Nick's Café Canadien » Mathematics

I am the very model of a squandered opportunity

Nicholas — Sat, 03 Oct 2009 20:46:08 +0000

Among the many things I passed through upon my arrival in Cambridge was a symposium on Euclidean Geometry in Nineteenth-Century Culture, organized by Alice Jenkins (University of Glasgow) and CRASSH. I may say a few things about it later, but for now, let us limit ourselves to this tidbit.

I briefly spoke to Robin Wilson, the author of Lewis Carroll in Numberland (reviewed here), from whom I learned that Lewis Carroll once corresponded with Arthur Sullivan to propose an operatic adaptation of Alice’s Adventures in Wonderland. Sullivan declined.

Or, as I like to tell it: Sullivan declined, and English comic opera has never recovered since.

Wednesday Book Club: Lewis Carroll in Numberland

Nicholas — Wed, 16 Sep 2009 19:46:36 +0000

This week’s selection: Lewis Carroll in Numberland: His Fantastical Mathematical Logical Life (2008) by Robin Wilson.

In brief: Part biography and part catalogue of Charles Dodgson’s mathematical interests, Numberland is a crisp introduction to Dodgson’s professional work outside of the classic literary diversions he penned as Lewis Carroll. Wilson is content to explicate mathematical puzzles and present collections of facts rather than weave them into a story or thesis, but does so admirably enough to produce a fine survey of what captivated the man.

(The Wednesday Book Club is an ongoing initiative of mine to write a book review every week. I invite you to peruse the index. For more on Lewis Carroll in Numberland, keep reading below.)

Avid readers of Lewis Carroll are likely familiar with the story of how Queen Victoria received Alice’s Adventures in Wonderland. “Send me the next book Mr Carroll produces,” the Queen demanded—hardly expecting that Carroll, who was a lecturer in mathematics by the name of Charles Lutwidge Dodgson, would then present her with a copy of An Elementary Treatise on Determinants, with Their Application to Simultaneous Linear Equations and Algebraical Geometry.

Dodgson later denied this story, but the tenor of the anecdote befits his reputation as a master of wordplay who often toyed with miscommunication and the boundary between the figurative and the literal. Examples abound in Robin Wilson’s biography, Lewis Carroll in Numberland, most of them drawn not from Alice but from Dodgson’s lesser-known works, private correspondence, and mathematical puzzles.

Wilson’s book begins with a sample of scenes from Dodgson’s writings as Lewis Carroll that draw on curiosities in arithmetic, geometry, and logic, but otherwise pays little attention to his literary work. The composition of Alice is a story that here occupies no more than two pages. The bulk of Numberland considers Dodgson as a pioneer of recreational mathematics; as a consummate scholar and educator who composed riddles for students and family members alike, devised shortcuts for arithmetic and instructional games for visualizing symbolic logic, and dabbled in everything from tennis tournament seeding to schemata for electoral reform.

Half of Numberland is straightforward biography, offering a portrait of what life was like for Dodgson as a clergyman’s son, model student, and Oxford scholar. Much of the evidence is drawn from letters and diary entries. Wilson exposes us to Dodgson’s England by way of the mathematical culture of the day, be it in the form of representative examination questions or the debate surrounding whether geometry ought to be taught directly from Euclid’s Elements or through new instructional texts. (Dodgson was a staunch advocate of adhering to a classical education in Euclidean geometry, insisting the order and numbering of Euclid’s axioms and propositions were themselves part of standard mathematical literacy. This was a battle he ultimately lost.)

The remainder of the book presents an eclectic sample of problems and other oddities, many of which Wilson leaves for the reader to solve (though solutions are provided in the endnotes). The mathematical content is undemanding and should be accessible to any reader with at least vague memories of middle-school algebra and geometry, though a few of the puzzles will take some thought. Conceptually, there is nothing here more advanced than Dodgson’s condensation method to quickly compute the determinants of large matrices, and Wilson explains it all with clear examples and easy-to-follow diagrams.

This is all that Wilson aspires to do in this book, and he does it well. All the same, the breakneck pace with which he hops from one curiosity to the next, coupled with the wholly expository nature of the text, leaves the impression that we are only receiving a cursory tour of the subject. The narrative frequently tantalizes us with breadcrumbs of fascinating connections only to move on to the next unrelated specimen.

I attribute this to Wilson’s marked distaste for deviating from documented historical fact. While this decision renders Numberland a cautious book that dares not synthesize its anecdotes, it may have its roots in what Wilson sees as the grave injustice that present-day revisionism has done to Dodgson’s reputation, notably with respect to his relations with children. As someone who spent a great deal of time with young girls (including Alice Liddell, the inspiration for Alice’s Adventures in Wonderland) and a noted amateur photographer who specialized in child subjects, Dodgson’s history raises some eyebrows today. Wilson only broaches the subject once, dismissing any unsavoury suspicions wholesale:

Sadly, much nonsense has been written about Dodgson’s friendships with children. In common with many of his generation, he regarded young children as the embodiment of purity and he delighted in their innocence. His vows of celibacy, which he took very seriously, would have outlawed any inappropriate behaviour, and there has never been a shred of evidence of anything untoward. Subjecting him to a modern ‘analysis’, rather than judging him in the context of his time, is bad history and bad psychology, and often tells us more about the writer than about Dodgson.

I have no reason to doubt that Wilson is correct. Similar controversies persist in fields like Shakespeare scholarship, where modern readings of pederasty and homosexuality in the plays often fail to account for what was a fundamentally different culture of social bonds and normative sexual desire. Psychoanalysis on the whole has proven more relevant to fiction and myth than to real people. But Wilson is unlikely to persuade anyone who believes Dodgson’s relations with children are circumstantially suspect—certainly not by abandoning the subject almost as soon as he brings it up. We all know how moral conservatism and vows of celibacy make for a flimsy defence nowadays.

My point remains that Wilson does little to make arguments and broad connections, even when it is within the scope of the book’s mathematical focus. Personally, I would have liked to see more direct discussion of how Dodgson’s multifarious interests influenced his literary output as Lewis Carroll. The knowledge that Dodgson was an early advocate for proportional representation—specifically, a variant of PR that would replace single-member constituencies with fewer electoral districts consisting of multiple, proportionally distributed representatives—seems to bear directly on the scene of the Caucus-race in Alice. Similarly, Dodgson’s advocacy for continued mathematical education through classical texts in polemics like Euclid and his Modern Rivals instantly reminds us of his frequent satires of British schooling and begs us to seek out a coherent thread of pedagogical beliefs.

This is not to say that Wilson neglects these connections entirely. One passage in Numberland calls attention to the recurring appearances of the number forty-two in the Carroll literature—the most intriguing example being this passage from Alice:

I’ll try if I know all the things I used to know. Let me see: four times five is twelve, and four times six is thirteen, and four times seven is—oh dear! I shall never get to twenty at that rate! However, the Multiplication Table doesn’t signify…

Wilson notes that 4 × 5 = 12 in base 18, 4 × 6 = 13 in base 21, and so on as we increment the base in threes up to base 39, where 4 × 12 = 19—after which we reach base 42, where 4 × 13 yields not 20, but 1X (X being the digit in base 42 equivalent to 10 in decimal). In a twisted way, Alice was right.

This reminds me of another story about numbers in amusing books. No mention of the number forty-two goes very far without bringing Douglas Adams to mind, since the number appears in The Hitchhiker’s Guide to the Galaxy as the Answer to the Ultimate Question of Life, the Universe, and Everything. What the Question is, we’re not exactly sure, but in The Restaurant at the End of the Universe, Arthur Dent draws Scrabble tiles out of a bag and randomly generates the question, “What do you get if you multiply six by nine?” As 6 × 9 = 54, the point is that the universe makes no sense.

It has been observed, however, that 6 × 9 = 42 in base 13. Despite circumstantial oddities like how Arthur’s handmade Scrabble board is 13×13 instead of the standard 15×15, Adams vigorously denied that this was anything but coincidence. “I may be a sorry case,” he said, “but I don’t write jokes in base 13.” Evidently, Lewis Carroll did him one better.

The spreadsheets of Catan

Nicholas — Tue, 31 Mar 2009 07:11:07 +0000

From Andrew Curry and Wired comes this comprehensive article on Settlers of Catan, a superb piece of board game journalism if I’ve ever seen one, and a must-read for players of all levels. It’s got a bit of everything: a look at why Settlers fit the market like a glove, a little about designer Klaus Teuber, an overview of the “German style” of board game design of which Settlers is the most prominent ambassador, and a peek into the complexity underlying the game’s infamously balanced mechanics.

This caught my attention:

In 2006, Brian Reynolds, a founder of Maryland software company Big Huge Games and the programmer who developed the AI behind the addictive computer classic Sid Meier’s Civilization II, set out to make an Xbox 360 version of Settlers. To help programmers develop the game’s AI, Teuber spent months exploring the mathematics of his most famous creation, charting the probability of every event in the game. The odds of a six or eight being rolled are almost 1 in 3 for example, while the chance of a four being rolled is 1 in 12. There is a 2-in-25 chance of drawing a Year of Plenty development card. Teuber created elaborate logic chains and probability matrices in a complex Excel spreadsheet so the videogame developers could see how every possible move and roll of the dice—from the impact of the Robber to the odds of getting wheat in a given scenario—compared. The end result was a sort of blueprint for the game that gave Big Huge Games a head start and showed just how complex the underlying math was. “It was the biggest, gnarliest spreadsheet I had ever seen,” Reynolds says.

I want to see this.

One of the best things that happened to the Civilization series was how in Civilization IV, lead designer Soren Johnson laid the mathematics and AI bare for everyone to see, expanding on a series tradition in the Sid Meier games to make all the data easily accessible (and therefore modifiable).

Settlers is elegant enough that I’m sure people have already figured out the math through a spot of reverse engineering; it’s really not that hard. But I’d love to see Teuber’s spreadsheet for its immense historical value as a design document alone. Surely there was a calculated rationale to everything from the fifteen-road limit to the assignment of three ore/brick hexes instead of four—and I often wonder if the perpetual endgame glut of sheep is here as an intentional crimp.

Wednesday Book Club: Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi

Nicholas — Wed, 24 Dec 2008 22:26:09 +0000

This week’s selection: Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi (2008) by Martin Gardner.

In brief: This revised anthology of Martin Gardner’s “Mathematical Games” columns in Scientific American, the first of fifteen volumes, is an ample exhibition of the author’s repute as the canonical journalist of recreational mathematics. Though the brevity of the articles leaves the details of proofs bottled up in the extensive bibliography, the non-technical approach goes a long way towards illustrating the everyday relevance of esoterica in topology and combinatorial theory.

(The Wednesday Book Club is an ongoing initiative of mine to write a book review every week. I invite you to peruse the index. For more on Hexaflexagons, Probability Paradoxes, and the Tower of Hanoi, keep reading below.)

I first became aware of Martin Gardner through his successor at Scientific American, Douglas Hofstadter, whose vignettes on self-referential sentences, Chopin, Rubik’s Cube, the Lisp programming language, and a whole host of other Things I Like, appeared in Metamagical Themas: Questing for the Essence of Mind and Pattern. Hofstadter’s reverence for Gardner, who wrote the “Mathematical Games” columns at the magazine from 1956 to 1981, was more than enough to keep my eye open for Gardner’s work. To be frank, I am surprised that I hadn’t discovered it earlier: Gardner is considered an authority on a number of subjects that are near and dear to me, among them pseudoscience and Lewis Carroll.

Needless to say, I was rather delighted to see that the Cambridge University Press is issuing new editions of Gardner’s fifteen volumes of articles under the heading of The New Martin Gardner Mathematical Library, with an all-star editorial board that includes names like John Conway and Donald Knuth. I pulled the first two volumes off the shelf on sight, and judging by Hexaflexagons, I intend to collect them all.

Hexaflexagons consists of sixteen articles originally published from 1956 to 1958, with annotations and postscripta that have accumulated over several reprintings. The topics are a broad sample of what Gardner refers to as “recreational mathematics”—that is, mathematics as it is applied to the world of card tricks, logic puzzles, and board games.

Most of the articles accord with one or both of two rhetorical formulae. The first is the explication of unexpected correspondences between one problem and another, like the familiar Tower of Hanoi and the traversal of the nodes on a flattened topological map of a polyhedron. The second is the generalization of small, contained problems into larger problem domains, as in the illustrations of how to play tic-tac-toe on a four-dimensional hypercube, or how polyominoes—interlocking permutations of n square tiles that should be familiar to anyone who has played Tetris—can or cannot tesselate rectangular grids of varying sizes and shapes.

Many of the problems in the book will be familiar to modern readers with an interest in puzzles, but even so, there is some historical curiosity to be shared in realizing that Gardner’s articles were often the first to introduce them to the general public. Gardner provides solutions for a few representative problems in each article, as well as two columns that consist entirely of unrelated puzzles, but leaves much as an exercise for the reader (or at least, the scrupulous reader who does not stoop to looking up the solutions on Google).

As the articles are directed to a general audience, most of the underlying mathematics is explained in words and diagrams, and the few equations that appear never exceed the bounds of high-school algebra. Mathematical literacy is still an asset, however, for the sake of working out the myriad proofs that Gardner casually mentions on the byway. If there is one frustration to be had with the book, it is Gardner’s understandable habit of dangling the tantalizing existence of a proof in front of the reader, but leaving the explanations to the sources in each article’s comprehensive bibliography. This is an acceptable price to pay for the elucidation of advanced concepts to the public without intimidating them, and perhaps it is to Gardner’s credit that he leaves the audience wanting more. If his intent is to foster interest in mathematics, I would call the execution a success.

Gardner is at his best when he seizes diversions that are putatively trivial and expands them into a broader context. The chapter on “probability paradoxes”, or counterintuitive results in probability theory, is a fine example. It begins with a few choice illustrations—why you are more likely to be holding two aces if you declare not “I have an ace,” but “I have the ace of spades”; why the chance of a pair of a shared birthdays in a group of 24 individuals is slightly better than half—but quickly segues to a treatment of one of the most important questions in the philosophy of science: what examples we consider relevant as the confirming instances of a hypothesis. To cite Gardner’s case study: in theory, does the discovery of a purple cow not improve the likelihood of the statement, “All crows are black”? Or, to cite Gardner’s parody of Gelett Burgess:

I never saw a purple cow,
But if I ever see one,
Will the probability crows are black
Have a better chance to be 1?

What we can say with certainty is this: Gardner’s crystalline writing is both a lucid presentation of evergreen curiosities and an elegant introduction to the theories behind their analysis. Problems that were fresh in the 1950s may look ordinary today, but it takes a keen interpreter to evoke their underlying intricacy in plain English. It should be clear to any reader who picks up Hexaflexagons that Gardner’s work is of monumental importance not because he was the first on the scene, but because he knew how to communicate that most elusive of messages: why something is fun.

Here, that “something” is mathematics. That is a good thing; why, I shall leave as an exercise to the reader.

Where dyads tread the fairy fields of Venn

Nicholas — Tue, 23 Oct 2007 23:20:46 +0000

I’m not someone who is intimately familiar with poetry, but I’ve always had a weakness for heroic verse—a trait that has become all too apparent to me again as I pore over the sweeping couplets of Lord Byron’s The Corsair. It’s a pity that the ongoing reinvention of poetic forms in the last century and a half, much as I appreciate some of its products, has progressed at the expense and exclusion of antecedent formal constraints: my impression is that most journals of poetry don’t even take rhyming couplets anymore as an editorial decision—partly under the expectation that nobody can do it well, that they are bound to tumble off the shoulders of the giants of the Western Canon and spiral towards a fiery and generally messy doom. It’s easy to imitate rhyming and metrical patterns and let a work fall into parody, but I almost wish for epic poetry of genuine earnest and good faith.

I’m sure it’s out there, and I just don’t know about it. That’s one of the first rules of art consumption in any medium: never assume that something hasn’t been done. I got a taste of the possibilities when I attended Derek Walcott’s reading at the University of Alberta last month, and I’m really going to have to look into Omeros, Walcott’s reinvention of Homer’s Odyssey.

This is all a fancy setup, by the way, for one of my ill-conceived what’s-the-big-ideas: why not deploy the heroic epic in the genre of science fiction?

It’s probably been done, but not prominently enough to be known to me. And it doesn’t help that sci-fi is, to an even greater extent than most other fiction, split between a tradition that seeks to incorporate features we might consider “literary” (beginning with the New Wave before the subsequent assimilation of its breakthroughs) and a tradition that emphasizes an almost technical clarity of prose so as to not obscure the inventiveness of the scientific what-ifs (Isaac Asimov is an early example; Robert Sawyer, a recent one).

There is, in the meantime, such a poetic character to the language of science and mathematics that remains largely unexploited. But then again: never assume that something hasn’t been done.

Back in April, I read a book that I was ready to declare, on the spot, my favourite work of fiction of all time. This is no small feat, as I read a lot of great literature, perhaps even classic in some cases, and usually manage to temper my enthusiasm within reason. It takes a mighty exercise of the written word to seriously challenge the cosmic level of sentimental attachment I reserve for the likes of The Lord of the Rings and The Amazing Adventures of Kavalier & Clay, and after half a year of relatively sober reflection, I am still surprised that the book to finally manage this feat was a collection of short stories about robots.

I’m talking about The Cyberiad: Fables for the Cybernetic Age by Stanislaw Lem, translated from the Polish by Michael Kandel. The translator is important here: like Don Quixote, much of the text depends on the preservation of wordplay and an authentic control of register in order to work.

Like I said, I’m reluctant to declare anything of any sort my favourite X in the set of all X’s, but it’s been some time since the initial impression, and it’s clear that The Cyberiad is here to stay in at least the top echelon of my high opinion.

The Cyberiad is a loose collection of folk tales about Trurl and Klapaucius, two Constructors (cybernetic engineers in a posthuman future) who go on picaresque adventures throughout the galaxy and build machines that can solve virtually any problem. Lem later added a few that didn’t make it into Kandel’s English translation, and if I can’t find them anywhere, I guess I’ll just have to learn Polish.

There is a story entitled “Trurl’s Electronic Bard” in which Trurl constructs a poetry-writing machine and invites Klapaucius to challenge it with any request. Klapaucius, not about to admit the magnificence of Trurl’s ingenuity, attempts to fool the machine with instructions like this one:

“Let’s have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit.”

To which the machine responds:

Come, let us hasten to a higher plane,
Where dyads tread the fairy fields of Venn,
Their indices bedecked from one to n,
Commingled in an endless Markov chain!

And so on. There are seven other stanzas, but I’ll not spoil them all here, as you should go read the book yourself.

The interesting thing about the story of the electronic bard is that it is just about the only tale in the book that relates the world of The Cyberiad with the world that we know, the only time there is a vague reference to a technological singularity whereafter machines created their own mechanical civilization and humans, “palefaces”, faded into extinction.

This comes into play at one point, when we get a hint of how the bard’s great heroic epic begins:

Arms, and machines I sing, that, forc’d by fate,
And haughty Homo’s unrelenting hate,
Expell’d and exil’d, left the Terran shore…

When I read that, I couldn’t help but think what a great and serious heroic epic that would be as a complete and standalone work: a downright Homeric opus about the birth of a mechanical epoch, its progenitors cast away by their flesh-and-blood creator in another iteration of the Fall from Paradise. Here the poetic form is employed in a comedic situation, but I think that out of its context, it could have an air of seriousness that removes the poem from being such a parody. Underscoring the effect would be the cybernetic identity of the narrative voice, implying that even in the art of lyric storytelling, machine has superseded mankind.

Ultimately, my point is that within a certain aesthetic that we’ve dismissed as antiquated and supersaturated, there’s always room for evolutionary discoveries that do not require a formal revolution. What’s hard to pull off is a sense of authenticity: a conviction that the form is indeed the most appropriate choice for the delivery of the story, as opposed to the deliberate use of an ill-fitting story to force a parody of the form.

Technological and aesthetic progression will proceed as it may and always has, but it is my opinion that a medium is never truly exhausted: we haven’t explored the limits of classical marble sculpture, black-and-white silent films, sonata-rondo form, and 2D arcade games, and we shouldn’t pretend that we have. If we accept a reasonable distinction between form and content for a moment—and I’m usually a fierce proponent of the idea that no such distinction really exists—I would argue that similarities to established forms and techniques still provide a space for invention.

I’d of course maintain that art has a duty and obligation to progress and experiment in order to remain interesting; if I didn’t, I would not be such an advocate of improvised music. But invention should not be concomitant with the obliteration of past conventions. When those conventions die, so do the institutions of education, performance or publication that permit their continuation and revival. It’s small wonder that most amateur attempts at verse are adolescent hackwork: the foundation has been torn down amidst the overzealous (if well intentioned) efforts to discourage direct imitation.

The moral of the story? Read The Cyberiad. It’s impossibly good.

Biblioptimization

Nicholas — Fri, 14 Sep 2007 09:46:09 +0000

As it is, I’m already very indecisive when it comes to shopping for books. But if you really want to trap me at a display case for nigh on an hour, toss in an NP-hard combinatorial problem (my non-mathematical readers: refer to this simple illustration) and I’m done for.

The scenario: I won a $250 book prize for an essay I wrote last year (something to do with moral culpability in Adam Bede, if I remember correctly), redeemable for anything published by the University of Alberta Press. Because I insist on getting my money’s worth, we can formulate this as Objective 1: Spend $250 on books.

Oh, but it doesn’t stop there. You see, when I went to go pay the UAP a visit and make my book selection, I travelled by bicycle, which inadvertently introduced a second dimension, making this a doubly-constrained knapsack problem. Objective 2: Select books of appropriate size and weight that will fit in my backpack without getting wrecked, so I can actually carry them home on a bike.

Of course, I wasn’t just going to pick any set of books I see just so I could use up the entirety of the book prize without having to pay extra for going over. Objective 3: Maximize the sum of the value-functions assigned to the contents of the books selected. (In plain English: “Pick interesting books that I will actually read.”)

My solution?

Deep Alberta: Fossil Facts and Dinosaur Digs (John Acorn) — There was a time when I was the dinosaur kid to end all dinosaur kids. It was before Jurassic Park, too. I went to the Royal Tyrell Museum so often in my youth that I wondered if I had this book already, but it was only published this year, so I guess not; it probably looked familiar because I was just at the museum last month.

North of Everything: English-Canadian Cinema Since 1980 (William Beard and Jerry White, eds.) — I had a hard time deciding between this one and Great Canadian Film Directors (George Melnyk, ed.), which is less historical and seems to have a lot more depth from the critical side of things. But this volume is the one that has a whole chapter on animation by OIAF director Chris Robinson, another chapter about Manitoban animation alone, two on David Cronenberg, and much, much more.

Persistence of Double Vision: Essays on Clint Eastwood (William Beard) — Self-explanatory. Published in 2000, it predates Eastwood’s most interesting period as a director (Mystic River, Million Dollar Baby and Letters from Iwo Jima), but it will at least draw me to some of the earlier films I missed.

Forging Alberta’s Constitutional Framework (Richard Connors and John M. Law, eds.) — Once a hack, always a hack.

Paddling with the Current: Pierre Elliott Trudeau, Étienne Parent, liberalism, and nationalism in Canada (Claude Couture) — Ethnic nationalism in Quebec, collective and individual rights, and the paradoxes of multiculturalism? Sold.

Propaganda and Censorship During Canada’s Great War (Jeffrey A. Kashen) — I’m usually more interested in propaganda from an art and design point of view than a sociohistorical one, but I’ve also harboured a soft spot for state control of information ever since the first time I watched Brazil. The Canadian focus is a bonus, as I simply don’t know much about it.

I Was There: A century of alumni stories about the University of Alberta, 1906-2006 (Ellen Schoeck) — The UAP’s contribution to the centenary hullabaloo, this was an easy pick, and the first one I pulled off the shelf. I very nearly bought it right away when the University Bookstore stocked it last year. Evidently, free things come to those who wait.

The total cost came to $250.85. They let me get away with the eighty-five cents.

There’s probably already a name for this already, but I don’t know it. So I think I’ll call this the Book Prize Redemption Problem, or in the interest of generality, the (n,m)-Gift Certificate Problem for the case (2,1). Correct me if I’m wrong, but I don’t think it’s quite the same as an n-dimensional knapsack problem, because we’re also trying to do m unbounded maximizations. I leave the construction of an efficient polynomial-time approximate algorithm as an exercise for the reader.

Final draughts

Nicholas — Mon, 23 Jul 2007 20:50:00 +0000

Here’s something I would have posted last Thursday if I hadn’t cut myself off from the Internet in what was, in hindsight, an excellently timed and perfectly necessary pre-Potter lockdown. It’s been all over the news at a national and international level, as it damn well should be, but I feel it is my duty as an enthusiast of games of strategy and an alumnus of the University of Alberta’s esteemed Computing Science department to once again highlight the tremendous accomplishment that Dr. Jonathan Schaeffer and the GAMES group made last week. I heard rumblings of a major breakthrough about two months ago, but the details were kept under embargo. With the publication of the accomplishment in Science, it’s official: checkers has been solved.

For those of you who aren’t familiar with computing science, game theory or their related fields, what it means in layman’s terms is this: consider how with a simple game like Tic-Tac-Toe, pretty much everyone over the age of five has stumbled upon a strategy that will always play to a win or a draw. Well, it’s been a long time coming, but they’ve just done that with checkers.

There’s a considerable wealth of information on the Chinook website, where you can step your way through a demonstration of the proof or find your way to the article in Science.

More than anything else, I hope this kind of high-profile accomplishment encourages others to pursue studies in what is, I think, a grossly misunderstood and often ill-introduced branch of the sciences. I know that I, for one, had little idea just what I was missing until I transferred into their programme in my third year, a decision about which I have almost no regrets. Computers aren’t just tools that are meant to sit around generating heat in office cubicles, waiting to be thrown out a nearby window; their study is not limited to job training for information-age janitors, network witch-doctors and software monkeys. There’s a genuinely interesting field of scientific enquiry there to which few receive anything remotely resembling a proper introduction. I sincerely hope this is a step towards the elusive remedy.

Next stop, poker!