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.

How well I played depended on the week. I was absorbed in a way I've only managed a handful of times since, and the rules became familiar enough that I kept using them to think about other things for the next twenty-five years.

Richard Garfield wrote his doctorate on combinatorial mathematics before he designed it, and that shows everywhere once you know to look. The game that shipped in 1993 gave us plenty to argue about when two cards interacted.

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, and the mistake carried into the comparisons I made with programming.

It also has an execution model, which became particularly useful to 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.

In my thirties I learned about a more formal connection to computation. 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).

Those results concern constructed positions and general questions about the rules. They don't describe the difficulty of the ordinary games we played as teenagers. I find the formal result interesting without needing it to explain what I learned at the kitchen table.

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.

The mapping helped me through a great deal of early learning, although I later found distinctions it could not represent.

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.

I don't think I would have learned as quickly without that comparison. Familiar relationships gave me somewhere to begin, even when the details needed correcting.

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.

I already understood what it meant for one thing to depend on another remaining in play.

Recognizing a useful comparison is another difficulty. A person can know an example without thinking to apply it to the problem in front of them. 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.

The difficulty of transferring learning deserves attention. 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).

In my case, I was deliberately reaching for a game I had spent four years learning. I did not have to discover an unfamiliar example and recognize its relevance at the same time.

That resembles the role of a hint in the experiment, although my experience is not a test of the same task. I was drawing on a familiar game as I learned to program.

The card game gave me a set of relationships I knew well. Programming gave me reasons to revise them.

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.

Research on how people judge their own understanding gave me another way to think about that feeling. 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). The exercise reveals a gap people may not notice when simply rating their understanding.

We also rely on knowledge held by other people and in the tools we use. There's a serious argument that the reach of your mind includes the notebook, tool, and reference you routinely consult (Clark & Chalmers, 1998). Research on cognitive offloading examines how people use external resources to reduce a task's demands (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.

I try to distinguish knowing how to use an idea from being able to explain it. 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. If the task requires a derivation, I need to produce it or ask someone who can.

Feynman left a line on his blackboard when he died. What I cannot create, I do not understand. Another line on the board told him to know how to solve every problem that has already been solved (Caltech Archives, 1988). I like finding both instructions there together.

There is also a speculative picture I keep returning to. The traditions that remind me of it don't establish that it is true.

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.

In the version I imagine, you 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).

These traditions differ substantially. The resemblance I notice is my own comparison, and does not establish a shared account of what the world is.

I don't know whether that resemblance says more about the ideas or about what attracts me to them.

Bostrom's simulation argument gives me another comparison to consider. He 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). That distinction limits what I can take from it.

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.

The lower endpoint needs a qualification. 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.

What I can describe most confidently is how I used the game while learning. I knew its relationships well enough to reach for them, and they helped me begin. Some comparisons held up. Others needed to change as I understood the new subject better.

I still enjoy the speculative part, including the holodeck and the sparks in the broken vessels. I don't have to settle it to keep thinking about it. The card game remains part of how I approach a new idea, even when I eventually have to leave the comparison behind.