See also Stone Logical Dimensions …
“Lord Arglay had a suspicion that the Stone
would be purely logical. Yes, he thought,
but what, in that sense, were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
Sunday, April 3, 2016
Logic
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Wednesday, February 23, 2022
Tuesday, February 16, 2021
Buffalo Logic
From a post of January 8, 2021 —
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
A Midrash for Emma —
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Friday, January 8, 2021
Welcome to Zombieland
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
“Don’t give a damn ’cause I done that already.” — Zombie Jamboree
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Wednesday, January 29, 2020
On the Road
From Mosaic Logic, a post of September 3, 2017 —
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
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Sunday, November 17, 2019
E-Elements Revisited
The German mathematician Wolf Barth in the above post is not the
same person as the Swiss artist Wolf Barth in today's previous post.
An untitled, undated, picture by the latter —
Compare and contrast with an "elements" picture of my own —
— and with . . .
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
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Sunday, September 3, 2017
Mosaic Logic
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
While you're waiting …
Click the above illustration for
some remarks on mosaics.
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Sunday, August 13, 2017
Logos
In memoriam —
Zadeh is known for the unfortunate phrase "fuzzy logic."
Not-so-fuzzy related material —
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
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Monday, June 12, 2017
Bubble
The "bubble" passage in the previous post suggests a review of
a post from December 21, 2006, with the following images —
Update of 11:01 PM ET the same day, June 12, 2017 —
Related material for the Church of Synchronology —
From a tech-article series that began on Halloween 2006 and
ended on the date of the above Geometry's Tombstones post —
Compare and contrast (from a post of Feb. 27, 2017) —
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
See also "The Geometry of Logic:
Finite Geometry and the 16 Boolean Connectives"
by Steven H. Cullinane in 2007.
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Monday, February 27, 2017
Logic for Jews
Adam Gopnik in The New Yorker today reacts to the startling
outcomes of three recent contests: the presidential election,
the Super Bowl, and the Oscar for Best Picture —
"The implicit dread logic is plain."
Related material —
Transformers in this journal and …
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
See also …
The above figure is from Ian Stewart's 1996 revision of a 1941 classic,
What Is Mathematics? , by Richard Courant and Herbert Robbins.
One wonders how the confused slave boy of Plato's Meno would react
to Stewart's remark that
"The number of copies required to double an
object's size depends on its dimension."
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Saturday, January 28, 2017
Cranking It Up
From "Core," a post of St. Lucia's Day, Dec. 13, 2016 —
In related news yesterday —
California yoga mogul’s mysterious death:
Trevor Tice’s drunken last hours detailed
"Police found Tice dead on the floor in his home office,
blood puddled around his head. They also found blood
on walls, furniture, on a sofa and on sheets in a nearby
bedroom, where there was a large bottle of Grey Goose
vodka under several blood-stained pillows on the floor."
See as well an image from "The Stone," a post of March 18, 2016 —
Some backstory —
“Lord Arglay had a suspicion that the Stone would be
purely logical. Yes, he thought, but what, in that sense,
were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
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Thursday, December 1, 2011
Paranoia Strikes Deep
Tens of Millions of Smartphones Come With Spyware
Preinstalled, Security Analyst Says
Published December 01, 2011 – FoxNews.com
For details, see comments at YouTube.
Related entertainment—
1. Tara Fitzgerald in "New World Disorder" (1999)—
We skipped the light fandango
turned cartwheels 'cross the floor
I was feeling kinda seasick
but the crowd called out for more
2. Tara Fitzgerald in "Broken Glass" (2011)—
And so it was that later
as the miller told his tale
that her face, at first just ghostly,
turned a whiter shade of pale
— Procol Harum song at beginning and end of "The Net" (1995)
“Lord Arglay had a suspicion that the Stone
would be purely logical. Yes, he thought,
but what, in that sense, were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams,
quoted here on Kristallnacht 2011
See also, from "The Net"—
Decompiling Wolfenstein
"In Wolfenstein 3D , the player assumes the role of an American soldier
of Polish descent… attempting to escape from the Nazi stronghold of
Castle Wolfenstein." — Wikipedia
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Wednesday, November 9, 2011
Polish Logic–
The Big Lukasiewicz
“Lord Arglay had a suspicion that the Stone
would be purely logical. Yes, he thought,
but what, in that sense, were the rules of its pure logic?”
—Many Dimensions (1931), by Charles Williams
See also Łukasiewicz in Wikipedia and Lukasiewicz in this journal.
The latter's Christian references seem preferable to yesterday's
link to a scene from the Coen brothers' film "The Big Lebowski."
For those who prefer a Christ-for-Jews there is
also Harvard's version. See The Crimson Passion.
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Tuesday, November 23, 2010
Tale
A reviewer says Steve Martin finds in his new novel An Object of Beauty "a sardonic morality tale."
From this journal on the day The Cube was published (see today's Art Object ) —
Monday February 20, 2006
|
See also a post on Mathematics and Narrative from Nov. 14, 2009.
That post compares characters in Many Dimensions to those in Logicomix—
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Sunday, November 15, 2009
The Dead Shepherd and…
Chinese Boxes
Continued from “The Dead Shepherd,” Jan. 24, 2007…
“James R. Lilley, 81, a longtime CIA operative in Asia who served as ambassador to China during the Tiananmen Square crackdown… died Nov. 12.”
James R. Lilley
From a page linked to here on the date of Lilley’s death:
“… the extraordinary set of nested Chinese boxes that we introduced earlier in this series….”
A seemingly unrelated item in today’s New York Times obituaries index:
This suggests an article on temporal logic at IBM Developer Works, which contains a link to Time-Rover.com.
This in turn leads to…
Shing’s CV at the Naval Postgraduate School affirms the usefulness of temporal logic.
Those who prefer metaphysics may consult the novel Many Dimensions referred to in yesterday’s entries and in “Relativity Blues” (Feb. 20, 2005)–
From Many Dimensions:
“Lord Arglay had a suspicion that the Stone would be purely logical. Yes, he thought, but what, in that sense, were the rules of its pure logic?”
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Tuesday, February 24, 2009
Tuesday February 24, 2009
Hollywood Nihilism
Meets
Pantheistic Solipsism
Meets
Pantheistic Solipsism
Tina Fey to Steve Martin
at the Oscars:
"Oh, Steve, no one wants
to hear about our religion
… that we made up."
|
From Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 117:
… in 'The Pediment of Appearance,' a slight narrative poem in Transport to Summer… A group of young men enter some woods 'Hunting for the great ornament, The pediment of appearance.' Though moving through the natural world, the young men seek the artificial, or pure form, believing that in discovering this pediment, this distillation of the real, they will also discover the 'savage transparence,' the rude source of human life. In Stevens's world, such a search is futile, since it is only through observing nature that one reaches beyond it to pure form. As if to demonstrate the degree to which the young men's search is misaligned, Stevens says of them that 'they go crying/The world is myself, life is myself,' believing that what surrounds them is immaterial. Such a proclamation is a cardinal violation of Stevens's principles of the imagination. |
Superficially the young men's philosophy seems to resemble what Wikipedia calls "pantheistic solipsism"– noting, however, that "This article has multiple issues."
As, indeed, does pantheistic solipsism– a philosophy (properly called "eschatological pantheistic multiple-ego solipsism") devised, with tongue in cheek, by science-fiction writer Robert A. Heinlein.
Despite their preoccupation with solipsism, Heinlein and Stevens point, each in his own poetic way, to a highly non-solipsistic topic from pure mathematics that is, unlike the religion of Martin and Fey, not made up– namely, the properties of space.
"Sharpie, we have condensed six dimensions into four, then we either work by analogy into six, or we have to use math that apparently nobody but Jake and my cousin Ed understands. Unless you can think of some way to project six dimensions into three– you seem to be smart at such projections."
I closed my eyes and thought hard. "Zebbie, I don't think it can be done. Maybe Escher could have done it."
|
A discussion of Stevens's late poem "The Rock" (1954) in Wallace Stevens: A World of Transforming Shapes, by Alan D. Perlis, Bucknell University Press, 1976, p. 120:
For Stevens, the poem "makes meanings of the rock." In the mind, "its barrenness becomes a thousand things/And so exists no more." In fact, in a peculiar irony that only a poet with Stevens's particular notion of the imagination's function could develop, the rock becomes the mind itself, shattered into such diamond-faceted brilliance that it encompasses all possibilities for human thought:
The rock is the gray particular of man's life,
The stone from which he rises, up—and—ho,
The step to the bleaker depths of his descents ...
The rock is the stern particular of the air,
The mirror of the planets, one by one,
But through man's eye, their silent rhapsodist,
Turquoise the rock, at odious evening bright
With redness that sticks fast to evil dreams;
The difficult rightness of half-risen day.
The rock is the habitation of the whole,
Its strength and measure, that which is near,
point A
In a perspective that begins again
At B: the origin of the mango's rind.
(Collected Poems, 528)
|
Stevens's rock is associated with empty space, a concept that suggests "nothingness" to one literary critic:
B. J. Leggett, "Stevens's Late Poetry" in The Cambridge Companion to Wallace Stevens— On the poem "The Rock":
"… the barren rock of the title is Stevens's symbol for the nothingness that underlies all existence, 'That in which space itself is contained'…. Its subject is its speaker's sense of nothingness and his need to be cured of it."
This interpretation might appeal to Joan Didion, who, as author of the classic novel Play It As It Lays, is perhaps the world's leading expert on Hollywood nihilism.
More positively…
Space is, of course, also a topic
in pure mathematics…
For instance, the 6-dimensional
affine space (or the corresponding
5-dimensional projective space)
over the two-element Galois field
can be viewed as an illustration of
Stevens's metaphor in "The Rock."
Heinlein should perhaps have had in mind the Klein correspondence when he discussed "some way to project six dimensions into three." While such a projection is of course trivial for anyone who has taken an undergraduate course in linear algebra, the following remarks by Philippe Cara present a much more meaningful mapping, using the Klein correspondence, of structures in six (affine) dimensions to structures in three.
Cara:
Here the 6-dimensional affine
space contains the 63 points
of PG(5, 2), plus the origin, and
the 3-dimensional affine
space contains as its 8 points
Conwell's eight "heptads," as in
Generating the Octad Generator.
Comments Off on Tuesday February 24, 2009
Wednesday, April 23, 2008
Wednesday April 23, 2008
Upscale Realism
or, "Have some more
wine and cheese, Barack."
Allyn Jackson on Rebecca Goldstein
in the April 2006 AMS Notices (pdf)
|
"Rebecca Goldstein’s 1983 novel The Mind-Body Problem has been widely admired among mathematicians for its authentic depiction of academic life, as well as for its exploration of how philosophical issues impinge on everyday life. Her new book, Incompleteness: The Proof and Paradox of Kurt Gödel, is a volume in the 'Great Discoveries' series published by W. W. Norton….
In March 2005 the Mathematical Sciences Research Institute (MSRI) in Berkeley held a public event in which its special projects director, Robert Osserman, talked with Goldstein about her work. The conversation, which took place before an audience of about fifty people at the Commonwealth Club in San Francisco, was taped…. A member of the audience posed a question that has been on the minds of many of Goldstein’s readers: Is The Mind-Body Problem based on her own life? She did indeed study philosophy at Princeton, finishing her Ph.D. in 1976 with a thesis titled 'Reduction, Realism, and the Mind.' She said that while there are correlations between her life and the novel, the book is not autobiographical…. She… talked about the relationship between Gödel and his colleague at the Institute for Advanced Study, Albert Einstein. The two were very different: As Goldstein put it, 'Einstein was a real mensch, and Gödel was very neurotic.' Nevertheless, a friendship sprang up between the two. It was based in part, Goldstein speculated, on their both being exiles– exiles from Europe and intellectual exiles. Gödel's work was sometimes taken to mean that even mathematical truth is uncertain, she noted, while Einstein's theories of relativity were seen as implying the sweeping view that 'everything is relative.' These misinterpretations irked both men, said Goldstein. 'Einstein and Gödel were realists and did not like it when their work was put to the opposite purpose.'" |
Related material:
From Log24 on
March 22 (Tuesday of
Passion Week), 2005:
|
"'What is this Stone?' Chloe asked…. 'It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"
— Many Dimensions,
For more on this theme
appropriate to Passion Week — Jews playing God — see
Rebecca Goldstein
Wine and cheese |
From
UPSCALE,
a website of the
physics department at
the University of Toronto:
|
Mirror Symmetry
"The image [above]
The caption of the
'That most divine and beautiful
The caption of the
'A shadow, likeness, or * Sic. The original is incomprehensibilis, a technical theological term. See Dorothy Sayers on the Athanasian Creed and John 1:5. |
For further iconology of the
above equilateral triangles,
see Star Wars (May 25, 2003),
Mani Padme (March 10, 2008),
Rite of Sping (March 14, 2008),
and
Art History: The Pope of Hope
(In honor of John Paul II
three days after his death
in April 2005).
Happy Shakespeare's Birthday.
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Monday, April 7, 2008
Monday April 7, 2008
“Lord Arglay had a suspicion that
— Charles Williams, Many Dimensions
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Monday, February 20, 2006
Monday February 20, 2006
The Past Revisited
From Log24 a year ago on this date, a quote from Many Dimensions (1931), by Charles Williams:
“Lord Arglay had a suspicion that the Stone would be purely logical. Yes, he thought, but what, in that sense, were the rules of its pure logic?”
For the rest of the story, see the downloadable version at Project Gutenberg of Australia.
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Monday, August 22, 2005
Monday August 22, 2005
The Hole
Part I: Mathematics and Narrative
Apostolos Doxiadis on last month's conference on "mathematics and narrative"–
Doxiadis is describing how talks by two noted mathematicians were related to
"… a sense of a 'general theory bubbling up' at the meeting… a general theory of the deeper relationship of mathematics to narrative…. "
Doxiadis says both talks had "a big hole in the middle."
"Both began by saying something like: 'I believe there is an important connection between story and mathematical thinking. So, my talk has two parts. [In one part] I’ll tell you a few things about proofs. [And in the other part] I’ll tell you about stories.' …. And in both talks it was in fact implied by a variation of the post hoc propter hoc, the principle of consecutiveness implying causality, that the two parts of the lectures were intimately related, the one somehow led directly to the other."
"And the hole?"
"This was exactly at the point of the link… [connecting math and narrative]… There is this very well-known Sidney Harris cartoon… where two huge arrays of formulas on a blackboard are connected by the sentence ‘THEN A MIRACLE OCCURS.’ And one of the two mathematicians standing before it points at this and tells the other: ‘I think you should be more explicit here at step two.’ Both… talks were one half fascinating expositions of lay narratology– in fact, I was exhilarated to hear the two most purely narratological talks at the meeting coming from number theorists!– and one half a discussion of a purely mathematical kind, the two parts separated by a conjunction roughly synonymous to ‘this is very similar to this.’ But the similarity was not clearly explained: the hole, you see, the ‘miracle.’ Of course, both [speakers]… are brilliant men, and honest too, and so they were very clear about the location of the hole, they did not try to fool us by saying that there was no hole where there was one."
Part II: Possible Worlds
"At times, bullshit can only be countered with superior bullshit."
— Norman Mailer
Many Worlds and Possible Worlds in Literature and Art, in Wikipedia:
"The concept of possible worlds dates back to a least Leibniz who in his Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. Voltaire satirized this view in his picaresque novel Candide….
Borges' seminal short story El jardín de senderos que se bifurcan ("The Garden of Forking Paths") is an early example of many worlds in fiction."
"Il faut cultiver notre jardin."– Voltaire
Background:
Modal Logic in Wikipedia
Possible Worlds in Wikipedia
Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)
Part III: Modal Theology
"The lapis was thought of as a unity and therefore often stands for the prima materia in general."
"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"
'…It is told that, when the Merciful One made the worlds, first of all He created that Stone and gave it to the Divine One whom the Jews call Shekinah, and as she gazed upon it the universes arose and had being.'"
— Many Dimensions, by Charles Williams, 1931 (Eerdmans paperback, April 1979, pp. 43-44)
"The lapis was thought of as a unity and therefore often stands for the prima materia in general."
— Aion, by C. G. Jung, 1951 (Princeton paperback, 1979, p. 236)
"Its discoverer was of the opinion that he had produced the equivalent of the primordial protomatter which exploded into the Universe."
— The Stars My Destination, by Alfred Bester, 1956 (Vintage hardcover, July 1996, p. 216)
|
"We symbolize
logical necessity with the box  )and logical possibility with the diamond  ).
"The possibilia that exist,
— Michael Sudduth, |
Comments Off on Monday August 22, 2005
Sunday, February 20, 2005
Sunday February 20, 2005
Relativity Blues
Today, February 20, is the 19th anniversary of my note The Relativity Problem in Finite Geometry. Here is some related material.
In 1931, the Christian writer Charles Williams grappled with the theology of time, space, free will, and the many-worlds interpretation of quantum mechanics (anticipating by many years the discussion of this topic by physicists beginning in the 1950's).
(Some pure mathematics — untainted by physics or theology — that is nevertheless related, if only by poetic analogy, to Williams's 1931 novel, Many Dimensions, is discussed in the above-mentioned note and in a generalization, Solomon's Cube.)
On the back cover of Williams's 1931 novel, the current publisher, William B. Eerdmans Publishing Company of Grand Rapids, Michigan, makes the following statement:
"Replete with rich religious imagery, Many Dimensions explores the relation between predestination and free will as it depicts different human responses to redemptive transcendence."
One possible response to such statements was recently provided in some detail by a Princeton philosophy professor. See On Bullshit, by Harry G. Frankfurt, Princeton University Press, 2005.
A more thoughtful response would take into account the following:
1. The arguments presented in favor of philosopher John Calvin, who discussed predestination, in The Death of Adam: Essays on Modern Thought, by Marilynne Robinson
2. The physics underlying Einstein's remarks on free will, God, and dice
3. The physics underlying Rebecca Goldstein's novel Properties of Light and Paul Preuss's novels Secret Passages and Broken Symmetries
4. The physics underlying the recent so-called "free will theorem" of John Conway and Simon Kochen of Princeton University
5. The recent novel Gilead, by Marilynne Robinson, which deals not with philosophy, but with lives influenced by philosophy — indirectly, by the philosophy of the aforementioned John Calvin.
From a review of Gilead by Jane Vandenburgh:
"In The Death of Adam, Robinson shows Jean Cauvin to be the foremost prophet of humanism whose Protestant teachings against the hierarchies of the Roman church set in motion the intellectual movements that promoted widespread literacy among the middle and lower classes, led to both the American and French revolutions, and not only freed African slaves in the United States but brought about suffrage for women. It's odd then that through our culture's reverse historicism, the term 'Calvinism' has come to mean 'moralistic repression.'"
For more on what the Calvinist publishing firm Eerdmans calls "redemptive transcendence," see various July 2003 Log24.net entries. If these entries include a fair amount of what Princeton philosophers call bullshit, let the Princeton philosophers meditate on the summary of Harvard philosophy quoted here on November 5 of last year, as well as the remarks of November 5, 2003, and those of November 5, 2002.
From Many Dimensions (Eerdmans paperback, 1963, page 53):
"Lord Arglay had a suspicion that the Stone would be purely logical. Yes, he thought, but what, in that sense, were the rules of its pure logic?"
A recent answer:
Modal Theology
"We symbolize logical necessity
with the box )
and logical possibility
with the diamond ).
— Keith Allen Korcz,
(Log24.net, 1/25/05)
And what do we
symbolize by 
?
"The possibilia that exist,
and out of which
the Universe arose,
are located in
a necessary being…."
— Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)
Comments Off on Sunday February 20, 2005
Thursday, February 17, 2005
Thursday February 17, 2005
Modal Theology
"We symbolize logical necessity
with the box )
and logical possibility
with the diamond ).
— Keith Allen Korcz,
(Log24.net, 1/25/05)
And what do we
symbolize by ?
On the Lapis Philosophorum,
the Philosophers' Stone –
"'What is this Stone?' Chloe asked….
'…It is told that, when the Merciful One
made the worlds, first of all He created
that Stone and gave it to the Divine One
whom the Jews call Shekinah,
and as she gazed upon it
the universes arose and had being.'"
– Many Dimensions,
by Charles Williams, 1931
(Eerdmans paperback,
April 1979, pp. 43-44)
"The lapis was thought of as a unity
and therefore often stands for
the prima materia in general."
– Aion, by C. G. Jung, 1951
(Princeton paperback,
1979, p. 236)
"Its discoverer was of the opinion that
he had produced the equivalent of
the primordial protomatter
which exploded into the Universe."
– The Stars My Destination,
by Alfred Bester, 1956
(Vintage hardcover,
July 1996, p. 216)
"The possibilia that exist,
and out of which
the Universe arose,
are located in
a necessary being…."
— Michael Sudduth,
Notes on
God, Chance, and Necessity
by Keith Ward,
Regius Professor of Divinity
at Christ Church College, Oxford
(the home of Lewis Carroll)
See also
The Diamond Archetype.
For more on modal theology, see
Kurt Gödel's Ontological Argument
and
The Ontological Argument
from Anselm to Gödel.