Log24

Saturday, September 15, 2018

Axioms

Filed under: Uncategorized — m759 @ 9:50 AM

Tieszen— 'Kurt Godel and Phenomenology' — 1992

Update of 10:18 AM the same day —

See also Logicomix  in this  journal and, at Harvard,

http://www.math.harvard.edu/~mazur/

  • September 6, 2018:  Eric Maskin, Amartya Sen and I
    are giving a course this semester: 'Axiomatic Reasoning'
    (PHIL 273B). Introduction to Axiomatic Reasoning gives a
    general sense of what we intend to cover.

Update of 10:48 AM the same day —

http://www.log24.com/log/pix18/180915-Tieszen_died-March-28-2017.jpg

See Log24 on the date of Tieszen's death.

Tuesday, December 20, 2016

The Project’s Central Problem

Filed under: Uncategorized — m759 @ 10:00 AM

From page 180, Logicomix —

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

Alfred North Whitehead in the first of
the above-named years, 1906 —

"But the project's central problem was always there."

"The deeper we got into our Quest…
The more I doubted its premises."

— Attributed to Bertrand Russell
by Apostolos Doxiadis and Christos
Papadimitriou in Logicomix  (2008-9)

Wednesday, April 8, 2015

The Crosswicks Curse

Filed under: Uncategorized — m759 @ 8:08 PM

Continues.

It was a dark and stormy night 

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

Wednesday, May 21, 2014

Through the Vanishing Point*

Filed under: Uncategorized — Tags: , — m759 @ 9:48 AM

Marshall McLuhan in "Annie Hall" —

"You know nothing of my work."

Related material — 

"I need a photo opportunity
I want a shot at redemption
Don't want to end up a cartoon
In a cartoon graveyard"

— Paul Simon

It was a dark and stormy night…

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

A photo opportunity for Whitehead
(from Romancing the Cube, April 20, 2011)—

IMAGE- Whitehead on Fano's construction of the 15-point projective Galois space over GF(2)

See also Absolute Ambition (Nov. 19, 2010).

* For the title, see Vanishing Point in this journal.

Friday, June 8, 2012

Cartoon Graveyard

Filed under: Uncategorized — m759 @ 2:01 AM

Whitehead and Russell, 'Logicomix' page 181

For some background, see "Cartoon Graveyard" and "Many Dimensions."

Wednesday, April 20, 2011

Romancing the Cube

Filed under: Uncategorized — m759 @ 1:00 AM

It was a dark and stormy night…

http://www.log24.com/log/pix11/110420-DarkAndStormy-Logicomix.jpg

— Page 180, Logicomix

“… the class of reflections is larger in some sense over an arbitrary field than over a characteristic zero field.”

– Julia Hartmann and Anne V. Shepler, “Jacobians of Reflection Groups

For some context, see the small cube in “A Simple Reflection Group of Order 168.”

See also the larger cube in “Many Dimensions” + Whitehead in this journal (scroll down to get past the current post).

That search refers to a work by Whitehead published in 1906, the year at the top of the Logicomix  page above—

http://www.log24.com/log/pix11/110420-Whitehead1906Axioms.jpg

A related remark on axiomatics that has metaphysical overtones suitable for a dark and stormy night

“An adequate understanding of mathematical identity requires a missing theory that will account for the relationships between formal systems that describe the same items. At present, such relationships can at best be heuristically described in terms that invoke some notion of an ‘intelligent user standing outside the system.'”

— Gian-Carlo Rota, “Syntax, Semantics, and…” in Indiscrete Thoughts . See also the original 1988 article.

Tuesday, November 23, 2010

Tale

Filed under: Uncategorized — Tags: , — m759 @ 8:00 PM

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

m759 @ 12:00 AM

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.

See also a post on Mathematics and Narrative from Nov. 14, 2009.

That post compares characters in Many Dimensions  to those in Logicomix

Whitehead and Russell, 'Logicomix' page 181

Saturday, November 20, 2010

Search

Filed under: Uncategorized — m759 @ 4:00 AM

An Epic Search for Truth

— Subtitle of Logicomix , a work reviewed in the December 2010 Notices of the American Mathematical Society  (see previous post).

Some future historian of mathematics may contrast the lurid cover of the December 2010 Notices

http://www.log24.com/log/pix10B/101119-AMSnoticesThumb.jpg

Excerpts from Logicomix

with the 1979 cover found in a somewhat less epic search —

http://www.log24.com/log/pix10B/101120-79T-A37-500w.jpg

Larger view of Google snippet —

http://www.log24.com/log/pix10B/101120-79T-A37-snippet.jpg

For some purely mathematical background, see Finite Geometry of the Square and Cube.

For some background related to searches for truth, see "Coxeter + Trudeau" in this journal.

Friday, November 19, 2010

Absolute Ambition

Filed under: Uncategorized — Tags: — m759 @ 10:30 AM

"It's my absolute ambition that you are touched to the core of your being with the content…."

— Julie Taymor on Spider-Man: Turn Off the Dark  (Playbill video, undated)

Another ambitious comic-book promotion —

"What Logicomix  does that few works in any medium do is to make intellectual passion palpable. That is its greatest strength. And it’s here that its form becomes its substance."

— Judith Roitman, review (pdf, 3.7 MB) of Logicomix: An Epic Search for Truth , in …

http://www.log24.com/log/pix10B/101119-AMSnoticesSm.jpg

 The December 2010 AMS Notices  cover has excerpts from Logicomix.

Related material:

"In the classical grammarians’ sense of the power of form over 'content' and style over 'substance,' he originated the phrase, 'the medium is the message.'"

— Joseph P. Duggan on Marshall McLuhan at The University Bookman

See also, in this  journal, The Medium is the Message, Wechsler, and Blockheads .

Sunday, February 7, 2010

Today’s Sermon

Filed under: Uncategorized — m759 @ 11:00 AM

Mathematics and Religion, continued–

Calvin Jongsma, review of an anthology titled Mathematics and the Divine

"Believers of many faiths have found significant points of contact between their religious outlooks and mathematics. Not all of these claims were made in the distant past or by certified crackpots…."

Edward Nelson in "Warning Signs of a Possible Collapse of Contemporary Mathematics"–

"The most impressive feature of Cantor’s theory is that he showed that there are different sizes of infinity, by his famous diagonal argument. But Russell applied this argument to establish his paradox: the set of all sets that are not elements of themselves both is and is not an element of itself."

Jongsma's assertion appears to be true. Nelson's appears to be false. Discuss.

Remarks:

Saying that someone applied some argument– any argument will do here– to establish a paradox– any paradox will do here– casts into doubt the validity of either the argument, the application of the argument, or both. In the Cantor-Russell case, such doubt is unnecessary, since the paradox is clearly independent of the diagonal argument. There is certainly an historical connection between Cantor's argument and Russell's paradox– see, for instance, Wikipedia on the latter. The historical connection is, however, not a logical connection.

For Russell discovering his paradox without the use of Cantor's diagonal argument, see Logicomix

Russell discovers his paradox

Click for some context.

Saturday, November 14, 2009

Mathematics and Narrative, continued:

Filed under: Uncategorized — Tags: — m759 @ 10:10 PM

A graphic novel reviewed in the current Washington Post  features Alfred North Whitehead and Bertrand Russell–

Whitehead and Russell, 'Logicomix' page 181

Related material:

Whitehead on Fano’s finite projective three-space:

“This is proved by the consideration of a three dimensional geometry in which there are only fifteen points.”

The Axioms of Projective Geometry , Cambridge University Press, 1906

A related affine six-space:

Grey cube, 4x4x4

Further reading:

See Solomon’s Cube and the link at the end of today’s previous entry, then compare and contrast the above portraits of Whitehead and Russell with Charles Williams’s portraits of Sir Giles Tumulty and Lord Arglay in the novel Many Dimensions .

It was a dark and stormy night….

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