News from today's New York Times:

The Rev. Dr. Theodore Alexander Gill Sr., a Presbyterian theologian, a
philosophy
teacher, and an influential provost emeritus of John Jay College of
Criminal Justice in
Manhattan, died at 85 on June 10 in Princeton.  In retirement from
John Jay, The Rev. Dr. Gill was theologian in residence at Nassau
Presbyterian Church in Princeton.

In memory of The Rev. Dr. Gill:

Religious Symbolism at Princeton
    (on Nassau Presbyterian Church),
Pro-Semitism
    (on number theory at Princeton),
For the Mad Musicians of Princeton,
     (on Schroeder and Bernstein),
Movie Date and its preceding entries
   (on Princeton's St. John von Neumann),
Why Me?
   (for Princeton theologian Elaine Pagels),
Notes on Literary and Philosophical Puzzles
   (Princeton's John Nash as Ya Ya Fontana), and
Go Tigers!
   (for the Princeton Evangelical Fellowship).

   "True joy is a profound remembering, and true grief is the same.

    Thus it was, when the dust storm that had snatched
Cal up finally died, and he opened his eyes to see the Fugue spread out
before him, he felt as though the few fragile moments of epiphany he'd
tasted in his twenty-six years-- tasted but always lost-- were here
redeemed and wed. He'd grasped fragments of this delight before. Heard
rumour of it in the womb-dream and the dream of love; known it in
lullabies. But never, until now, the whole, the thing entire.

    It would be, he idly thought, a fine time to die.

    And a finer time still to live, with so much laid out before him."

In a 1940 letter to his sister Simone,  André Weil discussed a sort of "Rosetta stone," or trilingual text of three analogous parts: classical analysis on the complex field, algebraic geometry over finite fields, and the theory of number fields.  

John Baez discussed (Sept. 6, 2003) the analogies of Weil, and he himself furnished another such Rosetta stone on a much smaller scale:

"... a 24-element group called the 'binary
tetrahedral group,' a 24-element group called 'SL(2,Z/3),' and
the vertices of a regular polytope in 4 dimensions called the
'24-cell.' The most important fact is that these are all the
same thing!"

For further details, see Wikipedia on the 24-cell, on special linear groups, and on Hurwitz quaternions,

The group SL(2,Z/3), also known as "SL(2,3)," is of course derived from
the general linear group GL(2,3).  For the relationship of this
group to the quaternions, see the Log24 entry for August 4 (the
birthdate of the discoverer of quaternions, Sir William Rowan Hamilton).

The 3x3 square shown above may, as my August 4 entry indicates, be
used to picture the quaternions and, more generally, the 48-element
group GL(2,3).  It may therefore be regarded as the structure
underlying the miniature Rosetta stone described by Baez.

"The typical example of a finite group is GL(n,q), the
general linear
group of n dimensions over the field with q elements. The student who
is introduced to the subject with other examples is being completely
misled."

 -- J. L. Alperin, book review,

    Bulletin (New Series) of the American

    Mathematical Society 10
(1984), 121

"The typical example of a finite group is GL(n,q), the
general linear
group of n dimensions over the field with q elements. The student who
is introduced to the subject with other examples is being completely
misled."

 -- J. L. Alperin, book review,
    Bulletin (New Series) of the American
    Mathematical Society 10
(1984), 121

"Beauty is the proper conformity
of the parts to one another
and to the whole."

-- Werner Heisenberg,
"Die Bedeutung des Schönen
in der exakten Naturwissenschaft,"
address delivered to the
Bavarian Academy of Fine Arts,
Munich, 9 Oct. 1970, reprinted in
Heisenberg's Across the Frontiers,
translated by Peter Heath,
Harper & Row, 1974

Related material:

The Eightfold Cube

(in Arabic, ka'b)

and