
Update from 10 minutes later:
Summary of the 1966 Landin paper in a Google AI Overview —
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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:
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.
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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 —
From the post "Well Plaid" of February 8, 2024 —
… and from "Moss on the Wall," a post of September 10, 2013 —
See also Big Apple and Brick Space.
Flashback to April 12, 2011 —
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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 —
Unity
—Roman numeral 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— , sounding a lot like — paraphrasing . 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.
"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 —
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 —
See as well the two Log24 posts of December 1st, 2018 —
Character and In Memoriam.
This journal on the above date —
Thursday, April 13, 2017
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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
Cool Mystery:
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 —
by Ashay Dharwadker (Author), Vinay Dharwadker (Author)
Product Details
See as well …
Con Vocation (Log24, Sept. 2, 2014).
"There is such a thing as a tesseract." — Madeleine L'Engle
An approach via the Omega Matrix:
See, too, Rosenhain and Göpel as The Shadow Guests .
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—
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—
A chess set previously mentioned in this journal—

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. |
or, Deja Vu All Over Again
Top two obituaries in this morning's NY Times list–
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David Simons, Who Flew High 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 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, 2010Space Cowboys
Google News, 11:32 AM ET today–
Related material: Yesterday's Easter message, |
April 6 —
Tuesday, April 6, 2010Clue
See also Leary on Cuernavaca, Team Daedalus"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\ |
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"At the moment which is not of action or inaction |
"And there we were all in one place,
A generation lost in space…"
— Don McLean, "American Pie"
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.'"
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–
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 .
Tuesday, June 15, 2010
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Google search result: Saint Anselm College https://www.anselm.edu › Documents › Brown 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
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From a Log24 search for the above phrase . . .
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"For many of us, the geometry course sounded the death knell — "Shape and Space in Geometry" © 1997-2003 Annenberg/CPB. All rights reserved. |
See also Annenberg Hall.
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 —
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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) —
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"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" |
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Gottschalk Review —
W. H. Gottschalk and G. A. Hedlund, Topological Dynamics, 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 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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