Ken's Blog

Continuing on my quest to make an interactive playground for creating Möbius stories in the spirit of Vi Hart’s Möbius story: Wind and Mr. Ug, I ran a computer analysis over about 56000 English words, looking for “Möbius words”.

I found 728 words that fit the bill: When “mirror-flipped” upside down, each one still looks like a word (although maybe a different word). Any Möbius story you write has to contain only Möbius words.

Below are the words I found in all their symmetric glory, printed in the Möbius story font. Now we just have to make Möbius stories out of them!

Today’s post, like yesterday’s was inspired by Vi Hart’s Möbius Story: Wind and Mr. Ug, a wonderfully twisted little tale about self-reflection and the unexpected turns that love can take.

I thought would be good to build an interactive tool for telling such stories. My first step is the font below (seen with its mirror image), which I call (in honor of Vi’s tale) the Möbius story font:

 

Following on discussions I had with Vi recently, the next step is to build a vocabulary from this font of words that make sense (although maybe very different sense) when read upside down.

Then of course, will come the fun part. Because, in the words of the great Shakespearean actor Sir Edwin: “I don’t want you to get the impression it’s just a question of the number of words… I mean, getting them in the right order is just as important.”

I walked one day on a Möbius strip
Just ’cause I felt like taking a trip.
It seemed so easy, ’til I found
A land where things were turned around

Yes, turned around! Try as I might
I couldn’t tell my left from right
The food they had all tasted funny
The print was backwards on their money!

Now, much as I do like to roam
I just wanted to go home
But I found out to my dismay
The path would only go one way.

They say you can’t go home again,
The world I’d known was gone. But then
“The hell with it,” I said. “Instead,
“Why don’t I just forge ahead?”

So I found another Möbius strip
And started on a second trip
It made no sense I know, and yet
How much wronger could things get?

And sure enough when I’d gone round
That second strip, it seems I found
Another land where things were good
And left to right went like it should

Food was yummy, words looked right
I thought I’d maybe spend the night
Now here I am, still on that trip
To the land beyond the Möbius strip

This was my last evening in Japan, and I was sad to be saying my final goodbyes to my friends before making my way back to my little Ryokon. I was also a bit anxious, because earlier in the week I had gotten thoroughly lost in the narrow winding streets around Kyoto University.

Fortunately, the previous evening my friends had pointed out a small Buddhist shrine that marks the proper turn to take off the main road. Wanting to make sure I had the correct directions this time, I said: “When I see the Buddha, I should take the right turn. Is that it?”

One of my friends looked at me a moment, and then replied: “You know, that’s a good philosophy for life.”

Here in Kyoto
An old temple smiles, as youth
Plays in its shadow

The PAD (pleasure / arousal / dominance) scale by Mehrabian et al provides a nice simple three axis model for classifying all sorts of emotional states, including Anxiety, Depression, Panic, Empathy, Achievement, Extroversion, Arousal Seeking, Loneliness, Emotional Stability, Dependency, Aggressiveness, and Fidgeting.

In my recent post about using simple face-only characters to create a story, I used only two of these three dimensions: eyebrows up/down for varying dominance, and mouth frown/smile for varying pleasure. After seeing a lecture today by Marc Cavazza in which he discussed the PAD scale, I realized that it’s easy to add the third (arousal) axis, simply by changing the shape of the eyes.

So I’ve created another version of this program in which I replaced the winking and blinking with eye shapes that evoke different levels of arousal: interested→neutral→bored. I also added a time-line! You can play with the new version by clicking on the image below:

Several years ago I was on the phone with a program officer at the National Science Foundation, and I was describing a possible approach to a topic I’ve discussed here before — “universal programming literacy” — the possibility of everyone learning how to program a computer.

Her response was interesting. She referred to the “five percent who are the math kids”. Basically, she argued, about five percent of the population is interested in how things work, in a way that makes those individuals disposed to become mathematicians or scientists. The other ninety five are just not highly drawn to that way of thinking.

I suppose this idea is analogous to similar ideas about other fields. For example, most of us are exposed to some form of classes about music or art when we are kids. Yet only a small percentage love creating music or art, to the extent that they grow up holding a guitar or a paint brush in their hands, and thereby find their life passion and vocation.

Just in the last day I heard somebody else repeat the phrase “the five percent” in exactly this context, and now I wonder whether it is a given that this is the way things work — that some small percentage of the population are predisposed to becoming scientists, another small percentage are predisposed to becoming musicians, etc. (even in that scenario of course, there will be cross-overs, such as Brian May, who is both lead guitarist for the rock group Queen and an astrophysicist).

We all know examples of siblings who were raised in the same household by the same parents, with essentially the same cultural influences, yet one sibling falls in love with science and the other with, say, literature. This tends to support the “five percent” theory, does it not?

Finding myself today on a long flight overseas without access to the internet, I started wondering what it would take to make a robot that moved like a millipede. My thought was that a robot millipede could move not merely forward and back, but in any direction.

The first thing I came up with works like the following, when seen in profile:

If you click on the above image you can play with the interactive applet. The basic idea is that as the surface undulates, the little “hairs” on the bottom spread out and come back together in such a way that they grip the floor and pull the robot along.

I was thinking that these “waves” of undulation could go in any direction, so at any moment the robot can move itself along the floor in any direction. One possibility is to put a regular arrangement of up/down actuators on the underside of the robot, like this:

Then it occurred to me that rather than make this a vehicle, one could cover an entire floor or table with this kind of thing. Then any object you put on the surface could be moved along under computer control. This is reminiscent of some wonderful work done by Dan Resnick a while back, in which he cleverly vibrated a table to make it move multiple objects at the same time. One problem with Dan’s approach was that the more objects you wanted to control, the slower everything moved. The millipede surface wouldn’t have that problem.

Of course it will come down to questions like “How cheap can you make an actuator that just moves slightly up and down?” Should you use solenoids, memory metals, piezoelectrics, or something else entirely? The whole thing can be scaled down to very small sizes and still work, so the answer might just come down to finding a mechanism that comes in a really low cost per unit area when the actuators are at some optimal scale.

Perhaps eventually there will be a nano-tech solution, and these things will become as cheap as wallpaper. Imagine the desk that can arrange your papers or bring you your coffee cup — or a floor that could rearrange your furniture for you. That would be very cool.

I was very excited when Doug shared with me the fact that his brother Mike’s math doodle has been posted on Vi Hart’s page. One person doing these things is already wonderful. Two people starts to look like a movement.

In this era of slick iPads and Flash and glossy screens, there is something immensely appealing about going back to telling animated stories with nothing but pencil and paper — albeit transformed by the relatively recent availability of digital video recording and internet sharing.

Also, this is a creative form that I can see children learning to do, to express their own original thoughts and ideas. Not only wouldn’t it require them to go through the intermediate step of learning some commercial software package or other, but it’s also more expressive. In fact, on a certain measure of expressiveness, it could be argued that there is nothing more powerful than the combination of human voice and drawing with pencil on paper.

Maybe the future has just become a little friendlier.

Doug pointed out, in response to yesterday’s post, that there are many possible surfaces with hyperbolic curvature in them here or there. This actually follows from my recent conversation with Vi. Even solid space itself can be curved, for as Einstein pointed out in his General Theory of Relativity, when a big object (like a planet or a star) gravitationally attracts things, it’s actually creating a complex distortion in the fabric of space-time in the vicinity of that planet or star.

So at different places in our own 3D universe, “flat” areas of space can actually have a slight curvature. Some places might look round, like a Reiman sphere, whereas others might be hyperbolic. It would be great to create a software design tool that lets you “dial in” a desired curvature at any point in space — creating a new kind of shape whose curvature changes from neighborhood to neighborhood of space.

If we had the freedom to play with this, imagine what kinds of virtual environments and architectures we could create!