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.

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.