.....The magic logician, he recently passed:
....................The Titleless Poem
.....He lived a long life, but it ended too fast.
.....His writings so many, so few, so clever.
.....This paradox mortal will live forever.
I dedicate the poem above, and the story below, to one of my childhood heros: Raymond Smullyan.
Smith and Jones
by Nack Ballard
A few days ago, I was invited to a posh club that is ironically named the MANLY SLUR. Underneath its banner is a sign stating that ONLY SURLY MADMAN need apply. Finally, a hand-scrawled sign looks like it has been freshly added: Sadly mourn Mr. Merlin, ally. All three have a hidden meaning, or so I heard.
Inside the club, I noticed that next to one of the backgammon tables, two smartly dressed members were just finishing their midday meal.
"Inasmuch as outwith I'd partaken of nowt since afore yestreen," remarked one, "I felt more than a trifle peckish for summat. 'Twas a fit nosh: the sarnies, chips and porridge in this gaff are corking!"
"Likewise for my Yorkshire pudding, rarebit and taters!" exclaimed the other. "Top notch grub."
"Stonking! We lead doddle and cushy lives. Shall we bods forgo the afters and resume, Sir Smith?"
"Capital idea, Dr. Jones! Let us waffle, dither or swither no longer."
The diagram below shows the position on their board. Sir Smith started shaking his dice. I assumed that Dr. Jones would match his motions in a moment, and that they would each roll out one die to begin a new game in the customary manner. However, I noticed an irregularity. Can you spot it?
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"Excuse the interruption, gentlemen," I spoke up in a respectful tone, "but I thought you'd like to know that you have forgotten to re-center the cube."
"Cobblers, my fine fellow!" quipped Jones, shaking his head and grinning broadly. "In point of fact, I possess this smashing cube. A jolly bloater 'tis, by jove, and that's a jammy do for me!"
I was puzzled. "Is Sir Smith spotting you a cube on 16, and does he give you that handicap every game?"
"Good Lord, nay, chap! We put a halt to the bloomin' spots in this establishment yonks ago. Moreover, this doubler isn't actually on 16, per se, but rather that is its stage within a cycle. When the cube reaches 64, we start over at 2 to represent 128, which is the first rung of the second cycle, and if the cube strays high enough we might reach a third cycle, and so forth."
"Cycle?" Clearly, I had not caught on. "Can you please tell me the current level of the cube?"
"Righto," interjected Smith. "While we physically turn the cube each time to honour tradition, it is principally a symbol of ownership. We keep track of the full monty, the genuine magnitude of our risk, with this brill thing-a-ma-jig." He pointed to a sleek little electonic box adjacent to the board. "Each time one of us coaxes the cube higher, we press a button. That causes the number displayed here, which denotes the exponent of 2, to increase by one."
I could see the number 64 clearly displayed. "Ah, that means the cube is actually on 64?"
"Jings, sirrah, you are full of beans and owt but potty or dim, but perhaps I should say a tad flummoxed," mused Smith. He spoke a bit more slowly and loudly, looking at me directly. "The 64 displayed on this ace gadget means that betwixt Dr. Jones and myself, we've raised the cube 64 times and it is therefore on 2 to the power of 64. If and when the cube is twisted again it will be on 2 to the power of 65. The point value of this epic battle is a bomb -- surely into the quintillions by now!"
"Well, I guess it's a good thing you're not playing for money, then!" However, my laugh trailed off into an uncertain chortle when Jones piped in.
"Ah, but we are, mate, though for a dowdy quintillionth of a quid per point. Now, I don't mean to haver or natter, but you'd have been gobsmacked to gander at the blinking, mucked up rules once employed here; a manky chuffer that really took the biscuit -- tosh! Aye, the gormless pillocks and aggro wazzocks may call me a blinkered, naff and shirty geezer... just a daffy, stroppy ol' codger making a kerfuffle over sodall, but that barmy rubbish isn't my cup of tea. Why, they had unlimited treble-hike automatics, and duff, yampy cube escalations during the bout as well, when either die matched that of the previous roll. Balmy and dotty as you please -- not batting on a full wicket, zounds! Lost the plot, daft as a bush, and mad as a bag of ferrets, those nutters... I dare say bloody bonkers, 'round the bend and off their trolley, cor blimey!"
I could sense that, any moment now, Jones would make his point. "To scupper the tommyrot and sort this shambolic niggle, albeit as a bodge job amongst gents, we decreed ickle wagers, in order that even the dodgier, shonkier gannets could fancy a flutter and still have enough brass for the whip round. Granted, this wintry one-off caused a higgledy piggledy, with a whinging wobbler from the cheesed off, narked and miffed cafflers. Nonetheless, titchy, wee-lolly stakes remain in place to this day, notwithstanding our samey reversion back to the most conservative, standard set of backgammon rules."
"Conservative?" I gasped. "How does a cube get into the quintillions before you've even started the game, unless you've got some very loose allowances about automatic doubles, or something like that?"
"We no longer sport automatics and such, not even those cheeky beavers. And why conjecture the game hasn't started, lad? Shash and balderdash. Our luncheon respite was merely an interlude! We've rolled 57 times apiece, and Sir Smith..." Jones gestured politely to his opponent, "...is soon to impart his 58th."
"By the by," Jones added, "Our gallus friends General Brown and Admiral White have been top banana, simply cracking! They arrived in a colossal lorry before brekkie to record our meet, and performed keenly stout XG rollouts on a dozen rapid terminals the entire forenoon -- 'til chinstrapped and shattered, ripe for a kip. For one, I'm quite chuffed at their unassailable tidings: both Sir Smith and I have conducted the checkers and doubling cube impeccably in this splendid contest, nary a clanger thus far. The expanse of the cube, whilst blinding, is utterly licit: there's been nuffin wonky or loose about its management!"
At that point, I felt that I'd delayed the "resumption" of their esteemed game long enough, and I had other places to be. Besides, with so much to mentally process, I had become bewildered and tongue-tied. In parting, all I could manage in spirit of the occasion was a disjointed, "Ta, blokes," "Pip pip" and "Cheerio!"
Let's recap what we were just told about this amazing game (in progress):
.....(1) Standard money rules were in effect.
.....(2) The checker play and cube action were perfect on both sides.
.....(3) Each player rolled 57 times (counting the opening roll, won by Smith).
.....(4) The cube was turned 64 times (and therefore not turned only 49 times)!
.....(5) The opening position was showing on the board.
Crikey, was I in a madhouse?
Or... Could Smith's and Jones' claims actually be true? If so, HOW?
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