Saturday, February 13, 2021

Bullshit Studies . . .

Filed under: General — Tags: , , — m759 @ 2:40 PM


Background reading — Math’s Big Lies and, more generally, Mazur.

Related news for fans of Language Games

Thursday, November 19, 2020

Alex Garland’s grandfather, P. B. Medawar, on Bullshit

Filed under: General — m759 @ 6:37 PM

From a review of Teilhard de Chardin’s
The Phenomenon of Man:

“It would have been
a great disappointment
to me if Vibration did not
somewhere make itself felt,
for all scientific mystics
either vibrate in person
or find themselves
resonant with cosmic

— Sir Peter Brian Medawar

See as well . . .

Tuesday, November 17, 2020

What Is . . . Bullshit?

Filed under: General — m759 @ 12:45 PM

… and  What Is . . . Fact?

Saturday, August 8, 2020

Bullshit Studies

Filed under: General — Tags: , — m759 @ 9:00 PM

In memory of Wilford Brimley:

“The polymorphic Thing, capable of absorbing the human
as but one among other morphological possibilities in its
seemingly infinite repertoire, can be understood, that is,
as the embodiment of evolution.”

— Eric White,  Science Fiction Studies  #61  (Vol. 20, Part 3, Nov. 1993),
The Erotics of Becoming: XENOGENESIS and The Thing

Friday, June 12, 2020

Bullshit Studies: “Hyperseeing”

Filed under: General — Tags: — m759 @ 12:13 AM

In memoriam —

Friedman co-edited the ISAMA journal  Hyperseeing .  See also . . .

See too the other articles in Volume 40 of  Kybernetes .

Related material —

Compare and contrast the discussion of the geometry
of the 4×4 square
in the diamond theorem (1976) with
Nat Friedman’s treatment of the same topic in 2001 —

Saturday, May 16, 2020

Bullshit Studies

Filed under: General — Tags: , — m759 @ 11:59 PM

From https://www.mathunion.org/outreach/logos/versions-all-logos

Click the logo for some IMU history.

Related bullshit

Hegel’s Conceptual Group Action

Click the banner below for the background of the logo

Friday, May 1, 2020

Bullshit Studies

Filed under: General — Tags: , , , — m759 @ 2:55 PM

The following passage is from Amanda Gefter’s  Trespassing
on Einstein’s Lawn  (Bantam Books, 2014).

“You know the story of Plato’s cave?” my father asked. “All the prisoners are chained up in the cave and they can’t see the real world outside, only the shadows on the wall? That’s supposed to be a negative thing, like they’ll never know reality. But the truth is, you have to be stuck inside a limited reference frame for there to be any reality at all! If you weren’t chained to your light cone, you’d see nothing. The H-state.”

I nodded. “You’d have no information. You need the broken symmetry, the shadow, to have information and information gives rise to the world. It from bit.”

I couldn’t help but grin with excitement. The message was clear: having a finite frame of reference creates the illusion of a world, but even the reference frame itself is an illusion. Observers create reality, but observers aren’t real. There is nothing ontologically distinct about an observer, because you can always find a frame in which that observer disappears: the frame of the frame itself, the boundary of the boundary.

“If physicists discover an invariant someday, the game will be up,” my father mused. “That would rule out the hypothesis that the universe is really nothing.”

That was true. But so far, at least, every last invariant had gone the way of space and time, rendered relative and observer-dependent. Spacetime, gravity, electromagnetism, the nuclear forces, mass, energy, momentum, angular momentum, charge, dimensions, particles, fields, the vacuum, strings, the universe, the multiverse, the speed of light— one by one they had been downgraded to illusion. As the surface appearance of reality fell away, only one thing remained. Nothing.

My path to Gefter’s father’s musing led from a quotation attributed,
probably falsely, to John Archibald Wheeler on page 52 of Octavio
Paz’s  Claude Lévi-Strauss: An Introduction  (Cornell, 1970)

“There is a point at which

‘something is nothing and nothing is something.’

The quote may actually be by AP writer John Barbour reporting
on a 1967 American Physical Society talk by Wheeler, “The End
of Time.”

Gefter mentions Wheeler 369 times:

See as well Introduction to Quantum Woo.

Thursday, October 4, 2018

Mage Studies: Art vs. Bullshit

Filed under: General — Tags: — m759 @ 10:32 PM


From an October 3 post


From an academic's website —

Friday, September 8, 2017

Applied Bullshit

Filed under: General — Tags: — m759 @ 8:08 PM

A page from a book suggested by the previous post

Another approach to "the midrash  of space" —


Bullshit Studies

Filed under: General — Tags: — m759 @ 2:02 AM

Or:  Nine, Eight, Seven . . .

See as well
Rainbow Countdown.

Sunday, May 28, 2017

Bullshit Studies

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

The previous post dealt with a symbol of an apparently
admirable "social development environment."

For a less admirable development environment, see a film
described in a July 2014 story from Film New Europe —

"Shooting started in Bucharest on 9 June 2014. . . ."

This  journal on 8-9 June 2014 —

Monday, April 10, 2017

Bullshit Studies Continued*

Filed under: General — Tags: — m759 @ 9:29 PM

Yin Yang Yung

* See also earlier posts on Bullshit Studies.

Monday, March 6, 2017

Bullshit Studies

Filed under: General — Tags: — m759 @ 1:19 AM

From The Chronicle of Higher Education  on March 2, 2017 —

These days, in a world totally dependent on microprocessors, lasers, and nanotechnology, it has been estimated that 30 percent of the U.S. gross national product is based on inventions made possible by quantum mechanics. With the booming high-tech industry and the expected advent of quantum computers, this percentage will only grow. Within a hundred years, an esoteric theory of young physicists became a mainstay of the modern economy.

It took nearly as long for Einstein’s own theory of relativity, first published in 1905, to be used in everyday life in an entirely unexpected way. The accuracy of the global positioning system, the space-based navigation system that provides location and time information in today’s mobile society, depends on reading time signals of orbiting satellites. The presence of Earth’s gravitational field and the movement of these satellites cause clocks to speed up and slow down, shifting them by 38 milliseconds a day. In one day, without Einstein’s theory, our GPS tracking devices would be inaccurate by about seven miles.

Robbert Dijkgraaf, Director, Institute for Advanced Study, Princeton

The above paragraphs are clearly propaganda, not physics.

For "It has been estimated," see

The "without Einstein 's theory" statement may or may not be correct.
See the lengthy discussion at


See also Princeton's March of Mediocrity Continues.

Thursday, February 23, 2017

Bullshit Studies

Filed under: General — Tags: , — m759 @ 1:21 PM


" The origin of new ways of doing things may often be
a disciplinary crisis. The definition of such a crisis
provided by Barry Mazur in Mykonos (2005) applies
equally well to literary creation. '[A crisis occurs] when
some established overarching framework, theoretical
vocabulary or procedure of thought is perceived as
inadequate in an essential way, or not meaning
what we think it means.' "

— Circles Disturbed :
The Interplay of Mathematics and Narrative

Edited by Apostolos Doxiadis & Barry Mazur
Princeton University Press, 2012. See
Chapter 14, Section 5.1, by Uri Margolin.

See also "overarching" in this journal.

Thursday, November 17, 2016

Bullshit Studies

Filed under: General — Tags: — m759 @ 6:00 PM


Click image to enlarge.

Thursday, June 2, 2016

Bullshit Studies

Filed under: General,Geometry — Tags: , — m759 @ 11:30 AM


"The allusion to 'the most precious square of sense' shows
Shakespeare doing an almost scholastic demonstration of
the need for a ratio and interplay among the senses as
the very constitution of rationality."

— Marshall McLuhan, The Gutenberg Galaxy ,
University of Toronto Press, 1962, page 13

"What Shakespeare refers to in Lear  as the 'precious
square of sense' probably has reference to the traditional
'square of opposition' in logic and to that four-part analogy
of proportionality which is the interplay of sense and reason."     

— McLuhan, ibid. , page 241

This is of course nonsense, and, in view of McLuhan's pose
as a defender of the Catholic faith, damned  nonsense.

Epigraph by McLuhan —

"The Gutenberg Galaxy  develops a mosaic or field
approach to its problems."

I prefer a different "mosaic or field" related to the movable
blocks  of Fröbel, not the movable type  of Gutenberg.

Tuesday, May 17, 2016

Bullshit Studies

Filed under: General,Geometry — Tags: , , , — m759 @ 1:06 AM

The originator of the phrase 'Fab Four' reportedly
died at 80 on Saturday, May 14, 2016.

This suggests a review of another noted four-set.

The above image is from a study of Lévi-Strauss's "Canonical Formula"

Midrash —

Log24 post titled 'As Is'

[Above photo of Lévi-Strauss and formula added June 6, 2016.]

Wednesday, November 6, 2013

Bullshit Studies

Filed under: General — Tags: , — m759 @ 3:12 PM

The essay excerpted in last night's post on structuralism
is of value as part of a sustained attack by the late
Robert de Marrais on the damned nonsense of the late
French literary theorist Jacques Derrida—

Catastrophes, Kaleidoscopes, String Quartets:
Deploying the Glass Bead Game

Part I:  Ministrations Concerning Silliness, or:
Is “Interdisciplinary Thought” an Oxymoron?

Part II:  Canonical Collage-oscopes, or:
Claude in Jacques’ Trap?  Not What It Sounds Like!

Part III:  Grooving on the Sly with Klein Groups

Part IV:  Claude’s Kaleidoscope . . . and Carl’s

Part V:  Spelling the Tree, from Aleph to Tav
(While  Not Forgetting to Shin)

The response of de Marrais to Derrida's oeuvre  nicely
exemplifies the maxim of Norman Mailer that

"At times, bullshit can only be countered
with superior bullshit."

Tuesday, June 21, 2011

Truth, Beauty, Bullshit

Filed under: General — Tags: — m759 @ 1:16 PM

This post is for the Stonehenge solstice crowd, who might,
like the London artist Steve Richards, confuse bullshit
with scholarship and inspire the same confusion
in others.

IMAGE- Motto of Forgotten Books, with pirated quotation from Shakespeare that might be appropriate for London's 'Piracy Project'

The image, apparently an epigraph put there
by the author, is from the Forgotten Books edition
of Cassirer's Substance and Function:
And Einstein's Theory of Relativity

This is a scanned copy of the 1923 original.
The egg-figure above, however, is from the publisher's
prefatory notes and not  from the original.

A check of other Forgotten Books publications
shows that the motto and the Bacon
attribution are those of Forgotten Books and
not  of the authors they reprint — in particular,
not  of Ernst Cassirer, who would probably
be dismayed to have this nonsense associated
with his work.

Why nonsense? The attribution to Francis Bacon is
false. The lines are from "The Phoenix and the Turtle"
by William Shakespeare.

Monday, February 15, 2021

Philosophy for Emma Stone

Filed under: General — Tags: — m759 @ 9:51 PM

From a post of August 30, 2015

“… recall the words of author Norman Mailer
that summarized his Harvard education —

‘At times, bullshit can only be countered
with superior bullshit.’ “

And at times, non-bullshit is required.

BS from The New York Times  Friday  on the mathematical fields
known as topology  and analysis  in the 1960s —

“The two fields seemed to be nearly irremediably divided,
because topology twists objects around, and analysis
needs them to be rigid.”

Some less ignorant remarks from 1986:

The above Gauss-Bonnet theorem (ca. 1848) is explained in a talk titled
Analysis Meets Topology” labeled with the above Emma Stone date —

Sunday, December 6, 2020

The Undoing

Filed under: General — m759 @ 10:16 PM

Today’s earlier post “Binary Coordinates” discussed a Dec. 6
revision to the Wikipedia article on PG(3,2), the projective
geometry of 3 dimensions over the 2-element field GF(2).

The revision, which improved the article, was undone later today
by a clueless retired academic, one William “Bill” Cherowitzo,
a professor emeritus of mathematics at U. of Colorado at Denver.
(See his article “Adventures of a Mathematician in Wikipedia-land,”
MAA Focus , December 2014/January 2015.)

See my earlier remarks on this topic . . . specifically, on this passage —

“A 3-(16,4,1) block design has 140 blocks
of size 4 on 16 points, such that each triplet
of points is covered exactly once. Pick any
single point, take only the 35 blocks
containing that point, and delete that point.
The 35 blocks of size 3 that remain comprise
a PG(3,2) on the 15 remaining points.”

As I noted on November 17, this is bullshit. Apparently Cherowitzo
never bothered to find out that an arbitrary  “3-(16,4,1) block design”
(an example of a Steiner quadruple system ) does not  yield a PG(3,2).

PG(3,2) is derived from the classical  3-(16,4,1) block design formed by the affine
space of 4 dimensions over GF(2).  That  design has 322,560 automorphisms.
In contrast, see a 3-(16,4,1) block design that is  automorphism-free.

Tuesday, November 17, 2020

“To Illustrate My Last Remark . . .”

Filed under: General — m759 @ 8:49 PM

The previous post  contrasted recent bullshit of Louis Menand
with some non-bullshit at Wikipedia.

But Wikipedia is hardly blameless —

The text on the left is bullshit. The illustration on the right is not.

Saturday, November 14, 2020

The Grossinger Interview

Filed under: General — Tags: — m759 @ 8:40 PM

The following image was suggested by today’s
New York Times  obituary  of Joanna Harcourt-Smith
and by earlier Log24 posts now also tagged Grossinger.

For some background, see a book that reportedly
was published on Devil’s Night (October 30) 1997 —

The interview  date above suggests some related material
for students of bullshit and for
the Church of Synchronology

Thursday, October 1, 2020

Annals of Academia

Filed under: General — Tags: — m759 @ 1:21 PM

New York  magazine’s “The Cut” —

JULY 14, 2016

Why It Took Social Science Years to Correct a Simple Error
About ‘Psychoticism’

By Jesse Singal

“What should we make of all of this? Partly, of course, this is
a story of conflicting personalities, of competitiveness between
researchers, of academics acting — let’s be frank — like dicks.”

Or, worse, like New York Times  reporter Benedict Carey —

A Theory About Conspiracy Theories

In a new study, psychologists tried to get a handle on the personality types that might be prone to outlandish beliefs.

By Benedict Carey, New York Times  science reporter,
on Sept. 28, 2020

. . . .

The personality features that were solidly linked to conspiracy beliefs included some usual suspects: entitlement, self-centered impulsivity, cold-heartedness (the confident injustice collector), elevated levels of depressive moods and anxiousness (the moody figure, confined by age or circumstance). Another one emerged from the questionnaire that aimed to assess personality disorders — a pattern of thinking called “psychoticism.”

Psychoticism is a core feature of so-called schizo-typal personality disorder, characterized in part by “odd beliefs and magical thinking” and “paranoid ideation.” In the language of psychiatry, it is a milder form of full-blown psychosis, the recurrent delusional state that characterizes schizophrenia. It’s a pattern of magical thinking that goes well beyond garden variety superstition and usually comes across socially as disjointed, uncanny or “off.”

In time, perhaps some scientist or therapist will try to slap a diagnosis on believers in Big Lie conspiracies that seem wildly out of line with reality. For now, Dr. Pennycook said, it is enough to know that, when distracted, people are far more likely to forward headlines and stories without vetting their sources much, if at all.
. . . .

Some elementary  fact-checking reveals that historical definitions
of “psychoticism” vary greatly. Carey forwards this bullshit without
vetting his sources much, if at all.

Tuesday, September 22, 2020

Vanity Fair Cover Girl

Filed under: General — Tags: , , — m759 @ 11:15 AM

Elle Fanning recently played Catherine the Great.

Starring J. J. Abrams as Leonhard Euler?

Thursday, September 17, 2020

Structure and Mutability . . .

Filed under: General — Tags: , , , — m759 @ 9:51 PM

Continues in The New York Times :

“One day — ‘I don’t know exactly why,’ he writes — he tried to
put together eight cubes so that they could stick together but
also move around, exchanging places. He made the cubes out
of wood, then drilled a hole in the corners of the cubes to link
them together. The object quickly fell apart.

Many iterations later, Rubik figured out the unique design
that allowed him to build something paradoxical:
a solid, static object that is also fluid….” — Alexandra Alter

Another such object: the eightfold cube .


Filed under: General — Tags: , — m759 @ 1:32 AM

“This article is a nexus of ideas and vision….”

— Jack Plotkin at Medium.com yesterday

As are many other things. See nexus  in this  journal
and . . .

“Show me all  the blueprints.”

— Howard Hughes, according to Hollywood

Monday, August 17, 2020

Art School Confidential . . .

Filed under: General — Tags: , — m759 @ 4:13 PM


See also  Obelisk  in this journal.

Monday, December 25, 2017

New Kids on a Block:

Filed under: General — Tags: — m759 @ 11:59 PM

A Midnight Special for Charles Wallace

Peter Block —

Old Kid on Peter Block —

See the remarks today of Harvard philosophy professor Sean D. Kelly
in The New York Times :

Alexander's "15 properties that create the wholeness and aliveness" —

This is the sort of bullshit that seems to go over well at Harvard.
See Christopher Alexander in this journal.

Saturday, September 9, 2017

How It Works

Filed under: General,Geometry — Tags: , — m759 @ 8:48 PM

Del Toro and the History of Mathematics ,
Or:  Applied Bullshit Continues


For del Toro


For the history of mathematics —

Thursday, September 1, 2011

How It Works

Filed under: Uncategorized — Tags:  — m759 @ 11:00 AM 

"Design is how it works." — Steven Jobs (See Symmetry and Design.)

"By far the most important structure in design theory is the Steiner system S(5, 8, 24)."
 — "Block Designs," by Andries E. Brouwer

. . . .

Sunday, July 30, 2017

Sunday School:

Filed under: General — Tags: , — m759 @ 9:01 AM

Bullshit Studies  Continued

The remarks by Mikhail Gromov on neuroscience in his papers
cited in the previous post suggest some related remarks —

Saturday, April 22, 2017

Science Marches On

Filed under: General — Tags: , — m759 @ 1:00 PM

Connoisseurs of bullshit who enjoyed the previous post
might also enjoy the following:

The previous two posts introduced Mazzola's noxious combination of 
category theory and Hegel. The current version (Rev. 254) of the above 
nLab "Science of Logic" article, though not by Mazzola, displays this
combination in its full hideous splendor.

Some posts in this  journal that might be viewed as leading up to 
the original Sept. 2, 2012, "Science of Logic" article are now tagged
Death Warmed Over.

Friday, October 7, 2016


Filed under: General — Tags: , — m759 @ 11:27 AM

The Paz quote below is from the last chapter
of his book, titled "The Dialectic of Solitude."

The phrase "dialectic of solitude" has been applied also to a 1967
book by the Colombian writer Gabriel García Márquez:

The conclusion of One Hundred Years of Solitude ,
a 1967 novel by Gabriel García Márquez —

"He was so absorbed that he did not feel the second surge of wind either as its cyclonic strength tore the doors and windows off their hinges, pulled off the roof of the east wing, and uprooted the foundations. Only then did he discover that Amaranta Úrsula was not his sister but his aunt, and that Sir Francis Drake had attacked Riohacha only so that they could seek each other through the most intricate labyrinths of blood until they would engender the mythological animal that was to bring the line to an end. Macondo was already a fearful whirlwind of dust and rubble being spun about by the wrath of the biblical hurricane when Aureliano skipped eleven pages so as not to lose time with facts he knew only too well, and he began to decipher the instant that he was living, deciphering it as he lived it, prophesying himself in the act of deciphering the last page of the parchments, as if he were looking into a speaking mirror. Then he skipped again to anticipate the predictions and ascertain the date and circumstances of his death. Before reaching the final line, however, he had already understood that he would never leave that room, for it was foreseen that the city of mirrors (or mirages) would be wiped out by the wind and exiled from the memory of men at the precise moment when Aureliano Babilonia would finish deciphering the parchments, and that everything written on them was unrepeatable since time immemorial and forever more, because races condemned to one hundred years of solitude did not have a second opportunity on earth."

Update of Saturday, October 8:

I do not recommend taking very seriously the work of Latin American leftists
(or American academics) who like to use the word "dialectic."

A related phrase does, however, have a certain mystic or poetic charm,
as pointed out by Wikipedia —

"Unity of opposites is the central category of dialectics,
and it is viewed sometimes as a metaphysical concept,
a philosophical concept or a scientific concept."

See also Bullshit Studies.

Saturday, August 27, 2016

Folk Notation

Filed under: General — Tags: , — m759 @ 2:01 PM

See the Chautauqua Season post of June 25
and a search for Notation  in this journal.

See as well the previous post and Bullshit Studies .

Tuesday, July 26, 2016

The Day of the Locus

Filed under: General — Tags: — m759 @ 9:48 AM

From A. Trehub's remarks on the "space-like retinoid system"
mentioned by Bernd Schmeikal in his masterpiece of bullshit,
"Four Forms Make a Universe" —

The Self Locus 

Trehub - 'Self as the neuronal origin of retinoid space'

For a different grounding of the self, see the previous post.

Monday, June 6, 2016

Intellect Limited

Filed under: General — Tags: — m759 @ 6:29 AM

Explorations in Media Ecology
Volume 12 Numbers 3 & 4
© 2013 Intellect Ltd Article.

For some background, see Bullshit Studies.

Sunday, October 25, 2015

Buyers and Sellers of Children

Filed under: General — Tags: , — m759 @ 6:45 AM


Featured on this morning's online front page of
The New York Times

Some further details —

An example of New York Times  culture is shown above —

"… Mondrian paintings at the Museum of Modern Art
blend symmetry with a tensile volatility."

(To be fair, this contemptible bullshit is from a picture caption,
not from the art review being summarized.)

Related cultural observations —

Math for Child Buyers  and  Fiction for Child Sellers.

Sunday, August 30, 2015


Filed under: General,Geometry — Tags: , , — m759 @ 11:01 AM

"We tell ourselves stories in order to live." — Joan Didion

A post from St. Augustine's day, 2015, may serve to
illustrate this.

The post started with a look at a painting by Swiss artist
Wolf Barth, "Spielfeld." The painting portrays two
rectangular arrays, of four and of twelve subsquares, 
that sit atop a square array of sixteen subsquares.

To one familiar with Euclid's "bride's chair" proof of the
Pythagorean theorem, "Spielfeld" suggests a right triangle
with squares on its sides of areas 4, 12, and 16.

That image in turn suggests a diagram illustrating the fact
that a triangle suitably inscribed in a half-circle is a right 
triangle… in this case, a right triangle with angles of 30, 60,
and 90 degrees… Thus —

In memory of screenwriter John Gregory Dunne (husband
of Joan Didion and author of, among other things, The Studio
here is a cinematric approach to the above figure.

The half-circle at top suggests the dome of an observatory.
This in turn suggests a scene from the 2014 film "Magic in
the Moonlight."  

As she gazes at the silent universe above
through an opening in the dome, the silent
Emma Stone is perhaps thinking, 
prompted by her work with Spider-Man

"Drop me a line."

As he  gazes at the crack in the dome,
Stone's costar Colin Firth contrasts the vastness 
of the Universe with the smallness of Man, citing 

"the tiny field F2 with two elements."

In conclusion, recall the words of author Norman Mailer
that summarized his Harvard education —

"At times, bullshit can only be countered
with superior bullshit."

Tuesday, December 9, 2014

Plan 9…

Filed under: General — Tags: — m759 @ 1:00 PM

Or:  Bullshit for Brit   continues.

From the new film "I Origins," starring Brit Marling —

Plan 9:

The protagonist of "I Origins" is led to the above billboard
by apparently chance encounters with 11 's — such as the
1111 on the following page —

Update of Dec. 10, 2014: The "bullshit" in the subtitle above refers
to the remarks of Joan Stambaugh, not those of Nicholas of Cusa.
The passage from Nicholas was added because it indicates a more
reliable source than Stambaugh, because it is relevant to lines
about the metaphorical significance of light in "I Origins," and 
because it contains the number 1111. 

Saturday, September 20, 2014


Filed under: General — Tags: , — m759 @ 9:00 PM

Once again, Harvard defeats Holy Cross.

IMAGE- Joseph Campbell, 'The Inner Reaches of Outer Space,' meditation on the number nine, the Goddess, and the Angelus

See also a related remark by Norman Mailer, and Plan 9 in this journal.

Presumably the Holy Cross defeat will please art theorist Rosalind Krauss (below).

(Click to enlarge.)

Friday, March 14, 2014

Whitewashing Picasso

Filed under: General,Geometry — Tags: , , — m759 @ 4:30 PM

A search today for Edward Frenkel's phrase
"portals into the magic world of modern math"
leads to a reprint of his March 2 LA Times  opinion piece
in The Salem News —

IMAGE- Edward Frenkel in The Salem News

To hell with Picasso, I'll take Tom Sawyer.

Sunday, October 28, 2012

Another Green Door, and…

Filed under: General — Tags: , , — m759 @ 3:48 AM

Another Bullshit Night in Suck City:

IMAGE- 'Another Bullshit Night in Suck City,' by Nick Flynn

For the 2012 film version, see

(Click image below for a review.)

Personally, I prefer the green door of last night's 10 PM post
written partly in honor of the body mentioned here on October 23).

The cover of the Nick Flynn book shows a green door beneath a tree.
For a different tree, but similar metaphor, see Confirmation (July 16, 2007).

Wednesday, July 18, 2012


Filed under: General — Tags: — m759 @ 9:48 AM

(Continued from Midsummer Eve)

"At times, bullshit can only be countered with superior bullshit."

— Norman Mailer, March 3, 1992, PBS transcript

"Just because it is a transition between incommensurables, the transition between competing paradigms cannot be made a step at a time, forced by logic and neutral experience. Like the gestalt switch, it must occur all at once (though not necessarily in an instant) or not at all."

Thomas Kuhn, The Structure of Scientific Revolutions , 1962, as quoted in The Enneagram of Paradigm Shifting

"In the spiritual traditions from which Jung borrowed the term, it is not the SYMMETRY of mandalas that is all-important, as Jung later led us to believe. It is their capacity to reveal the asymmetry that resides at the very heart of symmetry." 

The Enneagram as Mandala

I have little respect for Enneagram enthusiasts, but they do at times illustrate Mailer's maxim.

My own interests are in the purely mathematical properties of the number nine, as well as those of the next square, sixteen.

Those who prefer bullshit may investigate non-mathematical properties of sixteen by doing a Google image search on MBTI.

For bullshit involving nine, see (for instance) Einsatz  in this journal.

For non-bullshit involving nine, sixteen, and "asymmetry that resides at the very heart of symmetry," see Monday's Mapping Problem continued. (The nine occurs there as the symmetric  figures in the lower right nine-sixteenths of the triangular analogs  diagram.)

For non-bullshit involving psychological and philosophical terminology, see James Hillman's Re-Visioning Psychology .

In particular, see Hillman's "An Excursion on Differences Between Soul and Spirit."

Tuesday, July 14, 2009

Tuesday July 14, 2009

Filed under: General — Tags: — m759 @ 6:29 PM
Herschel’s Onion

The Herschel Chronicle, by Constance A. Lubbock, Cambridge University Press, 1933, page 139:

“Sir John Herschel has recorded that his father [astronomer William Herschel, 1738-1822], when observing at Datchet, ‘when the waters were out round his garden, used to rub himself all over, face and hands &c., with a raw onion, to keep off the infection of the ague, which was then prevalent; however he caught it at last.'”

Herschel and his onion appear in a large illustration on the cover of next Sunday’s New York Times Book Review.  A review, titled “Science and the Sublime,” states that Herschel and his sister

“spent endless hours at the enormous telescopes that Herschel constructed, rubbing raw onions to warm their hands….'”

Clearly the anti-ague motive makes more sense.

A quotation from the book under review, The Age of Wonder: How the Romantic Generation Discovered the Beauty and Terror of Science (published today, Bastille Day, 2009):

“The emphasis of on [sic] secular, humanist (even atheist) body of knowledge… was particularly strong in revolutionary France.”

This, apparently, is the terror part.

A related quotation from Publishers Weekly:

“It’s an engrossing portrait of scientists as passionate adventurers, boldly laying claim to the intellectual leadership of society. Illus. (July 14)”

On its front page next Sunday, The New York Times Book Review boldly lays claim to intellectual leadership with the following opening sentence:

“In this big two-hearted river of a book, the twin energies of scientific curiosity and poetic invention pulsate on every page.”

The sentence begins with an insult to Hemingway and ends with a cascade of vulgarized-science bullshit. Its author, Christopher Benfey, has done better, and should be ashamed.

Wednesday, March 18, 2009

Wednesday March 18, 2009

Filed under: General — Tags: — m759 @ 9:00 AM
Gallic Clarity

Yesterday’s entry Deep Structures discussed the “semiotic square,” a device that exemplifies the saying “If you can’t dazzle ’em with brilliance, then baffle ’em with bullshit.”

A search today for what the Marxist critic Fredric Jameson might have meant by saying that the square “is capable of generating at least ten conceivable positions out of a rudimentary binary opposition” leads to two documents of interest.

1. “Theory Pictures as Trails: Diagrams and the Navigation of Theoretical Narratives” (pdf), by J.R. Osborn, Department of Communication, University of California, San Diego (Cognitive Science Online, Vol.3.2, pp.15-44, 2005)

2. “The Semiotic Square” (html), by Louis Hébert (2006), professor, Université du Québec à Rimouski, in Signo (http://www.signosemio.com).

Shown below is Osborn’s picture of the semiotic square:


Osborn’s discussion of the square, though more clear than, say, that of Rosalind Krauss (who reverses the bottom two parts of the square– see Deep Structures), fails. His Appendix A is miserably obscure.

On the brighter side, we have, as a sign that Gallic clarity still exists, the work of Hébert.

Here is how he approaches Jameson’s oft-quoted, but seemingly confused, remark about “ten conceivable positions”–

The Semiotic Square,”
  by Louis Hébert


The semiotic square, developed by Greimas and Rastier, is a means of refining oppositional analyses by increasing the number of analytical classes stemming from a given opposition from two (life/death, for instance) to four (for example, life, death, life and death (the living dead), and neither life nor death (angels)) to eight or even ten.


The actantial model, isotopy and the semiotic square are undoubtedly the best-known theoretical propositions that have emerged from the Paris School of semiotics, with Greimas as its central figure. Like the actantial model and the veridictory square, the semiotic square is designed to be both a conceptual network and a visual representation of this network, usually depicted in the form of a “square” (which actually looks like a rectangle!). Courtés defines it as the visual representation of the logical structure of an opposition (cf. Courtés, 1991, 152). The semiotic square is a means of refining oppositional analyses by increasing the number of analytical classes stemming from a given opposition from two (for instance, life/death) to four (for example, life, death, life and death (the living dead), and neither life nor death (angels)) to eight or even ten. Here is an empty semiotic square.

Structure of the semiotic square

5. (=1+2) COMPLEX TERM
1. TERM A  
9. (=1+4)
10. (=2+3)

7. (=1+3)


6. (=3+4) NEUTRAL TERM

The + sign links the terms that are combined to make up a metaterm (a compound term); for example, 5 is the result of combining 1 and 2.


The semiotic square entails primarily the following elements (we are steering clear of the constituent relationships of the square: contrariety, contradiction, and complementarity or implication):

1. terms
2. metaterms (compound terms)
3. object(s) (classified on the square)
4. observing subject(s) (who do the classifying)
5. time (of the observation)

2.1.1 TERMS

The semiotic square is composed of four terms:

Position 1 (term A)
Position 2 (term B)
Position 3 (term not-B)
Position 4 (term not-A)

The first two terms form the opposition (the contrary relationship) that is the basis of the square, and the other two are obtained by negating each term of the opposition.


The semiotic square includes six metaterms. The metaterms are terms created from the four simple terms. Some of the metaterms have been named. (The complex term and the neutral term, despite their names, are indeed metaterms).

Position 5 (term 1 + term 2): complex term
Position 6 (term 3 + term 4): neutral term
Position 7 (term 1 + term 3): positive deixis
Position 8 (term 2 + term 4): negative deixis
Position 9 = term 1 + term 4: unnamed
Position 10 = term 2 + term 3: unnamed

These ten “positions” are apparently meant to explain Jameson’s remark.

Hébert’s treatment has considerably greater entertainment value than Osborn’s. Besides “the living dead” and angels, Hébert’s examples and exercises include vampires, transvestites, the Passion of Christ, and the following very relevant quotation:

“Simply let your ‘Yes’ be ‘Yes,’ and your ‘No,’ ‘No’; anything beyond this comes from the evil one.” (Matthew 5:37)

Friday, October 12, 2007

Friday October 12, 2007

Filed under: General — Tags: — m759 @ 9:10 AM
A Harvard Education
in a Sentence:

“At times, bullshit can
only be countered
with superior bullshit.”

Norman Mailer,
Harvard ’43

Illustration from
today’s Crimson:

Nobel Laureate Morrison
Reads at Opening Event

Friday, October 12, 2007 3:17 AM

From the reserved elegance of Memorial Church to the sweeping grandeur of Sanders Theatre, the Harvard community honored 28th University President Drew G. Faust with two festive events on the eve of her inauguration.

Thursday, October 11, 2007

Thursday October 11, 2007

Filed under: General — Tags: — m759 @ 9:26 PM
Words and Music
suggested by the recent
Princeton symposium
"Deep Beauty"

The image “http://www.log24.com/log/pix07A/071011-vonNeumann.jpg” cannot be displayed, because it contains errors.

1. From my childhood:

"You remind me of a man."
"What man?"
"The man with the power."
"What power?"
"The power of hoodoo."
"You do."
"Do what?
"Remind me of a man…."

— Dialogue from
"The Bachelor and the
Bobby-Soxer" (1947)

2.  From later years:

"When I was a little boy,
(when I was just a boy)
and the Devil would
call my name
(when I was just a boy)
I'd say 'now who do,
who do you think
you're fooling?'"

Paul Simon, 1973 

"At times, bullshit can
only be countered
with superior bullshit."
— Norman Mailer

(See A Harvard Education
in a Sentence.)

From Plato's Cave:

A description of caveman life
translated from German

John von

"Soon Freud, soon mourning,
Soon Fried, soon fight.
Nevertheless who know this language?"

(Language courtesy of
Google's translation software)

Picture of von Neumann courtesy of
Princeton University Library

More from Rhymin' Simon–

"one funny mofo"–

"Oh, my mama loves,
she loves me,
she get down on her knees
and hug me
like she loves me
like a rock.
She rocks me
like the rock of ages"

Related material:

The previous Log24 entries
of Oct. 7-11, 2007, and
the five Log24 entries
ending with "Toy Soldiers"
(Valentine's Day, 2003).

See also

"Taking Christ to the Movies,"
by Anna Megill, Princeton '06

Saturday, July 21, 2007

Saturday July 21, 2007

Filed under: General — Tags: — m759 @ 9:45 AM

Death of a Nominalist

“All our words from loose using have lost their edge.” –Ernest Hemingway

(The Hemingway quotation is from the AP’s “Today in History” on July 21, 2007; for the context, see Death in the Afternoon.)

Today seems as good a day as any for noting the death of an author previously discussed in Log24 on January 29, 2007, and January 31, 2007.

Joseph Goguen
died on July 3, 2006. (I learned of his death only after the entries of January 2007 were written. They still hold.)

Goguen’s death may be viewed in the context of the ongoing war between the realism of Plato and the nominalism of the sophists. (See, for instance, Log24 on August 10-15, 2004, and on July 3-5, 2007.)

Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf):

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.’ Similarly, the ‘situations’ in the situation semantics of Barwise and Perry, which resemble conceptual spaces (but are more sophisticated– perhaps too sophisticated), are considered to be actually existing, real entities [23], even though they may include what are normally considered judgements.5 The classical semiotics of Charles Sanders Peirce [24] also tends towards a Platonist view of signs. The viewpoint of this paper is that all formalisms are constructed in the course of some task, such as scientific study or engineering design, for the heuristic purpose of facilitating consideration of certain issues in that task. Under this view, all theories are situated social entities, mathematical theories no less than others; of course, this does not mean that they are not useful.”

5 The “types” of situation theory are even further removed from concrete reality.

[23] Jon Barwise and John Perry. Situations and Attitudes. MIT (Bradford), 1983.
[24] Charles Sanders Peirce. Collected Papers. Harvard, 1965. In 6 volumes; see especially Volume 2: Elements of Logic.

From Log24 on the date of Goguen’s death:

Requiem for a clown:

“At times, bullshit can only be
countered with superior bullshit.”

Norman Mailer

This same Mailer aphorism was quoted, along with an excerpt from the Goguen passage above, in Log24 this year on the date of Norman Mailer’s birth.  Also quoted on that date:

Sophia. Then these thoughts of Nature are also thoughts of God.

Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God….

Whether the above excerpt– from Hans Christian Oersted‘s The Soul in Nature (1852)– is superior to the similar remark of Goguen, the reader may decide.

Wednesday, March 7, 2007

Wednesday March 7, 2007

Filed under: General,Geometry — Tags: , — m759 @ 8:35 AM
Footprints for

The image “http://www.log24.com/log/pix07/070307-Baudrillard.jpg” cannot be displayed, because it contains errors.

"Was there really a cherubim
waiting at the star-watching rock…?
Was he real?
What is real?


— Madeleine L'Engle, A Wind in the Door,
Farrar, Straus and Giroux, 1973,
conclusion of Chapter Three,
"The Man in the Night"


"Oh, Euclid, I suppose."

— Madeleine L'Engle, A Wrinkle in Time,
Farrar, Straus and Giroux, 1962,
conclusion of Chapter Five,
"The Tesseract"

In memory of the French philosopher Jean Baudrillard, who died yesterday, Tuesday, March 6, 2007. 

The following Xanga footprints may be regarded as illustrating Log24 remarks of Dec. 10, 2006 on the Library of Congress, geometry, and bullshit, as well as remarks of Aug. 28, 2006 on the temporal, the eternal, and St. Augustine.

From the District of Columbia–
Xanga footprints in reverse
chronological order from
the noon hour on Tuesday,
March 6, 2007, the date
of Baudrillard's death:

District of Columbia
Beijing String
12:04 PM
District of Columbia
12:03 PM
District of Columbia
About God, Life, Death
12:03 PM
District of Columbia
A Library of Congress Reading
12:03 PM
District of Columbia
Binary Geometry
12:03 PM
District of Columbia
Prequel on St. Cecelia's Day
12:03 PM

Wednesday, January 31, 2007

Wednesday January 31, 2007

Filed under: General — Tags: — m759 @ 3:09 PM

“At times, bullshit can only be
countered with superior bullshit.”
Norman Mailer

“It may be that universal history is the
history of the different intonations
given a handful of metaphors.”
— Jorge Luis Borges (1951),
“The Fearful Sphere of Pascal,”
in Labyrinths, New Directions, 1962

“Before introducing algebraic semiotics and structural blending, it is good to be clear about their philosophical orientation. The reason for taking special care with this is that, in Western culture, mathematical formalisms are often given a status beyond what they deserve. For example, Euclid wrote, ‘The laws of nature are but the mathematical thoughts of God.'”

— Joseph A. Goguen, “Ontology, Society, and Ontotheology” (pdf)

Goguen does not give a source for this alleged “thoughts of God” statement.

A Web search for the source leads only to A Mathematical Journey, by Stanley Gudder, who apparently also attributes the saying to Euclid.

Neither Goguen nor Gudder seems to have had any interest in the accuracy of the Euclid attribution.

Talk of “nature” and “God” seems unlikely from Euclid, a pre-Christian Greek whose pure mathematics has (as G. H. Hardy might be happy to point out) little to do with either.

Loose talk about God’s thoughts has also been attributed to Kepler and Einstein… and we all know about Stephen Hawking.

Gudder may have been misquoting some other author’s blather about Kepler.  Another possible source of the “thoughts of God” phrase is Hans Christian Oersted. The following is from Oersted’s The Soul in Nature

“Sophia. Nothing of importance; though indeed I had one question on my lips when the conversion took the last turn. When you alluded to the idea, that the Reason manifested in Nature is infallible, while ours is fallible, should you not rather have said, that our Reason accords with that of Nature, as that in the voice of Nature with ours?

Alfred. Each of these interpretations may be justified by the idea to which it applies, whether we start from ourselves or external nature. There are yet other ways of expressing it; for instance, the laws of Nature are the thoughts of  Nature.

Sophia. Then these thoughts of Nature are also thoughts of God.

Alfred. Undoubtedly so, but however valuable the expression may be, I would rather that we should not make use of it till we are convinced that our investigation leads to a view of Nature, which is also the contemplation of God. We shall then feel justified by a different and more perfect knowledge to call the thoughts of Nature those of God; I therefore beg you will not proceed to [sic] fast.”

Oersted also allegedly said that “The Universe is a manifestation of an Infinite Reason and the laws of Nature are the thoughts of God.” This remark was found (via Google book search) in an obscure journal that does not give a precise source for the words it attributes to Oersted.

The image “http://www.log24.com/log/pix07/070131-OerstedGudder.jpg” cannot be displayed, because it contains errors.

Friday, December 29, 2006

Friday December 29, 2006

Filed under: General — Tags: , — m759 @ 11:01 AM
of Christ Church

"For every kind of vampire,
there is a kind of cross."
— Thomas Pynchon

Cover of Thomas, by Shelley Mydans: Sword and its shadow, a cross

Click on picture for details.

Today is the feast
of St. Thomas Becket.

In his honor, a meditation
on tools and causation:

"Lewis Wolpert, an eminent developmental biologist at University College London, has just published Six Impossible Things Before Breakfast, a pleasant, though rambling, look at the biological basis of belief. While the book focuses on our ability to form causal beliefs about everyday matters (the wind moved the trees, for example), it spends considerable time on the origins of religious and moral beliefs. Wolpert defends the unusual idea that causal thinking is an adaptation required for tool-making. Religious beliefs can thus be seen as an odd extension of causal thinking about technology to more mysterious matters. Only a species that can reason causally could assert that 'this storm was sent by God because we sinned.' While Wolpert's attitude toward religion is tolerant, he's an atheist who seems to find religion more puzzling than absorbing."

Review by H. Allen Orr in
The New York Review of Books,
Vol. 54, No. 1, January 11, 2007    

"An odd extension"–

Wolpert's title is, of course,
from Lewis Carroll.

Related material:

"It's a poor sort of memory
that only works backwards."
Through the Looking-Glass

An event at the Kennedy Center
broadcast on
December 26, 2006
(St. Steven's Day):

"Conductor John Williams, a 2004 Honoree, says, 'Steven, sharing our 34-year collaboration has been a great privilege for me. It's been an inspiration to watch you dream your dreams, nurture them and make them grow. And, in the process, entertain and edify billions of people around the world. Tonight we'd like to salute you, musically, with a piece that expresses that spirit beautifully … It was written by Leonard Bernstein, a 1980 Kennedy Center Honoree who was, incidentally, the first composer to be performed in this hall.' Backed by The United States Army Chorus and The Choral Arts Society, soprano Harolyn Blackwell and tenor Gregory Turay sing the closing number for Spielberg's tribute and the gala itself. It's the finale to the opera 'Candide,' 'Make Our Garden Grow,' and Williams conducts."

CBS press release

See also the following,
from the conclusion to

"Mathematics and Narrative"

(Log24, Aug. 22, 2005):

Diamond on cover of Narrative Form, by Suzanne Keen

"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 at 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

"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

Diamond in a square

"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,
  Christ Church College, Oxford
(the home of Lewis Carroll)

For further details,
click on the
Christ Church diamond.

Sunday, December 10, 2006

Sunday December 10, 2006

Filed under: General,Geometry — Tags: — m759 @ 12:00 PM
On This Date

“… in 1896 Alfred Nobel,
the inventor of dynamite and
founder of the Nobel prizes,
died in San Remo, Italy,
at age 63.”

— “Today in History,”
by The Associated Press

… And the Nobel Prize
     for Bullshit goes to…

David Titcher,

author and co-producer of
The Librarian: Quest for the Spear.

First Runner-up

A Piece of Justice.

From a summary of the novel:

The story deals with “one Gideon Summerfield, deceased.” Summerfield, a former tutor at (the fictional) St. Agatha’s College, Cambridge University, “is about to become the recipient of the Waymark prize. This prize is awarded in Mathematics and has the same prestige as the Nobel….”

Monday, July 3, 2006

Monday July 3, 2006

Filed under: General — Tags: — m759 @ 10:13 AM
Requiem for a Clown

For Jan Murray,
who died yesterday–

Into the Sunset, Part I:

The image “http://www.log24.com/log/pix06A/060703-Sunset.jpg” cannot be displayed, because it contains errors.

Into the Sunset, Part II:

The image “http://www.log24.com/log/pix06A/060703-Achelous21.jpg” cannot be displayed, because it contains errors.

Requiem for a clown:

“At times, bullshit can only be
countered with superior bullshit.”

Norman Mailer

See also 10/13.

Tuesday, January 17, 2006

Tuesday January 17, 2006

Filed under: General — Tags: — m759 @ 12:00 PM
The image “http://www.log24.com/log/pix06/060117-Globe.jpg” cannot be displayed, because it contains errors.
BBC News Jan. 17

Related material:
Log24  Sept. 27 and
Sept. 28, 2005,
as well as
The Harvard Crimson,
Jan. 13, 2006:
“President was resolute–
‘This is bullshit'”

The image “http://www.log24.com/log/pix06/060117-Nixon.jpg” cannot be displayed, because it contains errors.

Wednesday, November 30, 2005

Wednesday November 30, 2005

Filed under: General,Geometry — Tags: — m759 @ 8:20 PM


Brian Davies is a professor of mathematics at King’s College London.  In the December Notices of the American Mathematical Society, he claims that arithmetic may, for all we know, be inconsistent:

“Gödel taught us that it is not possible to prove that Peano arithmetic is consistent, but everyone has taken it for granted that in fact it is indeed consistent.
    Platonistically-inclined mathematicians would deny the possibility that Peano arithmetic could be flawed.  From Kronecker onwards many consider that they have a direct insight into the natural numbers, which guarantees their existence. If the natural numbers exist and Peano’s axioms describe properties that they possess then, since the axioms can be instantiated, they must be consistent.”

“It is not possible to prove that Peano arithmetic is consistent”…?!

Where did Gödel say this?  Gödel proved, in fact, according to a well-known mathematician at Princeton, that (letting PA stand for Peano Arithmetic),

“If PA is consistent, the formula expressing ‘PA is consistent’ is unprovable in PA.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Remarkably, even after he has stated correctly Gödel’s result, Nelson, like Davies, concludes that

“The consistency of PA cannot be concretely demonstrated.”

I prefer the argument that the existence of a model ensures the consistency of a theory.

For instance, the Toronto philosopher William Seager writes that

“Our judgement as to the consistency of some system is not dependent upon that system’s being able to prove its own consistency (i.e. generate a formula that states, e.g. ‘0=1’ is not provable). For if that was the sole basis, how could we trust it? If the system was inconsistent, it could generate this formula as well (see Smullyan, Gödel’s Incompleteness Theorems, (Oxford, 1992, p. 109)). Furthermore, [George] Boolos allows that we do know that certain systems, such as Peano Arithmetic, are consistent even though they cannot prove their own consistency. Presumably, we know this because we can see that a certain model satisfies the axioms of the system at issue, hence that they are true in that model and so must be consistent.”

Yesterday’s Algorithm:
    Penrose and the Gödel Argument

The relationship between consistency and the existence of a model is brought home by the following weblog entry that neatly summarizes a fallacious argument offered in the AMS Notices by Davies:

The following is an interesting example that I came across in the article “Whither Mathematics?” by Brian Davies in the December issue of Notices of the American Mathematical Society.

Consider the following list A1 of axioms.

(1) There is a natural number 0.
(2) Every natural number a has a successor, denoted by S(a).
(3) There is no natural number whose successor is 0.
(4) Distinct natural numbers have distinct successors: a = b if and only if S(a) = S(b).
(5) If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all the natural numbers.

Now consider the following list A2 of axioms.

(1) G is a set of elements and these elements obey the group axioms.
(2) G is finite but not isomorphic to any known list of finite simple groups.
(3) G is simple, in other words, if N is a subset of G satisfying certain properties then N=G.

We can roughly compare A2 with A1. The second axiom in A2 can be thought of as analogous to the third axiom of A1. Also the third axiom of A2 is analogous to the fifth axiom of A1, insofar as it refers to an unspecified set with cetain properties and concludes that it is equal to G.

Now, as is generally believed by most group theorists, the system A2 is internally inconsistent and the proof its inconsistency runs for more than 10000 pages.

So who is to deny that the system A1 is also probably internally inconsistent! Particularly since Godel proved that you can not prove it is consistent (staying inside the system). May be the shortest proof of its inconsistency is one hundred million pages long!

— Posted by Krishna,
   11/29/2005 11:46:00 PM,
   at his weblog,
  “Quasi-Coherent Ruminations”

An important difference between A1 (the set of axioms of Peano arithmetic) and A2 (a set of axioms that describe a new, unknown, finite simple group) is that A1 is known to have a model (the nonnegative integers) and A2 is not known to have a model.

Therefore, according to Seager’s argument, A1 is consistent and A2 may or may not be consistent.

The degree to which Seager’s argument invokes Platonic realism is debatable.  Less debatable is the quasireligious faith in nominalism proclaimed by Davies and Nelson.  Nelson’s own account of a religious experience in 1976 at Toronto is instructive.

I must relate how I lost my faith in Pythagorean numbers. One morning at the 1976 Summer Meeting of the American Mathematical Society in Toronto, I woke early. As I lay meditating about numbers, I felt the momentary overwhelming presence of one who convicted me of arrogance for my belief in the real existence of an infinite world of numbers, leaving me like an infant in a crib reduced to counting on my fingers. Now I live in a world in which there are no numbers save those that human beings on occasion construct.

— Edward Nelson,
   Mathematics and Faith (pdf)

Nelson’s “Mathematics and Faith” was written for the Jubilee for Men and Women from the World of Learning held at the Vatican, 23-24 May 2000.  It concludes with an invocation of St. Paul:

During my first stay in Rome I used to play chess with Ernesto Buonaiuti. In his writings and in his life, Buonaiuti with passionate eloquence opposed the reification of human abstractions. I close by quoting one sentence from his Pellegrino di Roma.  “For [St. Paul] abstract truth, absolute laws, do not exist, because all of our thinking is subordinated to the construction of this holy temple of the Spirit, whose manifestations are not abstract ideas, but fruits of goodness, of peace, of charity and forgiveness.”

— Edward Nelson,
   Mathematics and Faith (pdf)

Belief in the consistency of arithmetic may or may not be foolish, and therefore an Emersonian hobgoblin of little minds, but bullshit is bullshit, whether in London, in Princeton, in Toronto, or in Rome.

Tuesday, September 27, 2005

Tuesday September 27, 2005

Filed under: General — Tags: — m759 @ 6:23 AM
Mathematical Narrative

Gwyneth Paltrow is said to be 33 today.


The image “http://www.log24.com/log/pix05B/050925-Summers.jpg”  cannot be displayed, because it contains errors.


Anthony Hopkins in 'Proof'

Recommended reading
for Harvard's president:

The image “http://www.log24.com/log/pix05B/050925-Truth.jpg” cannot be displayed, because it contains errors.

Truth: A Guide,
by Simon Blackburn

Recommended reading
for Gwyneth Paltrow:

The image “http://www.log24.com/log/pix05B/050925-Bullshit.jpg” cannot be displayed, because it contains errors.

On Bullshit,
by Harry G. Frankfurt

The image “http://www.log24.com/log/pix05B/050927-Blackburn2.jpg” cannot be displayed, because it contains errors.


The image “http://www.log24.com/log/pix05B/050927-Frankfurt2.jpg” cannot be displayed, because it contains errors.


Monday, August 22, 2005

Monday August 22, 2005

Filed under: General — Tags: , — m759 @ 4:07 PM
The Hole

Part I: Mathematics and Narrative

The image “http://www.log24.com/log/pix05B/050822-Narr.jpg” cannot be displayed, because it contains errors.

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."



Modal Logic in Wikipedia

Possible Worlds in Wikipedia

Possible-Worlds Theory, by Marie-Laure Ryan
(entry for The Routledge Encyclopedia of Narrative Theory)

The God-Shaped Hole

Part III: Modal Theology

  "'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)
"We symbolize
logical necessity
with the box (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz 

The image “http://www.log24.com/log/pix05B/050802-Stone.gif” cannot be displayed, because it contains errors.

"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)

Saturday, August 20, 2005

Saturday August 20, 2005

Filed under: General — Tags: — m759 @ 2:07 PM
Truth vs. Bullshit

For an essay on the above topic
from this week’s New Yorker,
click on the box below.

The image “http://www.log24.com/log/pix05B/050819-Critic4.jpg” cannot be displayed, because it contains errors.

Representing truth:

The image “http://www.log24.com/log/pix05B/050820-Goldstein.jpg” cannot be displayed, because it contains errors.

Rebecca Goldstein

Representing bullshit:

The image “http://www.log24.com/log/pix05B/050820-Doxiadis.jpg” cannot be displayed, because it contains errors.

Apostolos Doxiadis

Goldstein’s truth:

Gödel was a Platonist who believed in objective truth.

See Rothstein’s review of Goldstein’s new book Incompleteness.

Doxiadis’s bullshit:

Gödel, along with Darwin, Marx, Nietzsche, Freud, Einstein, and Heisenberg, destroyed a tradition of certainty that began with Plato and Euclid.

“Examples are the stained-glass
windows of knowledge.” — Nabokov

Sunday, February 20, 2005

Sunday February 20, 2005

Filed under: General,Geometry — Tags: , , — m759 @ 2:20 PM

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 (box.gif (75 bytes))
and logical possibility
with the diamond (diamond.gif (82 bytes))."

Keith Allen Korcz,
(Log24.net, 1/25/05)

And what do we           
   symbolize by  The image “http://www.log24.com/theory/images/Modal-diamondbox.gif” cannot be displayed, because it contains errors. ?

"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)

Friday, November 5, 2004

Friday November 5, 2004

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

A Harvard Education
in a Sentence

Harvard alumnus Norman Mailer:

At times, bullshit can only be countered with superior bullshit.

For Harvard bullshit, see
The Crimson Passion.

For superior bullshit, see
Shrine of the Holy Whapping.

Tuesday, August 17, 2004

Tuesday August 17, 2004

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

The Zen of Abraham

Today’s Zen Chautauqua, prompted by the fact that this is Abrahamic week at the real Chautauqua, consists of links to

The Matrix of Abraham,

Matrix of the Death God, and

Happy Birthday, Kate and Kevin.

The real Chautauqua’s program this week is, of course, Christian rather than Zen.  Its theme is “Building a Global Neighborhood: The Abrahamic Vision 2004.”  One of the featured performers is Loretta Lynn; in her honor (and, of course, that of Sissy Spacek), I will try to overcome the fear and loathing that the Semitic (i. e., “Abrahamic”) religions usually inspire in me.

To a mathematician, the phrase “global neighborhood” sounds like meaningless politico-religious bullshit —  a phrase I am sure accurately characterizes most of the discourse at Chautauqua this week.  But a Google search reveals an area of research — “particle swarm optimization” in which the phrase “global neighborhood” actually means something.  See

A Hybrid Particle Swarm
and Neural Network Approach
for Reactive Power Control,
by Paulo F. Ribeiro and
W. Kyle Schlansker

This article includes the following:

Given the sophistication of his writing, I am surprised at Schlansker’s Christian background:

A good omen for the future is the fact that Schlansker balances the looney Semitic (or “Abrahamic”) teachings of Christianity with good sound Aryan religion, in the form of the goddess Themis.

 Themis, often depicted as “Justice”

For those who must have an Abraham, Schlansker’s paper includes the following:

A Themis figure I prefer to the above:

For more on religious justice
at midnight in the garden of
good and evil, see the Log24
entries of Oct. 1-15, 2002.

For material on Aryan religion that is far superior to the damned nonsense at Chautauqua, New York, this week, see

Jane Ellen Harrison’s Themis: a Study of the Social Origins of Greek Religion, with an excursus on the ritual forms preserved in Greek tragedy by Gilbert Murray and a chapter on the origin of the Olympic games by F. M. Cornford.  Rev. 2nd ed., Cambridge, Cambridge U.P., 1927.

Those who prefer the modern religion of Scientism will of course believe that Themis is purely imaginary, and that truth is to be found in modern myths like that of Carl Sagan’s novel Contact, illustrated below.

Jodie Foster (an admirer of
Leni Riefenstahl) and the
opening of the 1936 Olympics

“Heraclitus…. says: ‘The ruler whose prophecy occurs at Delphi oute legei oute kryptei, neither gathers nor hides, alla semainei, but gives hints.'”
An Introduction to Metaphysics, by Martin Heidegger, Yale University Press paperback, 1959, p. 170

“The lord whose oracle is in Delphi neither indicates clearly nor conceals, but gives a sign.”
Adolf Holl, The Left Hand of God, Doubleday, 1998, p. 50

Saturday, February 7, 2004

Saturday February 7, 2004

Filed under: General — Tags: — m759 @ 1:00 PM

Scholarship vs. Bullshit

“Examples are the stained-glass windows of knowledge.” — Vladimir Nabokov

An example of scholarship:

Paul Friedlander.

An example of bullshit:

Leo Strauss.

Further background:

Noble lies and perpetual war: Leo Strauss, the neo-cons, and Iraq.

Wednesday, August 6, 2003

Wednesday August 6, 2003

Filed under: General — Tags: — m759 @ 10:23 AM


“I had a lot of fun with this audacious and exasperating book. … [which] looks more than a little like Greil Marcus’s Lipstick Traces, a ‘secret history’ tracing punk rock through May 1968….”

— Michael Harris, Institut de Mathématiques de Jussieu, Université Paris 7, review of Mathematics and the Roots of Postmodern Thought, by Vladimir Tasic, Notices of the American Mathematical Society, August 2003

For some observations on the transgressive  predecessors of punk rock, see my entry Funeral March of July 26, 2003 (the last conscious day in the life of actress Marie Trintignant — see below), which contains the following:

“Sky is high and so am I,
If you’re a viper — a vi-paah.”
The Day of the Locust,
    by Nathanael West (1939)

As I noted in another another July 26 entry, the disease of postmodernism has, it seems, now infected mathematics.  For some recent outbreaks of infection in physics, see the works referred to below.

Postmodern Fields of Physics: In his book The Dreams of Reason, H. R. Pagels focuses on the science of complexity as the most outstanding new discipline emerging in recent years….”

— “The Semiotics of ‘Postmodern’ Physics,” by Hans J. Pirner, in Symbol and Physical Knowledge: The Conceptual Structure of Physics, ed. by M. Ferrari and I.-O. Stamatescu, Springer Verlag, August 2001 

For a critical look at Pagels’s work, see Midsummer Eve’s Dream.  For a less critical look, see The Marriage of Science and Mysticism.  Pagels’s book on the so-called “science of complexity” was published in June 1988.  For more recent bullshit on complexity, see

The Critical Idiom of Postmodernity and Its Contributions to an Understanding of Complexity, by Matthew Abraham, 2000,

which describes a book on complexity theory that, besides pronouncements about physics, also provides what “could very well be called a ‘postmodern ethic.’ “

The book reviewed is Paul Cilliers’s Complexity and Postmodernism: Understanding Complex Systems.

A search for related material on Cilliers yields the following:

Janis Joplin, Postmodernist

” …’all’ is ‘one,’ … the time is ‘now’ and … ‘tomorrow never happens,’ …. as Janis Joplin says, ‘it’s all the same fucking day.’

It appears that ‘time,’ … the linear, independent notion of ‘time’ that our culture embraces, is an artifact of our abstract thinking …

The problem is that ‘tomorrow never happens’ …. Aboriginal traditionalists are well aware of this topological paradox and so was Janis Joplin. Her use of the expletive in this context is therefore easy to understand … love is never having to say ‘tomorrow.’ “

Web page citing Paul Cilliers

“That’s the dumbest thing I ever heard.”

— Ryan O’Neal in “What’s Up, Doc?”

A more realistic look at postmodernism in action is provided by the following news story:

Brutal Death of an Actress Is France’s Summertime Drama


The actress, Marie Trintignant, died Friday [Aug. 1, 2003] in a Paris hospital, with severe head and face injuries. Her rock star companion, Bertrand Cantat, is confined to a prison hospital….

According to news reports, Ms. Trintignant and Mr. Cantat argued violently in their hotel room in Vilnius in the early hours of [Sunday] July 27 at the end of a night spent eating and drinking….

In coming months, two films starring Ms. Trintignant are scheduled to debut, including “Janis and John” by the director Samuel Benchetrit, her estranged husband and the father of two of her four children. In it, Ms. Trintignant plays Janis Joplin.

New York Times of Aug. 5, 2003

” ‘…as a matter of fact, as we discover all the time, tomorrow never happens, man. It’s all the same f…n’ day, man!’ –Janis Joplin, at live performance in Calgary on 4th July 1970 – exactly four months before her death. (apologies for censoring her exact words which can be heard on the ‘Janis Joplin in Concert’ CD)”

Janis Joplin at FamousTexans.com

All of the above fits in rather nicely with the view of science and scientists in the C. S. Lewis classic That Hideous Strength, which I strongly recommend.

For those few who both abhor postmodernism and regard the American Mathematical Society Notices

as a sort of “holy place” of Platonism, I recommend a biblical reading–

Matthew 24:15, CEV:

“Someday you will see that Horrible Thing in the holy place….”

See also Logos and Logic for more sophisticated religious remarks, by Simone Weil, whose brother, mathematician André Weil, died five years ago today.

Thursday, April 24, 2003

Thursday April 24, 2003

Filed under: General — Tags: — m759 @ 4:13 PM


A Terrible Beauty

On this date in 1905, Robert Penn Warren, the first poet laureate of the United States, was born.  

This is also the date of Ireland’s 1916 Easter Monday rebellion, of which Yeats wrote that “a terrible beauty is born,”  and the date of Vatican I’s 1870 attack on reason, Dei Filius.

My comment on Yeats’s remarks:

“No honourable and sincere man, said Stephen, has given up to you his life and his youth and his affections from the days of Tone to those of Parnell, but you sold him to the enemy or failed him in need or reviled him and left him for another. And you invite me to be one of you. I’d see you damned first.”

— James Joyce, Portrait of the Artist, published 1914-15 in serial form

My comment on the Vatican’s remarks:

“[Robert Penn] Warren taught for years at Yale and became toward the end of his life one of the most vocal critics of deconstruction, which had Yale as its headquarters. He is said to have exclaimed, ‘They got a whole new line of bullshit up here.’ ”

Dr. Gerald McDaniel 

Warren wrote that

“…only, only,
In the name of Death do we learn
    the true name of Love.”

For some clues as to whether this, too, is bullshit, see my note of Easter Monday 2003,

Time, Song, and Tragedy.

Friday, October 11, 2002

Friday October 11, 2002

Filed under: General — Tags: — m759 @ 5:10 PM

The Fourth Man:
In Lieu of Rosebud, Part III


Posted on Fri, Oct. 11, 2002

Carlos Castañeda, who led
El Nuevo Herald, dies at 70

Carlos Castañeda, the publisher emeritus of El Nuevo Herald whose passionate belief in a free press helped guide several newspapers across Latin America, died Thursday morning in Lisbon, Portugal. He was 70.

From a site titled
Enlightened Transmissions“:

The Active Side of Infinity

by Carlos Castañeda

Carlos’ last book before his untimely death. In his desperate search for meaning, Carlos recapitulates Don Juan’s teachings in perhaps his best effort. The nature of silence, and the statement that the egoic mind is a foreign implant, give deep resonance to these final teachings of Don Juan.

Perhaps a little too active.

Arthur Koestler’s somewhat more respectable mystical thoughts about infinity may be found here.  Related material: my September 5 entry, Arrow in the Blue.

Added ca. 10 to 11:40 p.m. October 11, 2002:

A review of Castaneda seems in order… the bad Carlos, not the good Carlos.  (The bad Carlos being, of course, the bullshit artist who apparently died in 1998, and the good Carlos the publisher who died yesterday.)

From the LiveJournal site of fermina —

Today’s Public Service Message:

Hi. You’re going to die.

My comment:

From a review of Carlos Castaneda’s last book, The Active Side of Infinity:

“We wind up learning something more of Castaneda but not much at all about the active side of infinity, which is mystically translated as ‘intent.’ It appears that we ought to live with intent, never forgetting that we will die, regardless. Death (and the knowledge of it) should thus inform all of our actions and relationships, providing a perspective and enforcing our humility. This is hardly an original idea, and it can’t justify wading through Castaneda’s welter of self-indulgence, which might translate better to a bumper-sticker adage.”

Hmm… What adage might that be?

As for the good Carlos, see “In Lieu of Rosebud, Part II,” below… As was said of Saint Francis Borgia, whose feast is celebrated on the day good Carlos died, he

rendered glorious a name which, but for him, would have remained a source of humiliation.


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