Son of Devil's Advocate, November 2003

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Son of Devil's Advocate

Stan Kelly-Bootle

Picture of Stan Kelly-Bootle

ROSODA: Return of SODA

Dear, dear fans. Your patience is herewith rewarded. But how to reward the doctors at UCSF Medical Center, to whom I owe these last few borrowed leap-seconds? Medicaid tried with $300,000+ but let's not mention cash and health in the same breath. There's no value one can place on avoiding death; except perhaps in my own case where my actuarial tables indicate a negative dollar ROI (Return On Investment).

As Mae West used to say, I feel like a new man (as in "a hard man nowadays is good to find") -- back straddling the saddle again. Not quite $billion bionically revamped, but with an embedded Pace Maker programmed to keep my ticker at 60 ticks/minute. Sodden thought, perhaps it was programmed by one of my failed C++ students?

Your views on embedded C++ in a life-death situation are invited.

BTW Bjarne Stroustrup, the "onlie begeter," has moved West to the academic life of one of those oil-rich Texan campi. Farewell to what Dr Spooner called Jew Nersey (actually related to me by the Rev Sharpton)

Let me not bore you with a gruesome, stitch-by-stitch medical saga. Suffice it to say that my least favourite movie title is "My Left Foot." My pet cliche is "Curse this Gammy Leg" (beware of the effete "Gamey"). And that my pending Oratorio, scored by fellow scouser David Ellis, is called "Toeless in a Gaza Strip Club."

You can follow the prolific Ellis story at We forgive him for his association with the famous Manchester School of Composers. Of course, he doesn't support the arch soccer enemy Manchester United, aka ManScum.

David and I are Liobians, that is to say we both attended the Liverpool Institute High School, or to use its scouse diminutive, "De Inny." (See previous SODA columns for the Beatle's Inny connection.)

Though currently daily-nursed and wheel-chair bound, I hope to be up and about, possibly even walking, before 2003 ends. BTW, I do impersonations of Ironside and Stephen Hawkings and challenge visitors to spot which is which. (Hint: the diction!)

I'm into short hobbles, such as computer to bed, bed to orchid, orchid to can using a wonderful British invention: pacer poles. They come in pairs, color coded left and right. Popular among cross-country trekkers since they reverse the evolutionary curse of bipedalism and give you effectively four "feet" for a cat-like tread (think Cheetah; think Gilbert & Sullivan). More at I need to thank Dr Frank Holland for making me a pacer pole kinda guy. If I were smoking (which is forbidden), I would switch to one of those macho brands popular on ski slopes and horsebacks.

With the first major break in my monthly Devil's Advocate (DA) columns and the Son Of DA (SODA) progeny since May 1984, it seems logical to call this new sequence ROSODA (Return of SODA)? I rather like the Japanese resonance. Losoda is the wife of the head warrior but has the other six on the side. Just a brief Samurai of the plot. [Kindly leave the site -- Ed]

Next: a sincere apology for my uncharacteristic torpor in answering email. I think I can claim some sort of record for mailbox gluttage by an Anglo-Irish resident of Petaluma. After a 30 day stay in hospital I found over 9,500 unread messages.

The sequences of spam were (still are) rather weird:

Seems I can lose weight in my sleep while enjoying a huge penile enlargement. Then come cures for blindness and wrist problems, surely due to the aforementioned priapic explosion. And even if you turn down all those Nigerian billions, they can extinguish your credit card debts with a few clicks. After which, you can afford those blind dates with hot Czech chicks and voluptuos Vladivostok viragos. If she has a headache, there's low-cost Vicodin without a prescription.

Anyroad, my DELirious finger may well have cleared some worthwhile messages. If you emailed me between say June and September and still seek a response, could you please re-send?

What follows, dear reader, is the original extended version of a piece I wrote seven years ago for the MAA (Mathematical Association of America). Editor Underwood (Woody) Dudley never overtly used the word "bloated," but he did leave yards of sparkling strings on the cruel cutting-room floor.

So, most of my review has never seen the light of print. For some reason, this reminds me of the narky Dorothy Parker who in a similar situation said:

"This is not a novel to be tossed aside lightly. It should be thrown with great force."

BTW Woody has an Erdös number of 1 (see this site passim). Of course I wish in vain that my "joint paper" with Woody might endow me with some surreal Erdös number, maybe 1.3333...

Sad to note that with the death of Paul Erdös, there will be no more Erdös number 1 qualifiers. But for n > 1, the list swells each month.

Keys to Infinity by Clifford A. Pickover John Wiley & Sons, Inc NY, 1996; ISBN: 0-471-11857-5

Extended Review by Stan Kelly-Bootle

I am delighted to add Clifford Pickover's latest recreational romp to my endless collection of books [ref 1] with at least one occurrence of the string "Infinity" on their spines. By definition, "popular" science and mathematics books are aimed at a wide, lay, mainly point-of-sale audience. Publishers, therefore, employ the keenest semioticians (the bigger Houses can afford full oticians) to create catchy titles and matching cover designs. Certain keywords are known to attract the casual browser The amateur reader is more likely to buy "Catastrophe" than "Morphogenetic Stability," and more tickled by "Chaos" than by "Feigenbaum Transformations." (Mrs Feigenbaum may disagree.) A rare exception was Springer-Verlag's Rotations of Coupled Rigid Bodies Around a Fixed Point which flourished briefly for the wrong reasons. These "hot" topics can come and go like Paris fashions, earning the passing buck, but the best-sellers since the first, incunabular top-ten have promised enduring, transcendental insights.

As permitted by the AMM rules for "extended reviews," I plan some nostalgic meandering before I focus on the book's title, price, target audience, style/contents, and my reasons for a "buy/borrow" signal. (If you are pressed for time, the gist of my essay is an old-soldier's "The young budding mathematicians of today are spoiled rotten"). En route, I'll cover diverse topics related to the genre that we fast-fading fogeys fondly refer to as "mathematics for the million, science for the citizen, and languages for the loom." It's mumble years (well, why be bashful, 60+) since Lancelot Hogben's alliterations over-heated my childish academic ambitions. There were also those wonderful penny-blue-backed Pelicans on astronomy (The Stars in their Courses! The Expanding Universe!) and archaeology (Ur of the Chaldees! Digging Up The Past!). However, Billy Baxter, also known as "Creeping Jesus," my maths master at "de Inny" (The Liverpool Institute High School for Boys) [ref 2] exposed the downside of "popular" exegesis with an early warning on the ambivalent term, "elitism." He caught me reading Sylvanus P. Thompson's anathematical Calculus Made Easy and swore that I was doomed to eternal hellfire. The book's opening heresy, "What one fool [the author] can do, so can another [the reader]," offered a painless path to the priesthhood (priests hate that sort of thing). Then came the unpardonable sin on page 2, "dx is a little bit of x," that drove Billy Baxter barmy. Years later, I discovered that this blasphemy, suitably formalized, is now part of the holy differential (nay, deferential) canon.

Paging the Past

If space-time allowed, it would be fun to re-read, as sequentially as possible, all those texts (formative and misinformative) of yore. Modern litcrit has moved beyond the vacuous "What do we really do when we d?" to the more promisingly spurious "What do we really, really do when we re-read?" [ref 3] Can we cross the same hurdle twice or re- parse the same sentence? In the case of R. Wagner (his prose works), F. Nietzsche, K. Marx, V. I. Lenin, G. B. Shaw, Earl B. Russell, J. B. S. Haldane, G. H. Hardy, et Al Hiss, it would be impossible to recapture my former, innocent gullibility. Well, so much history, some suffered firsthand, has intervened. Freeman Dyson ("Can Science Be Ethical?", New York Review of Books, April 10, 1997) who cites Haldane as "an honest prophet," seems to have forgotten the Lysenko controversy during which many Western geneticists, both card-carriers (such as JBS) and fellow- travelers, suspended their honest disbelief to keep (fat chance) in the "good books" of our Supreme Scientist, Uncle Josef Vissarionovich. Revisiting Jeans, Woolley, and Hogben also reveals facts and opinions that have failed to survive the relentless, Baconian march of time. However, these authors still reflect the undogmatic "suck-it-and-see" adventure of science that sparked my enthusiasm.

I was present when JBS addressed a British Communist Party rally at a packed Liverpool Philharmonic Hall in the 1940s, but such are the quirks of ear-witness accounts that all I remember is Haldane's unusual, possibly correct, pronunciation of "Himalaya." We say "HimalAya," JBS says "HimAlaya." Cole Porter says "Let's call the whole thing off." To be fair, Haldane and thousands of disillusioned Marxists left the party in 1956 following the Russian "re-liberation" of Hungary, an event that also had a profound effect on the world of mathematics. (One is tempted to say that anything that happens to Hungary, good or bad, has a profound effect on the world of mathematics.) Less well-known, and proof of man's infinite capacity for contrariness, is the fact that the Scottish Nationalist poet Hugh MacDiarmid re- joined the party in 1956 following the aforementioned invasion. Both Haldane and MacDiarmid (not to mention Turing, Besicovitch, Conway, Halmos, Thom, Smales, Churchill, Cardinal Heenan, and the Duke of Edinburgh) have chapters in my forthcoming autobiography: I Only Met X The Once. The template generates my brief encounters with the famous: "I only met Churchill the once. He was rushing out of the Savoy, as I recall, and tripped over my suitcase. 'You clumsy fool,' he snarled with that inimitable bulldog scowl. Our eyes met for a moment but in that moment a whole world of understanding passed between us. Then he was gone. We were never to meet again." "I only met Turing the once. Our bikes collided on Kings Parade, as I recall, ..." and so on.

Kiss Me Hardy

Hardy is on my must-re-read-regularly list for several reasons. Forget all those authorial suffixes -- Platonic, Euclidean, Cantoresque, Peanistic, de Manic, Foucauldian, Fishy, Rortyan, -- Hardy serves unmodified as a self predicate. (Add that to your small set of homologicals!) I re-dip with pleasure into his elegant "non-fiction," number-theoretic works, but his "Apologia" has lost some of its initial allure. At the age of 13 (1942), I won three book prizes at the Liverpool Institute, my choices being Lady Chatterley's Lover (unavailable and unsuitable), Das Kapital (denied), Finnegans Wake, The Waste Land, and A Mathematician's Apology. Lord, all that precocity and whom has it got me? Hardy's small book was a major revelation that pushed me into the grammar-school's unfashionable "science" stream. (I dropped Greek but kept up with the soteriologically minimum of Latin needed in those days for the Cambridge Open Entrance exams.) With hindsight, it's not easy to accept Hardy as a conscientious objector. Although I prefer his moral rather than the prevailing religious grounds for laying down sword and shield, there was a tragic confusion between 1939 and 1914. Meanwhile, milions were reluctantly "studying war," and dying to save his collection of "Inequalities" from the inequitable Nazi burning of the books.burnings.

I wonder if Hardy was misled by some of his pro-Hitler colleagues? It's quite bizarre to re-read The Case for Germany, (A. P. Laurie, M.A. Cantab [O Schmerz!], Berlin W 15, Internationaler Verlag) published in July, 1939, and dedicated "with admiration and the Fuehrer." Page 104 has the chilling:

"In accordance with this principle of preserving the healthy part of the German Nation, the National Socialist Welfare Society does not help those who are hereditarily diseased or suffering from incurable mental or physical diseases. These persons are cared for by the State."

Laurie on Hitler's foreign policy and the chances for WW2 is beyond Bayesian analysis:

"The maddest of all nightmares from which the [Chamberlain] Opposition suffer, is that Germany would attempt a military conquest of the Ukraine. Either she would have to march six hundred miles across Polish territory, to which Poland would naturally object, or if she marched through Czecho-Slovakia would find herself lost in the Carpathian mountains, with no railways or roads, and would still have to violate either Rumanian or Polish territory." (ibid, p. 98).

A few months later, of course, der Fuehrer's Blitzkrieg let slip Laurie's conditional hounds and overcame Poland's natural objections. Is there a fancy Greek name for arguments based on short-lived, misplaced rhetorical irony?

In retrospect, Hardy's "pure" and "applied" dichotomy also seems dangerously naive. The "pure" mathematics, which he boasted would do neither good (apart from tenuring a few harmless recluses) nor bad (apart from the occasional donnish-sniping duels in obscure journals) to anyone, has the sneaky habit of cropping up in the most real-world of contexts. Who would have thought that wars could be won by the side with the fastest prime-factoring algorithms, no doubt exploiting some of Hardy's clean-hands lemmata? And what on earth is this "pure physics," whereby topology can hardly keep pace with cosmology? Red-shifted fiber bundles, indeed! If Hardy were alive today, he'ld be turning in his grave. For a more modern apologia, today's young mathematicians should try Moshé Flato's Le Pouvoir des mathématiques (Hachette, Paris, France, 1990). There's an English mistranslation by Maurice Robine, full of charming faux amis (as in "degenerescent refinement," and "superchord theory"): The Power of Mathematics, MacGraw-Hill Horizons of Science Series, New York, NY, 1991 (ISBN 0-07-021258-9). Flato courageously deflates his native Bourbakisme and in the section "From Mathematical Physics to Physical Mathematics," quotes Wigner's comment on the miracle: "The unreasonable effectiveness of mathematics in the natural sciences."

Catchy Titles and Prices

If I do a really smart grep on my library index, I can find putative cognates for "infinity" ranging from the lofty "God," "Eternity," and "Cantor's paradise," to the mundane "ellipsis" (as many dots as it takes), and "lazy eight" (known in Cambridge as "the Oxford boat crew") [ref 4]. I also encounter the homophonic motor-car, Infiniti, that, foot down through the floor, reaches c from a standing start in 0 seconds (assuming that you can live with the terrible gas-mileage and reduced boot capacity). And here comes Infini-D, a Macintosh graphics package from Specular Inc., promising instant renderings of Hilbertian objects (forget those old 2D and 3D versions). In the more traditional sci-fi domain, I find The Infinity Link by Jeffrey A. Carver (Bluejay Books, New York, NY, 1984). Subtitled An infinite adventure...The ultimate love..., the story tells us of "intelligent, faster-than-light tachyon messages from the stars threatening Earth's billions with a thermonuclear holocaust." Whoever or whatever sent these warnings seems to have massively pre-estimated this planet's communications technology.

If I over-rev my search engine, I locate (Yahoo!) legions of chapters called "Infinity," including one such in Donald Knuth's dramatic (literally) Surreal Numbers (Addison-Wesley Publishing Company, Reading MA, 1974). El Don invokes the Bard to prove that love is countable, sort of, provided that the partners are equally-yoked:

Bill: (hugging her once again) Alice, I love you, in infinitely many ways. Alice: (giggling) "How do I love thee? Let me count the ways." 1, w, w^2, w^w, w^w^w...

There's also a touch of Milton and Dante as the lovers are expelled from Cantor's Paradiso and enter Conway's Inferno.

There is clearly an insatiable and supermarketable curiosity for all flavors of the "infinite" and every Jihad-rattling name of the one-true god -- dare I call it the least effable of profundities, the all-time, best-selling epitome of transcendality? It seems that we can never, ever get enough of those bottomless dreams. But, can our nutmeg minds really master unbounded space? Ah, 'tis now a consummation on sale to all devout consumers. Pickover's book offers the "keys to infinity" for an infinitesimal, canonical $24.95. Not $24.68 or $25.03, of course, both of which violate the publishers' axioms of affordability. In the UK, the book sells for pound-sign 17.99 (pushing the axioms to the risible limit), and I see myself slapping eighteen quid on a W. H. Smith counter with a debonair "Keep the change, my good chap!" How did this integraphobic, least-lower/greatest-upper bound pricing work in the super- inflationary Weimar Republic? I reckon the formula was something like (aleph0 - 1) + .95 Dm? Or, I'll take two eggs and your wheelbarrow?

The vendors' excuse for these exotically unrounded prices is depressingly convincing: they are effective even in a supposedly numerate market. The most outrageous pricing tease was probably the Adam computer from LOMAC (Logical Machines Corporation, Sunnyvale, CA), circa 1975, listed at $14,999.99. Perhaps the only uncontestable statement in the brochure was "Under $15,000." LOMAC founder John Peers, a fellow expat Brit, gained further notoriety by having an operator non-dressed up as Eve at the launch. Whatever language Adam the ur-person spoke, Adam, the machine, was programmed in the least unnatural and most popular of current natural languages, "English," to which Peers attached the provocative symbol (c). We used to joke that the Adam user's manual was the complete OED (Oxford English (c) Dictionary), not included in the $14,999.99. To those who mocked his legal claim to "English," Peers pointed out that the OUP (Oxford (c) University Press) claims a copyright on the equally ancient "Oxford." Whether you can escape litigation by using earlier variants such as "Oxonia" and "Oxenffordde," rests in grubbier hands than mine.

Who Owns What?

We do know that Irish Business Machines were forbidden to use their natural acronym by an army of heavy ex-Attorneys-General flown in to Wexford from Poughkeepsie. Similarly, even if your real name is McDonald, MacDowland, or Mecke Messer {* check Brecht's spelling of Mack the Knife -- skb *}, you are well advised not to open an eponymous fast-food graisserie. The habit has spread to everyday words such as Windows, Apple, Oracle, Maple, and Mathematica, which must not be bandied around without due caution. Musical terms and dead composers are especially popular -- damn near every entry in Groves has been purloined apart from Allegro ma non troppo. For ages, we've been attaching people to equations, theorems, curves, effects, advantages, and paradoxes (not always accurately), but now the great ones have been "productized." There's an Einstein for $19.95 and a non-fig Newton for $599.95 [ref 5]. Fonts can also be trademarked, so there's the pleasant prospect of an infinite string of qualifiers generated recursively by the mapping (tm) -> (t(tm)m(tm)). The fear of violating trademarks and copyrights has inspired several weaselly generic preambles: "All the fonts, names, and symbols in this book are or may be the trademarks or registered trademarks of, or are possibly copyrighted by, their respective owners."

Legal Firewalls

John Wiley & Sons, the publisher of Keys To Infinity, commendably avoids the vapid copyright cop out. Better still, there's no sign of that annoying "Iago" disclaimer ("who steals my code steals trash"): "The computer programs in this book are offered 'as-is' with no implied claim that they will compile and/or run on your or any platform." (Note that "as-is" remains singular, present tense, regardless of context. Compare the French "Accroche-ca-moi" for second-hand clothes. We would say "hand-me-down!"

However, the publisher does provide a related declaration intended to deflect the pandemic of frivolous liability litigation:

"This publication is designed to provide accurate and authoritive information in regard to the subject matter covered. It is sold with the understanding that the publisher is not engaged in rendering professional services. If legal, accounting, medical, psychological, or any other expert assistance is required, the services of a competent professional person should be sought."

It would take many Chomskian (I mean before he gave up linguistics) semesters to probe the deep structures lurking here. There's a hint of the Zen-Boolean XAND (A AND B, but not both), as in "having XAND eating your cake," or the quantum "wave XAND particle." There may also be the libelous suggestion that the author is an incompetent non-professional. I realize that publishers, indeed all vendors, are now forced to protect themselves as best they can, but, ironically, should you ever be tempted to obtain the services of a "competent professional person," you'll find a longer list of disclaimers attached to the invoice. The toothpick mode d'emploi label shows you where to find your teeth and warns you not to shove the product up your nose. And in the TV vacuum-cleaner ad showing a virtual-Fred Astaire dancing on the ceiling, the footnote caption says, "Don't try this at home if your room is subject to adverse gravitational forces."

It's still a shock, though, to find this caveat emptor in a book of mathematics. I can see the need for such cautions in, say, "Ballistic Tables Made Easy," but presumably the post-Hardy notion that all mathematics, including Pickover's purely playful explorations of infinity, is potentially harmful has influenced John Wiley's legal department. If so, I would suggest a more specific three-part caveat:

1. This book contains many insanely-arbitrary, incredibly large numbers (such as the Leviathan (10^666)!) that 'make the googol look kind of small,' and that you may find infinitely, fatally boring. [ref 6]

2. The 'Slides in Hell' chapter describes a playground chute peppered with personholes and discusses the probability of a slider surviving a sequence of slides. The publisher and the author stress that this example is intended as a stochastic Gedanken experiment and in no way condones or encourages violations of the Recreational Equipment (Infants) Safety Act, 1897.

3. According to the Logician-General, there are apodeictic flaws in the very fabric of set theory and in certain derived predicate calculi that are known to vitiate the foundations of arithmetic. Neither publisher nor author can therefore be held accountable for any numerical errors, inconsistencies, and other acts of god. Before accepting any proposition or result in this book as true, the services of a competent professional god should be sought. (For a succinct explanation of legal verbosity, see The Cambridge Encyclopedia of Language, David Crystal, CUP, 1987, pp 386-7, "The Language of the Law.")

Kronecker Update

Such caveats are not entirely farfetched. Consider the fact that Lotus Corporation (now owned by IBM) gained a lien ((c), (tm), (r), or whatever) on the string "1-2-3" when they unfurled their masthead spreadsheet in the early 1980s. The spreadsheet mechanism itself (mapping cells [i,j] to functions and macros, and stretching the horrific side-effects from "What if?" to "If only" and "Why not?") was, alas, never patented by Descartes, Artin, or VisiCalc, so Lotus were free to sue their smaller competitors out of business. Note that in our high-cost, litigatious climate, a formal victory by the shallow-pocketed often proves to be the kiss of Pyrrhus. Since we are talking of "law" as in "lawyer" rather than "Law" as in "Nature" or "Newton," the full meaning of the Lotus claim remains intentionally obscure, plus ultra mootable and billable, without due let and hindrance, as it pleaseth the bar. Some argue that "1-2-3" is protected "iconically" or "logotypically" rather than as a numerical sequence. Although untested by the courts, so far, the latter claim, coupled with Peano's public-domain axioms, might give Lotus predatory rights over Z+. To update Kronecker: Lotus owns the positive integers; the rest of mathematics is subject to litigation.

But not so fast! The Lotus position (sic) is vulnerable, and strange to relate, the attack is coming from the East. A powerful Hindu-Islamic consortium (a rare union of disjoint sects, including some Buddhists who object to a corporation calling itself Lotus) has re-asserted its ancient (prior art) rights to "zero" and, by implication, custody over "infinity" in the broadest possible sense of that word. Expect a protracted battle in the courts as a new breed of metamathematical attorneys disputes the rival claims. Jury selection will be a major hurdle. I propose a trick question: "Are you or were you ever a member of a null set?" Only those replying, "Don't you mean the null set?" would qualify. I see Pickover as the key expert witness against Lotus in spite of his IBM affiliations. (If he becomes non-grata at Big Blue, he could always "go evil," as we say, i.e., work for Microsoft's R&D cosmologist-chef, Nathan Myhrvold.) Keys to Infinity would be Exhibit A. In particular, m'lud, Chapter 26 discusses Ramanujan's "theory of reality using zero and infinity," whereby "zero represented 'absolute reality,'" and "infinity was the myriad manifestations of that reality...The product 0 x [infinity symbol] was not a single number but all numbers, each of which corresponded to an act of creation." The puny impugned Z+ of Lotus can't match this mystical flimflam when it comes to jury-swaying courtroom dramatics. All that remains is the problem of awarding infinitely punitive damages and settling the winning lawyers' 80% contingency fees. They reckon that 20% of infinity is better than 100% of nothing. Up my sleeve, awaiting the au juste (not to be confused with the American noun: "Would you like some more au jus on your beef?"), I have trademarked a spreadsheet called "0-1- 2-...w...," copyrighted all the decimal digits of pi, and changed my name to Mr Spigot. See you in court!

Math is Fun -- Maths are Funnier

We enjoy concerts and visits to the Hermitage. We'll never (hardly ever) fiddle like Nero [Menuhin? -- Ed.] or paint like Rembrandt. Our enjoyment and admiration is increased by "dabbling" or simply reading about the artists and their artforms. But there's often a brief tinge of despair and inadequacy. I see a similar happy-sad situation with mathematics. I skim the heavy journals through a glass darkly, pleasantly awed by even the glimmer of a gist. Yet without my regular fun diet of Math Horizons, The Mathematical Intelligencer, and the works of the popular popularizers (Gardner, Stewart, Rucker, Pickover, Dewdney, Dudley, ...), my appreciation of the "real thing" would be greatly diminished.


Pickover states early and often that The Keys to Infinity is not a formal mathematical treatise. It is not even recreational in the relax-on-the beach sense. The reader is regularly challenged to solve problems and run programs (there's no attached diskette, so you must type and compile the source-code listings). Each of the 31 chapters is an independent exploration of some aspect of infinity (or very large numbers headed in that direction), so dip into the book in any order. As with Pickover's previous Mazes for the Mind, computer-generated fractals are prominent and beautifully reproduced in rich colors.

Reviewers love to act the doryphore ("one who takes excessive delight in finding small errors"). The best I can do is to report a tiny mistake on page 200: Fibonacci(X) should be Fibonacci(N).

ref 1: You may take "endless collection" in the informal, everyday sense of a large, countable set that nobody bothers to count, but there's also a sneaky literal meaning: my shelves lack the traditional book-ends designed to maintain extensible, volumetric stability in the chiefly vertical environment.

ref 2: Old boys keep in touch via two chatspaces: liobians and liobanter. Both moderated with restricted membership. Sorry, like, dere!

ref 3: Rereading, Matei Calinescu, Yale University Press, 1993

ref 4: Zero to Lazy Eight -- the Romance of Numbers, Alexander Humez, Nicholas Humez & Joseph Maguire, Simon & Schuster, NY, NY, 1993

ref 5: "Let Us Now Exploit Famous Persons," Stan Kelly-Bootle, Computer Language, December, 1988.

ref 6: The well-known "proof" that all numbers are interesting can be readily reversed. The least-boring number may be interesting, but the least-interesting number is surely a big yawn. Still, there's a gulf between crazy-occult-obsessional numerology (you can now scan pi on the Web looking for your birthdate -- if mmddyy doesn't match, try ddmmyy or mmddyyyy or whatever) and the "off-duty" mathematician's delight in numbers with "curious" properties. The latter may remain isolates (such as Hardy's tram-ticket number and Pickover's "smallest power of 2 that contains the beastly subsequence 666"), or they may spawn useful generalizations, as with perfect numbers and pseudoprimes. In between, we have what Dudley calls the "Smith-number rathole," viz., the excessive formalizing of the trivial.

Stan's bio:

Liverpool-born Stan Kelly-Bootle has been exposed to computing, on and off and vice-versa, since 1953 when, after graduating in Pure Mathematics at Cambridge University, he switched to impure post-grad work on the wondrous EDSAC I. After some trenching with IBM and Univac in the 1960s and 70s, Stan opted for self-employment as a consultant, writer, folk-song revivalist, after-dinner entertainer, and cunning linguist.

His monthly DA ("Devil's Advocate") column ran and ran in UNIX Review (aka Performance Computing) from 1984 until January 2000 (a date that will live in infamy) but lives on as SODA ("Son of DA") via the homepage devoted to UNIX performance.

The latest of his umpteen books are "The Computer Contradictionary" (MIT Press) and "UNIX Complete" (Sybex). More on his biblio- and disco-graphy can be found on soon due for its millennial update.

Stan welcomes reader reaction:

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