The cover (pdf) of the Notices of the American Mathematical Society for April 2007 (Mathematics Awareness Month) features a naked disembodied brain (Log24, March 16), courtesy of researchers at the Catholic University of Louvain.

Log24, Jan. 26 "... at last she realized what the Thing on the dais was. IT was a brain. A disembodied brain...."   "There could not be an objective test that distinguished a clever robot from a really conscious person."   -- Daniel Dennett in TIME magazine, issue dated Mon., Jan. 29, 2007 Daniel Dennett, Professor of Philosophy and Director of the Center for Cognitive Studies at Tufts University, in his office on campus. (Boston Globe, Jan. 29, 2006. Photo © Rick Friedman.)

Update to
The Geometry of Logic:

A detailed description of a group of 16 "logical automorphisms" of the
16 binary connectives has been given in the paper
"Simetria y Logica: La notacion de Peirce para los 16 conectivos binarios," by Mireya
Garcia, Jhon Fredy Gomez, and Arnold Oostra. (Published in the
Memorias del XII Encuentro de Geometria y sus Aplicaciones,
Universidad Pedagogica Nacional, Bogota, June 2001; on the Web at

http://www.unav.es/gep/Articulos/SimetriaYLogica.pdf.)

The authors do not identify this group as a subgroup of the affine group of A (the finite affine geometry of four dimensions over the two-element field);
this can serve as an exercise.  Another exercise: determining whether the authors' order-16 group includes all transformations that might reasonably be called "logical automorphisms" of the 16 binary connectives.

Excerpt:

"We are left to conclude that there was something significant in
Hobbes's philosophy that motivated Wallis to engage in the lengthy and
vitriolic denunciation of all things Hobbesian.

In point of fact, Wallis made no great secret of his motivations for
attacking Hobbes's geometry, and the presence of theological and
political motives is well attested in a 1659 letter to Huygens. He
wrote:

But regarding the very harsh diatribe against Hobbes, the
necessity of the case, and not my manners, led to it. For you see, as I
believe, from other of my writings how peacefully I can differ with
others and bear those with whom I differ. But this was provoked by our
Leviathan (as can be easily gathered fro his other writings,
principally those in English), when he attacks with all his might and
destroys our universities (and not only ours, but all, both old and
new), and especially the clergy and all institutions and all religion.
As if the Christian world knew nothing sound or nothing that was not
ridiculous in philosophy or religion; and as if it has not understood
religion because it does not understand philosophy, nor philosophy
because it does not understand mathematics. And so it seemed necessary
that now some mathematician, proceeding in the opposite direction,
should show how little he understand this mathematics (from which he
takes his courage). Nor should we be deterred from this by his
arrogance, which we know will vomit poison and filth against us.
(Wallis to Huygens, 11 January, 1659; Huygens 1888-1950,* 2: 296-7)

The threats that Hobbes supposedly posed to the universities, the
clergy, and all religion are a consequence of his political and
theological doctrines. Hobbes's political theory requires that the
power of the civil sovereign be absolute and undivided. As a
consequence, such institutions as universities and the clergy must
submit to the dictates of the sovereign in all matters. This extends,
ironically enough, to geometry, since Hobbes notoriously claimed that
the sovereign could ban the teaching of the subject and order 'the
burning of all books of Geometry' if he should judge geometric
principles 'a thing contrary to [his] right of dominion, or to the
interest of men that have dominion' (Leviathan (1651) 1.11, 50; English Works**
3: 91). In the area of church government, Hobbes's doctrines are a
decisive rejection of the claims of Presbyterianism, which holds that
questions of theological doctrine is [sic] to be decided by the
elders of the church-- the presbytery-- without reference to the claims
of the sovereign. As a Presbyterian minister, a doctor of divinity, and
professor of geometry at Oxford, Wallis found abundant reason to reject
this political theory."

* Huygens, Christiaan. 1888-1950. Les oeuvres complètes de Chrisiaan Huygens. Ed. La Société Hollandaise des Sciences. 22 vols. The Hague: Martinus Nijhoff.

** Hobbes, Thomas. [1839-45] 1966. The English Works of Thomas Hobbes of Malmesbury, now First Collected and Edited by Sir William Molesworth. Edited by William Molesworth. 11 vols. Reprint. Aalen, Germany: Scientia Verlag.

"'It is a very difficult philosophical question, the question of
what "random" is,' he said. He plucked the rubber band with his
thumb, boink, boink."

-- Herbert Robbins in Richard Preston's "The Mountains of Pi" (The New Yorker, March 2, 1992)

The Logic of Dreams

From A Beautiful Mind--

"How
could you," began Mackey, "how could you, a mathematician, a man
devoted to reason and logical proof...how could you believe that
extraterrestrials are sending you messages? How could you believe that
you are being recruited by aliens from outer space to save the world?
How could you...?"

Nash looked up at last and fixed Mackey with
an unblinking stare as cool and dispassionate as that of any bird or
snake. "Because," Nash said slowly in his soft, reasonable southern
drawl, as if talking to himself, "the ideas I had about supernatural
beings came to me the same way that my mathematical ideas did. So I
took them seriously."

Ideas:

These
numbers may, in the mad way so well portrayed by Sylvia Nasar in the
above book, be regarded as telling a story... a story that should, of
course, not be taken too seriously.

Friday's New York numbers (midday 214, evening 711) suggest the dates 2/14 and 7/11. 
Clicking on these dates will lead the reader to Log24 entries
featuring, among others, T. S. Eliot and Stephen King-- two authors not
unacquainted with the bizarre logic of dreams.

A link in the 7/11 entry leads to a remark of Noel Gray on Plato's Meno and "graphic
austerity as the tool to bring to the surface, literally and
figuratively, the inherent presence of geometry in the mind of the
slave."

Also Friday: an example of graphic austerity-- indeed, Gray graphic austerity-- in Log24:

This
illustration refers to chess rather than to geometry, and to the mind
of an addict rather than to that of a slave, but chess and
geometry, like addiction and slavery, are not unrelated.

Friday's
Pennsylvania numbers, midday 429 and evening 038, suggest that the
story includes, appropriately enough in view of the above Beautiful Mind excerpt, Mackey himself.  The midday number suggests the date 4/29, which at Log24 leads to an entry in memory of Mackey.

(Related material: the Harvard Gazette of April 6, 2006, "Mathematician George W. Mackey, 90: Obituary"--  "A memorial service will be held at Harvard's Memorial Church on April 29 at 2 p.m.")

Friday's Pennsylvania evening number 038 tells two other parts of the story involving Mackey...

As Mackey himself might hope, the number may be regarded as a reference to the 38 impressive pages of Varadarajan's "Mackey Memorial Lecture" (pdf).

More
in the spirit of Nash, 38 may also be taken as a reference to
Harvard's old postal address, Cambridge 38, and to the year, 1938, that
Mackey entered graduate study at Harvard, having completed his
undergraduate studies at what is now Rice University.

Returning
to the concept of graphic austerity, we may further simplify the
already abstract chessboard figure above to obtain an illustration that
has been called both "the field of reason" and "the Garden of Apollo"
by an architect, John Outram, discussing his work at Mackey's undergraduate alma mater:

Let us hope that Mackey,
a devotee of reason,
is now enjoying the company
of Apollo rather than that of
Tom O'Bedlam:

For John Nash on his birthday:

I know more than Apollo,
For oft when he lies sleeping
I see the stars at mortal wars
In the wounded welkin weeping.

-- Tom O'Bedlam's Song

Queen's Gambit

That the topless towers be burnt

And men recall that face,

Move most gently if move you must

In this lonely place.

She thinks, part woman, three parts a child,

That nobody looks; her feet

Practise a tinker shuffle

Picked up on a street.
Like a long-legged fly upon the stream

Her mind moves upon silence.

-- W. B. Yeats, "Long-Legged Fly"

This is the epigraph to
the Walter Tevis novel
The Queen's Gambit.