magicdragon2 ([info]magicdragon2) wrote,
@ 2004-06-15 10:23:00
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Eric Temple Bell: Math Prof., Sci-Fi author, Liar?
I have recently acquired an archive of writings of the brilliant and controversial Eric Temple Bell, dating back to 1932. Based on Constance Reid's book (see below), he seems to have led a triple life: Math Professor at Caltech, Science Fiction author, and perhaps compulsive liar. You can find out about his most famous discovery( Bell Numbers) at any major Math site, such as mathworld.com. I shall be entering the debate on exactly what he did, when, as revised by my archives. It seems that he had his wife calculating recursive functions on some 1930-era mechanical computer. And it seems that he condemned String Theory decades before it was born!

The Search for E. T. Bell: Also Known as John Taine
by Constance Reid

An account of one of the century's most colorful mathematicians. Bell's Men of Mathematics (1937) presented mathematics and mathematicians in a way that had never been done before, fascinating many of his colleagues, irritating others, and inspiring young people to become mathematicians. Bell was also widely known as the science fiction writer John Taine. As a result of biographer Reid's discoveries about his early life, almost every statement now in print about Bell's family background and early life will have to be revised, and a new look taken at his extensive mathematical work and his science fiction.
[Annotation copyright Book News, Inc. Portland, Oregon]


Eric Temple Bell (1883-1960) was a distinguished mathematician and a best selling popularizer of mathematics. His Men of Mathematics, still in print after almost sixty years, inspired scores of young readers to become mathematicians.

Under the name of John Taine, he also published science fiction novels (among them The Time Stream, Before the Dawn, and The Crystal Horde) that served to broaden the subject matter of that genre during its early years.

In The Search for E. T. Bell, Constance Reid has given us a compelling account of this complicated, difficult man who never divulged to anyone, not even to his wife and son, the story of his early life and family background. Her book is thus more of a mystery than a traditional biography. It begins with the discovery of an unexpected inscription in an English churchyard and a series of cryptic notations in a boy's schoolbook. Then comes an inadvertent revelation, by Bell himself, in a respected mathematical journal. You will have to read the book to learn the rest.

[or follow this thread on the magicdragon2 blog!]

(36 comments) - (Post a new comment)

Quotes from Eric Temple Bell
[info]magicdragon2
2004-06-15 10:43 am UTC (link)
Quotes from Eric Temple Bell : The Development of Mathematics, [McGraw-Hill, 1945]:

p.248 : on the abstract method (since David Hilbert):

" .... viewing the vast accumulations in abstract geometry, abstract algebra and abstract analysis of the twentieth century ..... The root of these troubles seems to be the unimaginative lack of a clearly recognized objective. -- If the aim is merely to create new theories which many find intensely
interesting and even beautiful, then the abstract method keeps on reaching its goal."

p.510 : on specialization and communication:

"To interrupt one's own researches in order to follow those of another is a scientific pleasure which most experts delegate to their assistants. Consequently, the confusion of tongues increases as the square of the number of talkers, until only ever more select coteries of narrow specialists really understand the refinements of their esoteric vocabularies."

p.208: on rivalry and inertia in mathematics (re: vector and matrix analysis):

".... Frenchmen, Germans, and Italians, urging their respective substitutes for quaternions, added to the din. By the second decade of the twentieth century there was a babel of conflicting vector algebras, each fluently spoken only by its inventor and his few chosen disciples. If, at any time in the brawling half-century after 1862, the bickering sects had stopped quarreling for half an hour to listen attentively to what Grassmann was doing his philosophical best to tell them, the noisy battle would have ended as abruptly as a thunderclap. Such, at any rate, seems to have been
the opinion of Gibbs. In retrospect, the fifty-year war between quaternions and its rivals for scientific favor, appears as an interminable sequence of duels fought with stuffed clubs in a vacuum over nothing."

[magicdragon2 comments: Grassman was another of the mathematicians who was attacked as insane, because of the content of his theories ... which are now accepted as ahead of their time]

see also:

On abstraction, specialisation and divergence, quotes selected by Nico F. Benschop

(Reply to this)

E.T. Bell, on imagination
(Anonymous)
2004-06-15 10:46 am UTC (link)
"Nevertheless, the consuming hunger of the uncritical mind for what it imagines to be certainty or finality impels it to feast upon shadows in the prevailing famine of substance."

(E.T. Bell, on imagination)

(Reply to this)

Mathematics: Queen & Servant of Science
[info]magicdragon2
2004-06-15 10:53 am UTC (link)
Mathematics: Queen & Servant of Science
by Eric Temple Bell
[The Mathematical Association of America, September 1996]
ISBN 0883854473
Price $12.50

Review comment from mathematicsbooks.org/

I will keep this very brief. I am an electrical engineer and computer scientist, and, after a couple of decades in the "commercial world" , am always amazed at the "unreal effectiveness" of mathematics when applied to this and the real world. Bell's book captures this essence in a timeless tome that must be required reading and regular re-reading for all aspiring. and indeed, practicing, mathematicians, engineers and scientists. It is a source of both inspiration and "bringing back to earth" ...

By the way, the data on the previously mentioned book are:

Men of Mathematics: The Lives and Achievements of the Great Mathematicians from Zeno to Poincare'
E.T. Bell
ISBN 0-67162-818-6 (Paperback)
[Touchstone Books: 15 October, 1986]
Subjects: Mathematicians, Mathematics, History, Biography, Autobiography, Scientists -- General, History and Philosophy

(Reply to this)

E.T.Bell: anti-Semitic? anti-Celtic?
[info]magicdragon2
2004-06-15 10:59 am UTC (link)
Subject: Re: E.T.Bell
Author: Touhey@aol.com
Date: Mon, 19 May 1997 11:35:40 -0400

From the 1937 (fourth printing) Simon & Schuster edition of "Men of
Mathematics", with illustrations grouped after the table of contents.

pp 562-563

"Rightly or wrongly, Cantor blamed Kronecker for his failure to obtain the coveted position at Berlin. The aggressive clannishness of Jews has often been remarked, sometimes as an argument against employing them in academic work, but it has not been so generally observed that there is no more vicious academic hatred than that of one Jew for another when they disagree on purely scientific matters or when one is jealous or afraid of another. Gentiles either laugh these hatreds off or go at them in an efficient, underhand way
which often enables them to accomplish their spiteful ends under the guise of sincere friendship. When two intellectual Jews fall out they disagree all over, throw reserve to the dogs, and do everything in their power to cut one another's throats or stab one another in the back. Perhaps after all this is a more decent way of fighting - if men must fight - than the sanctimonious
hypocrisy of the other."

Surely insensitive, but anti-Semitic?

pg 342

"His disposition was genial and his temper - rather unusually so for a sturdy Irish boy - invariably even. In later life however Hamilton showed his Irish by challenging a detractor - who had called him a liar - to mortal combat."

Is this anti-Celtic?
We should note that no connection is drawn between Hamilton's alcoholism and his nationality. But with respect to Hamilton's drinking problem;

pg 353

"Still, even this handicap could not put him out of the race, although without it he probably would have gone farther and have reached a greater height than he did. However, he got high enough, and moralizing may be left to moralists."

Sound advice.

(Reply to this)

E. T. Bell inspired John Forbes Nash's Beautiful Mind?
[info]magicdragon2
2004-06-15 11:03 am UTC (link)
A reader from Fairmont, WV United States [on Amazon.com reviews of Men of Mathematics by E.T. Bell:

"I just wanted to mention that this was the book that mathematical genius John [Forbes] Nash read in high school. In case you didn't know, John Nash was the winner of the 1994 Nobel Prize in Economics for his development of the Nash Equilibrium he discovered for Non-cooperative games. There is a famous biographical movie about his life, which, apparently like the lives of the mathematicians in this book, is quite eccentric. The movie is A Beautiful Mind.

(Reply to this)

E.T. Bell: also a mule skinner, surveyor, and poet
[info]magicdragon2
2004-06-15 11:10 am UTC (link)
There's a fine historical summary of the life and works of Eric Temple Bell, by J. J. O'Connor and E. F. Robertson:

Eric Temple Bell
Born: 7 Feb 1883 in Peterhead, near Aberdeen, Scotland
Died: 21 Dec 1960 in Watsonville, California, USA

"... In the United States he supported himself with a variety of different jobs, from ranch hand and mule skinner to surveyor. He entered Stanford University in 1905, being awarded an A.B. with honours in mathematics two years later. He then studied for his Master's Degree at the University of Washington which he received in 1908. He received his doctorate from Columbia University in 1912 after one year of study for the dissertation The Cyclotomic Quinary Quintic. At Columbia his doctoral work was supervised by C J Keyser. Two years before he received his doctorate, Bell married Jessie Lillian Smith Brown. They had one son."

"Bell taught mathematics at the University of Washington from 1912 being appointed first as an Instructor but rose to the rank of Professor over the fourteen years he taught at the university. In 1926 he left Washington when he was appointed professor of mathematics at the California Institute of Technology, holding that post until illness forced him to retire a year before his death. Bell had the honour of being elected President of the Mathematical Association of America and he held the position during the years 1931-33...."

"... Bell did not confine his writing to mathematics and he also wrote sixteen science fiction novels under the name John Taine [3]
'... the excuse, Bell himself once wrote, being that if these popular novels made money, some publishers might be interested in more serious books. Finally we should mention another of Bell's interests. He wrote several volumes of poetry, and perhaps this was his greatest love, but he never received any real recognition for it.'"


References for Eric Temple Bell:

Biography in Dictionary of Scientific Biography (New York 1970-1990).

Biography in Encyclopaedia Britannica.

Obituary in The Times [available on the Web]

Books:

A Broadbent, Eric Temple Bell, Nature 4763 (1961).
C Reid, The search for E T Bell, also known as John Taine (Washington D.C., 1993).

Eric Temple Bell, New York Times (22 Dec, 1960).

J W Dauben, Eric Temple Bell, American National Biography 2 (New York, 1999), 502-503.

C Reid, The alternative life of E T Bell, Amer. Math. Monthly 108 (5) (2001), 393-402.

(Reply to this)

More Quotations by Eric Temple Bell
[info]magicdragon2
2004-06-15 11:17 am UTC (link)
More Quotations by Eric Temple Bell
[assembled by J. J. O'Connor and E. F. Robertson]

"Euclid taught me that without assumptions there is no proof. Therefore, in any argument, examine the assumptions."
[Quoted in H. Eves Return to Mathematical Circles., Boston: Prindle, Weber and Schmidt, 1988.]

"Wherever groups disclosed themselves, or could be introduced, simplicity crystallized out of comparative chaos."
[Mathematics, Queen and Servant of Science, New York, 1951, p. 164]

"It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences."
[The Handmaiden of the Sciences (Book by that title)]

"Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness."

"'Obvious' is the most dangerous word in mathematics."

"The pursuit of pretty formulas and neat theorems can no doubt quickly degenerate into a silly vice, but so can the quest for austere generalities which are so very general indeed that they are incapable of application to any particular."
[H.Eves Mathematical Circles Squared, Boston 1972]

"Abstractness, sometimes hurled as a reproach at mathematics, is its chief glory and its surest title to practical usefulness. It is also the source of such beauty as may spring from mathematics."

"If a lunatic scribbles a jumble of mathematical symbols it does not follow that the writing means anything merely because to the inexpert eye it is indistinguishable from higher mathematics."
[in J R Newman, The World of Mathematics, New York, 1956]

"The longer mathematics lives the more abstract -- and therefore, possibly also the more practical -- it becomes."
[Quoted in The Mathematical Intelligencer 13, (1, 1991)]

"The cowboys have a way of trussing up a steer or a pugnacious bronco which fixes the brute so that it can neither move nor think. This is the hog-tie, and it is what Euclid did to geometry."
[The Search For Truth, p. 191]

"If 'Number rules the universe' as Pythagoras asserted, Number is merely our delegate to the throne, for we rule Number."
[in H. Eves "Mathematical Circles Revisited" Boston, 1971]

"I have always hated machinery, and the only machine I ever understood was a wheelbarrow, and that but imperfectly."
[H. Eves "Mathematical Circles Adieu" Boston, 1977]

"Archimedes, Newton, and Gauss, these three, are in a class by themselves among the great mathematicians, and it is not for ordinary mortals to attempt to range them in order of merit."

"Had Poincare' been as strong in practical science as he was in theoretical he might have made a fourth with the incomparable three, Archimedes, Newton, and Gauss."

(Reply to this)

E. T. Bell's Science Fiction Bilbliography
[info]magicdragon2
2004-06-15 09:27 pm UTC (link)
Eric Temple Bell's Science Fiction Bibliography
Copyright (c) 1995-2004 Al von Ruff

Slightly annotated and adapted by magicdragon2:

Novels [under pseudonym John Taine]:

The Purple Sapphire [1924;
magazine appearance: "Famous Fantastic Mysteries", Aug 1948]
Quayle's Invention [E. B. Dutton & Company, 1927]
The Gold Tooth [as E. T. Bell; A. L. Burt Company, 1927]
The Greatest Adventure (1929; 1944; Ace, 1960]
The Iron Star [Dutton, 1930; Famous Fantastic Mysteries, Sep 1943]
The Time Stream [1931; serial in 4 parts, Wonder Stories, Dec 1931-Mar 1932]
Seeds of Life [Fantasy Press, 1931]
Before the Dawn [1934; in Portable Novels of Science, Donald A. Wollheim, ed., Viking Press, 1945; Famous Fantastic Mysteries, Feb 1946; in Behold the Mighty Dinosaur, David Jablonski, ed, Elsvier, 1981]
The Forbidden Garden [Fantasy Press, 1947]
Green Fire [FPCI, 1952]
The Crystal Horde [Fantasy Press, 1954; Expansion of "White Lily"]
G.O.G. 666 [Fantasy Press, 1954]

Magazine Serial [under pseudonym John Taine]:

Twelve Eighty-Seven [in 5 parts, Astounding Science Fiction, May 1935-Sep 1935]

Collection [under pseudonym John Taine]:

Three Science Fiction Novels [Dover, 1964)

Short Fiction [under pseudonym John Taine]:

"White Lily" [Amazing Stories Quarterly, Winter 1930]
"The Ultimate Catalyst" [1930; Thrilling Wonder Stories, June 1939; frequently anthologized]
Seeds of Life [Amazing Stories Quarterly, Fall 1931]

Science Fiction Essays/Articles [under pseudonym John Taine]:

"Why Science Fiction?" [Startling Stories, March 1939]
"Why I Selected 'The Ultimate Catalyst'" [in My Best Science Fiction Story
ed. Leo Margulies and Oscar J. Friend, Merlin Press 1949; Pocket, 1954]
"Writing a Science Novel" [Of Worlds Beyond: The Science of Science-Fiction Writing,
ed. Lloyd Arthur Eshbach, Advent Publishers, Inc. 1964]

(Reply to this)

Customer Review: The Search for E. T. Bell
[info]magicdragon2
2004-06-15 09:33 pm UTC (link)
Geometry Net: Customer Review: The Search for E. T. Bell, by Constance Reid

Eric Temple Bell, (1883-1960), was the first person to truly popularize mathematics with his classic 1937 book, Men of Mathematics. Many mathematicians, including Reid's own sister Julia Robinson, later to become famous as one of the finest early women mathematicians, cite this book as the reason why they turned to a career in mathematics.

But his early life was rather a mystery, and when Albers and Alexanderson, two mathematicians who were attempting to profile Bell, talked to Reid, she became intrigued by the contradictory statements and minimal evidence about where he lived up until the early 1920's. He'd always claimed to be Scottish--but was he born in Aberdeen or Peterhead? He said he'd traveled around the world as a teenager--but never said exactly when or how. He claimed to have been at the University of London, which didn't fit with what else was known about his education. Reid talked to Bell's son Taine, and soon decided that she had a mystery to unravel. Initially she agreed only to write the story of his early life, but eventually wrote a full biography.

The book is told in the present tense, as Reid walks us through her early discoveries. This is a device that works well in the early chapters, when she is talking to folks in Peterhead and San Jose, trying to find clues; but it palls later. By the twenties Bell's career was enough in the public record that it would have been pointless for him to lie about it, and from that point on Reid's occasional interjections in the present tense, as she relates a discovery or inconsistency, are a little jarring.

That's a minor point though. The book is fascinating, both in its portrait of Bell, who was multi-faceted--a distinguished mathematician, a prolific sf author, and a top-flight popular mathematics writer--and in the story of the detective work Reid had to do. Eventually Reid does uncover almost everything one could hope for, though Bell's motivation for lying about his past will probably never be known. It becomes apparent by late in the book that Bell never even told his wife the truth about his first years.

His mathematical career is covered in reasonable detail, with some input from Lincoln Durst, who has spent much time studying Bell's papers. It's clear that Bell was original and influential, though oddly it appears that the gift of smooth exposition so in evidence in his popular work was sometimes missing from his mathematical papers. Apparently there have been many instances when later mathematicians have rediscovered results originally due to Bell, mainly because his papers were often obscure or poorly written.

The only real criticism I have is the lack of a bibliography. Even a list of twenty or so important papers would have sufficed for the mathematics, but for the books I think it is a real omission. Other than that, however, this is a great biography and a fascinating read. Recommended.

(Reply to this)

E. T. Bell's "The Time Stream" Customer Review
[info]magicdragon2
2004-06-15 09:37 pm UTC (link)
Customer Review on Geometry Net:

How easy to get lost in the stream of time...Or is it?

Here's a fascinating tale by John Taine, who is actually mathematician Eric Temple Bell. As I read this, back in the Sixties, the book contained two other stories: "The Purple Sapphire", and "The White Lilly". All these stories are somewhat dated, but quite original pieces, that stand by themselves. The Time Stream follows several travelers, who make use of some rather interesting properties of time -- apparently it behaves like water flowing, and thus has eddy currents that can be used to move both forward and back if you know how. The Purple Sapphire is an adventure tale set in the wilderness of Tibet, and assumes there are places on this earth that are remote and mysterious. It's a good yarn, and well spun, if you can set yourself back to those times. The White Lilly is a fairly dated "jekyll-hyde" piece about the good and not-so-good aspects of experimentation with radiation, (something that has been done to death).

(Reply to this)

customer review: "Before the Dawn" by Eric Temple Bell
[info]magicdragon2
2004-06-15 09:41 pm UTC (link)
dave_42 from Belleville, Michigan, USA , review on amazon.com

Before the Dawn by Eric Temple Bell (using the pseudonym John Taine), was published originally in 1934. In 1949, it appeared on August Derleth's Arkham Survey of Basic SF Titles, tied for 13th. Time has not been very kind to this book, and it remains largely unnoticed today.

The story centers on an invention that allows people to view history by extracting the light which was absorbed by stones throughout history. In using the time viewer, the characters in the book watch the extinction of the dinosaurs, and in particular they follow one dinosaur which they name Belshazzar, who is a massive flesh eater.

The reasons this book is not mentioned with the greats today are clear; the science part of the book doesn't really make much sense, nor would it have even when the book was written. Likewise science has shown that the species of dinosaurs that interact in this story, almost certainly were not alive during the same periods of time. On the positive side, this is perhaps the first science fiction story to use the concept of a time viewer. Also, the story itself is fairly well written, and is enjoyable to read.

(Reply to this)

Archived Eric Temple Bell Papers, U. C. Santa Cruz
[info]magicdragon2
2004-06-15 09:47 pm UTC (link)
In ONLINE ARCHIVE OF CALIFORNIA:

Descriptive Summary

Title: Eric Temple Bell Papers, 1918-1991

Collection number: MS 58

Creator: Bell, Eric Temple

Extent: 7 document box, 1 flat box, 6 cartons
10 linear ft.

Repository: University of California, Santa Cruz. University Library. Special Collections and Archives
Santa Cruz, California 95064

Abstract:
This archive contains manuscripts, and typescripts for many of Bell's works both mathematical and science fiction. The archive also contains books authored by Bell and published in many languages (Turkish, German, Italian, Spanish, Italian, French, Yugoslavian, and Finnish); books from Bell's personal reference library; and books authored by contemporary science fiction authors and inscribed to Bell.

Physical location: Stored offsite at NRLF: Advance notice is required for access to these papers.

Administrative Information:

Access: Collection is open for research.

Publication Rights: Property rights reside with the University of California. Literary rights are retained by the creators of the records and their heirs. For permission to publish or to reproduce the material, please contact the Head of Special Collections and Archives.

Preferred Citation: Eric Temple Bell Papers, MS 58, Special Collections and Archives, University Library, University of California, Santa Cruz.

Acquisition Information: Gift of Drs. Janet and Taine Bell in May 1969.


(Reply to this)

The Cosmic Geoids, by Eric Temple Bell
[info]magicdragon2
2004-06-15 09:50 pm UTC (link)
The Cosmic Geoids, by Eric Temple Bell [as John Taine] [Fantasy Publishing Co. Inc., 1949] novel + story

I have a copy of this, but it is not listed in Al von Ruff's Internet Science Fiction Database. Details later, on another post.

(Reply to this)

A. Broadbent described E. T. Bell
[info]magicdragon2
2004-06-15 09:51 pm UTC (link)
A. Broadbent described E. T. Bell and his writing in the following way:

"His style is clear and exuberant, his opinions, whether we agree with them or not, are expressed forcefully, often with humor and a little gentle malice. He was no uncritical hero-worshipper being as quick to mark the opportunity lost as the ground gained, so that from his books we get a vision of mathematics as a high activity of the questing human mind, often fallible, but always pressing on the never-ending search for mathematical truth".

(Reply to this)

Eric Temple Bell as a mathematician
[info]magicdragon2
2004-06-15 09:56 pm UTC (link)
"... [Eric Temple Bell] also made contributions to analytic number theory, Diophantine analysis and numerical functions. The American Mathematical Society awarded him the Bocher Prize in 1924 for his memoir, Arithmetical Paraphrases, which appeared in the Transactions of the American Mathematical Society in 1921. Although he wrote 250 research papers, including the one which received the Bocher Prize, Bell is best remembered for his books, and therefore as an historian of mathematics. His books Algebraic Arithmetic (1927) and The Development of Mathematics, (1940) became classics."

[excerpt of Mathematical (not Science Fiction or Popular) bibiographic/bibliographic description of his papers in the U.C. Santa Cruz archives]

(Reply to this)

Eric T. Bell puzzled by Darwin evolution
(Anonymous)
2004-06-16 07:22 am UTC (link)
"Even stranger things have happened; and perhaps the strangest of all is the marvel that mathematics should be possible to a race akin to the apes."

~Eric T. Bell, The Development of Mathematics

(Reply to this)

Albert Einstein wrote about Mathematics
(Anonymous)
2004-06-16 07:26 am UTC (link)
"Pure mathematics is, in its way, the poetry of logical ideas."

~Albert Einstein


"Mathematics are well and good but nature keeps dragging us around by the nose."

~Albert Einstein

(Reply to this)

Gregory Benford, scientist/novelist, on Einstein and Math
[info]magicdragon2
2004-06-16 07:34 am UTC (link)
Einstein and his Mathematics were themselves commented on in a Science Fiction novel by Astrophysics professor Gregory Benford:

"There was a blithe certainty that came from first comprehending the full Einstein field equations, arabesques of Greek letters clinging tenuously to the page, a gossamer web. They seemed insubstantial when you first saw them, a string of squiggles. Yet to follow the delicate tensors as they contracted, as the superscripts paired with subscripts, collapsing mathematically into concrete classical entities - potential; mass; forces vectoring in a curved geometry - that was a sublime experience. The iron fist of the real, inside the velvet glove of airy mathematics."

Gregory Benford, Timescape

And an excerpt from a review of Timescape:

"First published in 1980, Greg Benford's Timescape won the both the Nebula and the John W. Campbell Memorial Award, so it is interesting to go back and see how well it has worn. The immediate answer is not well, as it has suffered the fate of many very-near-future stories, in that time has overhauled it."

"The story is split between the 'future' of 1998, largely in Cambridge, and the early sixties in California, and broadly tells of a project in 1998 to transmit a message via tachyon beams into the past to avert the environmental catastrophe that is threatens the millenial world. The group of scientists in Cambridge plan to influence the results of experiments carried out by American scientists in 1962, generating a tachyon beam that introduces a coded signal into the 1962 results. The best part of the book is the detailing of how scientists work, both the 10% inspiration and 90% perspiration that goes into it, plus the struggle to obtain funding to buy necessary equipment and keep the experiments going for long enough to achieve a publishable result."

"As a working physicist (and one who personally experienced the physics scene in California in the early 60s), Benford is on firm ground when he is telling the 60s part of the story. He's on more uncertain ground writing about England and Cambridge, portraying a rather dated (even for 1980) view of England, and its class structures, a dating that looks even more embarassing in the late nineties...."

[appeared in Vector, the British Science Fiction Association magazine]

(Reply to this)

Robert Heinlein wrote about Math in his Sci-Fi
(Anonymous)
2004-06-16 07:37 am UTC (link)
"Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable subhuman who has learned to wear shoes, bathe, and not make messes in the house."

~Robert Heinlein, Time Enough for Love

(Reply to this)

Famous Writers on Mathematics
[info]magicdragon2
2004-06-16 07:58 am UTC (link)
Life is complex; writers can capture that complexity.

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."
[John Louis von Neumann]

"I never did very well in math - I could never seem to persuade the teacher that I hadn't meant my answers literally."
[Calvin Trillin]

"Arithmetic is where numbers fly like pigeons in and out of your head."
[Carl Sandburg, "Arithmetic"]

"Arithmetic is numbers you squeeze from your head to your hand to your pencil to your paper till you get the answer."
[Carl Sandburg, "Arithmetic"]

"So if a man's wit be wandering, let him study the mathematics; for in demonstrations, if his wit be called away never so little, he must begin again."
[Francis Bacon, "Of Studies"]

"The essence of mathematics is not to make simple things complicated, but to make complicated things simple."
[S. Gudder]

"The mathematics are distinguished by a particular privilege, that is, in the course of ages, they may always advance and can never recede." [Edward Gibbon, Decline and Fall of the Roman Empire]

"The hardest arithmetic to master is that which enables us to count our blessings."
[Eric Hoffer, Reflections On The Human Condition]

"With my full philosophical rucksack I can only climb slowly up the mountain of mathematics."
[Ludwig Wittgenstein, Culture and Value]

"Still more astonishing is that world of rigorous fantasy we call mathematics."
[Gregory Bateson]

"We could use up two Eternities in learning all that is to be learned about our own world and the thousands of nations that have arisen and flourished and vanished from it. Mathematics alone would occupy me eight million years."
[Mark Twain]

"Mathematics is the supreme judge; from its decisions there is no appeal."
[Tobias Dantzig]

"The mathematics are usually considered as being the very antipodes of Poesy. Yet Mathesis and Poesy are of the closest kindred, for they are both works of the imagination."
[Thomas Hill]

"I used to love mathematics for its own sake, and I still do, because it allows for no hypocrisy and no vagueness...."
[Stendhal (Henri Beyle), The Life of Henri Brulard]

"One cannot escape the feeling that these mathematical formulas have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers..."
[Heinrich Hertz]

"Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too."
[Fyodor Mikhailovich Dostoevsky]

"I know that two and two make four - & should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 & 2 into five it would give me much greater pleasure." [George Gordon, Lord Byron]

"A man has one hundred dollars and you leave him with two dollars. That's subtraction."
[Mae West]

"I've dealt with numbers all my life, of course, and after a while you begin to feel that each number has a personality of its own. A twelve is very different from a thirteen, for example. Twelve is upright, conscientious, intelligent, whereas thirteen is a loner, a shady character who won't think twice about breaking the law to get what he wants. Eleven is tough, an outdoorsman who likes tramping through woods and scaling mountains; ten is rather simpleminded, a bland figure who always does what he's told; nine is deep and mystical, a Buddha of contemplation...."
[Paul Auster, The Music of Chance]

"Although I am almost illiterate mathematically, I grasped very early in life that any one who can count to ten can count upward indefinitely if he is fool enough to do so."
[Robertson Davies, "Of the Conservation of Youth," The Table Talk of Samuel Marchbanks]

"Why do we believe that in all matters the odd numbers are more powerful?"
[Pliny the Elder, Natural History]

"Uneven numbers are the gods' delight."
[Virgil, The Eclogues]

Welcome to the Quote Garden

(Reply to this)

Charles Babbage corrects Tennyson's poetry
(Anonymous)
2004-06-16 08:06 am UTC (link)
Your Thomas Hill quote about math and "poesy" reminded me on how 19th century computer pioneer Charles Babbage felt compelled to correct a line of Tennyson's poetry.

"'Every minute dies a man, Every minute one is born;' I need hardly point out to you that this calculation would tend to keep the sum total of the world's population in a state of perpetual equipoise, whereas it is a well-known fact that the said sum total is constantly on the increase. I would therefore take the liberty of suggesting that in the next edition of your excellent poem the erroneous calculation to which I refer should be corrected as follows: 'Every moment dies a man, And one and a sixteenth is born.' I may add that the exact figures are 1.067, but something must, of course, be conceded to the laws of metre."
~Charles Babbage, letter to Alfred, Lord Tennyson, about a couplet in his "The Vision of Sin"

(Reply to this)

Scientists and Mathematicians on Mathematics, 1
[info]magicdragon2
2004-06-16 08:34 am UTC (link)
Scientists and Mathematicians who are also writers have spoken:

"Mathematics - the unshaken Foundation of Sciences, and the plentiful Fountain of Advantage to human affairs."
[Isaac Barrow]

"I don't agree with mathematics; the sum total of zeros is a frightening figure."
[Stanislaw J. Lec, More Unkempt Thoughts]

"If equations are trains threading the landscape of numbers, then no train stops at pi."
[Richard Preston]

"Go down deep enough into anything and you will find mathematics." [Dean Schlicter]

"It is not the job of mathematicians... to do correct arithmetical operations. It is the job of bank accountants."
[Samuil Shchatunovski]

"Let us grant that the pursuit of mathematics is a divine madness of the human spirit, a refuge from the goading urgency of contingent happenings."
[Alfred North Whitehead]

"The tantalizing and compelling pursuit of mathematical problems offers mental absorption, peace of mind amid endless challenges, repose in activity, battle without conflict, 'refuge from the goading urgency of contingent happenings,' and the sort of beauty changeless mountains present to sense tried by the present-day kaleidoscope of events."
[Morris Kline, Mathematics in Western Culture (Kline is quoting Alfred North Whitehead - "refuge from...")]

"Mathematics is as much an aspect of culture as it is a collection of algorithms."[
Carl Boyer, 1949, calculus textbook]
magicdragon2 notes: this is the essential idea of Ethnomathematics

"Mathematics is not a careful march down a well-cleared highway, but a journey into a strange wilderness, where the explorers often get lost. Rigour should be a signal to the historian that the maps have been made, and the real explorers have gone elsewhere."
[W.S. Anglin]

"Mathematics is the only good metaphysics."
[William Thomson Baron Kelvin of Largs]

"The most savage controversies are those about matters as to which there is no good evidence either way. Persecution is used in theology, not in arithmetic."
[Bertrand Russell]

"Music is the pleasure the human mind experiences from counting without being aware that it is counting."
[Gottfried Leibniz]

"To most outsiders, modern mathematics is unknown territory. Its borders are protected by dense thickets of technical terms; its landscapes are a mass of indecipherable equations and incomprehensible concepts. Few realize that the world of modern mathematics is rich with vivid images and provocative ideas."
[Ivars Peterson]

"But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius."
[Harold Marston Morse]

"[T]he different branches of Arithmetic - Ambition, Distraction, Uglification, and Derision."
[Lewis Carroll, pseudonym of mathematician Charles Dodgson]

"Can you do Division? Divide a loaf by a knife - what's the answer to that?"
[Lewis Carroll, Through the Looking Glass]

"Although he may not always recognize his bondage, modern man lives under a tyranny of numbers."
[Nicholas Eberstadt, The Tyranny of Numbers: Mismeasurement and Misrule]

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."
[Albert Einstein, Sidelights on Relativity]

"[G]eometry is not true, it is advantageous."
[Henri Poincare']

"Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover."
[Bertrand Russell]

"If a healthy minded person takes an interest in science, he gets busy with his mathematics and haunts the laboratory."
[W. S. Franklin]

"Proof is an idol before whom the pure mathematician tortures himself."
[Arthur Stanley Eddington, The Nature of the Physical World]



(Reply to this)

Scientists and Mathematicians on Math, 2
[info]magicdragon2
2004-06-16 08:35 am UTC (link)
"One of the endlessly alluring aspects of mathematics is that its thorniest paradoxes have a way of blooming into beautiful theories." [Philip J. Davis]

"Pure mathematics is the world's best game. It is more absorbing than chess, more of a gamble than poker, and lasts longer than Monopoly. It's free. It can be played anywhere - Archimedes did it in a bathtub."
[Richard J. Trudeau, Dots and Lines]

"I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because like Spinoza's God, it won't love us in return."
[Bertrand Russell, 1912]

"The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization."
[John Kemeny]

I close with a quote from the man whom this Blog was initially about:

"A mathematician is a device for turning coffee into theorems."
[Paul Erdos]

Thanks again to Welcome to the Quote Garden

(Reply to this)

There was a young man from Trinity
(Anonymous)
2004-06-16 08:44 am UTC (link)
There was a young man from Trinity,
Who solved the square root of infinity.
While counting the digits,
He was seized by the fidgets,
Dropped science, and took up divinity.

(Reply to this)

Another "infinity" verse
[info]magicdragon2
2004-06-16 09:35 pm UTC (link)
Little Jack Horner
Sits in a corner
extracting cube roots to infinity.
An assignment for boys
that will minimize noise
and produce a more peaceful vicinity.

[The Space Child's Mother Goose, Verses by Frederick Winsor. Illustrations by Marian Parry, Simon & Schuster, 1958, hard back with dust jacket]

(Reply to this)

Paragrapg from The Time Stream (John Taine/E.T. Bell)
[info]magicdragon2
2004-06-22 11:29 am UTC (link)
ROBERT SMITHSON: Entropy And The New Monuments"

On rising to my feet, and peering across the green glow of the Desert,

I perceived that the monument against which I had slept was but one
of thousands.

Before me stretched long parallel avenues, clear to the
far horizon of similar broad, low pillars.

John Taine (Eric Temple Bell) "THE TIME STREAM"



(Reply to this)

"The Time Stream": keywords
[info]magicdragon2
2004-06-22 11:34 am UTC (link)
Excerpt from my "Timeline 1940s" page of The Ultimate Science Fiction Web Guide:

1946 John Taine [Eric Temple Bell]: "The Time Stream" (Providence RI:
Buffalo Book Co. & G.H.E.) superscience, time-travel, 1906
San Francisco quake, atomic energy, eugenics, libertarian
utopia, and more; reprint from "Wonder Stories" serial
(1931)

Magic Dragon Multimedia home page then click on "Timeline" and thebn choose that decade from the link list.

(Reply to this)

The Time Stream: eccentric publisher Tom Hadley
[info]magicdragon2
2004-06-22 11:47 am UTC (link)
excerpt from Joe Kennedy's two-part history of New York area Science Fiction fandom

New York Fan History, Part 2
After the Atom
by Joe Kennedy
[Spacewarp #42]

I. CONCEPTION ON A COUCH

Shortly after the atom bomb went off... providing John W. Campbell Jr. with a topic to write a non-fiction book about, things began getting back to normal. Rameses cigarets and Orbit chewing gum vanished from the market; newspapers went back to using small headlines; and George R. Fox of Rahway, New Jersey, decided to form a whiz-bang new science fiction club.

One balmy December day in 1945, this club was conceived on a couch in Fox's livingroom. Somebody sitting on the couch ... thought up a name for the organization. "World of Null-A" was running in Astounding at the time, and so the club was named "The (Null-)A-Men".

It was, as Moskowitz later remarked, the first time in fan history that a club had been named after a story which none of its members liked.

Ten people from Jersey and New York got together at Moskowitz's house the following January, to eat Moskowitz's liverwurst and paw with unwashed hands through his magnificent collection of rare fanzines in bound volumes. This was the second meeting of the A-Men.

In March 1946 the A-Men considered themselves sufficiently mighty to sponsor an affair which foundered under the official title of The First Post-war Eastern Science Fiction Convention.

Now, although George Fox and I lifted a couple of fingers to mimeograph and address a wad of circulars, the First Postwar Eastern was Moskowitz's show from start to finish. He hired the hall, he talked L. Sprague de Camp into giving a speech, and ran the affair like a veteran ringmaster.

More than a hundred people squeezed into Newark's gloomy Slovak Sokol Hall. For our heroic efforts on the convention committee, Fox and I were given the honor of sitting up on the speakers' platform. Manly Wade Wellman and Tremaine and Merwin and Robert Arthur and Wollheim spoke briefly; a little guy with horn-rimmed glasses stuttered forth a question and I didn't find out until a year afterward that this had been George Ebey; Helen Wesson was wandering around with an armload of The ... Things, looking beautiful and bewildered as she tried to locate all the people that the copies were supposed to go to. Afterward, an account of the proceedings somehow managed to get into -- of all places -- Harper's Magazine.

Tom Hadley was there, too.

Of the fabulous individuals whose fannish trajectories my own has crossed, Tom Hadley will remain one of the fabulousest. The man himself is surrounded in legend. His mother, some say, is a multi-millionaire. I do not know if there is any truth to the story that when Hadley, out driving, confounded a tree with the highway, he calmly phoned for another new Cadillac. At the Philcon, anyhow, the hotel staff leaped to his service as if motivated by springs.

Hadley had just published The Time Stream by John Taine, and he brought along a couple hundred copies which were offered for sale at the con. As the firewater rose higher in Hadley's head, the price of The Time Stream sank lower. Collectors who, minutes earlier, had relinquished three dollars for the volume, were mad as bloody hell when the book was suddenly offered for two.

At the auction Hadley was the biggest buyer. After a bitter bidding duel with Gerry de la Ree over a not-particularly good Lawrence original, Hadley peeled off fifteen dollars, took a close look at the drawing, and bellowed: "Migawd! What made me buy this?" He also paid five dollars for a batch of old Cosmic Circle Commentators.

It seems to me, though, that Hadley deserves much of the credit for starting the current stampede to cram sci-fic between hard covers. When The Time Stream first appeared, I heard fully a score of people opine that Hadley was throwing his money down a hole. There were not 2,000 stf fans who'd plunk down $3 for a book, said the prophets gloomily. The only reason Arkham House prospered was that it specialized in weird fiction, for which there was a larger audience.

(Reply to this)

"The Time Stream": British 1957 recollection
[info]magicdragon2
2004-06-22 11:56 am UTC (link)
Excerpt: The History of early British SF Conventions, magazines, fandom

THOSE WERE THE DAYS by Bert Lewis

The Early Days of Science Fiction Fandom

...

My first experience of conventions was just before the war. I was to attend a training course... at the Dollis Hill Research Station in London. Just before leaving, I had received an invitation from a London fan to a 'gathering' of fans. Happily the 'gathering' coincided with my course and I jumped at the chance.

I arrived at a small place called the 'Druids Hall' not knowing what to expect. My first impression of the venue was of biting cold. It was very early in the year and there was no such thing as central-heating. The only heating available was from a pair of portable paraffin heaters, and you had to touch them to feel any heat anyway. This, of course, meant that we had to wear our overcoats all the time. Maybe it was our enthusiasm which kept us warm! ... later in the day the 'piece de resistance' was produced. This was a film (silent of course) about a strange adventure in the mountains and the main scenery turned out to be snow - Brrr! Of course we all enjoyed the 'get together', being as it was something quite unique.

My next convention was during the war, in 1944... Most of the regular fans were either in the forces or on war work, but some young fans in Leicester had enough time to organise a convention. luckily, this one day event was held in summer, on a Saturday. I ... travelled to Leicester by rail. It was an overnight journey with two changes of train - each of these changes involved a long wait. Due to the rationing, no food was available on the journey. I was met at the station at 8 a.m., by the young organiser who took me back to his home where his mother cooked me a very welcome breakfast. This gesture can only really be appreciated by someone who has been through war time rationing.

The 'con' was to be held in a small room in the local school, courtesy of a friend of the organiser. As was to be expected, only 15 to 20 fans managed to attend. We did a lot of talking and the organiser produced a fencing sword and imitated John Carter of Borrough's [sic] Martian Trilogy.

It was good fun but the highlight of the event was still to come. As in present day conventions, the auction of S.F. items aroused a great deal of interest. It consisted mainly of books and American Science Fiction Magazines. In spite of the low attendance these were quickly snapped up. The final item, though provoked the greatest interest. It was a shining metal model of a spaceship made by the organiser's father who was an engineer at the local works. The bidding was keen even though wages and pocket-money were low at the time. When the bidding reached two pounds I began to despair. Then it went up to two guineas; an absolute fortune in those days. I raised it to two pounds five shillings and prayed. Luckily it was just enough and I clinched it. As it was all metal it was very heavy but its beauty outweighed any fault....

Attending cons such as these may seem rather mediocre, but the enthusiasm of the participants makes them memorable events which I look back on with great pride and pleasure.

The 1957 World SF Convention

In 1957 England managed to host the World Science Fiction Convention. It was held over Easter in a large hotel in London. A lot of events were crowded into the three days between Good Friday and Easter Monday ... this meant travelling overnight both there and back. So I was determined to cram as much in as I could.

One of the highlights of the convention was the auction... There were many U.S. first editions being bid for and I spent most of my money. There was one book I was particularly waiting for; The Time Stream by John Taine. I felt very tense as the bids rose up to and beyond the amount of money I had left to spend. Eventually a fellow from London got it, I think. I was disappointed but, as if to make up for it, someone I knew quite well phoned me up after the convention and asked if I wanted a copy of this book at the price I bid. Of course I jumped at it and became the proud owner of the prized title.

(Reply to this)

"Time Time Stream" and Hypnosis
[info]magicdragon2
2004-06-22 12:00 pm UTC (link)
"Time Time Stream" summarized on hypnosisinmedia.com:

A group of people in San Francisco, just before the 1906 Earthquake, experience past lives on a dying alien planet through hypnosis.

(Reply to this)

E. T. Bell: Poetry, math, science fiction market facts, 1
[info]magicdragon2
2004-06-22 12:15 pm UTC (link)

[excerpt] Science Fiction Studies
#62 = Volume 21, Part 1 = March 1994
R.D. Mullen
"Two Poets and an Engineer"
Constance Reid. The Search for E.T. Bell, also known as John Taine"
is what might be called a metabiography, a fascinating account of the author's search for the truth behind the silences and lies of a prominent mathematician;

In early 20th-century America poetry was everywhere: not only in books, literary magazines, and schoolrooms, but also in general magazines, pulp-paper fiction magazines, mass-circulation slick-paper magazines, Sunday supplements, and daily newspapers. The Browning Societies flourished, earnest women gathering in small towns and large to study the sometimes obscure works of the Victorian masters. The extent to which schoolchildren today read, memorize, and recite poetry I do not know, but in my day it was a major part of one's schooling.

Although Eric Temple Bell (1883-1960) was to set something of a record in the publication of mathematical papers (more than 200), he seems to have turned to research in mathematics only after failing as a poet. In England he had excelled in mathematics at a "modern school" and, with private tutoring, mastered Greek,4 "his earliest ambition" being "to know the Greeks at firsthand through their literature" (89). In 1902, 19 years old, he came to California and entered Stanford University, where he took a BA in mathematics in 1904. He worked at various things in and around San Francisco for three years, spent a year as a graduate assistant at the University of Washington (MA 1908), taught school for two years in a small California town, and then, in 1911, set off for New York and Columbia University with just enough money for one academic year. Accepted as a candidate, he enrolled in a few courses, submitted the dissertation he had already written, won his doctorate (1912), and then refused an instructorship at Columbia in order to return as an assistant professor to Washington, which was not yet a research university. He published one mathematical paper at this time, but locally rather than nationally, so that it went unnoticed by serious mathematicians (159-60).

All this time he had also been writing poetry, including ambitious book-length poems. During his first five years at Washington he seems to have regarded the teaching of mathematics only as a way to make a living:

In addition to his teaching, there is only one thing that I can say for certain Bell was doing. He was writing poetry. Reams of poetry. And trying very hard to get it published commercially. "Typescript copies of poems written at this time [were] sent out to publishers and regularly returned..." (168).

We are not told whether the "publishers" included newspapers and magazines, the readiest avenue to winning a reputation as a poet. In 1915-16 he published two volumes of verse through a vanity press at a cost of $1350 (a year's salary). There is no evidence that these volumes, published under a carefully guarded pseudonym, found any readers or that he became acquainted with other poets. In these years, then, he had isolated himself both from the world of serious mathematicians and from the world of poets, perhaps wishing to be known as a poet only after achieving great success and in the meantime guarding his anonymity so that in the event of failing at poetry he could try his hand at mathematics free of any embarrassing reputation as a scribbler of verses.

....

(Reply to this)

E.T. Bell: science fiction market realities, 2
[info]magicdragon2
2004-06-22 12:17 pm UTC (link)
[continued]

In 1917, Bell began to publish mathematical papers and to participate in professional conferences. His rise was rapid. There were visiting summer-session professorships at the University of Chicago and offers of permanent positions at Harvard and Columbia as well as at Chicago, but he would not leave the west coast. In 1927 came the ideal offer: a professorship at the California Institute of Technology. He had become a leader in his field and was later to win wider fame as a popularizer, especially with Men of Mathematics (1937).

Although Bell had in 1917 abandoned serious efforts to establish himself as a poet, he had not abandoned writing on non-mathematical subjects. In 1919 he devoted three weeks to what he called recreational writing and produced the first of his "scientific adventure stories" (Green Fire, 1928). Once or twice a year thereafter he allowed himself a three-week period for writing novels, of which five or six were written, rejected by publishers, and filed away by 1923....

In 1923, Bell's The Purple Sapphire, was accepted by Dutton for publication in 1924, as by John Taine. Its moderate success led Dutton in 1926 to contract for a second novel and for the publication "within the next three years of four other works of the same nature and already written" (223). Bell acknowledged Haggard as an influence on his fiction (183), which is obvious in The Purple Sapphire, but a more abiding influence on characterization and plotting would seem to be M.P. Shiel.

In "late 1927 or early 1928," [Stanton] Coblentz, having become aware of the magazine's existence, submitted one of his filed-away novels to Amazing Stories: "half-a-cent a word, though exceptionally low payment even in those days long before inflation, was measurably better than no cents at all" (78-79). In late 1929, with Dutton preparing to wind up its contractual obligation and refusing to publish any additional John Taine novels, Bell also turned to Amazing Stories. Coblentz's 'The Sunken World' appeared in the Summer 1928 Amazing Stories Quarterly, followed by, among others, 'After 12,000 Years' (Spring 1929), 'The Blue Barbarians (Spring 1931), and 'In Caverns Below'/Hidden World (Wonder Stories, March-May 1935).

Bell's White Lily/The Crystal Horde and Seeds of Life also appeared in Amazing Stories Quarterly (Winter 1930, Fall 1931), followed by The Time Stream in Wonder Stories (Dec-March 1931-32), all as by John Taine.6

What interests me at this point is, first, that these are the best book-length works, aside from reprints, to appear in any SF magazine up to 1940, and, second, that all these novels were written before the establishment of Amazing Stories in 1926 or at least before either Bell or Coblentz was aware of the SF magazines as a possible market. When we add that E.E. Smith's The Skylark of Space was also a rejected and filed-away work exhumed for the new market, we may begin to see how little influence Amazing and Wonder had on the actual writing of SF as opposed to simply opening a market for SF written in ways and on subjects already traditional.

(Reply to this)

Eric Temple Bell
(Anonymous)
2006-02-05 04:07 pm UTC (link)
Eric Temple bell was a lier who really never told anyone about with life. It was pretty much kept a sercet! To this day we have poeple still trying to figure out who this Bell was. But someday in the future or maybe today. We will fidn out who Eric Temple Bell really was.

(Reply to this) (Thread)
Re: Eric Temple Bell
[info]magicdragon2
2006-02-05 05:50 pm UTC (link)
I was at the Math Department of Caltech, where Eric Temple Bell had been professor, one afternoon this week. His name came up over cookies and coffee, as a visiting Math professor was talking about science fiction. I pointed out that Bell was from this department, and the visitor was surprised. The older professors agreed, and supported me on the story. Their attitude was neither pride nor embarrassment, but a kind of wry amusement, combined with being puzzled that anyone would do what he did. As to his famous book of biographies of Mathematicians, "Men of Mathematics," the comment was made "why let the truth get in the way of a good story?"

(Reply to this) (Parent)
Number of digits of Bell number
[info]magicdragon2
2006-03-03 07:02 pm UTC (link)
The following was posted on the Online Encyclopedia of Integer Sequences:

A113865 Number of digits of Bell number A000110(n).

1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 55, 57, 58, 59, 60, 62, 63, 64, 66, 67, 68, 70, 71, 72, 74, 75, 76, 78

OFFSET 0,5

COMMENT A113015 is the number of decimal digits in BellB[10^n]. The positive integers which are in the complement to this sequence are: 25, 34, 41, 46, 51, 56, 61, 65, 69, 73, 77, 80, 84, 88, 91, 94, 98, 101, ... because there is no Bell number with 25 digits (Bell[30] = 846749014511809332450147 has 24 digits, Bell[31] = 10293358946226376485095653 has 26 digits).

LINKS John Sokol, The First 1000 Bell Numbers.

FORMULA a(n) = ceiling(log_10 A000110(n)).

EXAMPLE a(0) = 1 because Bell(0) = 1, which has one digit.

a(1) = 1 because Bell(1) = 1, which has one digit.

a(2) = 1 because Bell(2) = 2, which has one digit.

a(3) = 1 because Bell(3) = 5, which has one digit.

a(4) = 2 because Bell(4) = 15, which has two digits.

CROSSREFS Cf. A000110, A113015: Number of decimal digits in BellB[10^n]. .

Adjacent sequences: A113862 A113863 A113864 this_sequence A113866 A113867 A113868

Sequence in context: A060151 A097330 A086861 this_sequence A029071 A104408 A008718

KEYWORD base,easy,nonn

AUTHOR Jonathan Vos Post (jvospost2(AT)yahoo.com), Jan 25 2006


(Reply to this)

A000110 Bell or exponential numbers
[info]magicdragon2
2006-03-03 07:04 pm UTC (link)


A000110 Bell or exponential numbers: ways of placing n labeled balls into n indistinguishable boxes.
(Formerly M1484 N0585)

1, 1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322, 1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372, 474869816156751, 4506715738447323

OFFSET 0,3

COMMENT Number of partitions of an n-element set.

a(n-1) = number of nonisomorphic colorings of a map consisting of a row of n+1 adjacent regions. - David Wilson, Feb 22, 2005

If an integer is square free and has n distinct prime factors then a(n) is the number of ways of writing it as a product of its divisors - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 23 2001

Consider rooted trees of height at most 2. Letting each tree 'grow' into the next generation of n means we produce a new tree for every node which is either the root or at height 1, which gives the Bell numbers. - Jon Perry (perry(AT)globalnet.co.uk), Jul 23 2003

Begin with [1,1], and follow the rule that [1,k] -> [1,k+1] and [1,k] k times, e.g. [1,3] is transformed to [1,4], [1,3], [1,3], [1,3]. Then a(n) is the sum of all components. [1,1]=2, [1,2],[1,1]=5, [1,3],[1,2],[1,2],[1,1],[1,2]=15, etc... - Jon Perry (perry(AT)globalnet.co.uk), Mar 05 2004

Number of distinct rhyme schemes for a poem of n lines: a rhyme scheme is a string of letters (eg, 'abba') such that the leftmost letter is always 'a' and no letter may be greater than one more than the greatest letter to its left. Thus 'aac' is not valid since 'c' is more than one greater than 'a'. For example, a(3)=5 because there are 5 rhyme schemes. aaa, aab, aba, abb, abc. - Bill Blewett (BillBle(AT)microsoft.com), Mar 23 2004

Asymptotic expansion of (0!+1!+2!+...+n!)/n! = a(0)+a(1)/n+a(2)/n^2+... - Michael Somos, Aug 22 2004

Also the number of equivalence relations in (alternatively, or the number of partitions of) a set of n elements. - Federico Arboleda (federico.arboleda(AT)gmail.com), Mar 09 2005

Number of partitions of {1, ...,n+1} into subsets of nonconsecutive integers, including the partition 1|2|...|n+1. E.g. a(3)=5: there are 5 partitions of {1,2,3,4} into subsets of nonconsecutive integers namely 13|24, 13|2|4, 14|2|3, 1|24|3, 1|2|3|4. - A. O. Munagi (amunagi(AT)yahoo.com), Mar 20 2005

Triangle (addition) scheme to produce terms, derived from the recurrence, from Oscar Arevalo (loarevalo(AT)sbcglobal.net), May 11 2005:

1

1 2

2 3 5

5 7 10 15

15 20 27 37 ... [This is Aitken's array A011971]

With p(n) = the number of integer partitions of n, p(i) = the number of parts of the i-th partition of n, d(i) = the number of different parts of the i-th partition of n, p(j,i) = the j-th part of the i-th partition of n, m(i,j) = multiplicity of the j-th part of the i-th partition of n, sum_{i=1}^{p(n)} = sum over i, and prod_{j=1}^{d(i)} = product over j one has: a(n)=sum_{i=1}^{p(n)} (n!/(prod_{j=1}^{p(i)}p(i,j)!)) * (1/(prod_{j=1}^{d(i)} m(i,j)!)) - Thomas Wieder (wieder.thomas(AT)t-online.de), May 18 2005

a(n+1) = the number of binary relations on an n-element set that are both symmetric and transitive. - Justin Witt (justinmwitt(AT)gmail.com), Jul 12 2005

If Jon Perry's rule is used, i.e. "Begin with [1,1], and follow the rule that [1,k] -> [1,k+1] and [1,k] k times, e.g. [1,3] is transformed to [1,4], [1,3], [1,3], [1,3]. Then a(n) is the sum of all components. [1,1]=2, [1,2],[1,1]=5, [1,3],[1,2],[1,2],[1,1],[1,2]=15, etc..." then a(n-1) = [number of components used to form a(n)] / 2 - Daniel Kuan (dkcm(AT)yahoo.com), Feb 19 2006

a(n) is the number of functions f from {1,...,n} to {1,...,n,n+1} that satisfy the following two conditions for all x in the domain: (1) f(x)>x; (2)f(x)=n+1 or f(f(x))=n+1.E.g. a(3)=5 because there are exactly five functions that satisfy the two conditions: f1={(1,4),(2,4),(3,4)}, f2={(1,4),(2,3),(3,4)}, f3={(1,3),(2,4),(3,4)}, f4={(1,2),(2,4),(3,4)}, and f5={(1,3),(2,3),(3,4)}. - Dennis P. Walsh (dwalsh(AT)mtsu.edu), Feb 20 2006

REFERENCES

[see website for references and more]

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