Mindstorms and Physics Microworlds

Spend some time in the Matrix before trying to see the 1s and 0s.

This is the second of three posts describing my experience trying to get to a place where I can share physics with you all that feels exploratory, wonderful and different from anything you’ll find in a textbook.

The first post is about what I tried to build. This post describes my encounter with the small, passionate culture of people trying to do the same for education; the next and final post will describe what I’m going to do about it, now that I know I’m not alone.


I wrote last time about my clash with the lack of good tools for sharing work from “Structure and Interpretation of Classical Mechanics”. I built what the authors must have wanted to exist — a system for writing papers that weave code and math, papers that you can execute on your computer and reproduce the same results.

But when I look at the dozens of exercises I've written up, they look like an extension of the textbook. They look damned hard, in the way that people expect physics exercises to be hard.

This is a problem for me. I want to share artifacts that are helplessly exciting for people who tried to learn this stuff the normal way and couldn’t lock in their intuition. We all live in the universe, and we’re drawn to physics by a fascination with the way the world ticks. It has to be possible to pull back the curtain without being forced out of the world and into a sequence of equations!

Maybe it’s hopeless. Maybe these fields just are tough, and it’s a pipe dream to think that it’s possible to infect other people with the sense of excitement I feel after hours working on these exercises. Maybe we already know the best way to teach physics… and if we have to instill deep Mathphobia in most of the population to find the 10% or so that can think this way, well, so be it.

If true, this is inhumane. So let’s pretend that we can improve.

I didn’t know how to teach, but I knew how I wanted it to feel. I want to be able to offer someone the experience that we have with the best puzzles or video games. You watch a friend tackling some level in Zelda, get more and more excited, and finally, when they start fumbling, helplessly reach for the controller. “Give me that!” “Let me try!” and you’re in the world yourself, exploring.

As this was unhappily swirling, I saw a tweet from my friend Avi Bryant, about a new programming language he’s building called “Loglo”:

Loglo is a play on LOGO, an old programming language that some of you may remember as the engine behind Turtle Graphics:

Small Basic: The History of the Logo Turtle - Microsoft Tech ...

I decided to read Mindstorms (pdf) by Seymour Papert, the creator of LOGO. I had no idea that this book would describe everything I’d been feeling is wrong about how we teach, and what to do about it.

Computers, Tools for Thinking

Mindstorms is a book about how education might be transformed by complete availability of computers to kids. (This doesn’t do it justice, but I’m trying to limit myself. You have to read Mindstorms. Just buy the damned book.) Total ubiquity of computers hadn’t happened yet in the 80s when Papert wrote the book, but it was obvious that it was coming.

He describes two possible outcomes for school in a world like this. The first, and the outcome that’s come to pass, is a future where computers are used to program children.

Take Khan Academy. I’m a product of the current system, and I love this site. If you browse their catalogue you’ll find hundreds of lessons in any topic you could imagine. But the site’s goal is to help School more efficiently train kids. There are a certain number of educational nuggets that we all have to digest to function as adults. Khan cooks them into nice meals, but the kids are still on a set program.

The second outcome is a world where computers have become tools for thinking, expanding the ability of kids and adults to think in the way that pencil and paper does. How would this work? When you program in LOGO, you control a small turtle by offering it commands in “Turtle Talk”. You can say things like


And the turtle will draw a square on the screen. You can also run the program on these Floor Turtles, big honking 1980s turtle-shaped robots that dragged a pen around a big sheet of paper on the ground.

Try writing down the program to draw a triangle. I bet you’ll write something like


… and it won’t work. You’ll have something that breaks in an interesting way. Why does it fail? Try actually walking the program out with your body. You’ve internalized the idea that “the angles of a triangle add up to 180 degrees”. But those are the inner angles, and the turtle has to turn the outer angles. An idea you’ll feel in your bones after drawing more and more complicated shapes in LOGO is a more useful theorem:

Any path the turtle walks that ends up back at the same place must turn a total of 360 degrees.

Kids who got free access to LOGO ended up building all sorts of fantastical things. Flocks of animals, gardens, brilliant fractal patterns. There’s a book called Turtle Geometry that builds up to the math behind General Relativity using LOGO programs and the turtle, all the way down.

And these kids were learning geometry, differential geometry, in the immersive way that kids who spend time in a new country pick up the language. The 360 degree theorem is a useful tool that makes it much easier to draw closed shapes like flower petals or components of robots.

The connection to what I’m trying to do gets tighter, but I have to say that I was hooked at this point, and went off on a separate bender trying to figure out how to make a floor turtle and get LOGO running. But the idea of total immersion into Mathland, physical, embodied experience with a technical field? That’s what I was missing!

Mental Lenses

I’m interested in physics because the field is a fertile source of new Mental Lenses. I want to look at the world and see it through the lens of fields and action, of infinitely dense particles of space, of quantum fluctuations.

This happened to me with software years ago. When I learned to program, I gained the ability to look at any software creation and think, “how would I make that?” When I can’t figure out the trick, I know that the effort of the attempt is giving me more pleasure than if I was just blindly seeing uniform Apps and Websites.

I can’t sum up the feeling I’m seeking better than Teller does in this short video. it’s only 90 seconds:

Anyone who’s written a textbook or tried to explain some idea they see through their personal Mental Lens is saying: “Trust me, this is completely amazing.“ There is far too much “Trust me…” going on in math and physics education. Papert was trying to remove any need for trust; no one, kid or adult, should have to already have the mental lens that allows them to see magic in symbolic equations to gain admittance to the Cave of Wonders that is humanity’s legacy of math and science.


Back to Mindstorms. The most important part of the book for us is Chapter 5, titled “Microworlds: Incubators for Knowledge”.

Here’s the paragraph that clarified everything for me:

Most physics curricula are similar to the math curriculum in that they force the learner into dissociated learning patterns and defer the "interesting" material past the point where most students can remain motivated enough to learn it. The powerful ideas and the intellectual aesthetic of physics is lost in the perpetual learning of "prerequisites." The learning of Newtonian physics can be taken as an example of how mathetic strategies can become blocked and unblocked. We shall describe a new "learning path" to Newton that gets around the block: a computer-based interactive learning environment where the prerequisites are built into the system and where learners can become the active, constructing architects of their own learning. (Mindstorms, p. 122)

Papert makes an analogy of a world where kids are forced to study written sheet music and musical notation for years before ever being allowed to listen to a score. Of course most kids would wash out, and most of them would hate sheet music for the rest of their lives.

It’s obvious that there is more to the story of Sheet Music, and kids hate being lied to. I think that it’s difficult to avoid resentment when it’s obvious we’re being cheated.

Papert goes on to describe the “Dynaturtle”:

Dynaturtles can be put into patterns of motion for aesthetic, fanciful, or playful purposes in addition to simulating real or invented physical laws. The too narrowly focused physics teacher might see all this as a waste of time: The real job is to understand physics. But I wish to argue for a different philosophy of physics education. It is my belief that learning physics consists of bringing physics knowledge into contact with very diverse personal knowledge. And to do this we should allow the learner to construct and work with transitional systems that the physicist may refuse to recognize as physics. (Mindstorms, p.122)

What are these transitional systems? They’re advanced forms of the Turtle Graphics world in LOGO. They are interactive computer worlds where the laws of physics are actually running the show, not as symbols on paper, but as the actual system of the world.

In the examples above, we told the turtle how to change its position. Imagine now that the turtle has some momentum, and keeps moving once it starts moving. Our job is to turn its head and update its speed, not its position.

Well, what are the equations of motion of classical mechanics? They are rules for updating the velocities of particles moving around in space. (If we know the velocity, we can update the position ourselves.)

Don’t force a kid to understand F = ma, says Papert. Give them a space game, or the tools to put orbiting planets into the Turtle’s world, and trace out glowing orbits; to speed up time, or reverse it, or add hundreds of particles weaving and bobbing and interacting.

The Problem with SICM

Papert’s criticisms of the School approach to physics resonate with my experience with SICM and other advanced textbooks.

Take the lowly pendulum. You can solve for the equations of motion on paper, and roughly understand that the pendulum is going to oscillate, sort of like a sine wave if you don’t kick it too hard to start. Now you decide to explore what happens if you kick the pendulum harder.

This is going to take a lot of visual imagination. SICM makes it easier to explore the system with code, but scmutils is clunky enough that to even have ideas to explore you’re going to need to know in advance what you’re looking for.

This is a problem for most of us. Just because you can’t run a simulation in your mind doesn’t mean you aren’t just as capable of gaining solid intuition for physics, or creating beautiful worlds with your new understanding.

Here’s what has me buzzing. SICM IS SO CLOSE! The first chapter of the book reads like a manual for how to write a fantastic software package to explore advanced dynamics. The exercises read like tests of that package. Everything in the book is itching to be animated and explored. The technology to make it all interactive just wasn’t there yet in the 80s when the book was conceived.

Physical Microworlds

It turns out that, thanks to a mammoth effort by Colin Smith to port scmutils to Clojure, we’re very close to being able to make the Dynaturtle for SICM.

I think I can build the Dynaturtle, and give you all a window into what’s going on in advanced mechanics, in orbital mechanics, and, maybe, do it in a way that will let us build games together and explore in the browser.

Beyond the browser, I think I can build a series of actual, physical Dynaturtles using Sphero BOLTs. the programs in SICM are all ripe for animation on a computer and for controlling physical systems.

Take a look at https://paperprograms.org/, and imagine space simulations playing out in light on the floor of a room in your house, responding to your inputs. Imagine an entire room like Dynamicland placing you in a ridiculously difficult game controlled by Lagrangian mechanics. You get your ass kicked… until you decide to load a Poincaré map of the system up on a tablet and look at how the system is evolving in phase space. Suddenly a tool of advanced mechanics becomes a tool in a video game.

I’m not abandoning the idea of sending “normal” posts out about how I managed to build up some intuition for a physics concept. But this style of learning could be immersive and amazing, and I feel a compulsion to build it and share it with you all.

What’s Next?

In the next and final post I’ll add more detail on the plan, reaching out to Colin Smith about his sicmutils package, and about how close we are to being able to generate physics microworlds using that system.

See you soon!

Appendix A: The Problem with “Why?”

Explaining to people why this is necessary seems to take a lot out of me. I hear myself talking, and I want to downplay why this is important. “This is more… education than research, right?“

I’m trying to get past the need for permission. I have a deep feeling that it’s not right that we can’t animate or explore any of this incredible work; not in a way that’s both useful and visual and built to teach. I don’t have that feeling very often, but I do know that it’s easy to kill.

Kevin Lynagh’s latest newsletter linked to On Cultures that Build, with this quote:

In the 21st century, the main question in American social life is not ‘how do we make that happen?’ but ‘how do we get management to take our side?’

I winced when I saw this. I sat with it for a while, and then decided to send a note to my boss at my current research lab and let him know that I’d be working on something strange and difficult to explain for the next month or so. Time to have a little courage, and make the space to build something that’s not so easy to justify.

Appendix B: Where are the turtles?

Check out this amazing sequence of old Floor Turtles. Here’s one that’s starting to look awesome:

Here’s a lovely essay on Papert and LOGO that gives some more flavor to Turtle Graphics, and what Papert was trying to achieve with his work.

What happened to his work? Can you buy a floor turtle? Strangely, you can’t. All Robotics kits these days seem to be targeted at kids 10 and up, and are made to be sort of tough to build.

This is the best floor turtle I’ve found: https://www.instructables.com/id/OSTR/ It’s honestly wonderful. I’m going to make one for myself, then see if I can get the author’s permission to sell them pre-built.

Please, read Mindstorms. Bret Victor hosts the pdf at his site.

Papert’s The Children’s Machine (pdf) is also inspiring. He wrote this a decade on from Mindstorms, and talks about his vision for how School might be replaced by something more personal and meaningful.

The best vision of personalized education still lives in Neal Stephenson’s The Diamond Age as “A Young Lady’s Illustrated Primer”.