Log24

Tuesday, October 1, 2019

Transylvania Revisited

Filed under: General — Tags: — m759 @ 2:10 PM

The previous post suggests . . .

Jim Holt reviewing Edward Rothstein's Emblems of Mind: The Inner Life of Music and Mathematics  in The New Yorker  of June 5, 1995:

"The fugues of Bach, the symphonies of Haydn, the sonatas of Mozart: these were explorations of ideal form, unprofaned by extramusical associations. Such 'absolute music,' as it came to be called, had sloughed off its motley cultural trappings. It had got in touch with its essence. Which is why, as Walter Pater famously put it, 'all art constantly aspires towards the condition of music.'

The only art that can rival music for sheer etheriality is mathematics. A century or so after the advent of absolute music, mathematics also succeeded in detaching itself from the world. The decisive event was the invention of strange, non-Euclidean geometries, which put paid to the notion that the mathematician was exclusively, or even primarily, concerned with the scientific universe. 'Pure' mathematics came to be seen by those who practiced it as a free invention of the imagination, gloriously indifferent to practical affairs– a quest for beauty as well as truth." [Links added.]

A line for James McAvoy —

"Pardon me boy, is this the Transylvania Station?"

Bolyai 'worlds out of nothing' quote

See as well Worlds Out of Nothing ,  by Jeremy Gray.

Friday, July 5, 2019

Ex Nihilo

Filed under: General — Tags: — m759 @ 10:50 AM

IMAGE- James McAvoy (left) and Michael Fassbender in 'X-Men: First Class'

The previous post suggests a line for James McAvoy —

"Pardon me boy, is this the Transylvania Station?"

Bolyai 'worlds out of nothing' quote

See as well "Out of Nothing" in this journal.

Sunday, May 19, 2019

The Building Blocks of Geometry

Filed under: General — Tags: , — m759 @ 10:21 PM

From "On the life and scientific work of Gino Fano
by Alberto Collino, Alberto Conte, and Alessandro Verra,
ICCM Notices , July 2014, Vol. 2 No. 1, pp. 43-57 —

" Indeed, about the Italian debate on foundations of Geometry, it is not rare to read comments in the same spirit of the following one, due to Jeremy Gray13. He is essentially reporting Hans Freudenthal’s point of view:

' When the distinguished mathematician and historian of mathematics Hans Freudenthal analysed Hilbert’s  Grundlagen he argued that the link between reality and geometry appears to be severed for the first time in Hilbert’s work. However, he discovered that Hilbert had been preceded by the Italian mathematician Gino Fano in 1892. . . .' "

13 J. Gray, "The Foundations of Projective Geometry in Italy," Chapter 24 (pp. 269–279) in his book Worlds Out of Nothing , Springer (2010).


Restoring the severed link —

Structure of the eightfold cube

See also Espacement  and The Thing and I.
 

Related material —

 
 

Wednesday, September 26, 2018

Analogies Between Analogies

Filed under: General — m759 @ 8:05 PM

On the new Netflix series "Maniac" —

(Spoiler alert)

"The treatment Owen and Annie sign up for promises to fix
its subjects’ brains with just three little pills—A, B, and C—
administered one after another over the span of three days.
The first forces you to relive your trauma;
the second exposes your blind spots; and
the third pill forces a confrontation."

— Kara Weisenstein at vice.com, Sept. 26, 2018, 12:19 PM

See also, from Log24 earlier 

A.  Monday — Mathematics as Art
B.  Tuesday — Trinity and Denkraum  Revisited
C.  Wednesday — Trinity Tale

'Out of nothing' opening of 'Maniac' at Netflix

Saturday, September 22, 2018

Symmetric Generation, by Netflix

Filed under: General — Tags: , — m759 @ 5:05 AM

Suggested by the previous post . . .

'Out of nothing' opening of 'Maniac' at Netflix

"The pattern is the pattern."

Monday, September 17, 2018

Lying at the Axis

Filed under: G-Notes,General,Geometry — m759 @ 12:00 AM

Or:  Zero Dark Zero

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

Thursday, May 17, 2018

Leap

Filed under: General — Tags: — m759 @ 9:45 PM

Quoted here on May 5, 2018

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

The page number  229 may also be interpreted, cabalistically,
as the date  2/29, Leap Day.

See Leap Day 2016 among the posts tagged Mind Spider.

Saturday, May 5, 2018

Galois Imaginary

Filed under: General,Geometry — m759 @ 9:00 PM

" Lying at the axis of everything, zero is both real and imaginary. Lovelace was fascinated by zero; as was Gottfried Leibniz, for whom, like mathematics itself, it had a spiritual dimension. It was this that let him to imagine the binary numbers that now lie at the heart of computers: 'the creation of all things out of nothing through God's omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing.' He also wrote, 'The imaginary number is a fine and wonderful recourse of the divine spirit, almost an amphibian between being and nonbeing.' "

— A footnote from page 229 of Sydney Padua's
    April 21, 2015, book on Lovelace and Babbage

A related passage —

From The French Mathematician
by Tom Petsinis (Nov. 30, 1998) —

0

I had foreseen it all in precise detail.
One step led inevitably to the next,
like the proof of a shining theorem,
down to the conclusive shot that still echoes
through time and space. 
Facedown in the damp pine needles,
I embraced that fatal sphere
with my whole body. Dreams, memories,
even the mathematics I had cherished
and set down in my last will and testament–
all receded. I am reduced to
a singular point; in an instant
I am transformed to .

i = an imaginary being

Here, on this complex space,
i  am no longer the impetuous youth
who wanted to change the world
first with a formula and then with a flame.
Having learned the meaning of infinite patience,
i  now rise to the text whenever anyone reads 
about Evariste Galois, preferring to remain 
just below the surface, 
like a goldfish nibbling the fringe of a floating leaf.
Ink is more mythical than blood
(unless some ancient poet slit his 
vein and wrote an epic in red):
The text is a two-way mirror 
that allows me to look into
the life and times of the reader. 
Who knows, someday i  may rise
to a text that will compel me 
to push through to the other side.
Do you want proof that i  exist? Where am ?
Beneath every word, behind each letter, 
on the side of a period that will never see the light.

Friday, December 18, 2015

Box of Nothing

Filed under: General,Geometry — m759 @ 9:00 PM

Images related to the previous post

Detail of the 1697 Leibniz medal

Leibniz, letter of 1697:

“And so that I won’t come entirely empty-handed this time, I enclose a design of that which I had the pleasure of discussing with you recently. It is in the form of a memorial coin or medallion; and though the design is mediocre and can be improved in accordance with your judgment, the thing is such, that it would be worth showing in silver now and unto future generations, if it were struck at your Highness’s command. Because one of the main points of the Christian Faith, and among those points that have penetrated least into the minds of the worldly-wise and that are difficult to make with the heathen is the creation of all things out of nothing through God’s omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing. And it would be difficult to find a better illustration of this secret in nature or philosophy; hence I have set on the medallion design IMAGO CREATIONIS [in the image of creation]. It is no less remarkable that there appears therefrom, not only that God made everything from nothing, but also that everything that He made was good; as we can see here, with our own eyes, in this image of creation. Because instead of there appearing no particular order or pattern, as in the common representation of numbers, there appears here in contrast a wonderful order and harmony which cannot be improved upon….

Such harmonious order and beauty can be seen in the small table on the medallion up to 16 or 17; since for a larger table, say to 32, there is not enough room. One can further see that the disorder, which one imagines in the work of God, is but apparent; that if one looks at the matter with the proper perspective, there appears symmetry, which encourages one more and more to love and praise the wisdom, goodness, and beauty of the highest good, from which all goodness and beauty has flowed.”

See also some related posts in this journal.

Saturday, April 25, 2015

Faustian Merry-Go-Round

Filed under: General — m759 @ 11:01 PM

Thanks to David Lavery for the following:

"Voilà! Stevens has managed to create out of nothing a palpable imaginative space, an interiority without material dimensions, replete with its own achieved and accomplished music. And in truth, in a world of Heisenbergian uncertainties and shifting star masses, it may be enough for the dizzying, ever-shifting merry-go-round of the Faustian mind simply to slow down and let itself come to rest, at least for the moment."

— Paul Mariani, "God and the Imagination," Aug. 10, 1996

http://imagejournal.org/page/journal/articles/issue-18/mariani-essays

Thursday, October 17, 2013

Finite Geometry and Physical Space (continued)

Filed under: General,Geometry — m759 @ 1:26 PM

On Monday, October 14, 2013, Jeremy Gray published
an article titled "Epistemology of Geometry" in the online
Stanford Encyclopedia of Philosophy.

Gray's article did not mention the role of finite  geometry
in such epistemology.

For that role, see Finite Geometry and Physical Space 
as a web page and as a Google image search.

See also my papers at Academia.edu.

Thursday, May 26, 2011

Life’s Persistent Questions

Filed under: General — m759 @ 4:01 PM

This afternoon's online New York Times  reviews "The Tree of Life," a film that opens tomorrow.

With disarming sincerity and daunting formal sophistication “The Tree of Life” ponders some of the hardest and most persistent questions, the kind that leave adults speechless when children ask them. In this case a boy, in whispered voice-over, speaks directly to God, whose responses are characteristically oblique, conveyed by the rustling of wind in trees or the play of shadows on a bedroom wall. Where are you? the boy wants to know, and lurking within this question is another: What am I doing here?

Persistent answers… Perhaps conveyed by wind, perhaps by shadows, perhaps by the New York Lottery.

For the nihilist alternative— the universe arose by chance out of nothing and all is meaningless— see Stephen Hawking and Jennifer Ouellette.

Update of 10:30 PM EDT May 26—

Today's NY Lottery results: Midday 407, Evening 756. The first is perhaps about the date April 7, the second about the phrase "three bricks shy"— in the context of the number 759 and the Miracle Octad Generator. (See also Robert Langdon and The Poetics of Space.)

Monday, May 16, 2011

Luck

Filed under: General — m759 @ 10:00 PM

From the Guardian  yesterday—

Stephen Hawking: 'There is no heaven; it's a fairy story'

In an exclusive interview with the Guardian, the cosmologist shares
his thoughts on death, M-theory, human purpose and our chance existence

http://www.log24.com/log/pix11A/110516-Hawking.jpg

Stephen Hawking dismisses belief in God in an exclusive interview with the Guardian.
Photograph: Solar & Heliospheric Observatory/Discovery Channel

What is the value in knowing "Why are we here?"

The universe is governed by science. But science tells us that we can't solve the equations, directly in the abstract. We need to use the effective theory of Darwinian natural selection of those societies most likely to survive. We assign them higher value.

You've said there is no reason to invoke God to light the blue touchpaper. Is our existence all down to luck?

Science predicts that many different kinds of universe will be spontaneously created out of nothing. It is a matter of chance which we are in.

So here we are….

New York Lottery today, May 16… Midday 374, Evening 430.

See also the Turner Classic Movies film now playing.

    Friday, December 25, 2009

    Brightness at Noon

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

    New York Times online front page
    Christmas morning:

    “Arthur Koestler, Man of Darkness”–

    NY Times front page, Christmas morning 2009

    The photo is of Koestler in 1931 on a zeppelin expedition to the North Pole.

    The Act of Creation is, I believe, a more truly creative work than any of Koestler’s novels….  According to him, the creative faculty in whatever form is owing to a circumstance which he calls ‘bisociation.’ And we recognize this intuitively whenever we laugh at a joke, are dazzled by a fine metaphor, are astonished and excited by a unification of styles, or ’see,’ for the first time, the possibility of a significant theoretical breakthrough in a scientific inquiry. In short, one touch of genius—or bisociation—makes the whole world kin. Or so Koestler believes.”

    – Henry David Aiken, The Metaphysics of Arthur Koestler, New York Review of Books, Dec. 17, 1964

    From Opus Postumum by Immanuel Kant, Eckart Förster, Cambridge U. Press, 1995, p. 260:

    “In January 1697, Leibniz accompanied his New Year Congratulations to Rudolf August with the design of a medal with the duke’s likeness on one side, and the ‘image of Creation’ in terms of the binary number system on the other. Concerning the inscription on this side, Leibniz writes: ‘I have thought for a while about the Motto dell’impresa and finally have found it good to write this line: omnibus ex nihilo ducendis SUFFICIT UNUM [To make all things from nothing, UNITY SUFFICES], because it clearly indicates what is meant by the symbol, and why it is imago creationis’ (G. F. Leibniz, Zwei Briefe über das binäre Zahlensystem und die chinesische Philosophie, ed. Renate Loosen and Franz Vonessen, Chr. Belser Verlag: Stuttgart 1968, p. 21).”

    Leibniz, design for medallion showing binary numbers as an 'imago creationis'

    Figure from Rudolf  Nolte’s
    Gottfried Wilhelms Baron von Leibniz
    Mathematischer Beweis der Erschaffung und
    Ordnung der Welt in einem Medallion…
    (Leipzig: J. C. Langenheim, 1734).

    Leibniz, letter of 1697:

    “And so that I won’t come entirely empty-handed this time, I enclose a design of that which I had the pleasure of discussing with you recently. It is in the form of a memorial coin or medallion; and though the design is mediocre and can be improved in accordance with your judgment, the thing is such, that it would be worth showing in silver now and unto future generations, if it were struck at your Highness’s command. Because one of the main points of the Christian Faith, and among those points that have penetrated least into the minds of the worldly-wise and that are difficult to make with the heathen is the creation of all things out of nothing through God’s omnipotence, it might be said that nothing is a better analogy to, or even demonstration of such creation than the origin of numbers as here represented, using only unity and zero or nothing. And it would be difficult to find a better illustration of this secret in nature or philosophy; hence I have set on the medallion design IMAGO CREATIONIS [in the image of creation]. It is no less remarkable that there appears therefrom, not only that God made everything from nothing, but also that everything that He made was good; as we can see here, with our own eyes, in this image of creation. Because instead of there appearing no particular order or pattern, as in the common representation of numbers, there appears here in contrast a wonderful order and harmony which cannot be improved upon….

    Such harmonious order and beauty can be seen in the small table on the medallion up to 16 or 17; since for a larger table, say to 32, there is not enough room. One can further see that the disorder, which one imagines in the work of God, is but apparent; that if one looks at the matter with the proper perspective, there appears symmetry, which encourages one more and more to love and praise the wisdom, goodness, and beauty of the highest good, from which all goodness and beauty has flowed.”

    See also Parable.

    Friday, December 12, 2008

    Friday December 12, 2008

    Filed under: General — m759 @ 12:24 PM
    Back to the Garden
    of Forking Paths

    “Somehow it seems to fill my head with ideas– only I don’t exactly know what they are!…. Let’s have a look at the garden first!”

    — A passage from Lewis Carroll’s Through the Looking-Glass. The “garden” part– but not the “ideas” part– was quoted by Jacques Derrida in Dissemination in the epigraph to Chapter 7, “The Time before First.”

    “‘For you… he… we aren’t meaning…’ She was almost stammering, as if she were trying to say several things at once…. Suddenly she gave a little tortured scream. ‘O!’ she cried, ‘O! I can’t keep up! it keeps dividing! There’s too many things to think of!'”

    — A passage from Charles Williams’s The Place of the Lion, Chapter 12.

    “He was thinking faster than he had ever done, and questions rose out of nothing and followed each other– what was to will? Will was determination to choose– what was choice? How could there be choice, unless there was preference, and if there was preference there was no choice, for it was not possible to choose against that preferring nature which was his being; yet being consisted in choice, for only by taking and doing this and not that could being know itself, could it indeed be; to be then consisted in making an inevitable choice, and all that was left was to know the choice, yet even then was the chosen thing the same as the nature that chose, and if not… So swiftly the questions followed each other that he seemed to be standing in flashing coils of subtlety, an infinite ring of vivid intellect and more than intellect, for these questions were not of the mind alone but absorbed into themselves physical passion and twined through all his nature on an unceasing and serpentine journey.”

    — A passage from The Place of the Lion, Chapter 10.

    Do you like apples?

    Good Will Hunting

    Friday, May 11, 2007

    Friday May 11, 2007

    Filed under: General — m759 @ 11:30 PM
    Today’s Lottery Commentary:

    Lonesome No More!

    In keeping with the spirit of previous Log24 entries, here is today’s Pennsylvania Lottery commentary.  This afternoon’s entry suggests an interpretation of today’s numbers as comments on the new film “Georgia Rule.”

    Pennsylvania Lottery today:
    Mid-day 384
    Evening 952

    Today’s mid-day number, 384, is the number of symmetries of the tesseract, a geometric figure illustrated on the cover of the novel The Gameplayers of Zan (see, for instance, May 10, 2007).  That novel suggests an interpretation of today’s evening number, 952, as addressing (literally) the subject of Life.

    See the address mathforum.org/library/view/952.html.

    From that address:

    “The Game of Life is played on a field of cells, each of which has eight neighbors (adjacent cells). A cell is either occupied (by an organism) or not. The rules for deriving a generation from the previous one are these: Death – If an occupied cell has 0, 1, 4, 5, 6, 7, or 8 occupied neighbors, the organism dies (0, 1: of loneliness; 4 thru 8: of overcrowding). Survival – If an occupied cell has two or three neighbors, the organism survives to the next generation. Birth – If an unoccupied cell has three occupied neighbors, it becomes occupied.”

    Relevance to the film “Georgia Rule”: lonesomeness, generations, and the Lord’s name–

    Georgia is a “lonesome and decent widow in wholesome Hull, Idaho…. her framed motto is ‘Count Your Blessings’ and she’s ready to ram [a] soap bar into your mouth if you insult the Lord’s name.” –David Elliott, San Diego Union-Tribune, May 11, 2007

    There is not universal agreement on just what is the Lord’s name. Perhaps it includes the number 952.

    From The Gameplayers of Zan:

    “The Game in the Ship cannot be approached as a job, a vocation, a career, or a recreation. To the contrary, it is Life and Death itself at work there. In the Inner Game, we call the Game Dhum Welur, the Mind of God. And that Mind is a terrible mind, that one may not face directly and remain whole. Some of the forerunners guessed it long ago– first the Hebrews far back in time, others along the way, and they wisely left it alone, left the Arcana alone.”

    From Bartlett’s Familiar Quotations:

    “Nothing can be produced out of nothing.”
    — 10th edition, 1919, page 952

    See also “Zen and Language Games
    and “Is Nothing Sacred?

    Tuesday, October 24, 2006

    Tuesday October 24, 2006

    Filed under: General — Tags: — m759 @ 9:00 PM

    Another illustration
    of the previous entry's concept of
    a "critical mass" of weblog entries,
    a concept reflected in
    the saying
    "You can't win the lottery
        if you don't buy a ticket." 

    Mathematics and Narrative:
    A Two-Part Invention

    Here are today's
    numbers from the
    Keystone State:

    The image “http://www.log24.com/log/pix06A/061024-PAlottery.jpg” cannot be displayed, because it contains errors.

    Here is an interpretation
    of those numbers:
    8/21 — Mathematics:

    The Wikipedia article on
    the Geometrization Conjecture
    ,

    revision of 13:22 UTC, 21 August 2006:
     

    "The geometrization conjecture, also known as Thurston's geometrization conjecture, concerns the geometric structure of compact 3-manifolds. The geometrization conjecture can be considered an analogue for 3-manifolds of the uniformization theorem for surfaces. It was proposed by William Thurston in the late 1970s. It 'includes' other conjectures, such as the Poincaré conjecture and the Thurston elliptization conjecture."

    The second sentence, in bold type, was added on 8/21 by yours truly. No deep learning or original thought was required to make this important improvement in the article; the sentence was simply copied from the then-current version of the article on Grigori Perelman (who has, it seems, proved the geometrization conjecture).

    This may serve as an example of the "mathematics" part of the above phrase "Mathematics and Narrative" — a phrase which served, with associated links, as the Log24 entry for 8/21.

    7/23 — Narrative:

    "Each step in the story is a work of art, and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination." –Freeman Dyson

    This quotation appeared in the Log24 entry for 7/23, "Dance of the Numbers."  What Dyson calls a "story" or "drama" is in fact mathematics. (Dyson calls the "steps" in the story "works of art," so  it is clear that Dyson (a former student of G. H. Hardy) is discussing mathematical steps, not paragraphs in someone's account– perhaps a work of art, perhaps not– of mathematical history.)  I personally regard the rhetorical trick of calling the steps leading to a mathematical result a "story" as contemptible vulgarization, but Dyson, as someone whose work (pdf) led to the particular result he is discussing, is entitled to dramatize it as he pleases.

    For related material on mathematics, narrative, and vulgarization, click here.

    The art of interpretation (applied above to a lottery) is relevant to narrative and perhaps also, in some sense, to the arts of mathematical research and exposition (if not to mathematics itself).  This art is called hermeneutics.

    For more on the subject, see the Stanford Encyclopedia of Philosophy article on Hans-Georg Gadamer, "the decisive figure in the development of twentieth-century hermeneutics."

    See also the work of Msgr. Robert Sokolowski of the Catholic University of America, which includes

    "Foreword" in Gian-Carlo Rota,
     Indiscrete Thoughts,
     Boston: Birkhäuser Verlag,
     1996, xiii-xvii, and

    "Gadamer's Theory of Hermeneutics" in
     The Philosophy of Hans-Georg Gadamer,
     edited by Lewis E. Hahn,
     The Library of Living Philosophers, Vol. 24,
     Chicago: Open Court Publishers,
     1997, 223-34.

    Wednesday, July 26, 2006

    Wednesday July 26, 2006

    Filed under: General — Tags: — m759 @ 1:44 PM
    Partitions,
    continued

    "Mistakes are inevitable and may be either in missing a true signal or in thinking there is a signal when there is not. I am suggesting that believers in the paranormal (called 'sheep' in psychological parlance) are more likely to make the latter kind of error than are disbelievers (called 'goats')."

    — "Psychic Experiences:
         Psychic Illusions,"
         by Susan Blackmore,
         Skeptical Inquirer, 1992

    For Harvard mathematician
    Frederick Mosteller,
    dead on Sunday, July 23, 2006:
     
    "… a drama built out of nothing
    but numbers and imagination"

    — Freeman Dyson, quoted in Log24
    on the day Mosteller died

    From Log24 on
    Mosteller's last birthday,
    December 24, 2005:

    The Club Dumas

    by Arturo Perez-Reverte

    One by one, he tore the engravings from the book, until he had all nine.  He looked at them closely.  "It's a pity you can't follow me where I'm going.  As the fourth engraving states, fate is not the same for all."

    "Where do you believe you're going?"

    Borja dropped the mutilated book on the floor with the others. He was looking at the nine engravings and at the circle, checking strange correspondences between them.

    "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."

    "Only gradually did I discover
    what the mandala really is:
    'Formation, Transformation,
    Eternal Mind's eternal recreation'"
    (Faust, Part Two)

    Carl Gustav Jung,   
    born on this date

    Today's other birthday:
    Mick Jagger

    "Pleased to meet you,
    hope you guess my name."

    Sunday, July 23, 2006

    Sunday July 23, 2006

    Filed under: General,Geometry — m759 @ 2:56 PM

    Dance of the Numbers, continued:

    Partitions

    Freeman Dyson on the role of the “crank” in the theory of partitions:

    “‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”

    Erica Klarreich in
        Science News Online, week of
        June 18, 2005, quoted in
       “In Honor of Freeman Dyson’s Birthday:
        Dance of the Numbers
        (Log24, Dec. 15, 2005)

    Paraphrase of Freeman Dyson’s remarks in The New York Review of Books, issue dated May 28, 1998:

    “Theology is about words; science is about things.

    “What is 256 about?”
    Reply to Freeman Dyson,
        (May 15, 1998)

    A partial answer to that rhetorical question: 256 is the cardinality of the power set of an 8-set.

    For the role played by 8-sets and by 23 (today’s date) in partitions of a different sort, see Geometry of the 4×4 Square.

    Thursday, December 15, 2005

    Thursday December 15, 2005

    Filed under: General — m759 @ 3:48 PM
    In honor of Freeman Dyson’s birthday:

    Dance of the Numbers

    “Mahlburg likens his approach to an analogous one for deciding whether a dance party has an even or odd number of attendees. Instead of counting all the participants, a quicker method is to see whether everyone has a partner—in effect making groups that are divisible by 2.

    In Mahlburg’s work, the partition numbers play the role of the dance participants, and the crank splits them not into couples but into groups of a size divisible by the prime number in question. The total number of partitions is, therefore, also divisible by that prime.

    Mahlburg’s work ‘has effectively written the final chapter on Ramanujan congruences,’ Ono says.

    ‘Each step in the story is a work of art,’ Dyson says, ‘and the story as a whole is a sequence of episodes of rare beauty, a drama built out of nothing but numbers and imagination.'”

    Erica Klarreich in Science News Online, week of June 18, 2005

    This would seem to meet the criteria set by Fritz Leiber for “a story that works.” (See previous entry.)  Whether the muse of dance (played in “Xanadu” by a granddaughter of physicist Max Born– see recent entries) has a role in the Dyson story is debatable.

    Born Dec. 11, 1882, Breslau, Germany.

    Died Jan. 5, 1970, Göttingen,
    West Germany.

    The image “http://www.log24.com/log/pix05B/051215-Born.jpg” cannot be displayed, because it contains errors.
    Max Born

    Those who prefer less abstract stories may enjoy a mythic tale by Robert Graves, Watch the North Wind Rise, or a Christian tale by George MacDonald, At the Back of the North Wind.

    Related material:

    “The valley spirit never dies. It’s named the mystic woman.”

    Tao Te Ching

    For an image of a particular
    incarnation of the mystic woman
    (whether as muse, as goddess,
    or as the White Witch of Narnia,
    I do not know) see Julie Taymor.

    “Down in the valley,
     valley so low,
     hang your head over,
     hear the wind blow.”

    Folk song

    “Which is the sound of the land
    Full of the same wind
    That is blowing in
        the same bare place

    For the listener,
        who listens in the snow,
    And, nothing himself, beholds
    Nothing that is not there
        and the nothing that is.”

    Wallace Stevens

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