In the references to The World Beyond Your Head I found an intriguing paper by Mizuko Ito, Mobilizing Fun in the Production and Consumption of Children’s Software, following the interactions between children and adults at an after-school computer club. It’s written in a fairly heavy dialect of academicese, but the dialogue samples are fascinating. Here a kid, Jimmy, is playing SimCity 2000, with an undergrad, Holly, watching:

J: (Budget window comes up and Jimmy dismisses it.) Yeah. I’m going to bulldoze a skyrise here. (Selects bulldozer tool and destroys building.) OK. (Looks at H.) Ummm! OK, wait, OK. Should I do it right here?

H: Sure, that might work… that way. You can have it …

J: (Builds highway around city.) I wonder if you can make them turn. (Builds highway curving around one corner) Yeah, okay.

H: You remember, you want the highway to be … faster than just getting on regular streets. So maybe you should have it go through some parts.

J: (Dismisses budget pop-up window. Points to screen.) That’s cool! (Inaudible.) I can make it above?

H: Above some places, I think. I don’t know if they’d let you, maybe not.

J: (Moves cursor over large skyscraper.) That’s so cool!

H: Is that a high rise?

J: Yeah. I love them.

H: Is it constantly changing, the city? Is it like …

J: (Builds complicated highway intersection. Looks at H.)

H: (Laughs.)

J: So cool. (Builds more highway grids in area, creating a complex overlap of four intersections.)

H: My gosh, you’re going to have those poor drivers going around in circles.

J: I’m going to erase that all. I don’t like that, OK. (Bulldozes highway system and blows up a building in process.) Ohhh …

H: Did you just blow up something else?

J: Yeah. (Laughs.)

H: (Laughs.)

J: I’m going to start a new city. I don’t understand this one. I’m going to start with highways. (Quits without saving city.)

As Ito puts it, “by the end Jimmy has wasted thousands of dollars on a highway to nowhere, blown up a building, and trashed his city.” So what’s the point of playing the game in this way?

Well, for a start, it lets him make cool stuff and then blow it up. That might be all the explanation we need! But I think he’s also doing something genuinely useful for understanding the game itself.

Ito mainly seems to be interested in the social dynamics of the situation – the conflict between Jimmy finding ‘fun’, ‘spectacular’ effects in the game, and Holly trying to drag him back to more ‘educational’ behaviours. I can see that too, but I’m interested in a slightly different reading.

To my mind, Jimmy is ‘sketching’: he’s finding out what the highway tool can do as a tool, rather than immediately subsuming it to the overall logic of the game. The highway he’s building is in a pointless location and doesn’t function very well as a highway, but that doesn’t matter. He’s investigating how to make it turn, how to make it intersect with other roads, how to raise it above ground level. While focussed on this, he ignores any more abstract considerations that would pull him out of engagement with the tool. For example, he dismisses the budget popup as fast as he can, so that he can get back to bulldozing buildings.

Now he knows what the tool does, he may as well just trash the current city and start a new one where he can use his knowledge in a more productive way. His explorations are useless in the context of the current game, but will give him raw material to work with later in a different city, where he might need a fancy junction or an overhead highway.

---

I first wrote a version of this for the newsletter last year. Reading it back this time, I noticed something else: Jimmy’s explorations are a great example of bricolage. I first learned this term from Sherry Turkle and Seymour Papert’s Epistemological Pluralism and the Revaluation of the Concrete, which I talked about here once before. In Turkle and Papert’s sense of the word, adapted from Lévi-Strauss, bricolage is a particular style of programming computers:

Bricoleurs construct theories by arranging and rearranging, by negotiating and renegotiating with a set of well-known materials.

… They are not drawn to structured programming; their work at the computer is marked by a desire to play with the elements of the program, to move them around almost as though they were material elements — the words in a sentence, the notes on a keyboard, the elements of a collage.

… bricoleur programmers, like Levi-Strauss’s bricoleur scientists, prefer negotiation and rearrangement of their materials. The bricoleur resembles the painter who stands back between brushstrokes, looks at the canvas, and only after this contemplation, decides what to do next. Bricoleurs use a mastery of associations and interactions. For planners, mistakes are missteps; bricoleurs use a navigation of midcourse corrections. For planners, a program is an instrument for premeditated control; bricoleurs have goals but set out to realize them in the spirit of a collaborative venture with the machine. For planners, getting a program to work is like ”saying one’s piece”; for bricoleurs, it is more like a conversation than a monologue.

One example in the paper is ‘Alex, 9 years old, a classic bricoleur’, who comes up with a clever repurposing of a Lego motor:

When working with Lego materials and motors, most children make a robot walk by attaching wheels to a motor that makes them turn. They are seeing the wheels and the motor through abstract concepts of the way they work: the wheels roll, the motor turns. Alex goes a different route. He looks at the objects more concretely; that is, without the filter of abstractions. He turns the Lego wheels on their sides to make flat ”shoes” for his robot and harnesses one of the motor’s most concrete features: the fact that it vibrates. As anyone who has worked with machinery knows, when a machine vibrates it tends to ”travel,” something normally to be avoided. When Alex ran into this phenomenon, his response was ingenious. He doesn’t use the motor to make anything ”turn,” but to make his robot (greatly stabilized by its flat ”wheel shoes”) vibrate and thus ”travel.” When Alex programs, he likes to keep things similarly concrete.

This is a similar mode of investigation to Jimmy’s. He’s seeing what kinds of things the motor and wheels can do, as part of an ongoing conversation with his materials, without immediately subsuming them to the normal logic of motors and wheels. In the process, he’s discovered something he wouldn’t have done if he’d just made a normal car. Similarly, Jimmy will have more freedom with the highway tool in the future than if he followed all the rules about budgets and city planning before he understood everything that it can do.

Alternatively, maybe I’m massively overanalysing this short contextless stretch of dialogue, and Jimmy just likes making stuff explode. Maybe he just keeps making and trashing a series of similarly broken cities for the sheer fun of it. Either way, mashing these two papers together has been a fun piece of bricolage of my own.

I’ve just read a fascinating paper, ‘Epistemological Pluralism and the Revaluation of the Concrete’ by Sherry Turkle and Seymour Papert. I’m lucky that I only found the paper recently: I love Papert but I’m not sure I’d have been able to stomach it even two years ago. The very first paragraph manages to combine a couple of ideas I’m seriously allergic to:

The concerns that fuel the discussion of women and computers are best served by talking about more than women and more than computers. Women’s access to science and engineering has historically been blocked by prejudice and discrimination. Here we address sources of exclusion determined not by rules that keep women out, but by ways of thinking that make them reluctant to join in. Our central thesis is that equal access to even the most basic elements of computation requires an epistemological pluralism, accepting the validity of multiple ways of knowing and thinking.

So, first of all, this is a paper about Women In STEM, considered capitalised as an Important Social Issue. Being lumped in with my gender automatically puts me on edge, as I tend to assume that I’m not going to fit in very well.

Then we have the phrase ‘ways of knowing’, which I’ve sort of unfairly come to associate with the worst of pomo nonsense. Like that anthropology course my flatmate did, where literally any bullshit explanation of anything ever advanced by some isolated tribe had to be taken seriously as an ‘equally valid’ way of understanding the world.

Put these two together and this article threatens to be about, er, ‘women’s ways of knowing in STEM’, a phrase which is literally making me cringe as I type it out. A couple of years I would have stopped here, unable to cope with the kind of associations this gave me with the awful gender-essentialist woo stuff that some women inexplicably find inspiring and not horrific. Like, stuff of the form ‘women have special kinds of intuition, which are probably to do with being really in touch with the earth or something, and also lots of feelings are going to be involved’.

Anyway I’ve calmed down about this a bit recently, to the point where I could possibly even extract something worthwhile from a full-fat gender-essentialist-woo piece of writing. And of course this paper is not like that.

Even so, this paper pretty much is about ‘women’s ways of knowing in STEM’ (in broad statistical strokes, rather than an essentialist claim that This Is How All Women Feel). And, um, it actually fits me rather well? Some of it is off, but it also includes the best description of my particular learning style that I have ever come across anywhere.

---

The basic setup here is one of those ‘two types of mathematician’ divisions I love. Except here there are two types of programmer. There’s this standard (straw? I don’t think so, but it’s hard for me to tell) idea of a programmer:

For some people, what is exciting about computers is working within a rule-driven system that can be mastered in a top-down, divide-and-conquer way. Their structured “planner’s” approach, the approach being taught in the Harvard programming course, is validated by industry and the academy. It decrees that the “right way” to solve a programming problem is to dissect it into separate parts and design a set of modular solutions that will fit the parts into an intended whole. Some programmers work this way because their teachers or employers insist that they do. But for others, it is a preferred approach; to them, it seems natural to make a plan, divide the task, use modules and subprocedures.

Then there’s ‘a very different style’:

They are not drawn to structured programming; their work at the computer is marked by a desire to play with the elements of the program, to move them around almost as though they were material elements — the words in a sentence, the notes on a keyboard, the elements of a collage.

Turkle and Papert call this ‘bricolage’, a term they got from Levi-Strauss. I know nothing about Levi-Strauss so can’t really say what he meant by it. The Wikipedia article on bricolage describes it as ‘the construction or creation of a work from a diverse range of things that happen to be available, or a work created by such a process’, which seems close enough to the usage in the paper.

Bricoleur scientists, apparently, work in the following way:

The bricoleur scientist does not move abstractly and hierarchically from axiom to theorem to corollary. Bricoleurs construct theories by arranging and rearranging, by negotiating and renegotiating with a set of well-known materials.

To which all I can say is:

!!!

This is the thing! This is a perfect description of the thing!

---

My favourite sort of problem is something that could probably be labelled ‘synthesis’, but at ground level looks like this: you have a bunch of concepts you don’t understand very well, but for some reason you’re convinced they can be combined. Sometimes this is a pointless exercise in making patterns out of noise, like staring at the Easyjet seat pattern for too long. Other times you have valid intellectual reasons for why they would fit together.

This is a bit vague, so here are some examples. There are some ideas in maths and physics that have this particular quality for me. They aren’t ones where I’m making much useful progress, and at least one is probably outright bad. They’re just examples of the kind of thing where once it’s in my head, it’s really in my head.

• There’s a variant form of general relativity called teleparallel gravity. GR takes place in curved spacetime, and one way of thinking of this mathematically is that as you move from place to place, your frame of reference rotates in a manner described by an object called the connection. The GR connection has nonzero curvature, but there’s also some other geometrical property it could have called torsion, that’s set to zero in GR.

It turns out that you can also make a perfectly good connection with zero curvature (it’s ‘teleparallel’ – parallel lines stay parallel). Instead, it has nonzero torsion. And if you choose some coefficients right in some Lagrangian, you can reproduce GR in some sense. Buh? The formulation is pretty opaque, so what’s really going on?

• Pedalling back a bit because we quite clearly need to, what are these curvature and torsion thingies? You can calculate quite well with limited understanding of what’s going on geometrically. GR people love to do this in a very opaque way with lots of shuffling little superscripts and subscripts around (it’s fast once you’ve learned it). In an intro course this is normally connected back to geometry at a specific ritual point, which involves shoving a vector round a loop and observing that it rotates a bit. This is not especially satisfying. It’s obviously possible to get a far better understanding, and people in the field manage this, but at least for me that’s involved extracting it painfully one piece at a time from many different sources.
• A subquestion of this that wasted hours and hours of my time over several years (this is the ‘probably outright bad’ one): there’s curvature and torsion of a connection, but there’s also the simpler idea of curvature and torsion of a a curve in 3D space. I’d convinced myself that there was some sort of analogy between them that had to do with taking a curve off a manifold and developing it in flat Euclidean space. In fact I even got it into my head that I’d read this one of Cartan’s own books! But a lot about the idea didn’t fit so well.

I eventually couldn’t stand it any more and risked asking about it on Mathoverflow, where I feel massively underqualified. Robert Bryant answered me, which was pretty amazing. There is probably nobody better placed in the world to answer questions about Cartan – he’s apparently read the whole lot. He very politely explained that he thinks it’s a red herring, and that Cartan had a different picture in mind when he introduced the torsion of a connection. And I can’t find anything about my brilliant idea in the Cartan book I read.

So it looks like there’s probably nothing there, but I can’t quite say it’s fully out of my head yet. It’s the Easyjet seat pattern of maths questions.

• A current one: what’s going on in QFT that makes it different to classical perturbation theory? Suddenly the diagrams have loops; why? OK, so some propagator’s nonzero at some point. What does that mean? Why can’t I get that out of a classical theory?

---

There’s two main parts to all these questions. One, how do the things fit together? And in order to answer this: two, what are these things really? Where ‘really’ is poorly defined, but just being able to reproduce a formal calculation definitely won’t cut it.

And the process for working on them? It’s exactly as in the quote: you do it ‘by arranging and rearranging, by negotiating and renegotiating with a set of well-known materials’. ‘Well-known’, because you’ve spent hours thinking about specific concrete instantiations, in the process of trying to understand what they ‘really’ are. Particular connections, particular propagators. ‘Negotiating and renegotiating’, because they’re your friends by now and you want them to get on. Maybe one side of your explanation meshes poorly with another side. Maybe there’s a reframing that can combine them.

---

Doing maths and physics in this style requires a certain stubbornness in the face of never getting taught that way. I lost confidence eventually, but I seem to have it back now. I’m convinced that it absolutely can work. It’s not some kind of second-prize way to flail around the curriculum, inferior to a more structured approach. It has its own distinctive methods and produces its own distinctive questions, which I think are often good questions.

It could work even better if it was supported better.

I’m a bricoleur scientist.