See also this journal on Jan. 8, 2013:
Tuesday, October 7, 2014
Ruler
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Sunday, January 10, 2021
From Fly-Bottle
Illustrations from posts now tagged Ved Mehta in this journal —
Epigraph to Fly and the Fly-Bottle: Encounters with British Intellectuals ,
by Ved Mehta , remarks first published in The New Yorker in 1961 and 1962 —
See as well the Wallace Stevens phrase “The Ruler of Reality.”
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Tuesday, May 12, 2020
Mehta Physics
Epigraph to Fly and the Fly-Bottle:
Encounters with British Intellectuals ,
by Ved Mehta , remarks first published
in The New Yorker in 1961 and 1962 —
See as well the Wallace Stevens phrase “The Ruler of Reality.”
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Saturday, June 16, 2018
Kummer’s (16, 6) (on 6/16)
"The hint half guessed, the gift half understood, is Incarnation."
— T. S. Eliot in Four Quartets
See too "The Ruler of Reality" in this journal.
Related material —
A more esoteric artifact: The Kummer 166 Configuration . . .
An array of Göpel tetrads appears in the background below.
"As you can see, we've had our eye on you
for some time now, Mr. Anderson."
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Saturday, February 10, 2018
Into the Upside Down
(Title suggested by the TV series Stranger Things )
" 'Untitled' (2016) is the most recent painting in the show
and includes one of Mr. Johns’s recurring images of a ruler."
— Image caption in an article by Deborah Solomon
in The New York Times online, Feb. 7, 2018
From a Log24 search for "Ruler" —
Related art —
See also, in this journal, Magic Mountain and Davos.
Einstein and Thomas Mann, Princeton, 1938
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Friday, May 5, 2017
For the Gods of Mexico*
A swimmer who won Olympic gold in 1936 reportedly died today.
Related material from August 4, 2008 —
Jodie Foster and the
opening of the 1936 Olympics
|
“Heraclitus…. says: ‘The ruler
— An Introduction to Metaphysics, |
Posts tagged Swimmer may or may not be relevant.
* See …
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Sunday, November 23, 2014
Remarks on Reality
Wallace Stevens in "An Ordinary Evening in New Haven"
(1950) on "The Ruler of Reality" —
"Again, 'He has thought it out, he thinks it out,
As he has been and is and, with the Queen
Of Fact, lies at his ease beside the sea.'"
One such scene, from 1953 —
Another perspective, from "The Osterman Weekend" (1983) —
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Style
Corrections to the NY Times obituary of Alexander Grothendieck
are shown below. For the original Sunday, Nov. 16, NY Times
print obituary (with its online date, Nov. 14), see a copy taken
from a weblog.
For another poetic remark in memory of Grothendieck,
see a Log24 post from November 13, the day of his death.
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Tuesday, February 4, 2014
Mystery Box
In honor of the tenth anniversary of Facebook
Viewed in the Chrome browser, a Facebook post from
January 29, 2014, displays an artist's Mystery Box*…
In the Internet Explorer browser, the mystery is solved:
Further details —
Related material — Lyche + Geometry in this journal.
See also the cat and triangle pictured by David Justice yesterday—
.
* A phrase of filmmaker J.J. Abrams. Click the link
for further details. See also a mystery box
in The New York Times on June 2, 2011.
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Tuesday, January 8, 2013
Vermont Throws Itself Together
"The way, when we climb a mountain,
Vermont throws itself together"
— Wallace Stevens, "July Mountain"
For another view of reality in New Haven, see the
brief biography of Vermont poet Frances Frost
at the Yale University Library. From that biography:
"She was survived by her son, the poet Paul Blackburn,
and by her daughter, Sister Marguerite of the Order
of St. Joseph."
See also a figure from The New York Times published
online on Epiphany, 2013:
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Friday, June 17, 2011
Bloomsday Lottery
This morning's exercise in lottery hermeneutics is unusually difficult.
Yesterday was Bloomsday (the date described in
James Joyce's Ulysses ) and the New York Lottery numbers were…
Midday numbers: 3-digit 181, 4-digit 9219.
Evening numbers: 3-digit 478, 4-digit 6449.
For 181 and 9219, see the following—
"With respect to every event, we must ask
which element has been subjected directly to change."
— Ferdinand de Saussure, Course in General Linguistics
(New York, The Philosophical Library, Inc., 1959), page 181
That Saussure page number was referenced in the following thesis
on James Joyce's other major novel, Finnegans Wake—
The thesis is from the University of Vienna (Universität Wien ).
The word Wien , in the derived form denoting an inhabitant of that city,
figured prominently in yesterday's news.
As for the evening numbers—
478 perhaps signifies the year 478 BC,
cited in Lawrence Durrell's Sicilian Carousel as the year
the ruler Gelon died.
For the evening 6449, note that the poem by Wallace Stevens quoted
here on June 15 in A for Anastasios deals with "the river of rivers"…
perhaps signifying time.
Interpreting 6449 chronologically yields 6/4/49.
The film artist John Huston, discussed in an essay from that date,
might appreciate the representation of the ancient Sicilian
river god Gelas as a man-headed bull on a coin from
around the year 478 BC.
For some perceptive remarks about Durrell, see the
article by Nigel Dennis in LIFE magazine's Nov. 21, 1960
issue (with cover noting Kennedy's victory in that year's
presidential election).
All of the above may be viewed as an approach to the aesthetic
problem posed by Dennis in yesterday's Bloomsday post—
"The problem that arises with this sort of writing is
one of form, i.e. , how to make one strong parcel
out of so many differently shaped commodities,
how to impose method on what would otherwise
be madness."
"The world has gone mad today…." — Cole Porter
For some related remarks, see page 161 of
Joyce's Catholic Comedy of Language *
by Beryl Schlossman (U. of Wisconsin Press, 1985)
and James Joyce in the final pages of The Left Hand of God
by Adolf Holl.
* Update of July 6, 2011—
This title is a correction from the previous title
given here, Moral Language by Mary Gore Forrester.
Google Books had Schlossman's content previewed
under Forrester's title.
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Monday, August 4, 2008
Monday August 4, 2008
Summer of ’36
Another Opening
of Another Show
“When I cast my mind back to that summer of 1936 different kinds of memories offer themselves to me. We got our first wireless set that summer– well, a sort of a set; and it obsessed us. And because it arrived as August was about to begin, my Aunt Maggie– she was the joker of the family– she suggested we give it a name. She wanted to call it Lugh after the old Celtic God of the Harvest. Because in the old days August the First was La Lughnasa, the feast day of the pagan god, Lugh; and the days and weeks of harvesting that followed were called the Festival of Lughnasa.”
— Michael in the play
“Dancing at Lughnasa”
“Dancing at Lughnasa”
From the film “Contact”–
Jodie Foster and the
opening of the 1936 Olympics
| “Heraclitus…. says: ‘The ruler whose prophecy occurs at Delphi oute legei oute kryptei, neither gathers nor hides, alla semainei, but gives hints.'” — An Introduction to Metaphysics, by Martin Heidegger, Yale University Press paperback, 1959, p. 170 |
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Sunday, June 8, 2008
Sunday June 8, 2008
| CHANGE TO BELIEVE IN |
Part I:
Part II:
16
|
Thus the ancient kings made music
In order to honor merit, And offered it with splendor To the Supreme Deity, Inviting their ancestors to be present. When, at the beginning of summer, thunder– electrical energy– comes rushing forth from the earth again, and the first thunderstorm refreshes nature, a prolonged state of tension is resolved. Joy and relief make themselves felt. So too, music has power to ease tension within the heart and to loosen the grip of obscure emotions. The enthusiasm of the heart expresses itself involuntarily in a burst of song, in dance and rhythmic movement of the body. From immemorial times the inspiring effect of the invisible sound that moves all hearts, and draws them together, has mystified mankind. Rulers have made use of this natural taste for music; they elevated and regulated it. Music was looked upon as something serious and holy, designed to purify the feelings of men. It fell to music to glorify the virtues of heroes and thus to construct a bridge to the world of the unseen. In the temple men drew near to God with music and pantomimes (out of this later the theater developed). Religious feeling for the Creator of the world was united with the most sacred of human feelings, that of reverence for the ancestors. The ancestors were invited to these divine services as guests of the Ruler of Heaven and as representatives of humanity in the higher regions. This uniting of the human past with the Divinity in solemn moments of religious inspiration established the bond between God and man. The ruler who revered the Divinity in revering his ancestors became thereby the Son of Heaven, in whom the heavenly and the earthly world met in mystical contact. These ideas are the final summation of Chinese culture. Confucius has said of the great sacrifice at which these rites were performed: "He who could wholly comprehend this sacrifice could rule the world as though it were spinning on his hand." |
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Wednesday, April 9, 2008
Wednesday April 9, 2008
A Yahrzeit for Baghdad
From Google News at
about 5:55 AM ET today:
Click to enlarge.
“When smashing monuments,
save the pedestals; they always
come in handy.”
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Saturday, December 1, 2007
Saturday December 1, 2007
Rhetoric, 1; Dialectic, 0.
— Robert M. Pirsig,
Zen and the Art of
Motorcycle Maintenance
— Robert M. Pirsig,
Zen and the Art of
Motorcycle Maintenance
(Pirsig is describing the response of Phaedrus to an obnoxious member of the Academy in a discussion of Plato’s figure of the horses and charioteer.)
Wallace Stevens,
opening lines of
The Necessary Angel:
“In the Phaedrus, Plato speaks of the soul in a figure. He says:
Let our figure be of a composite nature– a pair of winged horses and a charioteer. Now the winged horses and the charioteer of the gods are all of them noble, and of noble breed, while ours are mixed; and we have a charioteer who drives them in a pair, and one of them is noble and of noble origin, and the other is ignoble and of ignoble origin; and, as might be expected, there is a great deal of trouble in managing them. I will endeavor to explain to you in what way the mortal differs from the immortal creature. The soul or animate being has the care of the inanimate, and traverses the whole heaven in divers forms appearing;– when perfect and fully winged she soars upward, and is the ruler of the universe; while the imperfect soul loses her feathers, and drooping in her flight at last settles on the solid ground.
Let our figure be of a composite nature– a pair of winged horses and a charioteer. Now the winged horses and the charioteer of the gods are all of them noble, and of noble breed, while ours are mixed; and we have a charioteer who drives them in a pair, and one of them is noble and of noble origin, and the other is ignoble and of ignoble origin; and, as might be expected, there is a great deal of trouble in managing them. I will endeavor to explain to you in what way the mortal differs from the immortal creature. The soul or animate being has the care of the inanimate, and traverses the whole heaven in divers forms appearing;– when perfect and fully winged she soars upward, and is the ruler of the universe; while the imperfect soul loses her feathers, and drooping in her flight at last settles on the solid ground.
We recognize at once, in this figure, Plato’s pure poetry; and at the same time we recognize what Coleridge called Plato’s dear, gorgeous nonsense. The truth is that we have scarcely read the passage before we have identified ourselves with the charioteer, have, in fact, taken his place and, driving his winged horses, are traversing the whole heaven.”
Stevens, who was educated at Harvard, adds:
“Then suddenly we remember, it may be, that the soul no longer exists and we droop in our flight and at last settle on the solid ground. The figure becomes antiquated and rustic.”
Many who lack a Harvard education to make them droop will prefer to remember Robert Craig Knievel (Oct. 17, 1938 – Nov. 30, 2007) not as antiquated and rustic but as young and soaring.
Related material:
the previous entry
(a story for Gennie).
the previous entry
(a story for Gennie).
See also the entries for
last February’s
Academy Awards night:
Hollywood Sermon and
Between Two Worlds.
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Sunday, March 12, 2006
Sunday March 12, 2006
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.”
| 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 self-government. 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 non-euclidean 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
More interestingly, one can ask what kind of object
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
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
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 first-rate 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. 160-190 in A History of Scientific Thought, edited by Michel Serres, Blackwell Publishers (December 1995).
For the historically-challenged 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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Wednesday, October 6, 2004
Wednesday October 6, 2004
3:17:20 PM
Spin the Numbers
IN NOMINE PATRIS…
|
Today’s midday |
ET FILII…
|
2/24 Log24.net entry: |
ET SPIRITUS SANCTI…
|
|
“Heraclitus…. says:
‘The ruler whose prophecy
occurs at Delphi
oute legei oute kryptei,
neither gathers nor hides,
alla semainei, but gives hints.'”
— An Introduction to Metaphysics,
by Martin Heidegger,
Yale University Press paperback,
1959, p. 170
“The lord whose oracle is in Delphi
neither indicates clearly nor conceals,
but gives a sign.”
— Adolf Holl, The Left Hand of God,
Doubleday, 1998, p. 50
AMEN.
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Tuesday, August 17, 2004
Tuesday August 17, 2004
The Zen of Abraham
Today’s Zen Chautauqua, prompted by the fact that this is Abrahamic week at the real Chautauqua, consists of links to
Happy Birthday, Kate and Kevin.
The real Chautauqua’s program this week is, of course, Christian rather than Zen. Its theme is “Building a Global Neighborhood: The Abrahamic Vision 2004.” One of the featured performers is Loretta Lynn; in her honor (and, of course, that of Sissy Spacek), I will try to overcome the fear and loathing that the Semitic (i. e., “Abrahamic”) religions usually inspire in me.
To a mathematician, the phrase “global neighborhood” sounds like meaningless politico-religious bullshit — a phrase I am sure accurately characterizes most of the discourse at Chautauqua this week. But a Google search reveals an area of
This article includes the following:
Given the sophistication of his writing, I am surprised at Schlansker’s Christian background:
A good omen for the future is the fact that Schlansker balances the looney Semitic (or “Abrahamic”) teachings of Christianity with good sound Aryan religion, in the form of the goddess Themis.
Themis, often depicted as “Justice”
For those who must have an Abraham, Schlansker’s paper includes the following:
A Themis figure I prefer to the above:
For more on religious justice
at midnight in the garden of
good and evil, see the Log24
entries of Oct. 1-15, 2002.
For material on Aryan religion that is far superior to the damned nonsense at Chautauqua, New York, this week, see
Jane Ellen Harrison’s Themis: a Study of the Social Origins of Greek Religion, with an excursus on the ritual forms preserved in Greek tragedy by Gilbert Murray and a chapter on the origin of the Olympic games by F. M. Cornford. Rev. 2nd ed., Cambridge, Cambridge U.P., 1927.
Those who prefer the modern religion of Scientism will of course believe that Themis is purely imaginary, and that truth is to be found in modern myths like that of Carl Sagan’s novel Contact, illustrated below.
Jodie Foster (an admirer of
Leni Riefenstahl) and the
opening of the 1936 Olympics
“Heraclitus…. says: ‘The ruler whose prophecy occurs at Delphi oute legei oute kryptei, neither gathers nor hides, alla semainei, but gives hints.'”
— An Introduction to Metaphysics, by Martin Heidegger, Yale University Press paperback, 1959, p. 170
“The lord whose oracle is in Delphi neither indicates clearly nor conceals, but gives a sign.”
— Adolf Holl, The Left Hand of God, Doubleday, 1998, p. 50
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Friday, August 22, 2003
Friday August 22, 2003
Mr. Holland’s Week
On Monday, August 18, 2003,
a New York Times editor wrote
the following headline
for a book review:
Bending Over Backward
for a Well-Known Lout.
The word “lout” here refers to
author John O’Hara, who often
wrote about his native Pennsylvania.
On Thursday, August 21, 2003,
the Pennsylvania Lottery
midday number was
162.
For some other occurrences of this number,
see my entries of August 19, written
in honor of the birthday of
Jill St. John.
The “three days” remark referred to above
is from another St. John (2:19), allegedly
the author of an account of the last days
of one Jesus of Nazareth.
Those who share Mel Gibson’s
taste for religious drama may
savor the following dialogue:
|
Dramatis Personae:
Narrator: Those who had been healed did not join in with the throng at Jesus’ crucifixion who cried, “Crucify Him, crucify Him.” ….
Voice of Doom: It was a different story for the guilty ones who had fled from the presence of Jesus. Group 1: The priests and rulers never forgot the feeling of guilt they felt that moment in the temple. Group 2: The Holy Spirit flashed into their minds the prophets’ writings concerning Christ. Would they yield to this conviction? Voice of Doom: Nope! They would have to repent first! They would not admit that they were wrong! They knew that they were dead wrong. But they would not repent of it! And because Jesus had discerned their thoughts, they hated Him. With hate in their hearts they slowly returned to the temple. Voice of Hope: They could not believe their eyes when they saw the people being healed and praising God! These guilty ones were convicted that in Jesus the prophecies of the Messiah were fulfilled. As much as they hated Jesus, they could not free themselves from the thought that He might be a prophet sent by God to restore the sacredness of the temple. Voice of Doom: So they asked Him a stupid question! “What miracle can you perform to show us that you have the right to do what you did?” Voice of Jesus: “Destroy this temple and in three days I will build it again.” Voice of Doom: Those guys couldn’t believe it! |
Philosophers ponder the idea of identity:
what it is to give something a name
on Monday
and have it respond to that name
on Friday….
— Bernard Holland, The New York Times,
Monday, May 20, 1996
“Ask a stupid question…”
For further details, see
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Monday, October 21, 2002
Monday October 21, 2002
Birthdays for a Small Planet
Today's birthdays:
- Ursula K. Le Guin, 1929
- Frances FitzGerald, 1940
- Carrie Fisher, 1956
The entry below, "Theology for a Small Planet," sketches an issue that society has failed to address since the fall of 1989, when it was first raised by the Harvard Divinity Bulletin.
In honor mainly of Ursula K. Le Guin, but also of her fellow authors above, I offer Le Guin's solution. It is not new. It has been ignored mainly because of the sort of hateful and contemptible arrogance shown by
- executives in the tradition of Henry Ford and later Ford Foundation and Ford Motors employees McGeorge Bundy and Robert McNamara (see yesterday's entry below for Ford himself), by
- theologians in the tradition of the Semitic religions — Judaism, Christianity, and Islam — and by
- self-proclaimed "shamans of scientism" like Michael Shermer in the tradition of Scientific American magazine.
Here is an introduction to the theology that should replace the ridiculous and outdated Semitic religions.
"Scholarly translators of the Tao Te Ching, as a manual for rulers, use a vocabulary that emphasizes the uniqueness of the Taoist 'sage,' his masculinity, his authority. This language is perpetuated, and degraded, in most popular versions. I wanted a Book of the Way accessible to a present-day, unwise, unpowerful, and perhaps unmale reader, not seeking esoteric secrets, but listening for a voice that speaks to the soul. I would like that reader to see why people have loved the book for 2500 years.
It is the most lovable of all the great religious texts, funny, keen, kind, modest, indestructibly outrageous and inexhaustibly refreshing. Of all the deep springs, this is the purest water. To me it is also the deepest spring."
Tao Te Ching: Chapter 6
translated by Ursula K. Le Guin
The valley spirit never dies
Call it the mystery, the woman.
The mystery,
the Door of the Woman,
is the root
of earth and heaven.
Forever this endures, forever.
And all its uses are easy.
Sunday, September 29, 2002
Sunday September 29, 2002
New from Miracle Pictures
– IF IT’S A HIT, IT’S A MIRACLE! –
Pi in the Sky
for Michaelmas 2002
“Fear not, maiden, your prayer is heard.
Michael am I, guardian of the highest Word.”
Contact, by Carl Sagan:
Chapter 1 – Transcendental Numbers
In the seventh grade they were studying “pi.” It was a Greek letter that looked like the architecture at Stonehenge, in England: two vertical pillars with a crossbar at the top. If you measured the circumference of a circle and then divided it by the diameter of the circle, that was pi. At home, Ellie took the top of a mayonnaise jar, wrapped a string around it, straightened the string out, and with a ruler measured the circle’s circumference. She did the same with the diameter, and by long division divided the one number by the other. She got 3.21. That seemed simple enough.
The next day the teacher, Mr. Weisbrod, said that pi was about 22/7, about 3.1416. But actually, if you wanted to be exact, it was a decimal that went on and on forever without repeating the pattern of numbers. Forever, Ellie thought. She raised her hand. It was the beginning of the school year and she had not asked any questions in this class.
“How could anybody know that the decimals go on and on forever?”
“That’s just the way it is,” said the teacher with some asperity.
“But why? How do you know? How can you count decimals forever?”
“Miss Arroway” – he was consulting his class list – “this is a stupid question. You’re wasting the class’s time.”
No one had ever called Ellie stupid before and she found herself bursting into tears….
After school she bicycled to the library at the nearby college to look through books on mathematics. As nearly as she could figure out from what she read, her question wasn’t all that stupid. According to the Bible, the ancient Hebrews had apparently thought that pi was exactly equal to three. The Greeks and Romans, who knew lots of things about mathematics, had no idea that the digits in pi went on forever without repeating. It was a fact that had been discovered only about 250 years ago. How was she expected to know if she couldn’t ask questions? But Mr. Weisbrod had been right about the first few digits. Pi wasn’t 3.21. Maybe the mayonnaise lid had been a little squashed, not a perfect circle. Or maybe she’d been sloppy in measuring the string. Even if she’d been much more careful, though, they couldn’t expect her to measure an infinite number of decimals.
There was another possibility, though. You could calculate pi as accurately as you wanted. If you knew something called calculus, you could prove formulas for pi that would let you calculate it to as many decimals as you had time for. The book listed formulas for pi divided by four. Some of them she couldn’t understand at all. But there were some that dazzled her: pi/4, the book said, was the same as 1 – 1/3 + 1/5 – 1/7 + …, with the fractions continuing on forever. Quickly she tried to work it out, adding and subtracting the fractions alternately. The sum would bounce from being bigger than pi/4 to being smaller than pi/4, but after a while you could see that this series of numbers was on a beeline for the right answer. You could never get there exactly, but you could get as close as you wanted if you were very patient. It seemed to her
a miracle
that the shape of every circle in the world was connected with this series of fractions. How could circles know about fractions? She was determined to learn
The book said something else: pi was called a “transcendental” number. There was no equation with ordinary numbers in it that could give you pi unless it was infinitely long. She had already taught herself a little algebra and understood what this meant. And pi wasn’t the only transcendental number. In fact there was an infinity of transcendental numbers. More than that, there were infinitely more transcendental numbers that ordinary numbers, even though pi was the only one of them she had ever heard of. In more ways than one, pi was tied to infinity.
She had caught a glimpse of something majestic.
Chapter 24 – The Artist’s Signature
The anomaly showed up most starkly in Base 2 arithmetic, where it could be written out entirely as zeros and ones. Her program reassembled the digits into a square raster, an equal number across and down. Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.
The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover
— another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in. It doesn’t matter what you look like, or what you’re made of, or where you come from. As long as you live in this universe, and have a modest talent for mathematics, sooner or later you’ll find it. It’s already here. It’s inside everything. You don’t have to leave your planet to find it. In the fabric of space and in the nature of matter, as in a great work of art, there is, written small, the artist’s signature. Standing over humans, gods, and demons… there is an intelligence that antedates the universe. The circle had closed. She found what she had been searching for.
Song lyric not in Sagan’s book:
Will the circle be unbroken
by and by, Lord, by and by?
Is a better home a-waitin’
in the sky, Lord, in the sky?
“Contact,” the film:
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Recording: |
Columbia 37669 |
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Date Issued: |
Unknown |
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Side: |
A |
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Title: |
Can The Circle Be Unbroken |
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Artist: |
Carter Family |
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Recording Date: |
May 6, 1935 |
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Listen: |
Realaudio |
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The above conclusion to Sagan’s book is perhaps the stupidest thing by an alleged scientist that I have ever read. As a partial antidote, I offer the following.
| Today’s birthday: Stanley Kramer, director of “On the Beach.”
From an introduction to a recording of the famous Joe Hill song about Pie in the Sky: “They used a shill to build a crowd… You know, a carny shill.” |
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