___________________________________ WHY ARE LOGIC PUZZLES SO FASCIST? Dylan Holmes ___________________________________ 2021/Nov/2 You might've heard the one that goes like this: One day, a warden lines up one hundred prisoners in a single-file line and says, "I'll put a black or white hat on each of you. Then I'll start at the back of the line and ask each person to guess, using only logical inference, what color hat is on their own head. You can reply only with 'black' or 'white', nothing else. If you're right, you'll be freed from prison. If you're wrong, I'll shoot you right there---and everyone else in the line will know it." Now, prisoners in line can see only the people in front of them. If the prisoners are all perfect logical reasoners and are allowed to decide on a strategy before the game begins, what strategy should they use to save as many people as possible? What an inexcusable way to treat human beings, right? But I'm getting ahead of myself. This is a logic puzzle about prisoners. If you go looking, you'll find that a lot of very different logic puzzles take place in prisons: for example, the one about the hundred prisoners and a solitary room with a light bulb (), or the one about the hundred prisoners and a cabinet full of numbered slips (). Why do prisons crop up so often? Is it just coincidence? A cultural trope? Or is there a reason why the prison setting is an especially good fit for logical thinking? 1 Logic: sparse, abstract communication ======================================= The prisoner puzzles I know are all great fun---as logic puzzles. But they're monstrous if you think even a little about the world they describe: some tyrant playing life-or-death games with powerless people. Now, you can spoil the fun right away if you take logic puzzles seriously like that. You're really not supposed to, the same way you're not supposed to get too unorthodox in your answers, e.g. having the guards rebel against the warden or communicate surreptitiously by stomping their feet (This is the principle of circumscription, as defined by John McCarthy. ). The prison setting is just supposed to be a quick way to deliver the hard-and-fast logical structure of the problem. Maybe that's the answer: Every logic puzzle needs /some/ kind of setting for the story, and sometimes the setting is a prison. Maybe there's no deeper connection beyond that; after all, you could easily swap out the prison setting and still keep the same structure. Actually, I think it's more interesting than that! A logic puzzle needs a setting that communicates and explains what the rules of the world are. And logical worlds are, by nature, rigid and sparse: you've got a small number of available moves and a small number of important details, they're all enumerated in advance, and everything else is irrelevant, predetermined, or unquestionable. (Then the fun of a logic puzzle is finding a winning solution within this constrained form.) Note that a tyrannical prison is /especially/ suitable for setting up this kind of limited, logical world: - Why would anyone act in such a bizarre contrived way? You must or you die. An absolute authority wills the world to be this way. - What can I do? Only these allowed things. No further creativity is tolerated or even intelligible. - How could you treat people like this? That's not important. - Who am I? You are defined by your role in this problem; no other features matter. You are interchangeable with anyone else in the same role. - How do I act? Only according to the perfect logic of the situation. Individuality has nothing to do with it. The prison paradigm has exactly the features that help create a rigid, logical universe: the rules of the prison can be absolutely dictated by the warden (who is presumed to be unaccountable to anyone else), and the prisoners supply an interchangeable class of subjects whose inner lives and histories play no role. In fact, conversely, I'd argue that authoritarians love to develop systems which are orderly and simplistic in a way that suits logic puzzles. Wouldn't it be wonderful to make our messy world a little more rational and predictable? To reduce existence to a small number of dependable, meaningful, measureable variables so you could neglect the rest? Wouldn't it be wonderful if you could abstract away from individual circumstances, interacting with people only through their particular role in the system---medical patient, criminal defendant, student, consumer, prisoner, police officer, service clerk? Such systems are easy to build, inspect, and control from above, using a well-delimited set of levers. As we've seen, they are the prisons---and also the Amazon warehouses, the regimented hospitals, the retail stores, the compulsory schools. Such spaces are (at least in theory) sparse, cleanly defined, quantified, wholly knowable---a perfect image of high modernism. () Just imagine how easily I could have said: - One day, a warden decides to line up 100 prisoners... - One day, an Amazon supervisor lines up 100 warehouse workers... - One day, a principal lines up 100 students in assembly... - One day, a monarch lines up the 100 wisest advisors in the court... 2 The shackles of imagination ============================= In short, it's not just set dressing. Many logic puzzles are about prisons because prisons help evoke the key features of an artificially sparse and de-personalized world. To name them: 1. ABSOLUTE AUTHORITY. Know that our world, which is ordinarily so messy and inventive and idiosyncratic, has come to be defined by a small set of ironclad rules. The premises of this world cannot be questioned; that would unmake the game. 2. IMPERSONAL ABSTRACTION. Know that no details matter besides the ones you've been told. Props play their roles perfectly---no defects, no individual differences, no complicating history or pathos or interiority. In particular, people are dutifully rational---you can trust that even the capricious warden will act as promised. 3. RESTRICTED EXPECTATION. Know that you've been told everything you need in order to understand the world. There are no unnatural, spontaneous, unaccounted for events. The world is under perfect control; do not imagine anything else. This last feature about restricted expectations and possibilities deserves special emphasis. As I noted earlier, with logic puzzles, you're supposed to play along: the game comes from /humoring/ the rules. You won't get any points for treating it like a lateral thinking puzzle, bending the rules or introducing your own concepts (what if the prisoners rush the warden all at once? what if some of the /guards/ do? what if the gun misfires? what if the warden decides to shoot a few people even if they guessed correctly? what if the pattern of hat-colors spells out a predictable message? what if an attorney arrives and shuts down the entire corrupt prison?) Authoritarian regimes set similar limits on the possibilities---"Shut down your imagination and think within the framework of this universe." You've seen it in a small scale if you've ever had trouble filling out a form because none of the options seemed quite right---rigid expectation doesn't quite mesh with organic reality. Authority figures have the privilege of defining terms and ignoring the inner lives of their subjects (). In their one-size-fits-all unimaginativeness, they tend to prefer we be unimaginative, too. Let's be imaginative anyways. It's a bit whimsical, I know, to ask why logic puzzles are so fascist. But look at where it's led us. The key insight is that logic puzzles are fun for the same reason that fascist systems are governable---they're weirdly uncomplicated; you can easily wrap your head around the whole thing. Obviously, logic puzzles themselves are good clean fun---no real people are harmed, and there's something joyful about a world that follows simple rules. It's an ideal, and we can be curious about what is noble or lovable about that ideal. As we learn more, I wonder how we might develop logic puzzles whose stories don't depend on domination. Think about it: How do you create rigid rules without a dictator? How do you introduce an organizing principle without violent enforcement? Why else might a group of 100 people all wear strange hats and solve a logic puzzle? Gee, I don't know --- maybe they think it's fun. I wonder if we could use logic puzzles to expose the rigid institutions in our lives. Think of a setting for some new logic puzzle--- authoritarianism will be a lightning rod for your attention. A robotic mindset becomes a logic puzzle; a logic puzzle becomes satire. ("Guess whether your gendered hat is pink or blue".) And I wonder, most seriously, if we can use logic puzzles as a benchmark. Imagine making prisons, warehouses, schools, government agencies, hospitals, etc., that are no good whatsoever for logic puzzles because the human element in them is too huge to ignore.