This is from a book by five Dutch authors —
See as well . . .
“The bureaucratic innovations of the New Deal
fed into the powerful associative logic
of commonsense reasoning,
leading a number of Americans to equate science
with the technocratic, managerial liberalism
of Roosevelt and his allies.”
— http://bostonreview.net/sciencenature/
andrewjewetthowamericanscamedistrustscience
From a Log24 search for “Notes Toward” —
“Logos and logic, crystal hypothesis, Incipit and a form to speak the word And every latent double in the word….” — Wallace Stevens, “Notes Toward a Supreme Fiction“ 
Adam Gopnik in The New Yorker today reacts to the startling
outcomes of three recent contests: the presidential election,
the Super Bowl, and the Oscar for Best Picture —
"The implicit dread logic is plain."
Related material —
Transformers in this journal and …
“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?”
—Many Dimensions (1931), by Charles Williams
See also …
The above figure is from Ian Stewart's 1996 revision of a 1941 classic,
What Is Mathematics? , by Richard Courant and Herbert Robbins.
One wonders how the confused slave boy of Plato's Meno would react
to Stewart's remark that
"The number of copies required to double an
object's size depends on its dimension."
In memory of Theodore Sturgeon, Leonard Nimoy,
and William Thomas McKinley —
From the Boston Modern Orchestra Project today :
"In a good way"
New York Daily News , 2:55 PM EST today—
Joe Simon, who dreamed up the starspangled super hero Captain America while riding on a Manhattan bus during the early days of World War II, died Thursday [Dec. 15] after an undisclosed illness. He was 98.
New York Times , about 10 PM EST today—
Joe Simon, a writer, editor and illustrator of comic books who was a cocreator of the superhero Captain America, conceived out of a patriotic impulse as war was roiling Europe, died on Wednesday [Dec. 14] at his home in Manhattan. He was 98.
The discrepancy is perhaps due to initial reports that quoted Simon's family as saying he died "Wednesday night."
Simon was a cocreator of Captain America. For some background on Simon and a photo with his fellow comic artist Jerry Robinson, cocreator of The Joker, see a Washington Post article from this afternoon. Robinson died on either Wednesday, Dec. 7, or Thursday, Dec. 8, 2011.
Jerry Robinson, a pioneer in the early days of Batman comics and a key force in the creation of Robin the Boy Wonder; the Joker; Bruce Wayne’s butler, Alfred; and TwoFace, died Wednesday afternoon [Dec. 7] in New York City. He was 89.
CNN—
Cartoonist Jerry Robinson, who worked on the earliest Batman comics and claimed credit for creating the supervillain The Joker, died Thursday [Dec. 8] at the age of 89, his family confirmed.
A picture by Robinson—
The Joker in January 1943
with a Nov. 27 calendar page
A nonjoke from a more recent November 27—
“The book by Hesse has many facets ….” (Link added.)
— V. V. Nalimov, In the Labyrinths of Language ,
Ch. 1, “What Language Is,” p. 22.
Related philosophical speculation —
From Wallace Stevens —
"Reality is the beginning not the end,
Naked Alpha, not the hierophant Omega,
Of dense investiture, with luminous vassals."
— “An Ordinary Evening in New Haven” VI
From The Point magazine yesterday, October 8, 2019 —
Parricide: On Irad Kimhi's Thinking and Being .
Book review by Steven Methven.
The conclusion:
"Parricide is nothing that the philosopher need fear . . . .
What sustains can be no threat. Perhaps what the
unique genesis of this extraordinary work suggests is that
the true threat to philosophy is infanticide."
This remark suggests revisiting a post from Monday —
Monday, October 7, 2019
Berlekamp Garden vs. Kinder Garten

(A sequel to Simplex Sigillum Veri and
Rabbit Hole Meets Memory Hole)
” Wittgenstein does not, however, relegate all that is not inside the bounds
of sense to oblivion. He makes a distinction between saying and showing
which is made to do additional crucial work. ‘What can be shown cannot
be said,’ that is, what cannot be formulated in sayable (sensical)
propositions can only be shown. This applies, for example, to the logical
form of the world, the pictorial form, etc., which show themselves in the
form of (contingent) propositions, in the symbolism, and in logical
propositions. Even the unsayable (metaphysical, ethical, aesthetic)
propositions of philosophy belong in this group — which Wittgenstein
finally describes as ‘things that cannot be put into words. They make
themselves manifest. They are what is mystical’ ” (Tractatus 6.522).
— Stanford Encyclopedia of Philosophy , “Ludwig Wittgenstein”
From Tractatus LogicoPhilosophicus by Ludwig Wittgenstein.
(First published in Annalen der Naturphilosophie ,1921. 5.4541 The solutions of the problems of logic must be simple, since they set the standard of simplicity. Men have always had a presentiment that there must be a realm in which the answers to questions are symmetrically combined — a priori — to form a selfcontained system. A realm subject to the law: Simplex sigillum veri. 
Somehow, the old Harvard seal, with its motto “Christo et Ecclesiae ,”
was deleted from a bookplate in an archived Harvard copy of Whitehead’s
The Axioms of Projective Geometry (Cambridge U. Press, 1906).
In accordance with Wittgenstein’s remarks above, here is a new
bookplate seal for Whitehead, based on a simplex —
The disappearance of "Christo et Ecclesiae" at Harvard
Rabbit Hole
Memory Hole
The above Harvard seal in a PDF —
The same page, minus the seal, today at the Internet Archive —
For a larger image of the sealless page, click here.
Click to enlarge.
“Perhaps the philosophically most relevant feature of modern science
is the emergence of abstract symbolic structures as the hard core
of objectivity behind— as Eddington puts it— the colorful tale of
the subjective storyteller mind.”
— Hermann Weyl, Philosophy of Mathematics and
Natural Science , Princeton, 1949, p. 237
"The bond with reality is cut."
— Hans Freudenthal, 1962
From page 180, Logicomix — It was a dark and stormy night …
Update of 10:18 AM the same day —
See also Logicomix in this journal and, at Harvard,
http://www.math.harvard.edu/~mazur/ —
Update of 10:48 AM the same day —
See Log24 on the date of Tieszen's death.
 I was a teacher.  You're being modest, aren't you? You were a professor at Boston University... Isn't that right?  Yes, well, assistant professor.  And what'd you teach?  Philosophy. Truth and logic. That sort of thing. Read more: https://www.springfieldspringfield.co.uk/ movie_script.php?movie=gifted
Compare and contrast with a real Boston University professor,
John Stachel, quoted here on Sept. 5, 2017.
"But unlike many who left the Communist Party, I turned left
rather than right, and returned—or rather turned for the first time—
to a critical examination of Marx's work. I found—and still find—
that his analysis of capitalism, which for me is the heart of his work,
provides the best starting point, the best critical tools, with which—
suitably developed—to understand contemporary capitalism.
I remind you that this year is also the sesquicentennial of the
Communist Manifesto , a document that still haunts the capitalist world."
— From "Autobiographical Reflections," a talk given on June 5, 1998, by
John Stachel at the Max Planck Institute for the History of Science in Berlin
on the occasion of a workshop honoring his 70th birthday,
"SpaceTime, Quantum Entanglement and Critical Epistemology."
From a passage by Stachel quoted in the previous post —
From the source for Stachel's remarks on Weyl and coordinatization —
Note that Stachel distorted Weyl's text by replacing Weyl's word
"symbols" with the word "quantities." —
This replacement makes no sense if the coordinates in question
are drawn from a Galois field — a field not of quantities , but rather
of algebraic symbols .
"You've got to pick up every stitch… Must be the season of the witch."
— Donovan song at the end of Nicole Kidman's "To Die For"
Or: Coordinatization for Physicists
This post was suggested by the link on the word "coordinatized"
in the previous post.
I regret that Weyl's term "coordinatization" perhaps has
too many syllables for the readers of recreational mathematics —
for example, of an article on 4×4 magic squares by Conway, Norton,
and Ryba to be published today by Princeton University Press.
Insight into the deeper properties of such squares unfortunately
requires both the ability to learn what a "Galois field" is and the
ability to comprehend sevensyllable words.
From the Log24 post "A Point of Identity" (August 8, 2016) —
A logo that may be interpreted as oneeighth of a 2x2x2 array
of cubes —
The figure in white above may be viewed as a subcube representing,
when the eightcube array is coordinatized, the identity (i.e., (0, 0, 0)).
From page 180, Logicomix —
Alfred North Whitehead in the first of
the abovenamed 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 (20089)
This evening's New York Times —
"William Thomas McKinley, a prolific American composer
whose music was infused with the jazz he had performed
since childhood, died on Feb. 3 at his home in Reading,
Mass. He was 76.
He died in his sleep, his son Elliott said."
"William Thomas McKinley: Elegy for Strings (2006)
[Elliott McKinley]
137 views as of 9:45 PM ET Feb. 28, 2015
Published on Feb 11, 2015
Composed as an elegy and tribute for friends and family
that have passed, spurred by the passing of McKinley's
long time friend, drummer Roger Ryan. The performance
heard here is by the Seattle Symphony under the direction
of Gerard Schwarz.
Photos by Elliott McKinley (Rho Ophiuchi nebula complex…
and the Pleiades…) shot at Cherry Springs State Park."
Related material from the date of McKinley's death —
Expanding the Spielraum.
The previous post's Kirkridge link leads to
a mention of religious philosopher Parker J. Palmer.
From an Utne Reader page on Palmer:
See also Theodore Sturgeon's 1949 story "What Dead Men Tell"—
"… He’d read about it in a magazine or somewhere.
He took a strip of scrap film about eighteen
inches long and put the ends together. He turned
one end over and spliced ’em. Now, if you trace
that strip, or mark it with a grease pencil, right up
the center, you find that the doggone thing only
has one side!”
The doctor nodded, and the girl said:
“A Möbius strip.”
“That what they call it?” said Hulon. “Well, I figured
this corridor must be something like that. On that
strip, a single continuous line touched both sides.
All I had to do was figure out an object built so that
a continuous line would cover all three of three sides,
and I’d have it. So I sat down and thought it out…."
— and the following mathematical illustration —
"I thought I had an important idea.
It's part of a … call it a philosophy,
if that doesn't sound too high
falutin'," he said.
"It's a philosophy," she said.
"We can call things by their names."
Leonard Nimoy, 2015 :
"A life is like a garden.
Perfect moments can be had,
but not preserved, except in memory."
* A tale from Astounding Science Fiction
Vol. 44, No. 3, November 1949
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…
— Page 180, Logicomix
A photo opportunity for Whitehead
(from Romancing the Cube, April 20, 2011)—
See also Absolute Ambition (Nov. 19, 2010).
* For the title, see Vanishing Point in this journal.
For some background, see "Cartoon Graveyard" and "Many Dimensions."
It was a dark and stormy night…
— 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—
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.'”
— GianCarlo Rota, “Syntax, Semantics, and…” in Indiscrete Thoughts . See also the original 1988 article.
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

See also a post on Mathematics and Narrative from Nov. 14, 2009.
That post compares characters in Many Dimensions to those in Logicomix—
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
Excerpts from Logicomix
with the 1979 cover found in a somewhat less epic search —
Larger view of Google snippet —
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.
"It's my absolute ambition that you are touched to the core of your being with the content…."
— Julie Taymor on SpiderMan: Turn Off the Dark (Playbill video, undated)
Another ambitious comicbook 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 …
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 .
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 CantorRussell 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—
A graphic novel reviewed in the current Washington Post features Alfred North Whitehead and Bertrand Russell–
Related material:
Whitehead on Fano’s finite projective threespace:
“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
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 .
"Harvard seniors have
every right to demand a
Harvardcalibre speaker."
— Adam Goldenberg in
The Harvard Crimson
"Look down now, Cotton Mather"
— Wallace Stevens,
Harvard College
Class of 1901
For Thursday, June 5, 2008,
commencement day for Harvard's
Class of 2008, here are the
Pennsylvania Lottery numbers:
Midday 025
Evening 761
Thanks to the late
Harvard professor
Willard Van Orman Quine,
the midday number 025
suggests the name
"Isaac Newton."
(For the logic of this suggestion,
see On Linguistic Creation
and Raiders of the Lost Matrix.)
Thanks to Google search, the
name of Newton, combined with
Thursday's evening number 761,
suggests the following essay:
PHILOSOPHY OF SCIENCE:

Perhaps the Log24 entries for
the date of Koshland's death:
The Philosopher's Stone
and The Rock.
Or perhaps the following
observations:
On the figure of 25 parts
discussed in
"On Linguistic Creation"–
"The Moslems thought of the
central 1 as being symbolic
of the unity of Allah. "
— Clifford Pickover
"At the still point,
there the dance is."
— T. S. Eliot,
Harvard College
Class of 1910
"His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality."
—Allan Kozinn on Mstislav Rostropovich in The New York Times, quoted in Log24 on April 29, 2007
"At that instant he saw, in one blaze of light, an image of unutterable conviction…. the core of life, the essential pattern whence all other things proceed, the kernel of eternity."
— Thomas Wolfe, Of Time and the River, quoted in Log24 on June 9, 2005
"… the stabiliser of an octad preserves the affine space structure on its complement, and (from the construction) induces AGL(4,2) on it. (It induces A_{8} on the octad, the kernel of this action being the translation group of the affine space.)"
— Peter J. Cameron, "The Geometry of the Mathieu Groups" (pdf)
"… donc Dieu existe, réponse!"
(Faust, Part Two, as
quoted by Jung in
Memories, Dreams, Reflections)
"Pauli as Mephistopheles
in a 1932 parody of
Goethe's Faust at Niels Bohr's
institute in Copenhagen.
The drawing is one of
many by George Gamow
illustrating the script."
— Physics Today
'To meet someone' was his enigmatic answer. 'To search for the stone that the Great Architect rejected, the philosopher's stone, the basis of the philosophical work. The stone of power. The devil likes metamorphoses, Corso.'"
— The Club Dumas, basis for the Roman Polanski film "The Ninth Gate" (See 12/24/05.)
— The Innermost Kernel
(previous entry)
And from
"Symmetry in Mathematics
and Mathematics of Symmetry"
(pdf), by Peter J. Cameron,
a paper presented at the
International Symmetry Conference,
Edinburgh, Jan. 1417, 2007,
we have
The Epigraph–
(Here "whatever" should
of course be "whenever.")
Also from the
Cameron paper:
Local or global?
Among other (mostly more vague) definitions of symmetry, the dictionary will typically list two, something like this:
• exact correspondence of parts; Mathematicians typically consider the second, global, notion, but what about the first, local, notion, and what is the relationship between them? A structure M is homogeneous if every isomorphism between finite substructures of M can be extended to an automorphism of M; in other words, "any local symmetry is global." 
Some Log24 entries
related to the above politically
(women in mathematics)–
Global and Local:
One Small Step
and mathematically–
Structural Logic continued:
Structure and Logic (4/30/07):
This entry cites
Alice Devillers of Brussels–
"The aim of this thesis
is to classify certain structures
which are, from a certain
point of view, as homogeneous
as possible, that is which have
as many symmetries as possible."
"There is such a thing
as a tesseract."
The phrase “structural logic” in yesterday’s entry was applied to Bach’s cello suites. It may equally well be applied to geometry. In particular:
“The aim of this thesis is to classify certain structures which are, from a certain point of view, as homogeneous as possible, that is which have as many symmetries as possible.”
— Alice Devillers, “Classification of Some Homogeneous and Ultrahomogeneous Structures,” Ph.D. thesis, Université Libre de Bruxelles, academic year 20012002
Related material:
The above models for the corresponding projective spaces may be regarded as illustrating the phrase “structural logic.”
For a possible application of the 16point space’s “many symmetries” to logic proper, see The Geometry of Logic.
“His graceful accounts of the Bach Suites for Unaccompanied Cello illuminated the works’ structural logic as well as their inner spirituality.” —Allan Kozinn in Friday’s New York Times
A Circle of Quiet
From the Harvard Math Table page:
“No Math table this week. We will reconvene next week on March 14 for a special Pi Day talk by Paul Bamberg.”
Transcript of the movie “Proof”–
Some friends of mine are in this band. They’re playing in a bar on Diversey, way down the bill, around… I said I’d be there. Great. Imaginary number? It’s a math joke. 
From the April 2006 Notices of the American Mathematical Society, a footnote in a review by Juliette Kennedy (pdf) of Rebecca Goldstein’s Incompleteness:
^{4} There is a growing literature in the area of postmodern commentaries of [sic] Gödel’s theorems. For example, Régis Debray has used Gödel’s theorems to demonstrate the logical inconsistency of selfgovernment. For a critical view of this and related developments, see Bricmont and Sokal’s Fashionable Nonsense [13]. For a more positive view see Michael Harris’s review of the latter, “I know what you mean!” [9]….
[9] MICHAEL HARRIS, “I know what you mean!,” http://www.math.jussieu.fr/~harris/Iknow.pdf.
[13] ALAN SOKAL and JEAN BRICMONT, Fashionable Nonsense, Picador, 1999.
Following the trail marked by Ms. Kennedy, we find the following in Harris’s paper:
“Their [Sokal’s and Bricmont’s] philosophy of mathematics, for instance, is summarized in the sentence ‘A mathematical constant like doesn’t change, even if the idea one has about it may change.’ ( p. 263). This claim, referring to a ‘crescendo of absurdity’ in Sokal’s original hoax in Social Text, is criticized by anthropologist Joan Fujimura, in an article translated for IS*. Most of Fujimura’s article consists of an astonishingly bland account of the history of noneuclidean geometry, in which she points out that the ratio of the circumference to the diameter depends on the metric. Sokal and Bricmont know this, and Fujimura’s remarks are about as helpful as FN’s** referral of Quine’s readers to Hume (p. 70). Anyway, Sokal explicitly referred to “Euclid’s pi”, presumably to avoid trivial objections like Fujimura’s — wasted effort on both sides.^{32} If one insists on making trivial objections, one might recall that the theorem
that p is transcendental can be stated as follows: the homomorphism Q[X] –> R taking X to is injective. In other words, can be identified algebraically with X, the variable par excellence.^{33}
More interestingly, one can ask what kind of object was before the formal definition of real numbers. To assume the real numbers were there all along, waiting to be defined, is to adhere to a form of Platonism.^{34} Dedekind wouldn’t have agreed.^{35} In a debate marked by the accusation that postmodern writers deny the reality of the external world, it is a peculiar move, to say the least, to make mathematical Platonism a litmus test for rationality.^{36} Not that it makes any more sense simply to declare Platonism out of bounds, like LévyLeblond, who calls Stephen Weinberg’s gloss on Sokal’s comment ‘une absurdité, tant il est clair que la signification d’un concept quelconque est évidemment affectée par sa mise en oeuvre dans un contexte nouveau!’^{37} Now I find it hard to defend Platonism with a straight face, and I prefer to regard the formula
as a creation rather than a discovery. But Platonism does correspond to the familiar experience that there is something about mathematics, and not just about other mathematicians, that precisely doesn’t let us get away with saying ‘évidemment’!^{38}
^{32} There are many circles in Euclid, but no pi, so I can’t think of any other reason for Sokal to have written ‘Euclid’s pi,’ unless this anachronism was an intentional part of the hoax. Sokal’s full quotation was ‘the of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity.’ But there is no need to invoke nonEuclidean geometry to perceive the historicity of the circle, or of pi: see Catherine Goldstein’s ‘L’un est l’autre: pour une histoire du cercle,’ in M. Serres, Elements d’histoire des sciences, Bordas, 1989, pp. 129149.
^{33} This is not mere sophistry: the construction of models over number fields actually uses arguments of this kind. A careless construction of the equations defining modular curves may make it appear that pi is included in their field of scalars.
^{34} Unless you claim, like the present French Minister of Education [at the time of writing, i.e. 1999], that real numbers exist in nature, while imaginary numbers were invented by mathematicians. Thus would be a physical constant, like the mass of the electron, that can be determined experimentally with increasing accuracy, say by measuring physical circles with ever more sensitive rulers. This sort of position has not been welcomed by most French mathematicians.
^{35 } Cf. M. Kline, Mathematics The Loss of Certainty, p. 324.
^{36} Compare Morris Hirsch’s remarks in BAMS April 94.
^{37} IS*, p. 38, footnote 26. Weinberg’s remarks are contained in his article “Sokal’s Hoax,” in the New York Review of Books, August 8, 1996.
^{38} Metaphors from virtual reality may help here.”
* Earlier defined by Harris as “Impostures Scientifiques (IS), a collection of articles compiled or commissioned by Baudouin Jurdant and published simultaneously as an issue of the journal Alliage and as a book by La Découverte press.”
** Earlier defined by Harris as “Fashionable Nonsense (FN), the North American translation of Impostures Intellectuelles.”
What is the moral of all this French noise?
Perhaps that, in spite of the contemptible nonsense at last summer’s Mykonos conference on mathematics and narrative, stories do have an important role to play in mathematics — specifically, in the history of mathematics.
Despite his disdain for Platonism, exemplified in his remarks on the noteworthy connection of pi with the zeta function in the formula given above, Harris has performed a valuable service to mathematics by pointing out the excellent historical work of Catherine Goldstein. Ms. Goldstein has demonstrated that even a French nominalist can be a firstrate scholar. Her essay on circles that Harris cites in a French version is also available in English, and will repay the study of those who, like Barry Mazur and other Harvard savants, are much too careless with the facts of history. They should consult her “Stories of the Circle,” pp. 160190 in A History of Scientific Thought, edited by Michel Serres, Blackwell Publishers (December 1995).
For the historicallychallenged mathematicians of Harvard, this essay would provide a valuable supplement to the upcoming “Pi Day” talk by Bamberg.
For those who insist on limiting their attention to mathematics proper, and ignoring its history, a suitable Pi Day observance might include becoming familiar with various proofs of the formula, pictured above, that connects pi with the zeta function of 2. For a survey, see Robin Chapman, Evaluating Zeta(2) (pdf). Zeta functions in a much wider context will be discussed at next May’s politically correct “Women in Mathematics” program at Princeton, “Zeta Functions All the Way” (pdf).
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