

Filed under: General — Tags: , , — m759 @ 9:24 pm
 

  Rubik core:

 

Swarthmore Cube Project, 2008


Non- Rubik core:

Illustration for weblog post 'The Galois Core'

Central structure from a Galois plane

    (See image below.)

Some small Galois spaces (the Cullinane models)

Tuesday, May 16, 2023

The Cassirer in the Rye

Filed under: General — Tags: — m759 @ 11:01 am

From the American Mathematical Society today —

Robert Earl Tubbs (1954-2023)
May 15, 2023

"Tubbs, associate professor of mathematics at
the University of Colorado Boulder, died April 11, 2023,
at the age of 69. He received his PhD in 1981 from
Penn State University under the supervision of 
W. Dale Brownawell. His research interests included
number theory, especially transcendental number theory,
the intellectual history of mathematical ideas and mathematics,
and the humanities."

This  journal on the dies natalis  of Tubbs had the third of three
posts tagged "Space and Form."  Those posts dealt with European
cultural history related to Tubbs's interests. The "Space and Form"
posts, along with today's previous Log24 post, suggest a review of
the Nov. 10, 2021 post titled European Culture.  An image from that post —

Those who share Cassirer's enthusiasm for myth may regard the
above Josefine Lyche version of my work as a sort of "secret writing,"
to quote a phrase of Cassirer's I find very distasteful. But there is nothing
secret  about it, although there is some resemblance to written characters.

This  post's title was suggested by a Salinger quote in the European Culture post.

Update on the next day, May  17 —

Further reading in Cassirer's Mythical Thought  indicates that in the
passages above, on Schelling, he may be presenting a parody of
Schelling when he writes "a poem hidden behind a wonderful
secret writing."  Later, on page 10, he asks, sensibly, 

"… is there, perhaps, a means of retaining the question
put forward by Schelling's Philosophie der Mythologie
but of transferring it from the sphere of a philosophy of
the absolute to that of critical philosophy?"

There has reportedly been "an upsurge of interest" in Cassirer —

Sunday, February 26, 2023

TOE

Filed under: General — Tags: — m759 @ 2:24 am


 

Related images from The Crimson Abyss —

1984 —

IMAGE- 'Affine Groups on Small Binary Spaces,' illustration

2010 —

Logo design for Stack Exchange Math by Jin Yang

Thursday, July 28, 2022

The Gibson Gambit

Filed under: General — Tags: , — m759 @ 1:48 am
 

OPINION DYNAMICS ON DISCOURSE SHEAVES

By  JAKOB HANSEN AND ROBERT GHRIST

arXiv:2005.12798 (math)  [Submitted on 26 May 2020]

Funding: This work was funded by the Office of the Assistant Secretary of Defense Research & Engineering through a Vannevar Bush Faculty Fellowship, ONR N00014-16-1-2010.

HANSEN — Department of Mathematics, University of Pennsylvania, Philadelphia, PA (jhansen@math.upenn.edu)

GHRIST — Department of Mathematics and Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA (ghrist@math.upenn.edu)

See as well this  journal on the above date (26 May 2020) —

Tuesday, July 5, 2022

For Ron Howard, Tom Hanks, and Dan Brown — Symbology!

Filed under: General — m759 @ 1:22 am

Friday, March 18, 2022

Architectural Review

Filed under: General — Tags: , — m759 @ 12:30 pm
 

"Poincaré said that science is no more a collection of facts than a house is a collection of bricks. The facts have to be ordered or structured, they have to fit a theory, a construct (often mathematical) in the human mind.

… Mathematics may be art, but to the general public it is a black art, more akin to magic and mystery. This presents a constant challenge to the mathematical community: to explain how art fits into our subject and what we mean by beauty.

In attempting to bridge this divide I have always found that architecture is the best of the arts to compare with mathematics. The analogy between the two subjects is not hard to describe and enables abstract ideas to be exemplified by bricks and mortar, in the spirit of the Poincaré quotation I used earlier."

— Sir Michael Atiyah, "The Art of Mathematics"
     in the AMS Notices , January 2010

Gottschalk Review —

W. H. Gottschalk and G. A. Hedlund, Topological Dynamics,
reviewed by Paul R. Halmos in Bulletin of the American Mathematical Society  61(6): 584-588 (November 1955).

The ending of the review —

The most striking virtue of the book is its organization. The authors' effort to arrange the exposition in an efficient order, and to group the results together around a few central topics, was completely successful; they deserve to be congratulated on a spectacular piece of workmanship. The results are stated at the level of greatest available generality, and the proofs are short and neat; there is no unnecessary verbiage. The authors have, also, a real flair for the "right" generalization; their definitions of periodicity and almost periodicity, for instance, are very elegant and even shed some light on the classical concepts of the same name. The same is true of their definition of a syndetic set, which specializes, in case the group is the real line, to Bohr's concept of a relatively dense set.

The chief fault of the book is its style. The presentation is in the brutal Landau manner, definition, theorem, proof, and remark following each other in relentless succession. The omission of unnecessary verbiage is carried to the extent that no motivation is given for the concepts and the theorems, and there is a paucity of illuminating examples. The striving for generality (which, for instance, has caused the authors to treat uniform spaces instead of metric spaces whenever possible) does not make for easy reading. The same is true of the striving for brevity; the shortest proof of a theorem is not always the most perspicuous one. There are too many definitions, especially in the first third of the book; the reader must at all times keep at his finger tips a disconcerting array of technical terminology. The learning of this terminology is made harder by the authors' frequent use of multiple statements, such as: "The term {asymptotic } {doubly asymptotic } means negatively {or} {and} positively asymptotic."

Conclusion: the book is a mine of information, but you sure have to dig for it.  — PAUL R. HALMOS

The Dog Far Hence, or Ekphrasis for Anubis

Filed under: General — Tags: — m759 @ 1:26 am

IMAGE- Concepts of Space

The above image suggests a review of Sigaud in this journal and of . . .

Related material from the Web —

"Anubis, easily recognizable as an anthropomorphized jackal or dog,
was the Egyptian god of the afterlife and mummification. He helped
judge souls after their death and guided lost souls into the afterlife.
So, was he evil? No, and in fact just the opposite. In ancient Egyptian
mythology the ultimate evil was chaos. Nearly all of Egyptian mythology
was focused around maintaining the cycles of cosmic order that kept
chaos at bay. Few things were as significant in this goal as the rituals
maintaining the cycle of life, death, and afterlife. Therefore, Anubis was
not evil but rather one of the most important gods who kept evil out of Egypt."

— Christopher Muscato at Study.com

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