Two days ago I tried to post to my blog and realized I was locked out of the database. Unbeknownst to me said database had been gradually filling up with spam emails . When the bloat reached 150Mb (my database quota is 100Mb), the host site,, froze any access to the database that might increase its size (such as new posts or comments).

It took me a number of hours, using the onLine mySQL database tools at, to clear out all the garbage, and then another day for the host software to updated my official footprint — which is now back down to a slim and energetic 18Mb.

Since I’ve been blogging every day for over four years, without missing a day — until this — I decided, on an editorial level, to declare this an “Act Of God”, and to continue blogging daily as though nothing had happened. So my posts for the last two days were duly written on the appointed day, but uploaded this morning, when my blog returned to life.

The most unfortunate thing is that all reader comments during the AOG were annihilated. If you left a comment about, say, the recent Hypergeography post, it has been, I am sorry to say, savagely crushed, pulverized, zapped by a Martian death ray, sucked of all its life giving essential juices and left to die a sad and lonely death on the blasted shores of some internet wasteland.

So if you did leave a comment sometime in the last few days, please repost it. I would love to read it!!

Steam engine

NOTE: DB problems will lock me out of the server for two days, so this is written today but posted from the future. Will explain when that future arrives.

Today I attended a fascinating lecture by my old friend Debbie Deas about her recent visit to the New Library of Alexandria. As you undoubtedly know, the city of Alexandria, Egypt has the best library brand in history. The magnificent new library was opened in 2002 to celebrate that vision and bring it into the 21st century.

The photos Debbie took showed a huge number of young people from a nearby university crowding into the library’s beautiful space, taking up every available seat and study table. They were working alone or in small groups on their scholarly research under soaring ceilings, by the reader-friendly diffuse natural light that filled this magnificent building. An architect who attended the talk explained to me afterward that high ceilings and large windows are a desired feature of libraries partly because they create the ideal lighting conditions for reading.

But also, we tend to see high ceilings in places that connote honor or respect — such as court houses, churches, museums. And libraries, for a library is a place of pride and honor.

I also noticed the stacks of books, but the stacks were only partially filled. I had always associated the large vaulting spaces of libraries with the need to house stacks of books (which, after all, take up a lot of room). But here, if the photos were any guide, a transition was going on. Many of the students were using computers. They were surrounded by stacks of books but their own studies were drawn largely from the 3.5 petabytes of on-line storage the library provides.

And I was reminded of the steam engine. The magnificent old early locomotive (which I still love) with its gleaming boiler and towering smokebox, was an icon of the Victorian era — a perfect image of a particular kind of physical technology. Much more interesting to me than those sleek but featureless trains of the last seventy years, with their boring little diesel engines inside.

Similarly, the book is the very symbol of learning and erudition. But I wonder, looking at those students in the New Library of Alexandria, whether this symbol will slowly fade like the steam engine. With the rise of eBooks and tablets, we might very well be witnessing the beginning of the end of what might be called the Victorian phase of the information age.

Yet the libraries will remain. For the library is not primarily, as we might have thought, merely a place to house stacks of books. A library is fundamentally a sacred and quiet church of the mind, under whose lofted ceilings people will always gather to study, to learn, and to honor the magnificent possibilities of human thought.

Subtraction distraction

Today I created a sketch for a simple computer game. There is lots more to do before it is finished, but what I have so far will give you the basic idea.

I’m not sure if this game is an example of “less is more” or “less is less”. In any case, here it is, more or less. đŸ™‚

Try out the game for yourself by clicking on the image below:


Today I had a great brain-storming session with friends/colleagues Murphy Stein, Vi Hart and Charles Hendee (and briefly Jan Plass) about all sorts of things fun and mathematical. Among the many things we discussed, one that really resonated with me came out of this image, the original of which can be found in a wonderful discussion about Hyperbolic Geometry by Vladimir Bulatov.

This is a basically a PoincarĂ© disk model of the hyperbolic plane. That’s a way to look at the hyperbolic plane by cheating — distorting things to make them look smaller the further away they are from you. In the above picture the entire hyperbolic plane appears to fit inside the circle, but that’s just an illusion — things near the edge are really very very far away.

Unlike our boring old Euclidean plane, the angles of a polygon in the hyperbolic plane can vary, depending on the polygon’s size. And that makes the hyperbolic plane a lot of fun.

For example, in the picture above, the hyperbolic plane has been filled with regular pentagons of just the right size so that the edges at each vertex join at 90o. In the Euclidean plane you couldn’t do this — but the hyperbolic plane is way cooler than the Euclidean plane.

If you lived in a city based on the plan in the above picture, you could walk north, turn 90o right five times in a row, and end up where you started. Wherever you are standing, everything would look pretty normal, but objects that are far away would look weirdly distorted and too small — as though perspective itself were operating on overdrive.

When I look at this picture, I imagine a shared on-line world — maybe something like The Sims, but in a hyperbolic geography. People would live in pretty houses on nice streets, with manicured lawns, except that the city blocks would be shaped like pentagons, and five right angle turns will always get you back home.

Happy ending

This afternoon we were visiting a middle school in Brooklyn where several groups of seventh grade girls (mostly ages 12-13, all black or hispanic) were presenting their original ideas for math games. This is part of a Motorola Foundation funded project that we’re doing at the Games for Learning Institute. One of the girls showed a math puzzle containing the following algebra problem: “g / 6 = 36”. The goal was to figure out the value of “g”.

I wondered to myself whether she was really expecting kids to know the value of 36 × 6, or was just getting the algebra wrong (ie: whether what she’d really meant to write was “g × 6 = 36”).

So after her group was finished presenting its game idea, I asked her: “What’s the answer for ‘g’ in your equation ‘g / 6 = 36′”?

With no hesitation, she replied “Six!” Alas, it was as I had feared.

But then, about ten seconds later, another girl, a little 12 year old who had been very quiet up till that point, piped up — “Oh I know!”

“Ok, what is it?” I asked, trying not to get my hopes up.

“Two hundred and sixteen!”

Which completely made my day. A happy ending after all. And maybe even a future collaborator.

Gaze tracking

This weekend I had a sudden inspiration to use the i-Sight camera on my MacBook Air to write software that figures out where my eyes are looking on the computer screen. Such gaze tracking is definitely a hot topic these days. The newest Lenovo notebook computer has it built-in.

It turned out that the hardest part was finding code that would get anything at all from the i-Sight camera into Java. Once I found that out, the rest was pretty straightforward.

But one question kept nagging at me: I’ve been using one MacBook or another for almost two years now. Why did I suddenly, just this weekend, get an urge to implement a gaze tracker? And then it came to me — on some subliminal level I’m responding to the announcement of the IPad 2.

I never got an iPad when they first came out. I wasn’t even interested in the iPad. My response to all the hype was a consistent “Meh”. But the iPad 2 is not like the iPad. It has cameras — one facing you, and the other facing away from you. And that is interesting.

The camera facing you can be used to know where you are looking on the screen of the iPad 2. And the camera facing away from you can be used to create a cyber-enhanced (one might even say eccescopic) view of whatever lies on the other side of the iPad.

I think it is this possibility that the iPad can know where you are looking that matters here. Once millions of people can wander around in the world holding a consumer-friendly window into the internet, it becomes really interesting — empowering actually — for them to communicate through that window using their gaze and attention.

All of a sudden, just like that, after decades of interest by the geeky few, gaze tracking is actually about to become relevant to millions of people.


I’m listening to two people improvise together on a piano keyboard. And I am struck, as always on such occasions, by the “conversational” aspect of it. One person introduces an idea, the other takes it and riffs on it, the first person responds with their own variation / counterpoint, and before you know it they are off and running.

When one topic has been exhausted, they begin another, and seemingly in no time they are having an entirely different musical conversation together.

Of course this sounds a lot like what happens when two people start talking to each other. And I don’t think that’s a coincidence. I suspect that we have within us a much deeper instinct for “conversation” than could entirely be due to our species’ relatively recent development of language.

When we see two dogs or cats together, we see similar rhythms of back and forth. The ebb and flow how we spend time together — how we create time together — is a quality of our shared experience that I suspect stems from something deep into our mammalian brains, and perhaps underlies much of our common appreciation of music, as it underlies much that we find enjoyable in life.

Digital 3D recording

There was a time when you couldn’t make endless copies of a song. If you tried to play a recording, then record the copy you’d just played, then record that copy, after a few iterations it would all just turn into noise.

Same thing with images. If you scanned or photographed an image, then printed it, then made another scan, and repeated this a few times, you’d be left with nothing but snow.

This was the analog world we used to live in. Now of course we’re in a digital world, where you can make endless copies of things, because there are lossless digital formats.

Today I was talking to somebody who makes 3D scanners (exotic devices that do 3D scans of physical objects), and I had a sudden inspiration. I was thinking about the 3D printer I have at home, and I realized that if he were to scan an object I had made on my 3D printer, and I tried to 3D print the result, the shape would turn to mush after a few iterations. Just like it used to be for music and pictures.

And then I had a sudden inspiration. I said “Why can’t we do digital 3D printing?” In other words, why can’t we 3D print something losslessly, so that if we scan it, we get a perfect copy, no matter how many times we scan → print → scan → print, and so on.

But how do we do this? Well, let’s think about how much information we’re talking about here. Assume we have a reasonably accurate 3D printer — one that can print things to 0.1 mm accuracy.

Suppose I print a fairly complex object on this 3D printer. Let’s say it’s a famous sculpture that can be described on my computer as a polygonal mesh of 10,000 vertices. That means I need to encode 10,000 points. A point needs three numbers, for its x, y, and z coordinates. Each number needs about 16 bits (for the geeky among you: since one unit is 0.1 mm, 16 bits suffices to give an accurate position up to a length of 6.5 meters).

So we’re talking 16×3 bits × 10,000 points, or about half a million bits.

If our 3D printer can build up a model by depositing melted plastic filament with 0.1 mm accuracy, then we can “wiggle” that filament from side to side as we lay it down, so that it represents a zero bit when it wiggles to the left and a one bit when it wiggles to the right. This wiggling will make the filament take up twice as much room, so we need to make space for 1,000,000 bits.

But at a resolution of 0.1 mm, 1,000,000 bits takes up only 10mm × 10mm × 10mm, or one cubic centimeter.

Which means we can fill our 3D printed model with copies of this one cubic centimeter solid texture, made by our wiggling process. Even a fairly small fragment of the printed model will contain multiple copies of this information. If the printed model is scratched, gauged, cut into pieces or even smashed, we will still be able to recover the 500,000 bits of information that represent the 10,000 vertices that describe the model’s surface.

We don’t need to continue this wiggling all the way to the surface. The model can have a thin shell of solid material, so that if you look at it from the outside you will see only a smooth surface, just like the original sculpture.

I’m going to try some experiments along these lines with my little home 3D printer. If I succeed, then I might just help 3D printing to truly enter the digital age.

A boulder on the tracks

I’m writing this on a train, which is stopped because onto the tracks somebody rolled a very large boulder, which our train has hit. The collision with the boulder has caused sufficient damage to the train (which had been traveling 125 miles per hour) that we passengers now need to transfer to another train.

The conductor has announced that in about half an hour another train will come by, and then we will begin the process of moving everyone.

Sitting here, I am slowly absorbing how fortunate we all are to be alive and well. If our train had gone off its rails, many of us would have been either killed or seriously injured.

The oddest thing is that the conductors say they are quite sure, based on where the event occurred, that the boulder was placed there deliberately (as opposed, say, to having rolled down a hill).

Which leaves me trying to understand the mindset of someone who would roll a giant boulder onto train tracks. Were they just being stupid, or did they actually understand how close they came to causing death or injury to hundreds of people?

Snap together stories

I’m working on a way for people to build stories by snapping together words and phrases. The goal is for this to be collaborative — which means there’s going to be a server side, where the stories that people build together can live.

But first I’m working out the interaction — how you put the pieces together into larger pieces. This effort is very much inspired by the snap-together tiles approach used by the Scratch project at MIT. Except that I’m applying it to natural language.

I hope to have the server side connected soon. Meanwhile you can get a sense of it by clicking on the image below: