VolvelleDrawingIf I may muse for a bit, volvelles are a fascinating way to arrange a table. A pivoting table? Wheels within wheels. If you stack two logarithmic number lines, you have a slide rule. Clocks are volvelles with arms instead of discs. There are not only volvelles for calculation, but volvelles for remembering state capitals and volvelles for learning grammar rules. 

So many departures on a thing which turns upon itself. You might even wind up with Willie, Freddie, and Flaco.

Come back, come back to your arms again. I’ll come back to where you are.






Last Sunday’s trip to Brighton was a happy one, although it was cloudy for most of the day. image Here I am in front of Whirligig Toys, one of a handful of toy vendors who get it. They have the stuff: Kites and gyroscopes and Timberkits and a knitted version of the Brighton Ferris Wheel. Go there; have fun.

My Instructions


When you apply this to that, you begin a process of accretion, or concretization, that leads maybe out of a morass of tangled thoughts — the Sargasso Sea, the Bermuda Triangle, of the mind.

The this I talk about has to be a thing, a phenomenon. Things lead us somewhere. Two and two are four, but why not also say ii & ii = iiii, a thought leading to a picture or an object; or i | ii, then ii | iiii, two or three facts leading to a system?

We pursue linearity, speed, and virtuosity in mathematics to a fault. Those most capable of abstracting information get the brass ring. Yes, a certain number of east and middle European émigrés have changed history with their gigantic strides in math and science. Yes, Alan Turing helped turn the tide in WWII. Yes, NSF scholarship recipients are going on to make our lives better by crafting stents and optimizing airplane travel. But if we make science, engineering, and mathematics about elitism, don’t be surprised if 99 percent of us don’t become alienated from these subjects.

Mathematical thinking, logical thinking, inductive thinking, orthogonal thinking need to be spread like a skin-to-skin virus. I propose to do my part by creating or distributing manipulable things that make people think, cognitive artifacts, that lead them to mathematical ways of thinking that lead other people to mathematical ways of thinking, and so on.

We have actual things that make us think, according to Donald Norman, alphabets and algebra and methods to set up tables. These are every bit as important as things that do things, like knives and watches and plows.

I want to make things like the sector, also known as the proportional compass, using everyday objects. We likely don’t see sectors. No one needs to use them. We use calculators instead. At the dawn of enlightenment they were in the hands of astronomers, surveyors, engineers, and gunners.

The sector, also known as a proportional compass or military compass, was a major calculating instrument in use from the end of the sixteenth century until the nineteenth century. It is an instrument consisting of two rulers of equal length joined by a hinge. A number of scales are inscribed upon the instrument which facilitate various mathematical calculations. It was used for solving problems in proportiontrigonometrymultiplication and division, and for various functions, such as squares and cube roots. Its several scales permitted easy and direct solutions of problems in gunnerysurveying andnavigation. The sector derives its name from the fourth proposition of the sixth book of Euclid, where it is demonstrated that similar triangles have their like sides proportional. It has four parts, two legs with a pivot (the articulation), a quadrant and a clamp (the curved part at the end of the leg) that enables the compass to function as a gunner’s quadrant.

A scale is a this to that. As an adult education teacher I often introduced the concept of the table. The simple act of making a “T” shape on a black board or a piece of paper calmed the problem, at least for me. On the left side of the “T” you had a number, on the right side you have the number transformed, whether by the addition of two or the multiplication of eight or the application of an exponent — a powerful idea that you can put on a stick.

Image of two coffee stirrers connected on one end, forming a sector.

A sector made from coffee stirrers and a small brass fastener.

You can go to my Instructable to find out how to create and use a sector. In this case, you can imagine a series of equilateral triangles, the 1s spaced 1 cm apart, the 2s, 2 cm apart, the 3s, 3 cm apart. Using a ruler and a set of dividers, you can begin scaling things. The Science Museum in London had my favorite explanation for using the sector to make proportional measurements.

Suppose you want to divide a line six inches long into five equal parts. Measure off six inches with dividers, and open the sector until the distance between the 5 and 5 on the linear scales is six inches apart. By the principle of similar triangles, the distance between 1 and 1 on the linear scales is then one fifth of the distance of the distance between five and five. Measure the distance 1 to 1 with dividers and the five equal lengths can be measured off the original six inch line. 

And that’s just one function. What if you had a bunch of coffee stirrers and a way to easily connect them — a way that’s easier than my current method of poking a hole and adding a fastener? What if you had a specialized housing and a way of printing up coffee stirrers or card stock? Thousands of thisses to thatses in pockets on coffee tables, constant reminders of the comprehensibility of mathematics.

Let’s just call that my theses, my theses of thisses, “This to That for Everyone.”

Powerful Ideas

Resnick and Kay

Brian Silverman, Mitchell Resnick, and Alan Kay

Wow! A no longer blank page. I recently watched Alan Kay on Learning Creative Learning, MIT’s open course on programming and making. The one-hour session was called “Powerful Ideas.”

Science, the ability to not let our brains fool us, as it were, is a powerful idea. Though not explicitly mentioned, “computational thinking” is another powerful idea. I’m still thinking about the video because the subjects discussed have something constitutionally to do with why I’m starting this blog.

Kay’s comments were provocative, if not cantankerous. The beginning of the session, which took place on March 2013, had a conversational feel, but around the 32 minute mark, Kay gets on a hobby horse about people not getting the powerful idea of computing. For the next 10 minutes he unloads on the subject of most people not reaching a proper threshold in computer use.

I have trouble figuring out where to start writing about his beliefs, because he makes a number of different points. First, it’s good to understand his stance as a student of anthropology. Kay talks about cultures that accomplish certain things, but don’t achieve science.

Forgive me for not unpacking  this part of his discussion. For my purpose, I only want to establish that Kay thinks many people don’t get the powerful idea of computing even if they’re using a computer just like many cultures, advanced in their own way, don’t get science.

I think I’m being fair to Kay when I say that he believes you can tell stories and tinker without reaching a deeper understanding: “Scientific knowledge is not in the form of a story.” He makes an analogy to music, where he talks about Guitar Hero as an entry point to music in which the players only get a “pop culture” understanding and miss the bigger point. He says the same happens in computing. Students work on computers, but their understanding of the world goes no further than that of their parents.

He punctuates his remarks by saying, “Maxwell’s equations just [don’t] have a narrative. I’m sorry.” Something needs to be added. Students need to take the extra step toward understanding scientific concepts. Stories and tinkering just muddy the issue.

But if there weren’t stories about the enlightenment and this Maxwell you speak of, I believe, the equations would have been a little longer in coming. I now believe we live in a culture of computing, a fandom of computing, so that thousands of users inspire dozens of creators to press on.

I’m also biased against Kay because I feel like some of what he was doing was a form of breast beating. His own admission of living professionally amidst a culture of dissension and rivalry makes me think the primacy of knowledge was a matter of “eat or be eaten, beat or be beaten,” in the words of Iggy Pop. In a world differently networked than that of defense department funded academia, you will not be coming up with the inevitable, canonical answer. You are coming up with answers that satisfy numbers of people for a while (for example, the Windows operating system).

Some answers, like Unix and Lego, last longer. Should we say these were tinkertoys when we radically retool them or cast them out as we reach the new threshold? There will be more important operating systems in the future. There will be more important toys in the future. Operating systems and toys that are just stories to be told and impediments to Kay’s next step.

Kay does say that he only wishes to add the next step and not take anything away. I believe he contradicts himself with his statement about stories and culture muddying the issue.

He also waxes on the idea of zen and the art of archery: that programming doesn’t necessarily invoke virtuous behavior but it could. “Among the least enlightened people you might meet on the planet are programmers,” says Kay, invoking what he calls a makable generalization.

What stories are to be told? What thresholds are we approaching? What “powerful ideas,” to use Seymour Papert’s usefully ambiguous term, are we acquiring? Making an arrow fly through the air doesn’t make you more enlightened, but it can. We make things, shaped pieces of wood, skyscrapers, meccano-sets, and lines of code. What we think about those things makes all the difference.