Hi, this is Ray.

There's a memory from my high school chemistry class that I still think about sometimes. I had a teacher… I'll call her Ms. Davis because that wasn't her name but I don't want to embarrass her if by some cosmic accident she reads this… who had a particular pedagogical philosophy I now consider almost prophetic. She would deliberately get things wrong on the board. Not by accident. On purpose. She'd write out a chemistry equation, make a calculation error somewhere in the middle, and then watch us until someone caught it.

At the time, I thought this was unhinged. Why would a teacher deliberately produce wrong work? Why not just teach us the right way? I once raised this concern in class with the kind of self-righteous tone only a 16-year-old can produce. "Wouldn't it be more efficient to just show us the correct method?" Ms. Davis looked at me with what I now recognize as patient amusement and said something I didn't fully understand for another fifteen years: "The mistake is the teacher. I'm just the prop."

She was, it turns out, ahead of the research. The cognitive science on errors and learning has gotten increasingly clear over the past two decades, and the picture that's emerged is one Ms. Davis would have nodded at. Mistakes aren't obstacles to learning. They're not even side effects of learning. They are, in many cases, the actual MECHANISM of learning… the thing that triggers the neural changes that make new knowledge stick. The brain that never makes mistakes isn't learning. It's just running familiar patterns. Today's newsletter is about that. The science of what mistakes do to your brain, why they're so important, and how to actually use them as a deliberate learning tool. Let's get into it.

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Let me start with the neuroscience, because it's genuinely fascinating. When you make a mistake (even a small one, even one you're barely aware of consciously) your brain produces a very specific, measurable response within milliseconds. This response is so consistent that researchers have given it a name: the error-related negativity (ERN).

According to one accessible summary of the research, the brain creates a specific kind of brain activity when a person makes a mistake, called the error-related negativity or ERN, which happens almost at the same time that the error is made… it is as if the brain already knows we are making a mistake within fractions of a second, before we are even aware of it. The ERN signal originates in the anterior cingulate cortex (ACC), a brain region involved in monitoring conflicts between what you intended to do and what actually happened. The ACC is, in a real sense, your brain's error-detection department. It's running constantly in the background, comparing predictions to outcomes, and it lights up the moment those don't match.

This is profound when you sit with it. Your brain detects errors faster than you can consciously notice them. By the time you've thought "wait, that wasn't right," your ACC has already been firing for several hundred milliseconds. The error-detection system is automatic, fast, and constantly running. It's also doing real work… not just flagging mistakes but initiating the cognitive adjustments that should follow them.

A more recent study extended this finding with even more precision. According to the researchers, the human brain can identify an error as the cause of an unexpected outcome in about one second, and if human error is the reason for the outcome, the brain remains active for an additional two to three seconds… that means the brain realizes a mistake was made, and engages in a longer process to prevent future errors. The brain doesn't just detect the error and move on. It dwells on the error for several seconds afterward, doing additional processing that researchers believe is specifically about preventing the same mistake in the future. The mistake itself is the input. The post-mistake processing is the learning.

A Caltech-led team has even identified individual neurons involved in this process. Their work provides rare recordings of individual neurons located deep within the human brain, identifying the specific cells that monitor behavior, catch errors, and correct future actions. At the cellular level, your brain has dedicated machinery for error monitoring and post-error adjustment. This isn't an incidental feature. It's a core part of how human cognition works.

Okay, but WHY are mistakes such powerful learning signals? The mechanism is closely related to something I covered in the dopamine newsletter: prediction errors.

When you do something correctly that you expected to do correctly, your brain doesn't have much new to learn. The prediction matched reality. The neural pathway that produced the correct action gets a small reinforcement. Everything is as expected. The system updates very little because it doesn't need to.

When you make a mistake, the story is completely different. Now there's a mismatch between prediction and reality. The brain has to figure out: what happened? What did I expect? What actually happened? Why was my prediction wrong? What does this tell me about how the world actually works? This is rich computational territory. The neural machinery has actual work to do… updating predictions, adjusting models, encoding the new information that revealed the previous model was wrong.

As one analysis of error-based learning explained, when we expect one outcome and receive another, the brain registers what scientists call a prediction error, which signals that an adjustment is needed… the anterior cingulate cortex monitors conflicts between intended and actual outcomes, while the prefrontal cortex helps reorient attention and adjust strategies. The mistake triggers cognitive control mechanisms that don't get activated by smooth, error-free performance. The learning happens BECAUSE of the error, not despite it.

This is why purely passive learning (where you read or watch material without ever testing your understanding) produces such weak retention compared to active learning that involves attempts and corrections. The passive learning doesn't generate prediction errors. There's nothing for the error-detection system to detect. The neural machinery designed for learning sits idle. As one foundational neuroscience paper put it in language that's almost philosophical: we re-examine the commonly held view that learning and memory necessarily require potentiation of synapses… active synaptic connections are temporarily "tagged" and subsequently depressed if the resulting output turns out to be unsuccessful. Thus, all learning occurs by mistakes. That last phrase. "All learning occurs by mistakes." That's not a slogan. It's the underlying claim of a serious neuroscience model. The mistakes are the mechanism.

Now here's where it gets practically interesting. If mistakes are powerful learning signals, what happens when you DELIBERATELY make them? This sounds counterintuitive (surely the goal is to do things correctly?) but the research suggests that deliberate, well-structured errors can actually enhance learning beyond what error-free practice produces.

According to a 2025 paper on deliberate errors in learning, learners who make deliberate errors may focus more cognitive resources and attention on making and correcting errors, forming unique and memorable contextual traces in the brain, thereby enhancing learning through strengthened encoding. The mechanism is that intentional errors require you to actively engage with what's wrong about them… why they're wrong, what the correct version would be, how the wrong version differs from the right one. This active engagement produces deeper encoding than simply being told the right answer once and trying to remember it.

The same paper continued, deliberate errors require learners, once they know the correct answer, to consider what it is not, thereby increasing the discriminability of knowledge, which benefits long-term retention. When you've explored multiple wrong versions of an answer, the correct answer becomes more sharply defined in your memory. You don't just know what it is. You know what it isn't, in detail, which makes the knowledge more robust and harder to confuse with similar-but-wrong alternatives.

This is what Ms. Davis was doing. She wasn't being chaotic. She was deliberately producing errors so we'd have to actively process the difference between the wrong work and the right work. The processing was the lesson. The right answer alone wouldn't have produced it.

The research has even found that animals deliberately produce errors during learning as a strategy. A 2025 Johns Hopkins study found something striking. According to the researchers, mice continued making mistakes after learning, suggesting strategic exploration… when the mice continued to make errors, licking at the wrong times long after their neural activity showed they'd learned the task, their brain activity confirmed that the mice knew the rules of the game; they were just experimenting. Even mice (mice!) deliberately make errors after learning a task, apparently to test the boundaries of their knowledge and refine their understanding. The strategy is so universal that it shows up in basic mammalian learning behavior.

Before we get to how to handle mistakes well, let me flag the common ways people handle them badly, because the bad patterns are remarkably consistent.

Catastrophizing: Treating each mistake as evidence of fundamental inadequacy rather than as data. "I got this wrong, so I'm bad at this, so I should quit." This is the response that kills most ambitious learning projects. It's also a response that the brain's error-detection system never asked for. The ACC just flagged a prediction error. The catastrophe is something you added on top.

Avoidance: Staying in the parts of the material where you don't make mistakes. This is the comfort-zone trap I covered in a previous newsletter, applied specifically to error avoidance. If you never put yourself in situations where you might fail, you never get the learning signals failure produces. You stay smooth, comfortable, and not improving.

Hiding errors: Many learners try to conceal their mistakes from teachers, peers, or themselves. This prevents the social feedback that often catches errors you can't see yourself, and it prevents the honest self-assessment that makes correction possible. The hidden mistake doesn't go away. It just stops being available as a learning opportunity.

Quick-correction without analysis: Making a mistake, immediately doing the right thing, and moving on without actually processing what happened. This skips the post-error processing that produces most of the learning value. The brain noticed the error and was about to do its work. The quick correction interrupted the process. The error registered as a brief annoyance rather than as data.

Identity-based responses: "I'm not a math person, that's why I got that wrong." "I never could do this kind of thing." Treating each mistake as evidence for a fixed trait rather than as information about a specific gap in current knowledge. The growth mindset literature is full of this, and the research is fairly clear that learners who interpret mistakes as evidence of fixed limitations underperform learners who interpret them as information about current state.

Okay, the practical playbook. Based on the research and on a lot of years trying to do this well and badly, here's how to actually leverage mistakes for learning.

This is the foundational move. Pick learning material that's hard enough to produce regular errors. If you're not making mistakes, the material is too easy. You're operating in your comfort zone, where the error-detection system has nothing to do. The discomfort of being wrong is the price of the learning. Pay the price. Make the mistakes. Don't try to look smooth.

When you do make a mistake, don't immediately rush to the correction. Give yourself a few seconds to actually notice what happened. What did you expect? What did you get instead? Where did the prediction break down? This brief pause is when the post-error processing the research describes is happening. Don't short-circuit it by immediately moving on.

The Caltech and Johns Hopkins research suggests the brain stays active for a few seconds after an error, doing additional work. Match that biological rhythm. Don't interrupt the processing your brain is naturally trying to do.

Be specific about what went wrong. Not "I got it wrong"… what specifically did I get wrong? Was it a calculation error? A misunderstanding of the concept? A misreading of the question? A skipped step? The specific diagnosis matters because it points at what to actually work on next.

This is the same principle as the "find out what you suck at" newsletter. Mistakes are weakness identification in real time. Each one tells you something concrete about your current model that needs updating. Treat them as data, not as judgments.

After you've understood what went wrong, produce the correct version yourself rather than just being told what it should be. The active production strengthens encoding. If you're learning a concept and got an example wrong, work through several correct examples. If you're learning a skill and executed a move wrong, perform the correct version several times. The active reproduction is part of how the corrected knowledge gets locked in.

For material you're already studying, occasionally try to predict the wrong answer and explain why it would be wrong before working out the right one. Generate plausible-but-incorrect approaches before doing the correct approach. This is the "deliberate errors" technique the research validates. It feels strange. It works.

The principle: actively contrasting right from wrong produces deeper understanding than just knowing what's right. Build in the contrast explicitly. The mistake doesn't have to actually have been made by accident. The cognitive benefits come from processing the error, not from the error being unintentional.

This is one of the highest-leverage habits I've developed. When you make a meaningful mistake, write it down. What was the mistake? What was the right answer? What did you learn from it? Review the log periodically.

Most learners forget their mistakes within days. They make the same mistake again weeks later, having lost the lesson. A mistake log preserves the information. It also functions as evidence over time that mistakes lead to learning rather than to permanent failure. You can look back at last month's mistakes and see what you've corrected. The log becomes proof, against the catastrophizing voice, that you actually do improve.

If you're learning in a group context (a class, a study group, a community of practice), try to be the person who openly acknowledges mistakes rather than hiding them. This serves several functions: it makes your own learning more efficient (you can't hide the mistake and learn from it at the same time), it models for others that mistakes are part of learning rather than evidence of inadequacy, and it changes the culture of the group toward one where errors can be discussed and learned from collectively.

This is what good teachers do, including Ms. Davis. They make their own errors visible and processable. The students who watched her catch her own deliberate mistakes were learning two things at once: the chemistry, and the meta-lesson that mistakes are tools.

Here's what I want you to take from all this. The cultural script around mistakes is wrong in a deep way. We've been taught to fear errors, hide them, feel ashamed of them, treat them as evidence of inadequacy. The actual neuroscience tells a different story. Mistakes are some of the most important signals your brain processes. They trigger learning machinery that's specifically designed for them. Without mistakes, the machinery sits idle.

This doesn't mean you should be careless or aim to fail. It means you should accept that meaningful learning involves regular mistakes, and that the mistakes themselves are not the problem… the avoidance of mistakes is. The student who never gets anything wrong is the student studying material that's too easy for them. The student who makes mistakes regularly, processes them, and corrects them is the student who's actually learning.

If you've been treating your mistakes as something to be ashamed of, hidden, or rushed past, please consider that you might be wasting some of the most valuable signals your brain produces. The next time you make a mistake while learning something, pause. Notice what's happening. Let the error-detection system do its work. Analyze what went wrong specifically. Generate the correct version actively. Log it if it matters. Continue.

This isn't easier than fearing mistakes. It's actually harder, in the moment. The discomfort of being wrong is real and not something to suppress entirely. But the alternative (a learning life organized around avoiding errors) is one where the actual learning machinery never fully turns on.

Ms. Davis was right. The mistake is the teacher. You're just the prop.

Keep learning (and keep making the right kind of mistakes),

Ray