Son of Devil's Advocate
Combining parallel careers in mathematics and folksong, I am often faced with unexpected, nay, contradictory convergences. Euclidean parallels, by definition, never met until some post- classical smart-ass introduced the dubious "point at infinity," allowing all planar lines to intersect somewhere. You could argue that the evolution of mathematics has been haunted by this need to avoid exceptions. The quadratic x^2 = -1 must have two tangible roots however "imaginary." And as the limiting ratio dy/dx solved endless real-world problems, we learned to accept that infinitesimals were not quite zero, but effective, fleeting "ghosts." As you all know, we daily write if (x == 0) without always knowing which floating-point regime will eventually resolve the equality.
I dare not mention the ultimate "parallel" use-case. In the metaphysical parallel "universe" concept, I keep missing you as I write, and vice versa. There's a possibly valid column out there where I say "Solipsists of the World Unite?"
Here and now, when the great Leadbelly [ref 1] (Huddie Ledbetter [1885-1949]) sings "Some said one, I said 'More Yet,' some said two, I said 'More Yet'..." I think of the equally renownwed mathematician Giuseppe Peano.
Peano (1858-1932) was Leadbelly's near contemporary time-wise, yet widely separated spatially and culturally. Peano, had he known better, could have jazzed up his foundational arithmetic axioms. He started with ur-zero and posited a "successor" function that generates Z+, the majestically endless sequence of positive integers. Each member of this "set" has a unique "predecessor" except, of course, the magic zero. You could say, bypassing Shannan Hobbs' metaphysics, that this lack of a previous member is all you need to know about "zero."
Leadbelly's recursive trick is that the name of his song, revealed after the sour mash runs low, is "More Yet." Peano could well have added a multicultural footnote showing Leadbelly's twelve-string tablature, striking an early chord for what is now known as "ethno-mathematics.
This early venture into deriving "sums" from "pure logic" influenced Russell & Whitehead's vast Principia mathematica (1910-13). The injoke is that R&W get round to defining "1" on page 413. Further, the transition from a complete, consistent set theory to the everyday arithmetic we take for granted when we balance our check books turned out to be riddled with paradoxes.
Leadbelly was jailed twice in the deep chain-ganged South, for murder and attempted murder, but gained a Governor's pardon after intercessions from the folk-song collectors John and Alan Lomax. Sadly, Leadbelly never shared the huge royalties generated by such hits as "Goodnight Irene" and "The Rock Island Line." Polite, mainly white, tin-pan-alley groups oft bowdlerized his corpus. Thus his "I'll get you in my dreams," was toned down to"I'll see you in my dreams." Saddest of all, the Lomax's had Leadbelly dolled up in convict clobber and ankle chains performing at posh New York night clubs.
Have my parallel careers converged yet?
Thanks to Darius Thabit for directing me to the most curious of primes:
Briefly [sic], Phil Carmody (Lord knows how) has disovered that a certain C-source code that decrypts the DeCSS DVD movie encryption scheme can be expressed as a huge number that happens to be a prime. You can extract the source code from this sequence of digits using a legal Perl program written by Jamie McCarthy.
Here's the rub: "It's illegal to distribute this source code in the United States, so does that make the equivalent prime illegal?" (Caldwell -- Prime Curios! -- 1999-2000 [all rights reserved])
I see my expensive services in demand (either side of the bench, of course).
M'lud: all primes are curious. For, suppose there were a least curious prime? That would be most curious?
For Fred Avolio's insightful newsletter send a blank message to email@example.com
Bjarne Stroustrup reacted to my definition "A Language is a Dialect with its own Army and Navy," by suggesting that Ada may be the best-defended code. He also noted that Visual Basic and C# seem to have transcendental powers: the Oregon tectonic plates rumbled as soon as Bill Gates said "Slide One."
From esteemed fan Peter Kirwin:
"In case you missed this delightful Wakeanism:
'Some of those platforms are very small microcontrollers that don't have full-featured CPU sets. Typically they lack an MMU (Memory Management Unit). So Linux needs to be modified accodingly.'"
This Column 14 Years Ago
Devil's Advocate, April, 1987
Où Sont Les Chaddim d'Antan?
Serious fun-lovers seem able to party without troubling to dig up a valid excuse. For those whose conscience insists on a formal occasion, there are comforting "drinkers' diaries" that list the various options available. "Wow, it's the 163rd anniversary of the founding of the Bolivian Republic! This calls for a celebration." A more flexible ploy I encountered in Moscow was "If Vladimir Ilyitch were alive today, he would be 116 years, 4 months and 2 days old. Za zdorove Lenina!" But enough of these lame pretexts; you may now lift your glasses for a genuine toast.
Thirty-four years, 3 months and 4 days ago, to the very microsecond, I wrote my first computer program. It was keyed on a "blind" paper-tape perforator, verified using the Prayer method, then submitted to a room full of valves and mercury delay lines collectively known as EDSAC I (see this column October 1984 for detailed specifications).
WORUJ was a popular acronym in those days: Write Once, Read Until Jam.
Some aspects of computing have not changed. For example, programs were written with mnemonic op-codes, remarkably similar to present day assembly languages, although the limited single- address instruction set (18 ops each 18-bits long) might now qualify as "state-of-the-art" RISC!
Pieces of EDSAC I can still be seen at the Kensington Science Museum in London, but that early program of mine, a small roll of pink, 5-track teleprinter paper-tape, lovingly preserved for many years, has gone, alas, the way of all paper-tape. "Où sont les chaddim d'antan?" ("Where is the chad of yesteryear?") And whatever happened to all the suppliers of paper-tape support products: winders (the posh ones had electrified motors), splicers, duplicators, rubber bands and those cute little white storage boxes?
There I was at the very dawn of a new cyboconsciousness and freedom for the desk-bound masses, yet my fondest memories are of neat stacks of white, glossy cardboard containers, and sprinkling pink chad over a Pimm's Special!
Maurice Wilkes, who was then Director of the Cambridge Mathematical Laboratory and leader of the EDSAC I design team, has more cogent memories: "We realized that building the machine was only the start of the project; that there was a great deal to be learnt about writing programs...as soon as we started programming, we found to our surprise that it wasn't as easy to get programs right as we had thought. Debugging had to be discovered. I can remember the exact instant when I realized that a large part of my life from then on was going to be spent in finding mistakes in my own programs!" (Inaugural Lecture, Digital Computer Museum, 1979)
Most readers will identify with this chilling summary of the programmer's angst. Matters will not improve until the SKB Coding Rule is observed: "Avoid Debugging - Get it right first time!" Nowadays, of course, we have Software as a branch of Engineering, which suggests that someone, somewhere really knows what's going on. However, if you read "Comparing & Assessing Programming Languages," (Edited by Feuer & Gehani, Prentice-Hall, 1984) you find the experts sniping at each other over the basic tools of our trade. Perhaps conventional engineers have their differences and feuds, but I'm sure they all agree on the fundamentals of metallurgical methodology!
In the early 1950s the long-term prospects for paper-tape and its accessories appeared rosy, in spite of the rival claims of the punched card lobby. In fact, the card v. tape controversy raged for some years, mirroring the altercations between Fortran and Algol devotees. Those who saw salvation in "either/or" terms failed to recognize that both cards and tape would be condemned to near-extinction by data-entry and storage technologies not then dreamed of. Ah, the dangers of sales-forecasts. Perhaps in those rumored warehouses stuffed with unsold hoola-hoops and Davy Crockett hats, you can find 30,000 rusting Winders/Hand/Tape/Paper/Mk IIA? My own invention of paper-tape cartridges, by the way, was and still is ahead of its time. The seers of 1987, poring over the tabulations of past trends, often extrapolate without recognizing the essential discontinuities of technological progress. To add insult to injury the predictions are often made with stunning precision: "Micro software sales will increase by 18.392%..." The layperson suitably impressed by this spurious quantification. Who can dispute a number with three decimal places?
The definitive misuse of linear extrapolation occurred during a survey of London traffic in Victorian England. It was seriously estimated that vehicular traffic would squelsh to a nasty halt by 1925 because the roads, by then, would be covered in horse manure to a depth of 12.652 feet.
Everyone knows of the gross miscalculations made in the early 1950s just as the first leaps in electronic computing were being made. It was confidently predicted that three or four EDSACs would more than cope with all the foreseeable scientific computing requirements of the UK. This type of error arises from the belief that inventions fulfill existing needs rather than create new ones. Henry Ford did not start by conducting surveys on the demand for personal transportation. Had he done so he might well have devoted his talents to improving the railroads or equipping the road sweepers with bigger shovels.
With all this in mind, I limit myself to a very short-range prediction: It's good old Chaucerian "soote shoure drenchynge" Aprill again. If the Tax Man cometh can Baseball be far behind? Already I hear the whack of pine-tar on the jolly old spitball (Shurely shome mishtake here?...Ed.), the thump of crania as umpire and manager engage in rule-based paradigms:
We suspect that the rules of Baseball are incomplete, since all previous seasons have thrown up hitherto unexpected situations not covered by the Book. But, can any reader prove that the rules are consistent? Inconsistency would be established, for example, by describing a sequence of events after which two infallible umpires could give chapter and verse to uphold contradictory decisions. I will also accept proofs that the problem is undecidable.
Reassuring Quote for the Month: "But, so far, the ways in which AI systems can use knowledge to solve problems is still extremely limited as compared with humans." Ernest R. Tello, Dr. Dobb's Journal, Feb 1987.
ref 1: When Pete Seeger gave a concert in Moscow, announcing a song by Leadbelly, the audience reacted with unexpected ribaldry. Seems that the interpreter rendered our hero as "Tin Stomach."
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 www.sarcheck.com 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 http://www.feniks.com/skb/ soon due for its millennial update.
Stan welcomes reader reaction: firstname.lastname@example.org
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Portions © copyright Stan Kelly-Bootle 2001.