The Stack and the Spell

I learned how to think in a card game, and I've never been comfortable admitting that at dinner.

From about 1996 to 2000 I played an absurd amount of Magic: The Gathering. Kitchen tables. A shoebox of sleeved cards sorted by colour with dividers cut out of a cereal box. Somebody's basement that smelled the way basements smell. The back of a school bus, which is a terrible surface for a card game and we did it anyway.

Whether I was any good is beside the point, and honestly it depended on the week. I was absorbed in a way I've only managed a handful of times since, and I wasn't memorising a game. I was installing a filing system, and I've been hanging things on it for twenty-five years.

Richard Garfield wrote his doctorate on combinatorial mathematics before he designed it, and that shows everywhere once you know to look. What shipped in 1993 wasn't really a set of rules. It was a small legal system that happened to have dragons on it.

It has a type system. Instants, sorceries, enchantments, artifacts, creatures, lands. Each type carries its own law about when you may play it and how long it sticks around.

And an aura, the thing that attaches to another card, isn't its own type at all. It's a subtype of enchantment (Wizards of the Coast, 2026). I got that wrong for about fifteen years, which is going to matter later.

It also has an execution model, and this is the one that gets me. When you cast something it doesn't simply happen. It goes on the stack. Other people get a window to respond. Their responses go on top and resolve before yours, so the last thing said is the first to happen.

There's a whole automatic housekeeping pass that fires between actions and quietly kills anything that should not still be alive. There's a layering system that decides what order continuous effects apply in, settled by timestamp, and by dependency when timestamps aren't enough (Wizards of the Coast, 2026).

A call stack. Interrupts. A type system with subtyping. A garbage collector. A dependency-ordered resolution algorithm. I met every one of those in a game about wizards years before any computer science class introduced them. I was a kid arguing about them across somebody's kitchen table, years before I knew any of them had names.

And it goes further than a cute coincidence, which I didn't learn until my thirties. The rules are formally deep enough that you can build a legal board position that runs an arbitrary computer program, with every move forced, so that working out who wins the game is undecidable (Churchill, Biderman & Herrick, 2019). Playing perfectly in the general case is harder than merely undecidable: optimal play is non-arithmetic, which puts it outside the whole hierarchy the halting problem sits inside (Biderman, 2020).

That concerns a deliberately constructed board that nobody would ever arrive at by playing. No real game between two teenagers is undecidable, and I've watched people misuse this fact to sound impressive. What it does mean is narrower and stranger: a thing sold next to the batteries at a drugstore has a rule system deep enough to be undecidable. Almost nothing made for children is.

Then I started programming, and a mapping built itself without my deciding to. It was simply there.

A variable that lives for the whole program is an enchantment. It sits on the table, it keeps affecting things, and it stays until something removes it on purpose. A variable that hangs off another object is an aura. It's attached to something else, it dies the moment that thing does, and it goes to the graveyard alongside. Something that runs once at its proper moment and is finished is a sorcery. And something that fires out of turn, cutting in front of whatever was happening, is an instant.

That mapping carried me through an enormous amount of early learning. It's also wrong.

In actual computer science, scope and lifetime are two separate axes that vary independently. Scope is where in the text a name is visible. Lifetime is how long the storage exists. You can have a tiny scope and a whole-program lifetime at the same time, and my mapping can't represent that at all. And an instant isn't a scope thing in the first place. It's much closer to an interrupt.

So my beautiful system gets the shape right and the axes wrong. It was still enormously useful, and I don't think I'd have learned as fast without it. There's a reason, and it isn't that I'm clever.

When you map one domain onto another, what crosses over isn't the objects. Gentner calls it structure-mapping: the cargo is the system of relations between them (Gentner, 1983). My mapping was wrong about what an aura is and right about the only relation that mattered: one thing's existence depends on another's, and it dies when that other does.

That relation was the cargo. The wizards were the packaging.

There's a second condition, and it's the one that usually kills this whole idea. It isn't enough to have the structure. You have to find it at the moment you need it, and that's where almost everybody fails. In the classic experiments, ten percent solved the problem cold. Thirty percent solved it after reading a story that contained the answer. Seventy-five percent solved it when somebody added the single remark that the story was relevant (Gick & Holyoak, 1980). The middle group had the answer in their heads five minutes earlier and couldn't get to it.

That result is usually presented as depressing, and for the grand claims it is. Learning something in one place rarely helps you somewhere far away, and the question stays badly formed until you specify which kind of distance you mean (Barnett & Ceci, 2002).

But flip it over and it describes my exact situation. I never had to spontaneously retrieve anything. I had a source domain I had chunked to death over four years, and I was consciously, deliberately reaching for it.

That is analogy with the hint already supplied, which is the one condition where it reliably works. So the honest version of my thesis isn't "a card game taught me programming." That's a fun sentence and it's false.

It's: I showed up carrying a dense, well-organised source domain, and I used it on purpose. Much smaller claim. Also the one I can defend.

I use ideas constantly that I couldn't derive, that would collapse under a whiteboard, and that in a couple of cases I'd define wrongly if you woke me and asked. Entropy. Convolution. Eigenvector. Emergence. I know where each one sits. What kind of problem it answers to. What it neighbours. I couldn't tell you how most of them actually work. For a long time I thought this was a private fraud that I'd eventually be caught at.

It isn't, and there's a precise result about it. Ask people to rate how well they understand a zipper, or a flush toilet, or a helicopter. They rate themselves confidently. Then ask them to produce the explanation out loud, in order, all the way through.

The rating collapses, and the effect has a name: the illusion of explanatory depth. It shows up specifically for explanations rather than for facts or procedures or stories (Rozenblit & Keil, 2002). Almost everybody does this. The unusual thing isn't the gap. It's noticing you have one.

The reason we all survive this is that knowledge was never really stored in individual heads. We live inside a community that knows things, and we habitually mistake its knowledge for our own. That isn't purely a bug. There's a serious argument that the reach of your mind includes the notebook and the tool and the reference you always use (Clark & Chalmers, 1998), and the sturdy empirical core underneath all of it is simply that people hand thinking to the world whenever it is more reliable than they are, which is most of the time (Risko & Gilbert, 2016).

Underneath that sits an older distinction. Knowing how to do something is not a species of knowledge about it (Ryle, 1949). I can ride a bicycle. My explanation of why I don't fall over is wrong, and I've watched a physicist confirm that.

So my working position now is this. Using an idea well and understanding it are two separate achievements, and the actual error is confusing them. I don't need to derive a compiler to write a program, any more than lunch requires me to understand a liver. What I need is to know which of the two I'm doing at any given moment, and to say so out loud when the difference matters. The failure mode isn't shallow knowledge. It's shallow knowledge that has forgotten as much, walking confidently into a room where depth was the whole job.

Feynman left a line on his blackboard when he died. What I cannot create, I do not understand. Everybody quotes it. The line directly underneath, which nobody quotes, told him to know how to solve every problem that has already been solved (Caltech Archives, 1988). Even the patron saint of understanding-things-from-scratch kept a lookup table.

The evidence stops here. What follows is a picture I keep coming back to, and it isn't an argument. The names below are company, not support.

If you were something with no limits, and you could simulate anything you could conceive of, you would eventually run out of conceiving. Everything imagined, all of it staged, every arrangement run twice. When you can produce any experience on demand, none of them is news anymore.

The only move left is to divide yourself. Send out fragments that carry your nature but not your memory, so that whatever they meet is genuinely met. Then take it back when they come home. Not creation exactly. More like a way of getting outside your own knowing. I hold it loosely.

What surprised me is how much company the picture turned out to have, and its age.

In Plotinus, everything proceeds from the One by emanation, and there's a specific condition attached that I find genuinely remarkable: the source isn't diminished by what pours out of it (Kalligas, 2024). In Advaita Vedanta the individual self isn't similar to the ground of everything, it's numerically the same thing, temporarily under a misapprehension (Dalal, 2021). In Lurianic Kabbalah the divine contracts to make room for something other than itself, and then the vessels holding the light break, and the sparks scatter into the world (Scholem, 1941).

None of those people could have read each other. Two thousand years and no common language, arriving at the same shape.

That isn't evidence. It might mean the shape is true. It might mean something about the kind of mind that finds it attractive, which includes mine.

The nearest modern relative gets misquoted more than almost anything in philosophy. Bostrom didn't argue that we are in a simulation. He argued that at least one of three propositions must hold, and ours being simulated is only one branch (Bostrom, 2003). It's a trilemma. People remember the exciting third.

There's one piece of all this I could actually go and check, and I did, because I've been saying it out loud for years and it deserved to be tested. My claim has been that the inner world is bigger than the outer one. That the reach from a person down to the smallest thing we can talk about exceeds the distance out to the largest. It's true.

The Planck length is about 1.616 times ten to the minus thirty-five metres (NIST / CODATA 2022, 2024). A person is about 1.7 metres tall. The edge of the observable universe sits near 4.4 times ten to the twenty-sixth (Planck Collaboration, 2020).

Counting in powers of ten from where we stand: about thirty-five orders of magnitude down, and about twenty-six up. There's more room beneath us than above us, and it isn't close. The gap between the two is itself a factor of a few hundred million.

One guardrail. The Planck length isn't the floor of reality. It's where our current theories stop being trustworthy, which is a fact about them and not about the world. "The smallest length we can coherently talk about" is defensible. "The smallest thing there is" isn't. The count stands either way. And when I first read those numbers, in my twenties, I didn't feel astonished. I felt the thing you feel when a proof confirms something you had already assumed without permission.

So. I have a card game from 1993 sitting underneath a large portion of how I think. I didn't choose it. I couldn't remove it now if I wanted to.

The pieces I'm most confident about are the smallest ones. Analogy carries relations, not things. Finding the analogy is harder than having it, which means the real value of a rich source domain is that it's already indexed. Most people don't understand what they use, and the only actual sin is forgetting that. And there's a very great deal of room underneath us.

The rest of it, the splinters and the holodeck and the sparks in the broken vessels, I hold the way I held the aura mapping. Wrong in its particulars, almost certainly. Right about some relation I haven't managed to name properly yet, possibly. That is how I've used everything my whole life, and it hasn't failed me yet. I'm aware that isn't the same as being correct.