Episode 3 — It's Just Subtraction

Toye Oyelese

Welcome back. This is the episode people brace themselves for — the one with the formula in it. Take a breath. I'm going to walk you through it slowly, one piece at a time, and I think you'll be surprised how gentle it turns out to be. Here it is, in words. A-star equals arg-max over A of — open bracket — the probability of the good thing given your action, minus, in square brackets, the probability of fixable damage plus w times the probability of permanent damage — and w is greater than one. Now don't hold onto that. Let me translate it, every symbol, one at a time. A-star — that just means "the option you should pick." Arg-max over A — "look at all your options, score each one, and take the highest." That's all that grand-looking bit of notation is asking you to do. P of D given A — "the chance of the good thing, if you do this." That little bar in the middle just means "if you do." P of U-r given A — "the chance of fixable damage, if you do this." P of U-i-r given A — "the chance of permanent damage, if you do this." w — "how much extra permanent damage counts." And w greater than one — "and it always counts extra." So read it back in plain English: score each option — the chance of the good thing, minus the chance of fixable damage, plus the extra-weighted chance of permanent damage. Pick the highest score. That's the whole formula. It's subtraction, with one thing multiplied. That's it. Let's watch it work, using the original's own example. Say you're weighing some action, and you reckon: the chance it goes well is nought-point-eight — eighty percent. The chance of fixable damage, nought-point-one — ten percent. The chance of permanent damage, nought-point-nought-five — five percent. And you've set w equal to two, so permanent damage counts double. The penalty is nought-point-one, plus two times nought-point-nought-five. That's nought-point-one plus nought-point-one — nought-point-two. And the score is nought-point-eight minus nought-point-two — which is nought-point-six. Positive. So you'd take it, unless something else scored higher. Now look at what just happened, because it's the whole point of the design. The permanent harm was only a five percent chance — half the size of the fixable one. But after doubling, it contributed exactly as much penalty as the fixable harm did at ten percent. It punched above its weight. That's w, doing its job. And crank w up, and it gets dramatic. At w equals ten, that same five percent chance of permanent harm costs you nought-point-five — it would swallow most of your nought-point-eight benefit all on its own. As the original says plainly: as w gets bigger, even a small chance of permanent harm can come to dominate the decision. Which is exactly right. Small chances of unrecoverable things should dominate. That's not timidity. That is how anyone sane crosses a road. And now the most important thing I'll say in this episode. You will never have those numbers. Nobody walks around knowing there's a five percent chance of permanent harm. Real life does not hand you decimals. And that is perfectly fine — it isn't a flaw, and it isn't something to apologise for. The original says so directly: it does not claim formal probabilistic precision; its language is intentionally simplified to discipline reasoning, rather than to compute optimal solutions. So what is the formula for, if you can't compute it? It's for forcing the question. The value was never in the number that comes out. It's in what you have to do to get there. You have to stop, and ask: what's the permanent one, here? That question — that is the product. Most bad decisions in a life aren't made because someone did the arithmetic wrong. They're made because nobody ever separated out the box that couldn't be undone. It sat there, blended into everything else, invisible — cancelled out by a story about how the upside was huge. The formula is simply a machine for making you look in box three. Whether you can put a number in it barely matters. One more thing before we finish, about that w. It's a dial. Turn it up, and you get more cautious about permanent things. Turn it down toward one, and permanent harm counts the same as fixable harm — and the whole safety mechanism quietly switches off. So the framework insists: w greater than one. Always more than one. Permanent always counts extra. And then it does something I want you to notice, because it's rare. It asks a question it doesn't answer. Is w a fixed number? Or does it change, depending on what kind of permanent we're talking about? Because "permanent" isn't one thing, is it. Permanent loss of money; permanent damage to who you are; permanent damage to a relationship — are those the same weight? Should they be? The original raises this, and it leaves it open — it calls it the edge where this becomes dynamic, rather than rigid. It isn't answered. It's marked. And I rather respect that, because it would have been so easy to fill in a number and sound complete. Next time, we step back from the arithmetic and ask a deeper question — why permanent harm gets to come first at all. The answer is not the one you'd expect. See you there.