The End of Chance
Swordless and without a living adversary, I imagine Cirzpisława’s students saying in their best imitation of the master, “Untrue? Perrrrhaps. Not a trrrrifle. Okay, okay! But LOGICALLY necesarrrrry.”
“Oh hell, Donald,” was the last thing Cirzpisława Wolny, then 103 years old, said to me and perhaps the last thing he said to anyone before he died. Cirzpisława was the most promising student of Jan Łukasiewicz and the kind of mind given an office and students in the Other Institute of Princeton University,1 the shadow IAS adjacent to Dr. Ramsey Glutherfeld’s “men in basements”. Cirzpisława worked on the fringes of many-valued and modal logic and hated me because he (wrongly!2) thought I broke the heart of his granddaughter, Magdalena.
Do you know many-valued logic? Lord Dunsany is said to have said, “Logic, like whiskey, loses its beneficial effect when taken in too large quantities.” The many-valued logic studied by Cirzpisława is like the rare case of whiskey taken in such quantities that it causes levitation rather than liver failure. Simply put, many-valued logic does not exclude the middle. In the case of what I call the Wolny System,3 the unexcluded middle is populated by a frightening number of logical categories, which interact and reproduce with one another and are expressed in a notation system borrowed from Ge’ez (for an example of that holy language, see below) that has only a distant (metaphorical? satirical?) relationship to the ⊃, ≡, ⊻, ⟣, and ∄ we’re all familiar with.
The central and eventually only problem Cirzpisława and his students concerned themselves with was the “impossibility”4 of “random chance.” Their research consisted of playing long games of Yahtzee. Half the students would play while Cirzpisława and the remaining students wrote and analyzed each game action in the Wolny System notation. They were convinced of the “impossibility” of “random chance” after the first fifteen years, but intellectual probity, exemplified more by Cirzpisława than anyone since Gottlob Frege, forced him to check the research again and again for decades after. The collected Yahtzee analyses grew to some 40,000 pages, now held in a closed collection at the Seeley G. Mudd Manuscript Library.
I met Cirzpisława when I answered an ad in the newspaper for “a perspicacious young man to help an aged logician with his memoirs.” When I arrived at his small Princeton apartment—tidy and spare but not minimalist, with reproductions of Balthus’ landscapes on the east wall and an Olivetti Diaspron 82 Amharic-language manual typewriter on the desk—he ushered me to the couch, and we stared at each other in silence for a good while. He broke the silence thus: “When you’ve analyzed as many Yahtzee games as I have, you know how to look at a man.” Then he handed me a box full of notecards, each filled front and back with small, elegant handwriting. “Make sense of these. Be here in one week with a plan. Good day.” He moved me out of the apartment before I said a word.
The notecards recounted his life and elucidated the Wolny System, but the more I read the more the account of his life and the account of his System blended together or changed places. Some of the pages were filled with Ge’ez letters and modern logical notation: መሠ⊬ሐ⊼ተኀ⟛ሀለ⟢ሐ⥽ሰነ:⇔ረ⊃ቀበ. For reasons of honor and loyalty5 I cannot record here the contents of his memoirs.
After his death Cirzpisława’s students split into three opposing camps. The first we’ll call “The Traditionalists.” They continue with the same Yahtzee games and analysis on the same schedule in the same room. The second, “Practical Wolnians,” want to expand the research to include other games of “chance.” The third also call themselves “Practical Wolnians” and spurn laboratory experiments in favor of using the Wolny System to win card games and lotteries, which they do, frequently.
Don’t bother looking it up. It is real, but like anything interesting, you can only read about it here.
Please reassure my wife that I have never met Magdalena Ogórek, and, in any case, I doubt Magdalena is Cirzpisława’s granddaughter. A broken heart is no trifle, nor the accusation of heart breaking. Every night men draw swords over such accusations, and so would I, had I a sword and were Cirzpisława alive. Swordless and without a living adversary, I imagine Cirzpisława’s students saying in their best imitation of the master, “Untrue? Perrrrhaps. Not a trrrrifle. Okay, okay! But LOGICALLY necesarrrrry.”
A name rejected by Cirzpisława, I admit, but he offered no alternative!
“Impossibility” and “random chance” are not meaningful (full? complete?) terms in the Wolny System, but it’s the closest plain language equivalent I can think of.
But not to him!