I can recall a time when a referee report arrived for a paper with a coauthor. I’m blurring the details, because the details would identify them. They are strong, and in some quarters have a reputation for being less careful than good. The report had read the reputation before it read the paper. You could see it in the opening paragraph, before the mathematics started: the referee had decided what kind of paper this was going to be and then read it to find out where. They found typos. There were typos. There were a few other things of the sort you’d expect, and the report was right about each of them and wrong about the paper, which was careful where it mattered. We fixed the typos, ran the whole thing through every checker we could find, and polished sections that had never been in question. We answered a claim about my coauthor by treating the paper as if the claim were true.
Here is the other scene. My second problem in graduate school was to construct a counterexample to a certain version of the corona problem. For several weeks I computed, and each week I brought the computations to my advisor, and they weren’t right, weren’t closer, weren’t anything. At some point he said the problem wasn’t working and we should move on. What I remember is trusting that. I’d seen the work and seen it not arrive; he had seen this situation before and I hadn’t. I don’t recall taking it as a verdict on me, and I’ve tried.
Two failures. Weeks of computation that produced nothing is a larger failure than a typo. But only one of them left a mark, and the mark has nothing to do with the size of the failure. The difference was in the explanation, and in who supplied it.
Four different Mondays
The paper was rejected. That sentence can be filed as I’m not good enough, or I rushed the write-up, or that journal is a lottery, or problems in this area don’t get into journals like that. Same event, four different Mondays.
Psychologists have studied how people explain events since the 1950s, under the name attribution theory, and one version, built for success and failure, says those four explanations differ along three axes. Locus: inside me or outside me. Stability: the same next time or not. Controllability: could I have done something. Not good enough is internal, stable, uncontrollable. Rushed is internal, unstable, controllable. Lottery is external and unstable. That area is external and stable. The four textbook cells are ability, effort, task difficulty, and luck.
Each axis does different work afterward. Stability sets expectation: a failure explained by something stable is expected again, and expectation decides whether you try. Locus sets the emotions you direct at yourself; pride and shame attach to internal causes. Controllability sets the emotions other people direct at you: anger at a controllable failure, sympathy for an uncontrollable one, and on your side guilt for the first and something closer to shame for the second.
The one piece of this most people have heard of is the self-serving bias: successes are mine, failures belong to the circumstances. It’s real and large across ages and cultures. For a long time I assumed it was the whole theory. It’s one corner.
Outcomes and process
When I look at how I actually explain things, the self-serving bias is there, but only in one place. Outcomes I file generously. A rejection can be a bad draw, and I’ve seen enough of them to know there’s luck in it. That’s the self-serving direction, and I don’t apologize for it.
Process is different. When I’ve been stuck on a problem for months, I file it under my own failings: not the problem being hard for the known tools, but me not being able enough to do it. That’s the opposite of the self-serving bias. It’s a pattern described as the attributional signature of helplessness: failures explained internally, stably, and globally.
I don’t think this split is peculiar to me, and I think it lands where it does for a reason. Outcomes happen out in the world, with referees and panels and visible randomness, so external explanations are available and plausible. Process happens where you alone can see it. There’s no one else’s failure to compare yours against, and the one agent in view is you. You attribute externally where you can see other actors and internally where you can only see yourself. It’s the actor-observer asymmetry psychologists describe between people, running inside one person, split by whether anyone else is in the frame.
The consequence is uncomfortable. For most of a career, outcomes are a small fraction of the time and process is nearly all of it, so the protective bias runs on the part that matters least and the helpless one on the part that matters most. The split tilts by stage, and a postdoc in a market year will object that outcomes are not a small fraction of anything just now. They’re right; I’ll come back to them.
The empty table
A version of attribution theory is the one a mathematician would have invented. To explain an event rationally you want three pieces of data. Consensus: does this happen to everyone? Distinctiveness: does it happen to me only here, or everywhere? Consistency: does it keep happening? High consensus and high distinctiveness point at the situation. Low consensus, low distinctiveness, and high consistency point at the person. The interesting psychology is what people do when most of the table is empty, which in this profession is always.
Take a student four months into a thesis problem and stuck. The advisor’s table is full. They have consensus data: they’ve watched other students hit this kind of wall, they may remember hitting it themselves, they may know this particular step has stopped better people. They have distinctiveness data, because they’ve seen the student do other things well. So the advisor’s attribution comes out at the level of the task. Not out of kindness, and not out of indifference, though from across the desk the calm can look like either. Out of having the columns filled in.
The student’s table is empty. No consensus, because the field hides struggle; I argued in The Room Is Busier Than You Are that mathematicians are honest about not understanding things in private and almost never in public, and the same goes for being stuck. Thin distinctiveness, because the student has only ever been stuck on the one problem. And high consistency, four months of it. An empty consensus column with high consistency is exactly the configuration that resolves to the person. The student isn’t being neurotic. They’re running the correct inference on the table they were given.
And the advisor’s full table is invisible unless the advisor shows it. That’s what mine did when he said the problem wasn’t working. He wasn’t reassuring me. He was simply supplying the consensus column from a table I didn’t have, and he had the standing to make it stick. You’re doing fine is cheap and gets discounted. I was stuck at this step for a semester is data, and it lets the student run the inference the advisor is already running.
Doom spiral
A fourth axis for attribution exists: global versus specific. I made an error in Lemma 3 is internal and specific. I’m bad at this is internal and global. I shouldn’t be doing this is internal, global, and stable.
I know that spiral. It starts on something small, a computational slip, a wrong sign, and it moves fast: a silly mistake, I’m doing badly, I shouldn’t be here. What’s happening isn’t that the locus changes; you did make the mistake. It’s that the explanation gets wider at each turn, and each turn is a small, plausible generalization of the last, so none of them looks like the moment to stop.
I can usually catch it now, and I used to think that was age. I now think it’s the table. Thirty years of small mistakes that never predicted anything is consistency and distinctiveness data about myself, and I shouldn’t be doing this can be checked against the record and fails the check quickly. At twenty-five the same sentence arrived with no record to check it against, and it had the room to itself. If you’re there now, the one thing worth knowing is that the record accumulates whether or not you do anything about it. The waiting is the hard part, and it’s only waiting.
In the meantime, the question that stops the spiral is a stand-in for the data: what is this one event actually evidence about? A sign error is evidence about a sign. That question is close to the whole content of one of the better-supported interventions in the field. Wilson and Linville told struggling first-year students that their difficulties were unstable, the kind that go away, and grades went up. Growth mindset, which I wrote about in The Gap That Closes is attribute to effort, not ability, with a brand on it.
What it does downstream
A reputation is a stored attribution, and it can only be confirmed. The referee held a prior about my coauthor. The typos confirmed it. The careful parts of the paper didn’t disconfirm it, because, as I argued in Sounding Sure, success is low-information: a correct argument is consistent with careless, but got away with it this time. So any one paper can confirm the reputation or be uninformative about it. There’s no third outcome. Reputations are nearly irreversible by construction, not because anyone is unfair, and the ones confirmed once a paper at the level of a typo, while the global claim they carry stays wrong, are the most permanent kind.
Scrutiny manufactures evidence. I have coauthors whose sections I check more carefully than others’, especially in the places where I’ve seen problems before. I’d defend that; after enough joint papers I have the full table, where the referee had a rumor. But attributions direct attention, and attention produces findings. If you check section 4 three times as hard as section 2 you’ll find three times as many problems in section 4 regardless of the underlying rate, and each one confirms the reason you were looking. Nobody checks the base rate, because the prior is what set the checking. Once a reputation is steering where people look, it manufactures its own evidence.
The referee’s error runs in both directions. I wrote in The Outcome or the Message about why a wrong lemma reads as carelessness while a failed experiment reads as bad luck: the lemma was in your head and the check was available, and internal plus controllable is the configuration that draws blame. The other half is that reports usually carry the error twice. The referee explains the typos by the author’s character; the author explains the report by the referee’s. Neither considers that the author was rushing a deadline or the referee had a bad week. Ross called the habit of explaining other people by disposition rather than situation the fundamental attribution error, and a referee report is where two of them meet. We over-polished, and now a stranger’s claim about one person shapes how two people write, and the stranger will never know.
For a postdoc, the market is an attribution market. The file is short, so a single stored attribution carries more of its weight than it will at any later stage. The file is read for locus claims: he proved X and working with Y, he proved X are two explanations of one theorem, and the committee can only read the explanation. And the letters carry stored attributions from the last place into the next. Reputations are held by observers, and observers change, so the move built into the early career works, among other things, as a reputation reset. The reset is only as clean as the letters allow, and the letter writer is often the person whose prior is oldest. The people who can’t move, for all the reasons in Go Get an Outside Offer, don’t get the reset at all.
It selects. Everyone struggles. The people who stay through it are disproportionately the ones who explained the struggle as unstable or as the task’s, because that’s the explanation under which continuing makes sense. Some who left explained it as ability and were wrong. Some explained it as ability and were right; a stable attribution is sometimes the accurate one, and leaving is the correct response to it. Attribution theory can’t tell you which, and I’d distrust an essay that said it could. What I’d say to a student asking is that month four of a stuck problem is not when that question gets answered, by anyone. What the theory can tell you is that the survivors’ way of explaining struggle is the only one the next cohort hears, because the people who explained it differently and left aren’t in the room to say so.
What to do with it
Four things, in increasing cost.
Ask what the event is evidence about. Before the spiral starts, or when you notice it has. Width first, locus second: you may well have made the mistake, and the mistake is still evidence about one lemma.
Fill the consensus column yourself. Ask one person whether they were stuck here too. If you’re the student, ask your advisor directly whether other people stall at this step. The answer is data the field won’t give you unprompted.
If you’re the advisor, hand over the attribution. Say the task-level explanation out loud, with the consensus data attached, instead of the reassurance. I was stuck here for a semester. Three people have tried this step. It costs you a little authority, and that’s why it works.
If you have standing, audit the attributions you’re storing. Once a year, for each student and postdoc your working with, write the one-sentence explanation you’re holding about them, and then write what evidence would change it. If nothing would, you’re not holding an attribution. You’re holding a verdict, and it’s steering where you look. And when you write a letter, notice which locus claim each sentence makes, because that sentence is the attribution that travels.
The referee this year was right about the typos and wrong about the paper, and I’ll never know which of those they remember.
My advisor, that semester, said something wasn’t working in the problem. I’ve given his sentence to my own students since, and it always sounds like a judgment about mathematics. It is. It’s also the one explanation of a failure that doesn’t leave a mark, and he was the only person in the room with the data to make it.