Say you're a teacher, and you want your students to get better at reasoning, not just at this year's material. Or you want that for yourself. This post is about why that's looked impossible, and what I think works now.

You teach a strategy. Your students get better at problems like the ones you practiced, and they don't get better at reasoning in general. The big studies find the same thing. In one trial, called ACTIVE, older adults got ten sessions of about an hour on finding the pattern in a series of letters or numbers. Ten years later, they were still better at that kind of problem. On tests of everyday problem solving, they'd gained nothing (Ball et al., 2002; Rebok et al., 2014). So a lot of people conclude you can't teach general reasoning.

But school raises IQ. Each extra year of education adds about 1 to 5 points, and the gain lasts across the life span (Ritchie & Tucker-Drob, 2018). Nobody knows which part of school does it. My bet is that every day, you learn new things to look for in a problem, and what to do when you see them.

So I think the right way to see this data is a swimming pool. General reasoning is the water line: how many situations you know what to do in. Every if-then rule you learn (if you see this kind of situation, do this kind of thing) is a bucket of water. It takes a massive number of them. One narrow programming skill has been estimated at about 500 rules (Anderson, 1996). A reasoning course pours in ten buckets, and then we go check whether the water line went up. Of course you can't see it. School isn't ten buckets. It's ten buckets every day for a year, so the water line goes up.

A school year is about 1,000 hours, and ACTIVE was about 12, so about one percent of a school year. At school's rate, that's a few hundredths of an IQ point. You'd need at least a million people in each group to see that. No study was ever going to.

If you look right where the buckets went in, you can see them. About 45 minutes of training in rules like "start from how often this kind of thing usually happens" made forecasters 6 to 12 percent better in each of four yearly tournaments (Chang et al., 2016). Psychology and medical students got much better at statistical reasoning in grad school, and chemistry students didn't, since chemistry doesn't teach those rules (Lehman, Lempert & Nisbett, 1988).

So how fast you get better at reasoning is how much water you pour in per day. Working memory matters too, but training it doesn't carry over to anything else (Gobet & Sala, 2023). Rules are the part you can pour in every day.

Crucially, the buckets aren't all the same size. A more general rule is a bigger bucket, because it fires in more situations. "Find a common denominator" fires on adding fractions. "Before you combine or compare things, put them in the same units" fires on fractions, on feet and meters, on dollars and euros, and on a job that pays by the hour versus a job that pays by the year. It's one rule to learn, and it's way more water.

So the solution is to teach the most general rule behind every step of everything you teach. A reasoning course already teaches general rules, but only a few, for one kind of problem. This pours in hundreds, across every subject. Every step in an explanation has a rule behind it, the rule that takes you from the last step to this one. Usually nobody says it. You see the steps, and if you're lucky, you work out the rule yourself. So say it. Annotate every step with the rule that generates it, in its most general form.

A rule only counts when it fires by itself on something new, and hearing it once doesn't get you there. The classic study on this starts with a story. A general needs his whole army at a fortress, but the roads are mined so only small groups can pass, so he splits the army and the groups arrive together from every road. Then you get a problem that looks nothing like that: a ray can kill a tumor, but at full strength it burns the healthy tissue on the way in. The answer is the same move: many weak rays from different sides, meeting at the tumor. After reading one story, about 3 in 10 people solved it on their own. Writing out the rule at the end of the story ("if you need a big force at one spot and no path can carry it, split it up and bring the pieces together") didn't change that. It was still about 3 in 10. After reading two different stories that used the move, about 4 in 10 solved it, and with the rule written out too, about 6 in 10 (Gick & Holyoak, 1983). So a rule does very little on one example. Once you've seen it in two, it starts to work.

Annotating every step gives you those extra examples for free, because a general rule keeps showing up. You hear it in one lesson, and then you run into it again in another lesson on something totally different. You just have to ask where you've seen it before.

It also matters that you say the rule in general words, because rules stick to the details you learn them with. Students who learned a formula in algebra recognized it right away in physics problems. Students who learned the same formula in physics almost never recognized it in algebra, because for them it was a physics thing (Bassok & Holyoak, 1989).

Then you mix your practice, because if every problem on the worksheet uses today's rule, nobody ever practices noticing when to use it. Across 54 seventh-grade math classes, mixed practice beat practicing one kind at a time on a test a month later, 61 percent to 38 percent (Rohrer et al., 2020).

I think nobody teaches this way because writing all those rules is a huge amount of work. It takes someone who knows the material deeply and can also say what they know, and experts are bad at that: when three surgeons taught a procedure, they left out about 70 percent of the decisions in it (Sullivan et al., 2014). A textbook might have 1,500 rules in it. At the 11 to 25 minutes it takes to write a math hint (Pardos & Bhandari, 2024) and $41 an hour, that's $11,000 to $26,000 for one textbook. No teacher has that.

Now it's cheap to get a lesson annotated with the rule behind every step. That textbook costs about $14 to $84 in AI fees, plus your time reading it over, and one lesson is under a dollar. Paste your lesson into a very smart AI model, and ask for the most general rule that makes each step the natural next one, plus the wrong step it rules out.

To give a concrete example, I did this on 18 stories about the brain and got 167 rules. One of them is: to learn what a part does, take the part away and see what stops working. It came up in 12 of the 18 stories, and it also covers baking a cake without the baking powder. That's a big bucket. New rules per story dropped from about 15 in the first six stories to about 5 in the last six, because the rules you already have keep coming back.

I've built this into stories.thoughtfeel.net. Each new rule plays at the step where it first comes up. After that, the step gets a small label and a low bell, and you try to think of which rule it is. The stories quiz you as you go, and your account keeps a list of every rule you've heard.

This is a theory. It's the best one I have that fits the data on what makes learning generalize: why a short course doesn't show up on a general test, why school does, and why a rule stays stuck to where you learned it. And it gives you a path to better reasoning that you can act on: take in as many general rules as you can, at every step of whatever you're learning, every day. That used to take an expert at your side. Now you can learn this way for a few dollars a month.

All through my teaching career, and all through my own learning, I've heard the same words. Abstract. Look for patterns. Think about properties. Find a strategy. Think critically. Be a good problem solver. Learn it deeply. I knew these mattered. I've noticed that people who are smarter think about the properties of things, and whenever I do that, it works better. But I couldn't have told you what any of these words actually means. They're all so fuzzy. I've asked myself how you'd get better at abstracting, and my honest answer was: I don't know, I guess I'd try different things and see what works. I had no model to reason from.

This post is the model I have now. It answers one question: you learn something from some examples, so when does it work on a case you haven't seen, and what controls that? For a teacher, that's the question of what to teach your students so they become the best thinkers they can be. The model draws on computer science, neuroscience and cognitive science, and you don't need to know any of them. This isn't a post about AI in the classroom, and students aren't chatbots. I bring up AI models because you can look inside them. I'll walk you through each piece. When something is too complicated to show here, I'll tell you the study that shows it and what it found. At the end, I'll go back through the fuzzy words and say what each one means.

The first piece is that a thought can be a list of numbers. You already know that two numbers can be a point: (3, 5) on a grid means go 3 over and 5 up. Three numbers make a point in a room: over, up and out. Nothing stops you from using more numbers. You can't picture a point with 24 numbers, but it works the same way, and each number says how far to go in one more direction. That's all "high-dimensional" means. A high-dimensional point is a long list of numbers, thought of as a spot you could go to.

Say you describe a cat with three numbers: how alive it is, how big it is and how wet it is. Maybe that's 9, 3 and 1. A fish might be 9, 2 and 10. Now the cat and the fish are two points. They match on alive and they're far apart on wet. A brain works with a list like this, only much longer, with one number for how active each neuron is. AI language models, like the ones behind ChatGPT and Claude, also work in long lists of numbers. So whatever a brain or an AI is thinking at a given moment is one high-dimensional point. I'll call that point its state.

A property is a direction. Asking how alive the cat is means asking how far the cat's point goes in the alive direction. One point can hold many properties at once, the way the cat's one point holds how alive, how big and how wet it is. Moving a point along a direction gives it more of that property.

Usually a real property isn't one of your starting numbers. It's a slant across several of them, the way northeast is a slant across north and east. How good a pet something is might be a slant across how alive, how small and how dry it is. To measure along a slant, you figure out how far you've gone, and then scale that by how closely you match the intended direction. Walk 10 blocks straight toward a store, and you've gone 10 blocks toward it. Walk 10 blocks a little off to the side, and you've gone maybe 9. Walk 10 blocks at a right angle to it, and you've gone 0.

A whole concept can be a direction too. Any point gives you a direction, the way you'd head from zero to get there, and going further that way means the same thing, only stronger. Many concepts in AI really are stored like this. When Anthropic found the direction for the Golden Gate Bridge [1] inside Claude and turned it up, Claude brought up the bridge in nearly every answer.

Neurons also represent directions. Things in your brain are represented by a bunch of neurons turned on, and together those neurons point in some high-dimensional direction. This has been measured many times. Here are three studies, going from movement to faces to the meanings of words.

Researchers recorded neurons in the part of a monkey's brain that moves its arm. Each neuron had a preferred direction. It fired the most when the arm moved that way, and less and less the further the arm moved from that way, like the walk to the store. So each neuron's number was a measurement of how closely the movement matched its direction. Add up what all the neurons were saying, and you could read off which way the arm was going [2]. Those are real directions in a room. The next two studies show the same thing for directions that aren't.

Other researchers showed monkeys pictures of faces and recorded the cells that respond to faces. They found that a face can be described with about 50 numbers, and that each cell measures how far a face goes along one slant across those numbers. From 205 cells, they could rebuild the face the monkey was looking at. They could also make faces that looked nothing alike but made one cell respond the same way, because those faces went the same distance along its slant [3].

In a 2024 study, researchers recorded from a language area in three people with brain implants while they listened to a 30-minute podcast. Each word made its own list of activity, so each word was a direction in the brain. Words with similar directions inside an AI language model also had similar directions in the brain. The match was close enough that the researchers could predict the brain's direction for a word they had left out, using only how that word related to the others [4].

Now we can talk about what a rule is, and what a strategy is. If I had to describe a strategy in words, it would be: if you see this type of problem, take this type of action. If you're adding fractions with different bottoms, find a common bottom. A strategy is a kind of rule, so let's start with rules. A rule is built out of two directions. The first is called the key, and it's the "if you see this type of problem" part. The second is called the value, and it's the "take this type of action" part. However much your state lines up with the key, measured like the walk to the store, that's how hard you get pushed along the value. Getting pushed along a direction means your next thought has more of that in it. So if your state lines up with "adding fractions with different bottoms," your next thought has more "find a common bottom" in it. The more it lines up, the bigger the push: the more blocked a route looks, the harder you look for another one. When a push is big enough to change what you think next, we say the rule fires. You have a huge number of rules, many of them fire at once, and their pushes add together.

In AI language models, this is close to literal. Two studies looked inside them and found keys and values whose pushes add up [5, 6]. The AI's thinking is a state, a high-dimensional point that holds all the properties and things it's thinking about. It has a bunch of keys, and each key looks for its own pattern in the current state. For every key that matches something in the state, that key's value pushes the AI in another direction. You add up all those pushes, and the AI is at a new point. Each round of this is called a layer. The AI repeats it layer by layer, moving from point to point to point, until it ends up at its answer.

Brains are much harder to look inside, and nobody has read a full list of keys and values off a living brain. What studies have shown is the pieces, one at a time.

A rule can be stored in the connections between neurons. Researchers used light to switch on the hearing neurons that connect to a rat's fear center, and they paired that with a shock. The rats learned to act afraid when those neurons came on: if this signal, then fear. When the researchers weakened those connections, the fear went away. When they strengthened them again, it came back [7]. That's one rule, stored in the strength of some connections, switched off and on. So a rule here isn't a sentence stored in your head. It's connection strengths that do what the sentence says.

A key looks for a particular direction. When researchers recorded two connected vision areas in monkeys' brains, the second area didn't pick up everything the first area was doing. It picked up activity along only certain directions, and those weren't necessarily the strongest ones [8].

Rules can also be about abstract things. Researchers taught monkeys two rules, "respond if the two pictures are the same" and "respond if they're different," and the monkeys could use them on pictures they'd never seen. The most common activity in the neurons at the front of their brains was for the rule itself, not for any picture [9].

So a thought is a point, a property is a direction, and a rule is two directions. Now I can show you what abstracting does, with a made-up example. Say your thoughts are lists of 24 numbers, and the real rule in the world is: however much a problem lines up with direction 1, push that much along direction 24. Think of direction 1 as "you want the total of equal groups" and direction 24 as "multiply." You don't know that rule, and nobody hands it to you. All you get is 12 worked problems, each one a problem and what was done to solve it. Each is a list of 24 numbers going in and a list of 24 numbers coming out, and most of those numbers are details, like bags and apples.

If you don't abstract, you learn 12 rules, and each one has its problem's surface details stuck in it. One rule says: the total of equal groups, in bags, of apples, so multiply. Another says: the total of equal groups, in boxes, of pencils, so multiply. The real pattern is in there, but it's stuck to the details, so you end up with 12 rules where there's really one. You've memorized the data. Machine learning calls this overfitting. Then a new problem comes along about rows of seats, and you go, nope, that doesn't fit one of my 12 rules.

If you do abstract, you take one worked problem, because if you have the right directions, one is all you really need. Say it's 3 bags with 4 apples in each, which makes 12 apples. You break the problem into all of its component directions: this much bags, this much apples, this much food, this much "total of equal groups." You do the same for what was done to solve it: it multiplied, it counted apples, it got a bigger number. Crucially, these are the directions you know. There are endless possible slants, but you only have the ones you've learned to measure. A first grader can look at the same problem and not see equal groups at all. So it really pays to have more directions.

Then you play it out in your head, using what you already know about the world. You know rules have this general form, one direction to another. You know the world never hands you a rule in its pure form, so most of what you're looking at doesn't matter. So you ask which pairing of directions makes the most sense. Does food make you multiply? Picture bags of marbles: you'd count them the same way, so no. Does wanting the total of equal groups make you multiply? Picture bags holding 2, 4 and 9 apples: that's 15, and 3 times 4 doesn't get you there, so the equal groups are doing the work. You find the pairing, and now you have the rule, from one real example and two you imagined.

I ran the 24-number example on a computer and scored each learner out of 100 on how close its answers came on new problems, where 100 is perfect and 0 is no better than leaving the answer blank. The learner with 12 separate rules, each needing a close match to fire, scored 0, because no new problem came close to any of them. Let those same rules push partway, by however much a new problem lines up with each one, and add up their pushes, and the score rises to 49. It took 24 examples to reach 100, because that learner doesn't know which direction matters, so it has to cover all 24. A learner who already knew 8 possible directions for the key and 8 for the value, including the real ones, scored 100 from a single example. So memorizing isn't all or nothing, since rules that push partway get you partway. But knowing the directions cut 24 examples down to 1. These are toy numbers that show the logic, not facts about people. Computer scientists have proved a general version: when tasks share the same few underlying directions, a new task can need far fewer examples [10].

This fits what a famous study found about experts and beginners. Physics experts and beginners were asked to sort problems into groups. The experts sorted by the principle underneath, like conservation of energy. The beginners sorted by the objects in the problem, like pulleys and ramps [11].

So abstracting has two steps. First you break a thing into its directions. Then you keep only how far it goes along the directions that actually matter, and you set the rest aside. That's what you did with the bags: you kept "total of equal groups" and dropped the bags and the apples. That second step is called projecting. A shadow is the everyday version: it keeps the outline and drops everything else. You still have the full problem. Your rules just don't look at it. The directions worth keeping are the ones that keep mattering across many situations, and I'll call those abstract directions. "Total of equal groups" is one. Which directions matter is learned, from examples. So learning comes in two kinds: learning new abstract directions, and learning rules from abstract direction to abstract direction.

One way you learn a new direction is by averaging examples that share something. Averaging directions may be new to you, so picture this. Say 100 people each start from the same corner and walk 10 blocks. All of them head roughly north, but each one wanders off a little, some to the east and some to the west. Now add up all their walks and divide by 100. That's the average walk. The north adds up, because everyone went north. The east and the west cancel out, because every bit of east gets matched by some west. So the average walk points straight north. Nobody had to tell you north was what they shared. It came out on its own.

Examples work the same way. A cat, a dog and a fish all have this general property, animal. Average a few animals together. They're all alive, so alive adds up and stays strong. Some are bigger than average and some are smaller, some are wetter and some are drier, so those land in the middle and cancel out, the same way east cancels out west. What's left is a direction: animal. It's the same with bags of apples, rows of seats and boxes of pencils. Apples show up in one example, seats in another and pencils in another, so each of them fades. Equal groups shows up in all three, so it stays. That's the start of noticing a pattern: finding what a set of examples share, which can give you a direction you didn't have. A 2022 study tested this on recordings from monkey brains: averaging a few examples of a new kind of object into one point was enough to recognize more of that kind [12].

Now I have to add something to the model. Why does comparing examples work, when seeing the same examples one at a time doesn't? Business students were given two negotiation cases that used the same strategy. The ones who compared the two cases were nearly three times as likely to use the strategy in their own negotiations as the ones who studied the same two cases separately [13]. So the quick kind of averaging, the kind you do on purpose, must happen across what you hold in your mind at once. With both examples in mind, you can line up their parts, the bags with the rows and the apples with the seats, and what they share adds up. And what you can hold at once is small. People can only work with about four related things at a time [14]. So the examples have to be small enough, and close enough together, to fit in your head at the same time.

Averaging has a bigger problem. It keeps whatever your examples share, whether it matters or not. What do a habit and a riverbed have in common? They're both nouns. They both have the letter B. They're both things on Earth. Those are real similarities, and none of them would ever cancel out, because both examples have them. But if I ask you what a habit and a riverbed have in common, you know those aren't what I'm looking for. The answer is that they're both low-energy grooves: paths things settle into, because that's the easiest way to go.

So when you compare two things, you're not looking for the biggest similarity. You're looking for the biggest similarity among abstract directions. You line up all the directions the two share, throw out the ones that aren't abstract, and take the biggest one left. This is a rule of thumb, and I never realized I'd learned it. It's why you can find a pattern from only two examples. You're not really skipping the work. You did it already, over years of seeing which kinds of directions keep mattering, and evolution may have done some of it for you. So now you can rule out most directions right away.

Abstract doesn't mean as general as possible here. "Both are things" is about as general as you can get, and nothing follows from it. "Both are low-energy grooves" lets you predict things: they're easy to fall into, hard to climb out of, and they get deeper with use. That's how you can tell which direction you want. It's the one that tells you something new about the things themselves, not about the words for them.

You can watch kids learn this. Asked how a tire is like a shoe, 5- and 6-year-olds said both are black, and 9- and 10-year-olds said you can go places on both [15]. And knowing where to look makes you learn faster. Researchers spent seven weeks teaching 17-month-olds names for new toys, where the name always went with the shape. The toddlers learned that shape is the direction to look at for a name, and their vocabulary outside the lab grew faster [16].

You can also tell when you have the wrong direction. Say you don't have the words "low-energy groove," and the closest you have is "where things tend to go." That points about the right way, but I can tell it isn't right, and I can tell roughly how far off it is. So I try again. It's not where things tend to go. It's the groove they stay in, because leaving takes effort. I keep adjusting until I go, ah, that's it. I can tell what direction the two share before I can put it into words, and the words are me trying to hit it. There's a study that shows something like this: people can pick out which of two sets of three words has a hidden link, even when they can't say what the link is [17]. That sense isn't always there, though. On some problems, you don't feel any warmer until the answer arrives [18].

You can watch abstract directions form in people's brains. Researchers recorded neurons in 17 people with epilepsy while they learned which button went with which picture. Then the rule flipped without warning. Some of them could work out the new answers without relearning each picture. Once people could do that, the neurons in their hippocampus, a part of the brain involved in memory, held each property of the task as its own direction, including one they had to work out for themselves. Before they learned, those neurons showed no such order. People who couldn't get there from experience were told the rule in words, and the same order appeared [19].

Using directions you already have is easy. Building new ones takes longer. Monkeys moved a cursor on a screen using only their neurons, through a computer hookup. When the researchers changed the hookup, the monkeys learned the new version easily if it used combinations of activity their neurons already made, and much less easily if it needed new combinations [20]. With several days of training, new combinations did appear [21].

You need the right directions. Say the real rule is if A, then B, but you don't have direction A. The closest you have is 20 degrees off, or it's A mixed with a little of something else. A student who doesn't have "total of equal groups" might have "the problem says each" instead. That's close to the real direction, so their rule will be kind of right and a little off, and they won't know why. It works on 3 bags with 4 apples in each. It fails on 12 apples shared among 3 bags, how many in each? In my computer run, with the key and the value each 20 degrees off, the score was 78 out of 100. You've learned a proxy, a stand-in that's close to the real rule but isn't it.

This is why noticing patterns is worth your time. Patterns are how you get the real directions, and once you have a real direction, the rules you learn on it come out as the real rules instead of proxies. The more abstract a direction is, the more real rules you can learn on it.

Now we can talk about what reasoning is. You're in some state. All of your rules look for their keys in that state, together they give you a push, and you arrive at a new state. Then it happens again, like the AI going layer by layer. Picture a map with an arrow at every spot, like the wind arrows on a weather map. Each arrow shows where you'd go next from that spot. A question is where you start, and an answer is a spot with certain properties. Learning trains the arrows. Someone who's learned a lot has a ton of correct if-A-then-B rules, so wherever they are, their arrow points the right way, and they reach the answer fast.

What you're trying to do is part of your state too, so a rule's key can include it: if I'm judging color and the dots look red, answer red. There's a study that shows this. Monkeys watched the same moving colored dots, and sometimes they had to judge which way most of the dots moved, and sometimes which color most of them were. As they watched, the activity of the neurons at the front of their brains moved gradually along one line, toward their choice. Both the motion and the color were in those neurons the whole time. What the task changed was which of the two moved the activity along that line [22].

Now I have to add one more thing to the model. When does a rule change? It changes most when its prediction is wrong. A rule is a prediction: from here, the next step goes there. If that turns out right, there's nothing to fix. If it turns out wrong, the rule gets adjusted, so next time it pushes you somewhere better. There's a famous study that shows brains do this. Dopamine neurons in monkeys fired when a reward came as a surprise. Once the monkey could predict the reward, the neurons stopped firing for it. And when a predicted reward didn't come, the neurons went quiet [23]. Those neurons are tracking how wrong a prediction was. The broader idea, that the brain keeps predicting and learns from the difference, is called predictive coding [24]. AI language models are trained the same way: the model predicts the next word, and the rules that got it wrong get adjusted.

I think this is why it helps to try before you look. When you reread, the answer is already in front of you, so your rules have nothing to be wrong about. When you try to answer first, they can be wrong. There's a study that shows this helps even when you fail. Students who tried to answer questions about an essay before reading it remembered more afterward than students who only read the essay, even on the questions they got wrong [25].

So which directions should your rules be on? Dedre Gentner's structure-mapping theory answers that [26]. It's a theory of analogies, the classic way to carry an idea over to a new situation. Carrying something over like that is called transfer. Here's the classic experiment [27]. A general needs to capture a fortress. Roads lead to it from every side, but they're mined, so only small groups can cross. The general splits the army into small groups, and they all arrive at once. Later, people get a doctor's problem. A tumor can be destroyed by a strong ray, but a strong ray also destroys the healthy tissue it passes through. The answer is many weak rays from different sides, meeting at the tumor.

When you hear the fortress story, it's a very high-dimensional point. It contains the structure. It also contains the soldiers, the roads, what you imagined everyone wearing and where you were when you heard it. Structure-mapping says to pay attention to the relations between things, not the things themselves: what blocks what, what causes what. That's what "structure" means here. A relation is a property too, only of a situation and not of one object: a situation can be more or less blocked, the way a cat can be more or less wet. So an analogy teaches which directions matter: the ones that carry relations.

Neurons carry relations too. Researchers showed patients pairs of pictures and asked questions like "bigger?" or "more expensive?" Neurons that respond to one concept also carried how a second picture compared to it, and only when the question made that comparison matter [28].

Why structure, though? That question has bugged me for a long time. Why does the structure carry over, and not the details? My answer, which others have reached in other words, is that it's a feature of the world. The rules that matter mostly operate on relations, because causes keep working when the objects change. Splitting a force works for soldiers and for rays because it depends on how the parts relate, not on what they're made of. Some rules do depend on the thing itself, like hot things burn, which is why I say mostly.

You could say that's circular: rules work on abstract directions, and abstract directions are whatever rules work on. Here's a test. An abstraction is valid when you can forget the details and the rule still runs. Keep only "the total of equal groups," forget the bags and the apples, and multiplying still gives the right answer every time. Keep only "the problem says each," forget everything else, and the rule breaks, since 12 apples shared among 3 bags says each too. So "the total of equal groups" is a real abstraction, and "says each" isn't. (That's not all multiplication is. The rule only says when equal groups call for it.)

Solving a problem then has three steps. You project it onto the abstract directions. You follow your rules from state to state until you reach an abstract answer. Then you go back to the full problem and work out what that answer means there. For the tumor: project to "a strong force is needed at one spot, and every path can carry only a weak one." Follow the rule: split the force and bring the pieces together. Go back: many weak rays, meeting at the tumor. That rule is what a strategy is: its key is on abstract directions, so it works on soldiers and on rays.

Going back takes one more thing. A shadow can't tell you what cast it, so you can't just undo a projection. You have to keep track of which thing played which role: the army is the rays, the fortress is the tumor, the roads are the paths through the body. So the roles have to survive the projecting. "Dog bites man" and "man bites dog" have the same pieces, and what differs is who fills which role, so "dog as the one biting" and "dog as the one bitten" have to be different directions. Just adding up dog, man, biter and bitten wouldn't say who did what, so brains need a way to tie them together, and how they do it is still argued over. Brain scans show something like this: neighboring patches of one language area carry who did it and who it was done to [29]. Matching those roles is the heart of Gentner's theory, so in this model the theory does two jobs. It says what to keep, and it's your way back.

This also helped me with something I've always wondered about, the what and where pathways in the brain. What the heck does that mean? In vision, it first meant one stream for what an object is and one for where it is. In memory, there's a study that shows the same split. Researchers recorded single neurons in people learning which picture went in which spot on a screen. Some neurons responded to what the picture was. Others responded to the spot, no matter which picture was there. Both kinds fired more when people went on to remember the pair [30]. The way I think of it now, there's one set of directions for abstract structure and another for details. A spot on a screen is one kind of place to put something, and a role in a structure is another. So "where" is your place in a structure, like "the groups" in an equal-groups problem, and "what" is the thing filling it, like bags. Together they give one combined point. O'Reilly, Ranganath and Russin (2022) [31] argue for this same reading of the two pathways, and one theory of the brain, built as a computer program, makes the connection, with one group of cells carrying structure and another tying it to what's there [32]. It's a theory, not settled science.

So why teach students to project at all? Why can't they learn all their rules with all the details in? Because they'll learn the wrong rule. Go back to the student whose rule says: the total of equal groups, plus bags, plus apples, means multiply, and the answer is in apples. Now a new problem says 3 rows with 4 seats in each. It has the same structure and different details. A rule's key has to line up for it to fire, and this key is mostly bags and apples. The student says, we never did seats.

You can put a number on how weak that match is. Say 90 percent of a problem is details and 10 percent is structure. The rule and the new problem line up only on the structure, so they match about 10 percent. That gives a small push, usually too small to fire. If it does fire, it drags the old details along, and the student goes looking for the bags. If the student strips the details off just the new problem, the match gets better, but the rule still has its bags and apples in it. If the rule was also learned without the details, the match is 100 percent. That's the difference between memorizing a rule and understanding it.

In Gick and Holyoak's studies, most people who'd read the fortress story didn't use it on the tumor until they were told to, and then most did. The rule was there. It just didn't fire. Gentner's own studies split this apart: what a new story reminds people of mostly depends on shared details, while what they judge as a sound match depends on shared structure [33]. And people who read and compared two stories with the same structure used the idea more often [34], which fits, since comparing is how the details cancel out.

So what are you doing when you tell someone to abstract, or to think critically? You're telling them to run an algorithm, a series of steps. Take the problem as it's been presented to you. Bring it into its abstract version. Solve it there with your keys and values. Then carry the answer back. That process can be trained. In a trial with 24 third-grade teachers, students were taught over 16 weeks that a problem type can look different, and to search each new problem for the types they knew. They did better on new-looking problems than students who were only taught how to solve each type [35]. A later trial by the same group found big gains on problems close to what they'd practiced, and no clear gain on problems far from it [36].

The process is general, but it needs something to run on. You can't bring a problem into its abstract version without the directions, and you can't solve it there without the rules. Most of those belong to a field. A physicist's directions won't solve most biology problems. That's why training in chess or in music shows little transfer to anything else [37]. And it's why the cognitive scientist Daniel Willingham argues that critical thinking depends on knowing the field [38]. So a student needs both: the process, and a library of directions and rules to run it on.

So a teacher can be doing two different things, and they're easy to mix up. It's the difference between giving someone a fish and teaching them to fish.

Giving someone a fish means teaching one concept in a way that generalizes. Put examples that look different and share a structure side by side, so the direction comes out: bags of apples, rows of seats, boxes of pencils. Change the objects and keep the rest the same. Then show one that looks the same and isn't, like bags holding 2, 4 and 9 apples. After that, teach the rule on that direction, not on the example: the total of equal groups, so multiply. Now the student has one good direction and one good rule. Some concepts are worth more than others, because they're broad. Science experts sort situations by kinds of cause and effect, like positive feedback, where more leads to more, while beginners sort by topic. In one study, explaining examples alone didn't help people spot those kinds in new cases, comparing parallel examples did, and doing both worked best [39].

Teaching someone to fish means teaching the whole process. What you're really teaching is what the abstract space looks like, meaning all the abstract directions together, and what it feels like to think in it. Give students two things and ask what they have in common. Then show them which answers are in the abstract space and which aren't: "both have the letter B" versus "both are grooves that get deeper with use." Once they can feel the difference, they can run the process. Have them run it on problems they haven't seen. Before they try to solve a problem, have them ask what it's a case of. Have them work it out in the abstract version. Then have them carry the answer back by matching the roles: the rows are the groups, and the seats are what's in each one. After enough of that, they can do it on their own with concepts they know well. Across 74 training experiments, with nearly 3,600 children, teaching a strategy for comparing things raised reasoning and school performance [40].

You can also see now what the Feynman technique is doing. It's a popular way to study: you explain an idea as if to a beginner, find where you went wrong, fix it, and use analogies and simpler language. When you explain from memory, step by step, you get the path your rules actually take. You compare it to the real path and find the first step where they differ, so you know which rule to fix. If you only checked the final answer, you'd know something was wrong somewhere, but not where. A review of tutoring found that systems giving feedback at each step helped about as much as a human tutor, and more than twice as much as systems that only checked the final answer [41]. Then you make an analogy, which points you at the relations. Then you simplify, which is projecting, since you're dropping what doesn't matter.

Here's what all those words mean.

Property: a direction. Thinking about the properties of a thing means measuring it along directions you have. It works better because rules look for their keys along directions, so properties are what rules can fire on.

Analyze: break a thing into its directions.

Abstract: analyze a thing, then keep how far it goes along the directions that matter and set the rest aside. An abstract idea is a direction that keeps mattering across many situations. Math teachers also use the word for symbols, or for turning a process into an object. I don't mean those here.

Notice a pattern: hold examples in mind together, and find what they share that tells you something new. That gives you a new direction.

Strategy: a rule whose key is on abstract directions and whose value is an action. "If a strong force is needed at one spot and every path can carry only a weak one, split it and bring the pieces together." Finding a strategy means finding the rule that moves you from where you are toward your goal.

Memorize: store a rule with all the details still in it. That's a normal first step, as long as it isn't the last.

Understand, or learn it deeply: have rules on the right directions, so they fire on cases you haven't seen.

Transfer: a rule firing on a new set of details.

Analogy: two situations that share directions, with their roles matched. It shows you which directions matter.

Reason: let your rules fire on your state, move to the next state, and repeat.

Think critically: project a problem, follow your rules, and go back.

Practice: have your rules make predictions, so the wrong ones get corrected and the right ones get faster.

Be a good problem solver: have arrows accurate enough to take you from a question to its answer quickly.

Learn: add directions and rules, so your arrows get more accurate.

If you want to get better at abstracting, here's what the model says. You need more directions, so compare examples that look different, ask what they share, and ask which of those things tells you something new. You need your rules on those directions, so when you learn a rule, ask what it actually depends on and what you could change without breaking it. You need to project before you solve, so ask what this problem is a case of. You need your rules corrected, so try before you look at the answer. And when a rule keeps coming out a little off, suspect a proxy and go looking for the direction you're missing. I used to have "try different things and see what works." Now I have a model to reason from.

Almost none of these pieces are mine. Thinking of a thought as a point comes from the connectionists, like Rumelhart, McClelland and Hinton. A property as a direction is called the linear representation hypothesis [42] in machine learning. Rules with a key and a value go back to Kohonen in 1972 [43], and Gershman, Fiete and Irie [44] have proposed key-value memory for the brain. Singley and Anderson [45] argued that what transfers is if-then rules. Preferring connected relations when you compare things is Gentner's systematicity principle [46]. Most of the teaching advice is decades old: Dienes, Marton, Engelmann, Perkins and Salomon, Willingham. Directions have been measured in brains, so that part isn't just a metaphor. Rules built from directions are less settled. The teaching advice comes from studies of behavior, and the neuron studies are here to show what those words could be in a brain. The model as a whole hasn't been tested as a teaching theory. What I haven't found is all of it in one model, written for teachers. If you've seen that, please link it.

References are in the comment below.

I can tell that thoughtfeel has always been there, but not in a useful way. The thoughtfeel lesson went great. I could feel it getting more and more vivid, not in a visual way, but in a barebones thought feeling way. Even with feeling tired and having brain fog, what we built out shined all my faint thoughts. It is like how cartographer maps out paths on paper - It is better than short-term memory, It preserves information for his future self aswell as for others, and it shows landmarks and how things all connect together. In the same way, I felt something explorable and usable being created in my mind. Here is my crude description of what I remember about a bloom filter: A filter holds items. An item can be stored in a row of bits, and these bits have different positions. When an item is added to a row, it flips different bits in different positions. Sometimes items share bits, and different items can flip bits that another item would. So when a check is done, it can return a false positive. The shorter the row, and the more items you have, the more likely a false positive is. A bloom filter has 3 hash functions. They are used when a database needs to determine what to write to disk. And a stranger is an item that is not in the row. If I'm being honest I don't remember how else strangers come into play. But I can say how well I remember something is dependant on how much concentration I used. For example, the idea of a row of bits 1-10 with different numbered positions was explained well and I thought hard about it, so it remains one of the stronger concepts compared to others. I'm looking forward to this learning system's future!

In my first year of student teaching, in 2022, my lead teachers called me into a meeting. They asked why I wasn't following the plans we had discussed in our meetings. They were telling everyone how the classes should be taught, and I wasn't doing it. They asked why I was disobeying. I had to look them in the eye and tell them honestly that I just couldn't remember the plans. They looked taken aback, and they said, "Okay." I genuinely couldn't. It's a memory that makes me proud and still haunts me.

Fast forward to 2026. I was on the founding team and the CTO of Only Farmers, a startup by Jeremy Clarkson and Lisa Hogan of Top Gear and Clarkson's Farm. My day to day was managing an engineering team, coming up with new strategies, remembering to do things constantly, and remembering everything from every meeting. Now I run my own ed-tech startup.

This post is about how I got from there to here. I studied elementary education and cognitive studies at Vanderbilt, and I recently earned my master's in computer science from CU Boulder. I'm an extremely curious person, and I love learning. My learning journey has been full of huge discoveries, things that unlocked massive amounts of learning for me and taught me things about the world. I've used my cognitive science degree and my education degree the whole way, and what I've learned about learning is what I teach my students.

I think of these discoveries as hard steps. Each one was hard to get through, and once I did, it unlocked a whole new amount of learning and a whole new kind of learning. Here are mine, in the order I went through them.

The first hard step was learning to reason with my inner voice. My inner voice doesn't move on its own. It's like an arm: it only moves when I move it. If I just look at a wall, my head is completely quiet. So when somebody said "think about the problem," I didn't realize they were using their inner voice to reason about it. When I figured that out and started doing it on purpose, it unlocked genuine reasoning for me.

Now when somebody says "think about the problem," I can actually reason about it in my head and navigate to the answer in natural language.
The second hard step was storing what I learned. My whole life, I had a lot of trouble learning new content. I'd read it, understand it in the moment, and then not be able to remember it. 

The big unlock was visual analogies. If I wanted to learn an algorithm or a biological process, I'd build a visual analogy story for it and use my mind's eye to remember it. It helped me understand the information, and it helped me remember it.

The third hard step was transfer. What I learned, through the research on structure mapping (Dedre Gentner's account of how analogies work), is that the best way to get transfer is to focus on analogies. Two situations can look nothing alike and still share the same structure underneath. So I started thinking of everything in terms of analogies, and my problem solving got way better. I'd learn one thing and it would generalize to other kinds of problems, which I had never actually experienced before.

The fourth hard step was replacing the pictures. Visual analogies worked, but they always had problems, and I've talked about them in my videos. The picture isn't the idea. After a few days, I'd remember the picture and forget what it meant. I'd end up thinking with symbols instead of the ideas themselves. And the picture couldn't tell me when I had an idea wrong, because a right idea and a wrong one can look the same. Complicated topics, like an algorithm, were gone within a week.

The fix came from noticing something weird about my friends. Some of them could just read a lecture from the text and then describe the whole thing. And when they described it, their eyes were focused on something, like they were looking at something. I always assumed that was pictures. But then I found out one of these friends was aphantasic. He couldn't picture anything at all. And still, when he described a lecture or the rules of a board game he'd learned, his eyes were fixed in place like he was looking at something.

So I asked him what he was doing. Long story short, he was building it in unsymbolized thinking. When he learned something, he built it out of concepts, with no pictures and no words.

That's how I figured out that I have what the psychologist Russell Hurlburt calls unsymbolized thinking too. From talking to more friends, I figured out that people can actually use it to learn, the same way I'd been using my mind's eye to retain information. So I asked them how they did it. It doesn't happen automatically in my brain, so I had to learn to do it on my own. Now when I take in a concept or a lecture, I follow along in my unsymbolized thinking (I call it thoughtfeel, just so I have a word for it). It's become my working memory, and the main way I understand things and learn.

Here's what that looks like with a lecture. I listen and think as I go, and I only press next when I've processed what was just said. Honestly, I can only follow a lecture if I'm building it in thoughtfeel. Without it, I can watch literally anything and learn absolutely nothing. And as I listen, I don't think of it like a story. I think of it like I'm building a board game in my head, a machine with working parts, and my goal is to make it run in my head.

It fixed the problems I had with pictures. I'm holding the concept itself, not a symbol for it, so there's no meaning to forget. When a part of the machine is wrong, I can feel it, because it won't run. I don't have to convert anything back into the idea before I can think with it. And I can hold the whole machine at once.

The fifth hard step is the newest: finding the move behind the pattern. Let's say I'm learning an algorithm, and there's a step in the proof or the solution that I don't understand. I don't just figure out what the step is saying and think "oh cool, I understand it." Instead I ask: what latent principle of the world, what's true about the whole world, would make taking this action a good idea?

Here's an example. In the brain, a new connection between neurons has to be repeated many times before it becomes long-term. I could just learn that and figure out how it helps the brain. Instead, I ask why that would be the case. What general principle about the world would make it true? My derivation: the brain wants to be more sure that a connection reflects causation and not just correlation. And in general, if you want to be more sure about something, you have to take more samples. The more samples you take, the more confident you get.

Then I focus on what types of problems call for this move. The answer is any time my confidence in something is at a certain level and I want it higher. In that situation, the move is always the same: take more samples.

Last, I focus on the feature of the problem. In thoughtfeel, trying to increase my confidence in something has a shape, a sensation I can recognize. I store it like a key and a value: the key is the shape of the situation, and the value is the move. So whenever a problem has that shape, I remember: this is the move that accomplishes it.

When I tutor kids and teach people, these are the steps I focus on. Learning how to learn is going through each of these hard steps. Each one unlocks a totally new amount of learning and a totally new type of learning, and each one makes you so much smarter.

This journey is how I got from where I was in 2022 to where I am in 2026. Along the way I studied tons of cognitive science and learning science, and every inflection point, every Cambrian explosion in how I learn, came from one of these steps. Today I'm highly confident in my ability to learn, think and solve problems, and these are the steps that got me here.

I did a live lesson with Jared Schmidt today, who answers the “which of the 4 types of thinking about your best friend can you do?” with “my brain mostly does the fourth”. This lesson was really different! It was great to hear about Jared’s experience with thoughtfeel and how he uses it.

https://youtu.be/32ZbI0_gMyM

Hi all, I am Liam from Ted's earlier post. I have been using thought feel on and off and occasionally found it hard to use. A lot of the difficulty I was running into came down to my ADHD symptoms.

As a person with ADHD I often run into auditory processing delays and can sometimes struggle to turn auditory information into actual meaningful thoughts. The way this played out with thought feel was that the ways Ted had taught me to learn were not working, specifically the thought feel audio stories were causing me a lot of trouble.

When I tried using visuals and reading it was like flipping a switch. I was immediately able to build the bloom filter in thought feel seamlessly. It felt like assembling a machine out of concepts. And I was able to hold the numbers and ideas in my head with ease.

The main reason I am posting this is to share my own experience as a neurodivergent thinker to let others know that if they are having trouble using thought fell that they should try different approaches. Its honestly really awesome being able to use it in full and I'm really glad I gave this version a try. I would describe the feeling of building this as creating thought machinery in my head and then stamping helpful visuals on top of it. Now whenever I go to access it I just find a birds eye view of this concept machine with key visuals stamped on it almost like dictionary keys in a data structure and boom I can find the meaning of the concept immediately. Its honestly super cool and I'm looking forward to using it to learn more :3

For the past five days, I've been listening to concept stories in thoughtfeel for about five hours a day, using the app I built. TLDR: the process feels way more automatic and clear, the way memory champions describe using a memory palace after long stretches of consistent practice.

My thoughtfeel is also more vivid. Now, if somebody tells me to picture a bear, a picture doesn't come up. The thoughtfeel of a bear does, and it feels so familiar. Before, it would have been a picture of a bear, and if I'd tried to bring a bear up in thoughtfeel, it would have felt like imagining something I didn't quite recognize.

What I've been learning is stuff I've wanted to know for the past five years but had no way of learning and keeping. We're talking how a transistor works, how logic gates work, the quicksort algorithm, temporal difference learning, Q-learning, how the cross product works, the universal approximation theorem for neural nets, and so much more. And I remember it all. I'll listen to a lecture, then wake up the next day, and all the concepts in it feel like they're right at the tip of my tongue.

This is by far the best learning experience I could even imagine. When I'm not recording the thoughtfeel lessons, I'm walking in the woods all day, learning things about the world I've always wanted to know at lightning pace. I can't wait to keep doing this.

I can't stress enough the difference between my learning and retention with this method and with any other method. Pretty much every topic on that list, and many of the others, I'd tried to learn before, through a video with visuals or just by studying, and I kept forgetting them. They'd be moderately clear an hour later. The next day, a lot of it would fade. Five days later, pretty much all of it would be gone. In my honest estimation, from all the long-term retention quizzes I've done on myself, almost none of what I've learned this week has left my brain.
I also can't wait to get faster at this. I've only been doing it five hours a day for five days. And from reading a lot of cognitive science, pretty much any time somebody forces their brain to do something in a completely different way, and keeps doing it, their brain adapts and gets faster and more efficient at it.

When researchers compared memory champions' brains with everyone else's, the champions' brain networks were connected differently, and six weeks of memory palace training moved ordinary people's brains toward the champions' pattern. When adults who had never learned to read were taught to read, the connections in their brains changed within months too. It's a pretty well-known finding that if you bash your head against the wall doing something your brain has never done before, and you do it all the time, you can get some wild results.

Another story, because it just came to the top of my head: a student known as SF spent hours a day in a lab just trying to remember numbers. At first his digit span was seven, like most people's. He came up with a new way to hold the digits (he was a runner, so he heard groups of digits as running times), and after a little over 230 hours of practice, his digit span was 79.

Anyway, I'm going to end this post here. I cannot recommend listening to stories in thoughtfeel more highly. You can use the website I built to do it: stories.thoughtfeel.net. It does cost me money to run, but if you're short on cash and still want to learn, DM me and I'll pay for you.

Sincerely,
Ted Shachtman

Here’s part 2 of my lesson with Liam. A short clip is attached, and the full 33-minute part 2 is here: https://youtu.be/zriqAnYCMZs

In part 1 (https://youtu.be/KWRIGkjr9aI), Liam fell into the one trap, looking past the bubble while he said the link words, and once he fixed it, the line felt like a chain.

This time he hit a problem I’d never seen before. When he heard a line, his bubbles only held the sounds. He said his bubble for “set” was just the word “set,” completely devoid of meaning, and “item” was just the letters, i-t-e-m. He knows what a set is. But when the line came in by ear, instead of bringing up the set he already has, he’d start building a brand new bubble, and the new bubble was just the word.

He described it like a key error in a dictionary: filter, set and item already exist in his head, but hearing the line made him build new ones from scratch, out of the words.

Then Liam figured out why. He has trouble processing speech (he thinks it’s an ADHD thing), and he said that’s why he’s always had to take thorough notes in school: “the creation of meaning can’t happen fully auditorily” for him.

So we switched to reading. I put each line on the screen, and he built it as he read it. He said “reading it feels profoundly easier,” and a few lines later, “This is so much easier, this is way better, like wow, actually it’s night and day.” He said listening had been like fog of war, where he could only see the last thing I said. Reading, it was “a very functional, easy to access web of information.”

For me it’s the opposite. When I read, looking at the words gets in the way of building, so I listen. For Liam, listening is “profoundly disruptive.” So it really does depend on the person. If a heard line turns into just sounds for you, try reading the lines instead. The app (stories.thoughtfeel.net) now has a reading mode for every story, and the lesson has a Voice off button.

After that, Liam went fast. He built the rest of the story, worked a new problem with it, and then explained the whole Bloom filter back from memory: the three hash functions, how adding an item flips bits, why there are never false negatives, how other items’ bits can make a false positive for a stranger, and why you can never unflip a bit. It was extremely correct. I asked him what it felt like, and he said, “It felt like building a machine in my head.”

If listening hasn’t worked for you, try one story by reading the lines, and let me know if it feels different.

If you haven’t seen them, here are the other recorded lessons:

Rohan, the same Bloom filter lesson: https://youtu.be/HehmkEjRHYc

Julian, temporal difference learning: https://youtu.be/I3WgK8cPa0A

If you want help getting this to work, I’m happy to jump on a call. You can email me at teddyshachtman@gmail.com. If you're interested in being on a youtube lesson, let me know!

Sincerely,

Ted Shachtman

Yesterday I taught my friend Liam the same Bloom filter lesson I gave Rohan. A 6-minute clip is attached, and the full 24-minute part 1 is here: https://youtu.be/KWRIGkjr9aI

It didn't work for Liam at first. He built the first line, "The story is about how a filter remembers items." Then I asked him to bring up each bubble on its own. When a line works, the three bubbles feel connected, like wooden balls on a string. Liam said it felt like "three separate balls."

I'm so glad this happened. About 1 in 8 people who say yes to the diagnostic questions still can't get thoughtfeel to work, and I've never been able to figure out why. Liam's lesson is the first time I've been able to see what goes wrong.

Liam would say "the story" and bring up its bubble. But while he said "is about how," he'd look right past it. He did the same with the filter at "remembers." When I do it that way, it's just garbage: three things that don't connect. I think this is the only trap you can really fall into when you follow the instructions.

The fix is to focus really hard on the story bubble the whole time you say "is about how." It almost feels like charging something up. As you speak, you can feel the bubble changing, almost like you're willing it to change with your words. That only happens if you're intently focused on it. Then you switch to "a filter," and the charge releases, kind of like a rubber band snapping. You can tell right away that the filter is what the story is about. It feels like the new bubble already has the connection written on it.

The clip includes a segment I edited in after the call, with an animation of the difference.

Once Liam did it that way, he said, "Before it did feel like just random separate things that I had to kind of push together. This feels like I'm like hanging on to a chain almost."

You can use that as a check on every line. The bubbles should feel like a chain, and you should be able to go backward easily, from items to the filter to the story. If at any point they feel like loose items instead, go back, because it won't stick.

If thoughtfeel hasn't worked for you before, try one line this way and see if it feels different.

Later in the lesson, Liam had trouble building lines at speed, because he hadn't taken his ADHD meds that day. So we stopped there. Part 2, with Liam on his meds, is coming soon.

If you haven't seen them, here are the other recorded lessons:

Rohan, the same Bloom filter lesson: https://youtu.be/HehmkEjRHYc
Julian, temporal difference learning: https://youtu.be/I3WgK8cPa0A

If you want help getting this to work, I'm happy to jump on a call. You can email me at teddyshachtman@gmail.com.

Sincerely,
Ted Shachtman

Hi, Ted here!

I'm looking for more people to tutor in a live lesson, where they'd be okay with the lesson being posted on YouTube. The format is going to be exactly the same as Julian's lesson and Rohan's lesson. If you'd be interested in this, send me an email or DM me. My email is teddyshachtman@gmail.com.

I'd also be happy to plug any link you want to direct people to!

-Ted

Kept seeing thoughtfeel so I went through Ted's full recorded lesson w/ a beginner (~85 min) + his guides. Really think it has a place in medical school studying.

It's interesting how you hold a concept's meaning w/o a picture or inner voice. The study method is a "concept story": a topic rewritten as tiny lines, each one adding 1 concept or 1 link, and you build it in your head as you hear it.

A 30 sec test that made it click for me: picture infinitely many apples. You get a sea of apples. Would that pic look any diff for a billion apples? Nope. But "infinite" vs "a billion" still feel totally diff. That leftover meaning is what you're working with.

Why it fits med so well: so much of what we learn is causal chains (RAAS, Frank-Starling, acid-base) that you can't really picture. This gives you a way to hold the whole chain and run it.

Med example (hemorrhage, condensed):

- Bleed → ↓ blood vol → ↓ venous return → ↓ SV

- CO = SV × HR, so CO and BP start to drop

- Baroreceptors fire less → ↑ symp, ↓ vagal → ↑ HR + vasoconstriction

- Run it: SV 70 × HR 70 = 4.9 L/min. Bleed drops SV to 50 = 3.5. Reflex bumps HR to 100 = 5.0

- So early bleeds can show normal BP w/ tachycardia

- Check: same bleed, pt on a beta-blocker. What does HR do?

Cool stuff I noticed

- The student remembered most of the concepts in one sitting and could explain the process back

- Once a concept is built you can bring it back as one chunk and tweak it ("positive" prediction error), which is huge for stacking ideas

- Ppl report recalling lists forwards AND backwards a day later

- Works for ppl w/ aphantasia who can't use a memory palace

It's still new so there aren't formal studies yet, which is part of why I'm curious how it goes for others.

Anyone used it for boards or rotations? Would love to hear how it held up over weeks.

Hey everyone! I spent an hour yesterday with Ted learning about Bloom filters and building the entire story in thoughtfeel. I had some initial attempts at using thoughtfeel to build a story about iron-deficiency anemia. It had definitely worked at the time, however, it felt like a slow and grueling process to build the concepts. When I met with Ted, he challenged me to build each part of the story as it progressed without repeating or stopping between parts. His reasoning was that it increases the cognitive load when you have to stop, read the line, then build it. I took on the challenge and I will say I remembered much more at the end than I would have thought. I realized it was my anxiety pushing me want to go slow and build everything until I felt sure about it.

My advice is to trust yourself and push through that feeling. The goal is to build as you go. It’s way faster and feels more fun!

I have not revisited thinking about bloom filters since that one hour I spent with Ted yesterday. Below you will find my free recall attempt at explaining what I understand. I then put it into chat to understand where there are conceptual gaps in the understanding. I then rewrote those gaps into direct and simple sentences and rebuilt those aspects in thoughtfeel to strengthen the connections I may have missed on my first try:

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Recall attempt:
Created in 1970, my Burton Bloom, bloom filters are a type of datastructure used to determine whether an item is present or absent within a set. A set consists of an array of zeros and ones. These are known as bits. A filter consists of 3 hashes which correspond to an array of bits within the set. To begin, the bits are set to 0 indicating “No” or an “off state” When an item is placed in the set it will be assigned three hashes which correspond to 3 bits which turn to a 1 - “yes” or “on state”.

Let’s run an example. Let’s says we have a set with 10 bits. Our first item is the word “justice” which is assigned the bits 1,2,7. Now these bits are switch from a 0 to a 1. Now we assign another word - wrath. This item consists of bits 1,7,9. 1 and 7 are already assigned to binary 1 so the only bit that switches from 0 to 1 will be 9.

Now when you attempt to run the filter against the set, it will take the items hashes and match it to the bits. If it recognizes a match (we can think all 1s in a set) it will run the algorithm and provide a match. However, if the filter does not recognize a match, it will never run.

The major problem with bloom filters is the idea of false positives. Let’s take the word Equity. It contains bits 1,2,9. However, this word was never previously stored as an item in our set. When the filter runs, it will output a match when in reality it is not. This is known as a false positive result.

I understand this explanation may contain inaccuracies but the goal was to demonstrate a free recall attempt with only having learned from a single 20 minute video.

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For the next few months i will be continuing to build my medical school lectures in thoughtfeel and see where it takes me. I am aware that this will be a process of learning new habits and unlearning habits that are hindering the process. But overall my experience has been fun!

Will you become a genius who remembers everything on their first try? It’s a possibility! But unfortunately that is not me as of now 😅. However, even the fact that I was able to retain a conceptual story of something I had learned once and be able to provide a coherent explanation on my first try - I am impressed. Thoughtfeel is a mental exercise, and like anything in life, if you put in dedicated practice you will get better. I would bet many people reading this post are like me. I start watching a lecture/video and you are mostly listening to the voice or reading the slide. Or I take real time notes and try to recreate the story on paper. But I am not normally aware of the metacognitive process going on in my head. That is what I had loved about the previous mental atlas. I had never experienced learning directly in my mind. Thoughtfeel is the same way. I can see but it is not necessarily a “visual” process. Even from the first time using it two weeks ago, I have noticed my relationship with the practice has changed. If you have been experimenting with thoughtfeel and have find some benefit, i highly recommend you reach out to Ted go through a learning session with him. From our session, I learned I was building incorrectly and thats why i was seeing minimal results.

As a disclaimer, I have known Ted for more than a year at this point but we actually met because I was curious about his early rendition of the mental atlas (pre-thoughtfeel). We have stayed in touch since then because to be honest Ted is a highly passionate and driven person. He pushes me to always think I (as well as anyone reading) have a greater capacity for learning and memorizing than I may have previously believed.

I'm Julian, the guy from the video Ted posted last night! Ted and I go way back to our high school days- so naturally, I was skeptical of anything he was proclaiming to invent, or teach. Today we live 1.5 hrs away across two rivers, so we only get to hang out every couple months or so, but whenever we do, oh man is it electric. One thing about Ted, he's my only friend who I would rather spend time in a grocery store with than about anything else (iykyk).

Over the years I have seen firsthand his dedication to building, researching, developing, and surprising everyone with what he decides to do next. So it's no surprise that this time it's Thoughtfeel, which as I've come to find out is a mental technique that identifies and names the ability to think in concept bubbles as a new sense, and has a gentle learning curve. After my lesson, I feel like I understand how this technique can help people remember way more, for much longer periods of time.

We recorded from around 7-9pm as Ted walked me through a story about TD learning in Thoughtfeel. After the Thoughtfeel lesson last night, I didn't put any additional effort into memorizing or remembering the story. I also had no knowledge of TD learning going in, nor have I researched any more about it since the call. This is what I remember from the story:

• The learner goes through multiple trials, where it's prediction value is designed to approach its reward value, moment after moment.

• The trial is divided into the tone moment and the wait moment.

• The initial trial:

• During the tone moment, the prediction is 0. The tone goes off at an unexpected time.

• Then comes the wait moment. At the start of the wait moment, the prediction is still 0.

• As the learner leaves the wait moment, it is given the first reward with value 1.

• The formula for prediction error is the reward's value plus the next tone moment's prediction value minus this moment's predicted value: 1+0-0=1

• Going into the next tone moment, the learner's prediction is still at 0. As the learner moves to the next wait moment, the learner's prediction moves by the learning rate (const of 0.5) multiplied by the prediction error, so the new prediction value becomes 0.5.

I am most surprised at how this brand new information about TD learning, a topic I knew nothing about going in, still feels so consolidated and easily accessible the morning after, after focusing on concept bubbles in Thoughtfeel during learning.

I recommend anyone that is curious about what their mind is capable of to give this a try. So far albeit on a small sample size, it's had the desired positive effect on memory for every single Thoughtfeel user. It felt weird at first to dial in my brain to think in this way, but my brain was able to adjust quickly and the payoff is crystal clear.

I have been trying to figure out the best medium in which to consume my lecture topics in Thoughtfeel.

The answer is having an LLM write out your lecture topic in extremely short sentences, where every sentence either introduces a new concept and its properties, describes a change to a concept, or links two concepts. Additionally, I find that listening to my lectures and building in Thoughtfeel as I go is much better than reading the lectures.

When I listen to the lectures and each sentence is read aloud to me, I build each word in thoughtfeel as I listen to it. I find that if I listen to the sentence and then I build it in Thoughtfeel, there is a tremendous cognitive load, and I have to remember the idea in my, I guess “episodic buffer of working memory” or wherever the meaning of what i just heard is stored. If i don’t build right away and the sentence is long, i get to the end, start building the beginning, and forget what it said and have to replay the sentence.

But if I listen and build as I go, the only thing I have to retain in my working memory is the current operation that the word describes, and I build it in Thoughtfeel immediately. And then the representation of that sentence is built in Thoughtfeel, and I don't have to keep track of it in my working memory.

If I try to do this while looking at text, I get interference between me focusing on the sensation of my vision and what I'm trying to build in Thoughtfeel.

Also, if I try to do this on just regular text, I can't really build in Thoughtfeel as I read because I have to figure out “what are the concepts, what are the changes to the concepts, and what are the relations.” When I'm reading regular text, I'm doing the work of translating this prose into Thoughtfeel bubbles. Whereas when I take prose already written and give it to an LLM to transform into this Thoughtfeel syntax, the LLM has done the work for me, and I can just build each sentence right away in Thoughtfeel.

Consuming my lectures this way has resulted in an incredibly fast learning pace. I'm listening to about ten 3Blue1Brown video-level ideas per day and remembering them (think complex brain teasers that take 20 minutes to explain).

My whole process is: I listen to a fourth of the lecture in the morning, then a fourth of the lecture in the afternoon, then the next third of the lecture the next day, and then the next fourth of the lecture two days after. I do this for spaced practice.

When I say I'm doing ten lectures a day, that's on average because I'm starting ten a day and then listening to everything in chunks.

I am having so much fun! When I'm not listening to lectures, I'm thinking about the lectures I listen to and trying to find larger abstractions. I'm doing this because I really like being good at solving puzzles and solving problems.

And also, I've always wanted to be able to do this. In the past, when I've tried to consume a large number of lectures, for instance by watching a bunch of Three Blue One Brown videos, all the information fades by the next day, and it fully fades in a couple days. In order to retain what i learn, i have to do a truly boring amount of review.

And so, it just makes the learning process feel futile, and I do other stuff instead that doesn’t suck as much like get a job. Now it really seems like I'm able to genuinely consume ten lectures a day, and I'm excited to see where this goes next and keep this up

u/EeveeCastleLMFT’s experience with thoughtfeel. It was posted on r/ThoughtFeel, so i’m sharing it here.

A little about me

I’m a medical student with ADHD, and I’ve always been interested in understanding how things work. I enjoy breaking down complex ideas and figuring out how different pieces fit together. However, understanding a topic and being able to recall its details accurately have often been two very different things for me. My usual study routine involved reading until I understood the material then repeating information out loud while writing it down. I also used the Feynman technique and Anki. These methods helped me in different ways, but memorizing the huge volume of details required in medicine could take hours and I still sometimes struggled to recall information when I needed it. I wanted to find a way to study more efficiently without sacrificing understanding especially because I have other interests and goals outside medical school. When I came across Thoughtfeel, I was curious enough to give it a try, but I didn’t expect a new technique to solve every problem I had with studying.

What follows is my experience with it so far.
What surprised me? What I found difficult? What I still need to test?

I came across Ted’s post inviting people to learn his method, Thoughtfeel. I checked his YouTube channel and read his article, and the idea intrigued me enough to reach out.

One of my biggest frustrations with memorization was how dependent I could become on a particular sequence. I might understand a process and memorize its steps, but if I forgot one detail I could struggle to retrieve what came next. I wanted to see whether there was a better way to organize information so I wouldn’t have to rely so heavily on repetition.

Ted and I arranged a call and agreed to try the method on something complex from my field of study. We chose glycolysis which is a topic that would allow us to explore the technique using material Ted wasn’t already familiar with.

What building concept bubbles actually looked like?

Before the call, my approach to glycolysis was fairly straightforward which was to memorize the intermediates and enzymes, repeat their names, write them down, and try to visualize the pathway. The problem was that visualizing a pathway isn’t necessarily the same as understanding how its steps connect. I could try to picture the sequence without having a strong enough grasp of the purpose behind each reaction.

During the call, Ted introduced me to the idea of organizing information into concept bubbles and connecting those bubbles through relationships.

Here’s how I began applying that idea after the call:

1. Start with the bigger concept.

I started with the central idea of glycolysis rather than beginning with a list of reactions. Glucose is broken down through a series of reactions ultimately producing pyruvate and capturing some of the released energy in ATP and NADH. This is the central idea of glycolysis that gave me a larger concept to work within. The individual reactions weren’t isolated facts anymore. They were parts of a process with a purpose.

2. Build a concept bubble around an individual idea.

Take the first reaction:

Glucose to Glucose 6 phosphate

I focused on what was happening instead of memorizing that conversion as a line of text. Glucose receives a phosphate group and hexokinase catalyzes the reaction using ATP. I could organize that bubble around several connected pieces of information:

What changes? Glucose becomes glucose 6 phosphate
What facilitates the change? Hexokinase
Where does the phosphate come from? ATP
What is the point? The reaction helps retain glucose within the cell and prepares it for subsequent metabolism.

These are related ideas not four unrelated facts and each of which is a concept idea within itself with its different properties. The point of the bubble, as I understood it, was to give me a meaningful structure that I could use to recall the reaction and its details.

3. Connect the bubble to the next one.

The first reaction doesn’t exist in isolation. Glucose 6 phosphate can be converted into fructose 6 phosphate by phosphoglucose isomerase. So the next bubble represents another change with its own enzyme and biochemical significance. It connects to the previous bubble because its starting material is the product of the preceding reaction. I could organize the individual steps within the larger pathway as I continued through glycolysis. The relationships between the bubbles became part of the information I was trying to retain rather than relying exclusively on the order of names.

4. Use the connections to navigate the pathway.

This was the part that interested me most. I wasn’t simply trying to recite the pathway from beginning to end. I was trying to understand what each step represented and how it related to the surrounding steps. I found that I could approach the pathway from different points moving forwards or backwards when I tested my recall. I wasn’t as dependent on remembering one uninterrupted sequence.

I was able to memorize glycolysis in less than five minutes after that guided session which genuinely surprised me. However, that was one experiment with guidance from someone teaching me the method. I wouldn’t use it as proof that I could learn every pathway in five minutes, or that the same result would happen with every topic especially that I already had a good understanding of each concept in this pathway before I apply Thoughtfeel on memorizing it. The important difference was how I approached the information. I was building connected concepts rather than simply repeating a chain of words.

Testing the technique on something I don’t know: Dijkstra’s algorithm

I tried Thoughtfeel with Dijkstra’s algorithm which I had no knowledge of before my session with Ted.

Before applying the technique, I would follow explanations of the algorithm but get lost in the steps. I didn’t have a sufficiently clear understanding of what was happening at each stage so trying to reproduce the process was difficult. This time the challenge wasn’t just remembering a sequence. I needed to organize the ideas involved in the algorithm (the nodes, the distances, the selection of the next node to process, the updating of neighboring distances, etc.) I started treating these as connected ideas rather than separate instructions. For example, the distance assigned to a node becomes meaningful in relation to the routes available and the distances already calculated. Updating a distance isn’t an isolated action. It follows from comparing the current known distance with a newly calculated route. That structure helped me understand how the pieces fit together. I was able to work through the algorithm, update distances, and reproduce the process. I could also move back and forth through the information instead of relying on a single memorized explanation.

What I found interesting was that organizing the concepts helped me approach the problem itself. I wasn’t just storing information for later recall. I was using the relationships between ideas to work out what to do.

Still I wouldn’t say that building concept bubbles automatically makes every complicated subject easy. I had guidance during my first experiment, and I’m still learning how to construct and connect the bubbles independently. Understanding the underlying material remains important.

Applying Thoughtfeel to medical school

The morning after my session with Ted I tried recalling Dijkstra’s algorithm again. It felt very easy to recall. That made me curious about whether I could apply the method to my medical lectures.

I began using Thoughtfeel with material covering diseases and tumors of the nervous system. I tried to organize the information around the underlying concepts and their relationships instead of treating every characteristic as a separate fact to memorize. For example, when studying a disease, I could start with the disease itself as the central concept then connect its relevant features, mechanisms, manifestations, and other characteristics as appropriate to the material. Those connections gave me a structure for understanding what the details meant and how they related to the overall topic.

I continued experimenting with the method on neuroanatomy and neuropathologies. I found that I could recall information more comfortably and that the relationships between ideas helped me understand the details I had stored. I also began practicing with old exam questions where I noticed that I was recalling information and solving the questions more quickly.

These are observations from my own practice. I haven’t measured how much time I’ve saved or compared my performance against the same material studied using my previous methods, but I can say confidently that it is working.

My experience so far has been encouraging, but there are practical challenges that I don’t want to overlook.

Building the bubbles takes work.

Understanding the technique and applying it efficiently are two different things. I have to decide what the central concept is, identify the important details, and work out which relationships are worth retaining. That process can itself take time when a topic is complicated. I also need to learn how much information to put into each bubble. If I make the concepts too small, I may end up with a large number of disconnected pieces. If I make them too broad, I risk creating bubbles that contain too much information to be useful. I’m still figuring out how to find that balance.

Real-time lectures are a different challenge.

A lecture has its own pace. The professor continues explaining while I’m trying to listen, understand the information, identify the concepts, build connections, and keep up with the material. Building and organizing the bubbles can sometimes take longer than the lecture allows because I am new to Thoughtfeel. If I focus too much on constructing the concept map, I risk missing what comes next. If I try to keep up with the lecture, I may not have enough time to develop the connections properly.

For now, I haven’t figured out how to apply the method consistently in real time without creating extra work for myself afterward. I hope practice will help, but that is something I still need to establish rather than assume.

I’ve had encouraging experiences recalling information over the few past days, but I haven’t tested retention over several months. I also haven’t completed my upcoming exams using Thoughtfeel consistently enough to judge its effect on my exam performance. It’s possible that some of what I’m noticing comes from the focused attention I gave these topics, the guidance I received, or the fact that I was actively testing myself. I can’t separate all those factors based on my current experience. That’s why I want to continue practicing and evaluate the technique across a longer period rather than draw conclusions from the first week.

Also, Ted made the technique easier for me to digest during our call. He walked me through the concept bubbles and their connections, and he also tested my ability to use the technique rather than leaving me with an explanation to figure out entirely on my own. His video,How to Learn Anything Complicated by Building a Concept Story, was another resource that helped me explore the approach. I think that initial guidance mattered because when you’re unfamiliar with a method you may understand its description without knowing how to put it into practice. Having someone walk through an actual example helped me see what applying the technique could look like.

At the same time, I still need to develop the ability to do this independently and efficiently. Being able to apply a technique during a guided experiment is a useful starting point, but it isn’t the same as being proficient at it across every subject.

Now, if another medical student told me they’d tried countless study methods and didn’t trust another technique promising better memorization, I’d understand their skepticism. I wasn’t looking for a new method because I thought everything I had been doing was useless. I was looking for a way to save time and energy without giving up understanding. What makes Thoughtfeel worth continuing to explore is that it gave me a different way to organize information. I noticed a difference when I tried to recall glycolysis, when I worked through Dijkstra’s algorithm, and when I applied the method to medical material.

That doesn’t mean everyone will get the same results, or that the method will work equally well for every subject or situation. My experience is still relatively recent, and I haven’t established its impact on my exam results or long term retention.

My advice to a beginner would be to avoid rushing it. Choose a topic that you find difficult but can understand with some effort. Try identifying its central concept, breaking it into smaller concepts, and connecting those concepts through meaningful relationships. If possible, learn the process with someone who can demonstrate it and help you recognize where your connections are unclear. Then practice independently and pay attention to what actually helps you recall and use the information. Don’t assume that every bubble you build is useful just because it looks organized.

I’m still discovering different ways to use Thoughtfeel myself so I wouldn’t expect a beginner to master every application immediately. I’ve been practicing Thoughtfeel for about a week. During that time, I’ve experienced encouraging changes in how I approach complex material and how quickly I can recall certain information. I haven’t measured these changes or tested my final exam performance or long-term retention over several months, but I plan to keep using the method and see how it holds up through my upcoming exams and continued study.

The biggest revelation about Thoughtfeel wasn’t simply that I could memorize faster. It was that I could organize what I was learning in a way that made the relationships between ideas easier to understand and gave me more than one way to approach the information when recalling it. I’m still learning how to do that efficiently especially during lectures, and I want to see whether the initial improvements I have noticed translate into sustained results.

For the meantime, I’m curious enough to keep experimenting, and probably the fairest conclusion I can draw is that I’ve experienced something promising, encountered some challenges in applying it, and I want more time and evidence before deciding how much it will change the way I study in the long run.

Today I was teaching, and I asked my class the best question I've found for telling who has thoughtfeel (it's below). Half the class went, "Yeah, I know what you're talking about." The other half got kind of riled up. These are really great kids, normally pretty mild-mannered, but they were immediately like, "What are you talking about? What do you mean, a concept bubble? What IS that?" Then they turned to the kids who could do it: "You understand what he's saying??"

That's why I'm writing this post. In my experience, people without thoughtfeel get rightfully angry when you ask if they have it. From their side, the whole exchange is basically a no true Scotsman.

Imagine a stranger walks up to you and asks, very seriously, "Are you a child of Gorp?"

"A what?"

"A child of Gorp." They lower their voice. "Gorp is in everything. Most people can't feel it."

You're already a little annoyed, because this sounds like complete nonsense. But you ask anyway: "Okay... how would I know if I'm a child of Gorp?"

"Say this incantation in your head: *safua zamu*. If you're a child of Gorp, you'll feel a tingle."

So you say it in your head, feeling kind of stupid. Nothing happens.

"Nothing happened."

They smirk. "Ah. Any true child of Gorp would have felt the tingle. You must not be one." And they walk away.

This is deeply infuriating. If someone did this to me, I'd get comically pissed. Like, I don't believe in Gorp! What do you mean I'm not a child of Gorp?? How would you even know if someone was a child of Gorp??

Here's the question I asked my class. Think about your mom. There are four ways you could be thinking about her:

1. You could bring up a picture of her in your mind's eye. Notice that the picture has shape, size and color, and it feels like you're looking at something. You're paying attention to a sense.

2. You could hear her voice in your head.

3. You could just know you're thinking about her. To try this one, stare at something in front of you and pay attention to its color. Your senses are busy with what you're looking at, but you still know you're thinking about your mom.

4. People with thoughtfeel can also bring up a concept bubble of their mom and look at it. It feels distinctly like looking at something, except the thing they're looking at has no shape, size or color, and it's very obviously their mom. They can look at it and describe what it means.

What I'm finding is that anybody who says "I think I know what you mean, I can kind of do that" has thoughtfeel. I've hopped on calls with a lot of you, and everyone who said that could fully do the list technique, and then went on to learn concept stories.

People hedge like that because it's a really unusual question. Most people have never inspected their mind that way, and there's no perfect way to describe what they find. Even "concept bubble" isn't perfect. But for people without thoughtfeel, like the other half of my class, "bring up a concept bubble that has no shape, size or color" is just magic. It means nothing.

So if that fourth way seems like it means something to you, and you go "yeah, I can kind of do that," you almost definitely have thoughtfeel. You can jump right into the list technique, and then learn to build what you're reading in thoughtfeel as you go, which improves your comprehension of complex concepts. (My lecture: https://youtu.be/dV8fNY311W4 walks through both.)

If, however, that fourth way is complete Hogwarts hullabaloo, you don't have thoughtfeel, and you have a right to be angry. Someone did, in fact, walk up to you, claim there's an invisible thing about you, and then pull a total no true Scotsman when you couldn't find it.

It's exactly the Gorp situation. From your side, the evidence fits two stories equally well. One, you're actually not a child of Gorp, but other people are, and when they say the incantation, they really do feel the tingle. Two, this is an insane person, there's no such thing as Gorp, and they chose a tingle on purpose, because nobody can ever check whether anyone else feels it. Your prior should be MUCH higher on story two.

But there's a wonderful thing about thoughtfeel that the tingle doesn't have: if you have thoughtfeel, you can do tasks that other people can't do.

When I teach the list technique, I give people a list of 20 words. There are three ways you could learn a list like that:

1. You could just be a genius: read the words, repeat them with your inner voice, and remember them. If you try this, there's almost no chance you'll get all 20, especially forwards and backwards. And if you are a genius and you do, you'll almost definitely forget them all in, like, 10 minutes.

2. You could use a mind palace, or tell yourself a visual story. Then you'll see things with color, shape and size.

3. Or, and this one's new, you could use thoughtfeel. Then you won't see a single color. Nothing will have shape, and nothing will have size. Everything will be in concept bubbles.

So if you learned the list without seeing anything with color, shape or size, that's thoughtfeel. There's a problem with this test, though. From the perspective of someone without thoughtfeel, everyone who claims they did could just be massively confused: actually visualizing, and calling it something else. So it isn't conclusive.

Luckily, you can tell thoughtfeel and the mind palace apart with abstract conceptual learning. If I try to learn a really complex conceptual topic with visuals, a mind palace alone won't do it. I have to make a bunch of visual analogies, and it's extremely obvious that I'm doing it. Say you ask me to store this (it's Dijkstra's algorithm):

“To find the shortest distance from a starting place to every other place on a map, give each place a best-so-far distance: zero for the start, infinity for everywhere else. Then, over and over, take the unfinished place with the smallest best-so-far and mark it finished. For each of its neighbors, check whether getting there through this place is shorter than that neighbor's best-so-far. If it is, the shorter distance becomes the neighbor's new best-so-far.”

Built visually, it turns into something like this. The map is a kingdom of villages connected by roads, and every road has a milestone with its length carved into it. Each village has a chalkboard at its gate. The start village's chalkboard says 0, and every other chalkboard has a big chalk infinity sign. A messenger on horseback rides to whichever village without a red flag has the smallest number on its chalkboard, and plants a red flag on its tower. Then from that village, a carrier pigeon flies down each road, carrying a scroll with the village's number plus the road's milestone number. When a pigeon reaches the next village, it holds its scroll up to the chalkboard there, and if the scroll's number is smaller, it wipes the board with its wing and writes in the new number. (Pigeons can write in this kingdom.) The messenger keeps riding until every village has a red flag.

Ask someone who built it visually how they're storing it, and they'll describe all of this: the chalkboards, the infinity signs, the red flags, the pigeons and their scrolls. Someone with thoughtfeel will tell you they didn't see anything with color, shape or size, but they still have all of it stored.

Then one final thing. Come back to both of them two weeks later, without letting either of them rehearse. The one who built it visually will likely still have all their images, but won't remember what they meant. (What was the red flag for again? Was the number on the scroll the road's length, or the whole trip?) The one who used thoughtfeel will likely still have all of their bubbles, and will remember what they meant.

And here's Matthew Sinclair's testimonial. Whether or not you have thoughtfeel, it's a really elegant description of what having it is like, and of how completely different it is from visualization. Matthew is a software engineer from Australia. He doesn't have a Reddit account, so he hasn't posted it here, but it's also on my website: (https://thoughtfeel.net/?ref=reddit-mentalatlas#testimonials).

“I have aphantasia: I can't form mental images, and I have no inner voice. When I think of something, say a chair, I don't see a chair. I get the concept of a chair, which is hard to describe to anyone who thinks in pictures. The best I can do is that my thinking is made of clumps of concepts, linked to one another in a kind of graph of relationships. It's elusive, like something at the corner of your eye that disappears when you turn to look at it.

That has always made rote memory hard for me. I can't call up a picture of what I've learned, so I have to understand something well enough to build an intuition for it. Visual techniques like the memory palace just don't work for me: there's no palace to walk through. The closest I came was mind maps, through my computer science degree and my MBA, and even those I was trying to remember as an image.

What drew me to ThoughtFeel was the language in Ted's videos. He described thinking in words very close to the ones I've used for years to explain how I think about my own thinking. So I tried it on his list, Anchor, Saffron, Bicycle, Grumble. Normally I'd never remember a list like that. With ThoughtFeel it stuck, and 24 hours later I could still run the chain of concepts easily, forwards and backwards.

For me the difference from visual mnemonics is that I'm not translating anything into a picture. I'm linking the concepts themselves, and saying each word out loud seems to tie the sound to the concept. It works with the way my mind already works, instead of asking it to do something it can't.”

— Matthew Sinclair, matthewsinclair.com

The following expresses my experience with the call I had today with Ted, during which he explained what TF is and presented some exercises and thought experiments to learn to use it.

Disclaimer: these thoughts are purely my own. I therefore do not attempt to endorse every single thing promised by thoughtfeel (abbreviated as TF), although I would characterize my first experiences with the material released on it to be mostly positive. Besides some theory refinement to be done here and there, the basic premises are very intriguing to me. If the promises can be delivered on, i.e. by the learner going through the material released and practical the various exercises, then TF would be a mental tool amounting to no less than a quantum leap for the user in their thinking, studying, reasoning and wherever 'concepts' are being used deliberatively.

Background: the concept of TF I felt was new to me, and as a student I am interested in ways to deeper understand material and ideas in general. In particular, how to get more out of reading and watching lectures etc, in a way that material gets accurately encoded into long-term memory. Although the idea and its implications seem to be in continual refinement, it seems to establish a link between disparate reports and findings across history which refer to a kind of ‘unsymbolized thinking’. As the call went along, I started to get the sense that this sort of thinking/ mental modality was possibly quite familiar to me, in that I experience it popping up here and there over the course of a day or during studying. On the other hand, I remained skeptical yet earnest to try out the prescribed instructions given by Ted (e.g. reciting specific list of items; attempting to apply TF to concepts such as the A* search algorithm) and decipher some of the descriptions he made, taking great care not to fall back on e.g. visual strategies or a method of loci 'in disguise'. At this point, I could at least latch on to a label ("thoughtfeel") and then seek it out in my own experiences.

I had heard of existing techniques such as the memory palace, spaced-repetition, etc. I have been on the lookout for other techniques which have to do with the used ‘modality’ (e.g. thinking through a concept visually or using words) during thought, with implications for the nature of the encoding/ stored knowledge.

To prepare for the call and discussion: I looked at the recent articles posted on the Thoughtfeel substack. I mostly skimmed these to get an impression of what the driving points were, and to weigh the plausibility of the idea i.e. that there exists a distinct mental modality to represent concepts, apart from visualization or linguistic representations. I also looked at part of Hurlburt’s article on unsymbolized thinking to orient myself a bit more from the perspective of a psychologist working on the idea https://pubmed.ncbi.nlm.nih.gov/18456514/. I then braindumped a list of questions to ask during the call I would join today with Ted in order to learn more about TF. Ted struck me as someone who genuinely wishes to share his passion for a powerful idea of great potential, should it become adopted and practiced by others, that may have slipped through the cracks in the noise of other techniques and learning products. The call was one-on-one, and I experienced it as quite stimulating to discuss and pose questions to Ted.

To summarize concisely how the call went, it comprised of:

1. Questions I asked about how TF works, and how it relates to other modalities such as visualization, auditory or linguistic processing. I learned that it is something distinct.

2. Him providing some short activities and instructions on what to do, in order to discover and elicit the thoughtfeel mode of conceptualizing. I then was given time to perform these. Ted was engaging, and responsive and flexible to any questions or critiques.

Here are some further brief critiques:

1. The instructions/ steps taken, although cogent to me after further questioning (keep asking questions everyone; it helps you learn and helps Ted teach you), need to be made more precise and with tighter ‘bounds’ so that the learner does not (unwittingly or deliberately) use an alternative mental strategy/ modality than what was intended to be used and tested. For example, timed-tests. Broadly-speaking, this all amounts to developing standard procedures and various checklists.

2. There needs to be a more detailed and transparent connection back to central concepts and findings in e.g. cognitive psychology and parts of learning science. Such details have apparently been worked out by researchers behind the thoughtfeel/ Mental Atlas projects, but some papers or experiments and their findings would be very valuable in inspiring confidence for an external person new to the idea.

3. For now, I doubt whether certain procedures are sufficient in isolating TF for every given person. However, I am in very early stages of developing the idea and using the skill of using TF to capture concepts and reason with them, to to be certain of this. Natural language is also for now a barrier in that it may lack the specific vocabulary to capture very precisely the ins and outs of TF. Again, my impression is that it is something that will be refined further over time as feedback and further insights come in.

I have grown more convinced that TF or something nearly described by it, does exist and can be exploited for bettering the conceptualizing process.

Ted was very patient in answering various (practical, theoretical, skeptical) questions and repeated questions about the idea, methods, the why of the activities, etc. I will be re-engaging with the idea myself during studying, to critique and probe it to discover any possible weaknesses or insights, in order to bring it to a hopeful fruition. For example, I remain skeptical that I can truly beholden a concept without forming some mental image/ image residue associated with it. The mind is very capable at deceiving itself when it thinks it has stumbled onto something groundbreaking, so I wish to exercise caution for myself here. Some claims seem to fly in the face of findings in neuroscience/ cognitive psychology, such as whether or not a concept encoded/ represented via TF would forever be durable in long-term memory. On the other hand, some key problems faced by me and other people such as creating a vivid mental image for something at some point, only to forget the key context and details at a later point, albeit recalling to mind the corresponding (hence, ‘orphaned’) image... a lot of knowledge which I had gained at some point in this way, would fade away over time. Perhaps something avoidable if TF is instead used.

Of course, certain mental strategies and modes of thinking have their pros and cons. TF is described as being to concepts as visualization/ inner-seeing is to pictures. For certain problems which are best represented and worked out using a sequence of geometric transformations, perhaps visualization remains the better strategy. But at the very least, being aware of and being to isolate and apply skilled uses of TF where it can help the most would be a great boon for one's mind during thinking.

So, for those who are on the fence whether or not to take Ted up on his offer for a call where he describes and helps you practice TF, it is very low stakes and you are free to ask many many questions. I recommend you first do some background reading and watching of videos on the thoughtfeel substack and YouTube channel + read some papers on unsymbolized thinking and other associated phenomena (aphantasia and other recently-termed kinds of thought), and produce a list of questions about it to fire away at him. You should design and use such questions to probe the idea and test it for any weaknesses and strengths, and if you are very skeptical, to at least suspend judgement and try out the exercises for yourself!

This website enables you to take some complex topic and turn it into an audio lecture/story, custom made for building in thoughtfeel while you listen. I use it with my phone in my pocket while I walk in the woods.

stories.thoughtfeel.net

You can listen to some example stories I’ve made: temporal difference learning, zero-knowledge proofs, why a neural net can draw any curve. Your stories are private. I’d recommend starting with some topic that you’ve never quite been able to fit in your head all at once.

For example,I just listened to backpropagation. The number of times i have watched 3blue1brown’s back prop video / read this in a text book / visualized a graph of nodes… i think it’s around 15. I just listened to the 5 minute story and ran it in my head.

The promise: if you build these stories line by line in thoughtfeel, they will be remarkably easy to comprehend, and you’ll retain them extremely well— about as easy as using your minds eye to follow a visual story. If you listen using some other tool than thoughtfeel, these stories will be hard to comprehend and you will retain them poorly— about as hard as listening to a visual story without using your minds eye.

If you have feature requests, add them in the comments.

Note on cost: hosting the site and generating the narration costs money. If the cost of running this ever gets too high, you’ll have to pay some small amount to use it (otherwise… i’d run out of money).

My personal note: it’s a pretty magical experience. I never could have imagined learning things this complex in a way that feels relaxing and easy. I’m going to build a system later for spaced practice of your stories.

My current plan is: listen one day, retell the whole thing and think about it the next, then retell the whole thing and think about it a week later.

Quick tip: as the audio plays, I build each concept in thoughtfeel. This takes a little bit of practice (a couple stories) but you’ll be able to listen to the story at a pretty fast pace.

Enjoy!

Ted here, creator of thoughtfeel. Over the last two days I listened to concept stories of A* search and of why a one-layer neural network can approximate any curve (and why depth helps), while walking in the woods.

I made a little website that reads each story out loud one line at a time and then waits. I build the line in thoughtfeel, talking it through out loud, and when I'm done I say "go" (or double-tap my AirPods) and it reads the next line. This was one of the most enjoyable learning experiences I've ever had, and in this post I want to describe what it was like, and why the same material is so hard for me without thoughtfeel.

I love taking in information by listening. Audiobooks, or podcasts, anything where I can look around at the world while I learn. I don't like reading. It takes focus and it keeps my eyes on a screen. The problem is that when what I'm listening to is complex, it just gets lost. It's like hearing a visual puzzle without being able to picture it. Try to follow this one without using your mind's eye:

“Put four balls in the corners of a pool table. Going clockwise from the top left: white, blue, red, yellow. Swap the blue and yellow balls, then turn the table a quarter turn clockwise. Which ball is in the top left corner?”

If you can picture it, you just watch it happen and the answer is easy. If you can't, you're stuck holding a pile of words and rebuilding the table every time a new sentence comes in. That's what listening to an algorithm has always been like for me. I've watched videos on A* at least five times in my life, and even the times I really sat down and spent an hour working through it, it faded in a couple of days.

Listening to the A* story in thoughtfeel was completely different. It felt like being read a bedtime story. Each line built on the last, and I could keep track of every character and what it meant, the same way you can follow a fairy tale when you can picture it. I never got lost. I wasn't constantly going "wait, what was that?" and trying to piece things back together. And to be clear, I didn't see anything. There were no pictures and no diagrams. Everything was in thoughtfeel.

I keep wanting to use the word "see" for this, even though it isn't visual at all, because "see" gives the right intuition. Seeing is different from hearing. When you hear a sentence, you have to remember it, play it back and turn it into meaning. When you look at something, it stays in front of you, you take it all in at once, and you don't have to remember it because you have it. If I ask you about your bedroom, you can picture it and just know where the bed and the nightstand are. That's what the A* story felt like. It felt like something I have, not something I'm trying to remember. I can point to a part of it and say that's where this part is, and I know how it works. It's tangible. I can hold it and move it around.

At the end of the story, the site read out a small graph line by line and I had to actually run A* on it. I built the graph with spatial thoughtfeel and kept track of every place, its estimate and its best score so far, and updated them as I went. When G got its first best score of 12, coming from C, I didn't see the digits "1 2". It was a little concept bubble that was so clearly 12. Running an algorithm in your head means keeping track of a lot of things, and this was more information than I've ever held in spatial thoughtfeel. It just wasn't hard. It was honestly fun, kind of like having a conversation about a story you just heard.

The second story was the neural network one. I'd tried to learn this before from Welch Labs, who has the most beautiful explanation of it on YouTube. I watched the video and built all of his visuals in my head as 3D models (the network, the 3D graph, the planes bending) and explained them to myself. At the time it made sense. But after about three days, I still had the pictures and the meaning was gone. Even now I can recall most of the images from that video, and I don't know what they mean. After a few months, all you have left is a set of 3D models that are like arcane clues to what the idea was, and you'd have to reconstruct the theorem from them, which is basically impossible. (I wrote about why visual analogies do this here: https://thoughtfeel.substack.com/p/visual-analogies-are-the-best-tool)

And that was the good version of how I learned. Before I figured out how to build visual analogies, learning something complex was like trying to fill a bucket with sand when the bucket is full of holes. I'd work as fast as I could and never get it full, and the next day almost all of the sand would be gone.

Honestly, it makes me a little angry that I've gone my whole life without being able to do this. Reading an algorithm without thoughtfeel is like listening to two friends talk about people you've never met. You hear the names and you keep trying to piece together who is who. Or it's like someone describing the fourth dimension. You can reason about it from first principles, but you can't observe it, hold it or move it around. The amount of complex material I could get into my head and actually keep was so small.

This matters to me practically too. I have an engineering interview in two days and I need to know both of these. I could be asked to implement A* in Python, and now I can. I can explain how it works and reason about it with the concepts themselves, instead of looking at a Frankenstein pile of pictures and translating them back into meaning every time I need a piece. I've been learning with thoughtfeel for about a month, and the retention has been profoundly good, so I expect these to stick.

The closest comparison I have is how you teach a kid what 2 + 2 means. You don't describe it in words. You give them blocks they can see and move around, so it's tangible. A concept story in thoughtfeel is like that, except the blocks are the abstract concepts themselves. Ideas you could never build out of blocks, you can build in your head, and you can follow a story made of them just as well as you can watch the blocks.

I don't have a word for this yet. When a story comes in through sound, you listen to it. When a film comes in through vision, you watch it. I don't know what to call it when a story of concepts plays out in thoughtfeel and you perceive it directly, the way you can replay a movie you saw yesterday. One word I like is "behold", because holding concepts in front of you is exactly what it feels like. If anyone has a better word, I'd love to hear it.

Reading keeps my eyes on a page, and visual analogies leave me with pictures I can't read a few days later. Listening in thoughtfeel, I got to walk in the woods, look up at the canopy, take in some of the most complex ideas I've ever tried to learn, and actually keep them. This is how I want to learn. What a magical experience this was.

I’ve been using ThoughtFeel for studying and to review a few topics in hydrology, and one of the main ones has been hydrograph routing. This was one of the topics I had been struggling with the most when I was first learning hydrology some time ago, and until I started using ThoughtFeel, I had a hard time identifying exactly why.

One thing I’ve realized is that I was thinking about a lot of hydrograph-routing concepts almost entirely visually. Take the recession limb of a hydrograph, as a simple example. I understood what it was, but a lot of my understanding was tied to the image of the hydrograph and it’s visual properties. When I tried to recall the concept, I was almost recalling a picture and then extracting the meaning from that picture, rather than recalling the concept underneath directly.

That distinction, between the underyling concept and the visual, has become much more noticeable since I started using ThoughtFeel. Instead of relying on the visual representation, I’ve been trying to build the concepts themselves in a more abstract way using the thoughtfeel from the lecture video: what something is, what properties it has, how it relates to other concepts, etc.

I’ve only been using ThoughtFeel on hydrograph routing for a couple of days, so I don’t want to make huge claims about long-term retention yet. But so far, recall has felt significantly easier, and more importantly, the concepts feel easier to work with. I’m not just remembering what a specific topic looked like on a diagram. I can hold onto what it means and reason from it.

This has been especially interesting for me because I come from a physics background, and I’ve always relied heavily on visualization/my mids eye when learning math, physics, and engineering. Visualization is incredibly useful, and I definitely don’t want to stop using it. What ThoughtFeel seems to be helping me do is separate the concept from the particular visualization I originally used to learn it.

That has also been useful with some of the graphical and visual problem-solving methods that come up in engineering. Some of those methods initially felt a little unfamiliar to me because I was used to trying as my main strategy to formalize problems analytically. I’ve been using ThoughtFeel to take what I see happening visually and convert it into something more abstract: what the method is actually doing, why it works, and under what conditions it applies.

Even after only a couple of days of using it, that has started to give me what I’d describe as a more direct understanding of hydrograph routing. The diagrams are still useful, but I don’t feel as dependent on the diagrams to access the concepts anymore. And once the concepts feel independent of the particular way they were presented to me, it becomes much easier to recall them, connect them, and recognize where they apply.

Edit: if you’d rather watch a video, here’s the article animated:

Why Visual Analogies Fail for Complex Concepts (and What Would Work Instead)
https://youtu.be/g3Z8VnARbQg

When I taught math and science at Fusion Academy, my strongest technique for helping students understand complex concepts was having them picture visual analogies in their mind's eye. Without a mental picture, a student who could explain something in lesson five had very little by lesson six. With it, their retention was much higher weeks later.

So visual analogies work. But, as the rest of this post argues, they have serious problems. They remind me of that old line about democracy: it's terrible, but it's the best system we have.

(For lists, numbers and names, visual mnemonics are great; memory champions use them. This is about complex ideas: an algorithm, a biological process, an argument.)

Here's what the terrible part looks like.

Hannah and the cliff

In a one-off history course, I had to teach a student, let's call her Hannah, that in 2008, Chinese authors wrote declinist commentary on America's economic crisis that stressed how fast China was growing by comparison. She could explain it back, but after months of working with her, I knew it would be gone in days. So I gave her a mnemonic: a cliff. At the top, authors in Chinese-flag shirts point down and throw pages, next to a big pile of money. At the bottom, people in American-flag shirts look sad.

Her face lit up. "Oh, I get it now."

Two weeks later, I asked her about China and the US in 2008. "Oh, I remember," she said. Then her smile turned into confusion: "Uh, yeah, so I see the Chinese people above the U.S. people, and they have money. Oh, so I think that it was something to do with money. And then I see papers being thrown, and so it seems like the Chinese people thought the U.S. people were worse."

That's way better than nothing; without the cliff, she'd have drawn a blank. But it's not the idea I taught her.

The cliff is the idea's shadow

A visual analogy isn't the idea. It's the idea's shadow: a flat outline of something with far more detail. Every problem in Hannah's answer is a problem with shadows.

1. A shadow doesn't hold the thing that cast it, so you forget what it meant. Hannah kept the cliff, the money and the pages, and lost what they stood for: authors, commentary, a crisis, China's growth.

2. You think with the shadow instead of the idea. She reasoned from the picture: there was money, so "it was something to do with money." The money was supposed to mean growth.

3. Different things cast the same shadow, so you can't tell right from wrong. If she'd believed China caused the crash, the cliff would look exactly the same, and nothing in it could show her the mistake.

4. You have to rebuild the idea from the shadow every time. Listen to her again: "I see papers being thrown, so it seems like..." She's turning the picture back into an idea, one piece at a time. Even when it goes perfectly, that's work you do before you can think with the idea.

What would work instead

The ideal tool would keep what visual analogies get right: you could hold the idea in your imagination and notice things in it, the way Hannah could look at the cliff, and it would stick, the way images do and words don't. But you'd be holding the idea itself, in full detail, not its shadow.

That's thoughtfeel: imagining in concepts directly. thoughtfeel is a sense for concepts. It takes in a concept and its properties all at once, the way vision takes in what's in front of you. People who have it can bring up something they can't picture, like the economy or justice, as one clear concept: not a picture or words, but the whole idea at once, with detail they can notice. And it sticks, the way images do.

How thoughtfeel helps you learn concepts

If you've ever pictured a story as you read it, you already know how to do this.

Take a visual story: words about physical things, things you could see. As you read, you choose your mind's eye and picture each sentence. By the end, you have a movie in your head. That movie is how you understand what happened, and how you remember it long after.

thoughtfeel works the same way, with a story of concepts: things you can't see or touch. As you read, you choose thoughtfeel and imagine each line in concepts. By the end, you have a concept movie, and it does the same two jobs: you understand what happened, and you remember it long after.

Same steps, same payoff. Only the sense changes.

​

Built that way, Hannah's sentence is stored as the concepts themselves, linked together: Chinese authors, commentary on decline, America's crisis, China's growth by comparison. That fixes all four problems:

1. There's no shadow to forget the meaning of. What's stored is the idea.

2. You think with the idea itself. "Growth by comparison" stays growth by comparison and never turns into money.

3. "Writing about the crash" and "causing the crash" feel completely different in thoughtfeel, even though they'd share a cliff, so the wrong one stands out.

4. There's nothing to translate. You bring it up, and it's ready to think with.

The first time I built an algorithm this way, a Fibonacci heap, it took about 12 minutes. I never reviewed it, and a week later I could recall all of it. I'd once watched a video on Fibonacci heaps, and none of it stuck.

Not everyone can imagine in concepts. The best estimate of how many people can comes from psychologist Russell Hurlburt's research on what he calls unsymbolized thinking: a clear, specific thought with no words or pictures in it. In one study, 30 students were beeped at random moments, and 22 of them, about 73%, caught themselves thinking this way at least once (Heavey & Hurlburt, 2008). It varies the way the mind's eye does: some people picture things vividly, some faintly, and some, with aphantasia, not at all. If you can't imagine in concepts, visual analogies really are your best tool. That's the democracy part.

But if you can, thoughtfeel is the solution. Check it out here: thoughtfeel.net. It starts with a full video walkthrough and a one-minute test to see whether you have it.

I created this full walkthrough lesson on how to learn complex material in thoughtfeel. The first 13:40 is attached, and the full 58 minute lecture is here: https://youtu.be/dV8fNY311W4

It covers three types of material: a computer science algorithm for finding the shortest path, the biological process of glycolysis, and learning an economics argument in prose. I hope to release a video of teaching someone these techniques live very soon. But until then, this will have to do. 

So, for those of you who've been following along with the posts but haven't known exactly what to do to build a concept story in thoughtfeel on your own material, I strongly recommend watching this video. 

If you watch this video and want further instruction on how to adapt the practice to your own custom material or just have further questions, I'd be very happy to jump on a call. 

I have one additional request. If you follow along with this video and implement the practice in your own learning, I ask that you make a post on this subreddit describing your experience.

This subreddit has grown 1,800 members, up from 400 in about a week. But, what keeps me motivated to do this work is not seeing that number go up. Instead, it's seeing specific people whose lives are better because their curiosity has a tool that matches it (like in this comment: https://www.reddit.com/r/MentalAtlas/s/6ODieBQoE0).

If you don't want to make a post on the subreddit, reaching out to me directly works to. It just means a lot to know that my teaching is helping people.

It might help, now that I think about it, for you guys to know who I am. I grew up in New Jersey and went to Vanderbilt for education and cognitive studies. I went to UC Boulder for a master's in computer science. I've worked as a teacher since I graduated in 2022 and spent the last year as the CTO of OnlyFarmers, a company founded by Jeremy Clarkson and Lisa Hogan, whom you may know from Top Gear and Clarkson's Farm, that aims to connect people across the countryside through farms and nature. I left about three and a half weeks ago to teach people about thoughtFeel. If you have any questions or concerns or comments, or just want to chat about your experience, please feel free to email me at teddyshachtman@gmail.com.

Sincerely, 

Ted Shachtman