Saturday, November 7, 2015

Clarifying Dyson

Filed under: General,Geometry — m759 @ 12:00 PM

The previous post quoted a passage from Turing's Cathedral ,
a 2012 book by George Dyson

A passage in 'Turing's Cathedral' that recalls the Go chip in 'Wild Palms'

It should be noted that Dyson's remarks on "two species of
bits," space, time, "structure and sequence" and logic gates
are from his own idiosyncratic attempt to create a philosophy
based on the workings of computers.  These concepts are not,
so far as I can tell, part of anyone else's approach to the subject.

For a more standard introduction to how computers work, see
(for instance) a book by an author Dyson admires:

The Pattern on the Stone , by W. Daniel Hillis (Basic Books, 1998).


I etch a pattern of geometric shapes onto a stone.
To the uninitiated, the shapes look mysterious and
complex, but I know that when arranged correctly
they will give the stone a special power, enabling it
to respond to incantations in a language no human
being has ever spoken. I will ask the stone questions
in this language, and it will answer by showing me a
vision: a world created by my spell, a world imagined
within the pattern on the stone.

A few hundred years ago in my native New England,
an accurate description of my occupation would have
gotten me burned at the stake. Yet my work involves
no witchcraft; I design and program computers. The
stone is a wafer of silicon, and the incantations are
software. The patterns etched on the chip and the
programs that instruct the computer may look
complicated and mysterious, but they are generated
according to a few basic principles that are easily
explained. . . . .

Hillis's title suggests some remarks unrelated to computers —

See Philosopher + Stone in this journal.

Friday, December 19, 2014

Turing’s Church

Filed under: General — Tags: — m759 @ 12:23 PM

This post was suggested by the book Turing's Cathedral  and by
comments 29 and 31 on Scott Aaronson's Dec. 16 post about
"The Imitation Game."

See Church-Turing thesis at Wikipedia and Church Logic here.

Tuesday, April 10, 2012

Turing Gate

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

In memory of Christine Brooke-Rose,
an image from the date of her death

IMAGE- Excerpt from book 'Turing's Cathedral'

See also A Little Story and Before Dehors.

Monday, July 15, 2019

Possibility and Necessity: Kierkegaard Meets Nietzsche

Filed under: General — m759 @ 7:29 AM

The previous post's search for Turing + Dyson yielded a
quotation from Kierkegaard on possibility and necessity
Further details —

See also . . .

Nietzsche, 'law in becoming' and 'play in necessity'

Nietzsche on Heraclitus— 'play in necessity' and 'law in becoming'— illustrated.

The Chosen One

Filed under: General — m759 @ 6:55 AM

See also Turing + Dyson in this  journal.

Friday, December 30, 2016

ZZZ Accounting

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

Or:  Lost in Conversion

The main title is the name of Ben Affleck's firm in "The Accountant."
The subtitle was suggested by religious remarks in the previous post.

From "The Man Who Tried to Redeem the World with Logic" —

"The following June, 1945, von Neumann penned
what would become a historic document entitled
'First Draft of a Report on the EDVAC,' the first published
description of a stored-program binary computing machine—
the modern computer."

Image from von Neumann's report

Version converted to text —

See also "Turing + Dyson" in this journal . . . 

For a character  that "spans both worlds,"
see posts tagged "Oscar Day 2007."

Related image data —

" 'No views' is good." — Christian Wolff

Friday, November 6, 2015

Girard’s Transition

Filed under: General — m759 @ 10:15 AM

"Eight is a gate." — Mnemonic rhyme

Girard reportedly died at 91 on Wednesday, Nov. 4, 2015.

Sunday, December 14, 2014

Time, Space, Code

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

Some words and an image related to today's posts —

IMAGE- Excerpt from book 'Turing's Cathedral'

Saturday, April 13, 2013

Princeton’s Christopher Robin

The title is that of a talk (see video) given by
George Dyson at a Princeton land preservation trust,
reportedly on March 21, 2013.  The talk's subtitle was
"Oswald Veblen and the Six-hundred-acre Woods."


Thursday, March 21, 2013

Geometry of Göpel Tetrads (continued)

m759 @ 7:00 PM

An update to Rosenhain and Göpel Tetrads in PG(3,2)
supplies some background from
Notes on Groups and Geometry, 1978-1986,
and from a 2002 AMS Transactions  paper.

IMAGE- Göpel tetrads in an inscape, April 1986

Related material for those who prefer narrative
to mathematics:

Log24 on June 6, 2006:


The Omen:

Now we are 


Related material for those who prefer mathematics
to narrative:

What the Omen narrative above and the mathematics of Veblen
have in common is the number 6. Veblen, who came to
Princeton in 1905 and later helped establish the Institute,
wrote extensively on projective geometry.  As the British
geometer H. F. Baker pointed out,  6 is a rather important number
in that discipline.  For the connection of 6 to the Göpel tetrads
figure above from March 21, see a note from May 1986.

See also last night's Veblen and Young in Light of Galois.

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

Wednesday, March 21, 2012

Digital Theology

Filed under: General,Geometry — Tags: , — m759 @ 7:20 AM

See also remarks on Digital Space and Digital Time in this journal.

Such remarks can, of course, easily verge on crackpot territory.

For some related  pure  mathematics, see Symmetry of Walsh Functions.

Monday, January 29, 2007

Monday January 29, 2007

Filed under: General,Geometry — Tags: — m759 @ 9:00 AM

By Indirections
(Hamlet, II, i)

“Michael Taylor (1971)…. contends that the central conflict in Hamlet is between ‘man as victim of fate and as controller of his own destiny.'”– The Gale Group, Shakespearean Criticism, Vol. 71, at eNotes

Doonesbury today:

The image “http://www.log24.com/log/pix07/070129-Robot4A.gif” cannot be displayed, because it contains errors.

“Personality is a synthesis of possibility and necessity.”– Soren Kierkegaard

On Fate (Necessity),
Freedom (Possibility),
and Machine Personality–

Part I: Google as Skynet

George Dyson
The Godel-to-Google Net [March 8, 2005]
A Cathedral for Turing [October 24, 2005]

Dyson: “The correspondence between Google and biology is not an analogy, it’s a fact of life.”

Part II: The Galois Connection

David Ellerman–
“A Theory of Adjoint Functors– with some Thoughts about their Philosophical Significance” (pdf) [November 15, 2005]

Ellerman: “Such a mechanism seems key to understanding how an organism can perceive and learn from its environment without being under the direct stimulus control of the environment– thus resolving the ancient conundrum of receiving an external determination while exercising self-determination.”

For a less technical version, see Ellerman’s “Adjoints and Emergence: Applications of a New Theory of Adjoint Functors” (pdf).

Ellerman was apparently a friend of, and a co-author with, Gian-Carlo Rota.  His “theory of adjoint functors” is related to the standard mathematical concepts known as profunctors, distributors, and bimodules. The applications of his theory, however, seem to be less to mathematics itself than to a kind of philosophical poetry that seems rather closely related to the above metaphors of George Dyson. For a less poetic approach to related purely mathematical concepts, see, for instance, the survey Practical Foundations of Mathematics by Paul Taylor (Cambridge University Press, 1999).  For less poetically appealing, but perhaps more perspicuous, extramathematical applications of category theory, see the work of, for instance, Joseph Goguen: Algebraic Semiotics and Information Integration, Databases, and Ontologies.

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