Month: August 2010

Jenny was starting to get the hang of it. If you turned this way twice, it was the same as turning that way three times. There were patterns to moving in higher dimensions, even if it seemed crazy. She had the thought that it was a little like finding yourself in a strange new kind of Rubik’s cube. You didn’t really need to understand what each individual turn meant, as long as you learned the patterns.

Maybe, she thought, this is what magic incantations are all about. The reason an incantation doesn’t seem to make any sense is that we can’t see the space it works in — because it’s not the space we live in. An incantation is really a kind of map — each line, when spoke aloud, turns something in just the right way, and by the time it’s done, you’re there.

She never would have believed in magic incantations, of course, if she hadn’t seen them working with her own eyes. In a way it was reassuring to realize that magic is really just physics in a different world. In a way, she mused, it’s so much more comforting to think that there really are rules about these things. She thought of something she’d read in a comic book once, a line she’d really liked. Except now she’d say it differently: “With great power comes the need for a great sense of direction.”

She saw Josh and Mr. Symarian staring at her, and she realized she had said it aloud. But before she had time to be embarrassed, the teacher spoke up. “Yes, quite,” he said. “I believe you have caught the essence of it. And I am pleased to say,” he added, nodding toward Josh, “that our young friend here has an exceedingly fine sense of direction.”

It was only in that moment that Jenny realized that they were back again in normal three dimensions. They were standing in a small room, empty but for a very lovely queen size bed. And on that bed, apparently fast asleep, was her grandmother Amelia.

Rather than write just one daily post,
I could write two — or three at the most.

Writing more posts could really be fun,
Although I’d upload just the one.

The others I would set aside,
And then one day, when I have died,

Even though I’d gone away,
I could keep blogging, once a day!

As the years went by, Amelia found it harder and harder to remember how to act “normal” about time. Although she always knew when it would happen, she found it unpleasant when her husband would catch her staring off into space, and she would see that look of vague fear upon his face.

It was easier with the children. They seemed to understand the hidden world that everyone keeps inside, and how different it is from that world created by grownups, of days and weeks, of time diced into meaningless little calendar boxes. There was a point when she began to wonder whether growing up is a kind of forgetting, an erasing of the ability to see how time is a sculpture, a world of beautiful shapes carved forever into the fabric of the Universe.

Sometimes she wished they could see what she saw — past and future twisting together, frozen moments stretching as far as the eye could see, like glistening stalactites in a beautifully wrought cave of ice. But there was no way to show anyone, nobody to tell who would have the slightest idea what she was talking about.

And so, as the years went by, she spent more time with the shadow, as she knew she would. Until one day, when the time came to make a choice.

I was having dinner with some good friends this evening, and the subject came up of the question of the “artist” mindset versus the “scientist” mindset. Questions from that discussion are still rattling around in my head.

I’ll just say, right at the outset, that I don’t believe there are two different subspecies of human that can be labeled “artist” or “scientist”. Rather, such identities are part of a dialectic that operates within every individual mind. When you are thinking like a scientist, you are concerned with mechanism: “How does this work? What are the operating principles here? What do I need to build to get from here to there?”

In contrast, when you are thinking like an artist, you are focusing on the deeper meaning itself, and the mechanism is merely a tool to get you there.

The myth that the “artist” and “scientist” are different people is quite prevalent in our society. So much so, that many people are surprised when the myth is questioned. There are many social structures that reinforce this myth. Children are told, from the time they are little, that they need to self-define with a narrow identity. Academic and professional societies are structured in a way that forces a “scientist” to act in a particular way, and punishes professional behavior that seems too “artistic”. Science is not supposed to ask “why”. Yes, an individual scientist can be socially responsible — this is actually encouraged. But this concern with outcomes is not considered part of the process of science itself.

Similarly, to succeed in the art world, one needs not to be seen focusing on the means by which things are done, but rather on the larger purposes and meaning. Starting in the second half of the twentieth century, Clement Greenberg and other influential voices in the art world called upon a renunciation of “mere technique”, in favor of a concept of art that rises above technical means, and focuses rather on ideas expressed, independent of the means used to express those ideas.

And so art and science have formed themselves into two opposing ghettos, each trapped by its own self-imposed limitations.

In my view, “art” and “science” are really two sides of the same coin. Within any individual, the practice of each is impoverished without the practice of the other. Great artists tend to be inventors, and great scientists tend to be driven by a higher purpose that is somewhere on the spectrum from romantic to spiritual.

Frank Capra was constantly inventing new techniques on the set to express his films, which was not surprising, since he had a Ph.D. in Engineering. He self-defined primarily as an artist — which means he was more concerned with getting the shot, and capturing an emotion on film, than he was with how he got it done. Nonetheless, Capra was perfectly comfortable tapping into his scientist self to refine and improve upon the techniques of cinema. The artist within him did not squelch the scientist within him, and this was part of the reason for the great effectiveness of his films.

Albert Einstein and Richard Feynman, among other great physicists, were driven by a larger sense of purpose, of beauty, of intrinsic meaning in the universe around them. When they were identifying and communicating those ideals to others, they are being artists. When they are implementing those ideals by developing mathematical bridges to greater understanding of the workings of the Universe, they were being scientists.

Leonardo da Vinci was of course artist and scientist both, in a way that was so completely integrated that it is impossible to draw a line between those complementary aspects of his creative genius.

Wouldn’t it be wonderful if we had the courage to teach our children to follow in his footsteps?

At first Jenny wasn’t sure what was going on. The door was in front of them, and then suddenly it was, somehow, off to the side. But in a funny way, like it was squashed sideways. She saw that Josh, a little ways ahead of them, had a look of intense concentration on his face. Then, to her horror, Josh’s face became squashed too. Before she could shout or scream, she heard his voice, sounding shockingly normal.

“This way,” he said, and she felt Mr. Symarian take her arm, and somehow turn. As she turned to follow their teacher’s lead, Josh’s face seemed to change back to its normal shape. At that moment, she realized just how much she liked Josh’s face.

She realized she had been holding her breath. As Jenny took a deep breath, she was mildly surprised to find that the air seemed perfectly normal. Was there air in the fourth dimension, she wondered, or had they somehow taken it with them? In any case, she was very glad to find out that you could still breathe in the fourth dimension.

Very glad indeed.

Several years ago I became fascinated by 3D mazes. These are like the 2D mazes we’re all familiar with, except they form 3D paths within a cube, rather than 2D paths within a square. To explore these fascinating shapes (which look a lot like the Borg mothership), I created an interactive Java applet, which lets you create virtual objects that look like this:

 

As long as I am at the Banff Centre, it seemed like a good idea to print one of these things out in the real world. So I modified the Java applet to create a file that the 3D printer can read. It seemed like a good idea to print out the first one very small — you never know how safe you are with the Borg. And this is the first thing that resulted:

 

There is something wonderful about having one of these out in the physical world, where I can touch it and hold it in my hand. It’s a much more visceral experience than merely looking at an image on a computer screen.

As usual, I’ve included the trusty Banff Centre pen, to give you a sense of scale. I must say I am rather pleased. Now I’m trying to decide which of my Java creations to next bring out into our physical world.

I am open to suggestions. 🙂

“I don’t think I can go through that door again,” Jenny said with a shudder. “Talking to it — him — plays funny games with your head.”

“Well,” said Mr. Symarian, “It would appear that the only way for you to reach your grandmother is to proceed by stealth.”

“But how?” Josh said. “There’s only one door into that room.”

“Kid, I don’t think he’s talking’ about using the door,” Sid said.

“Wait,” said Charlie, “this doesn’t make any sense. You’re talking about getting into a room that has only one door, without going through the door? I could see maybe blasting your way in, but that doesn’t seem very, um, stealthy.”

“It is quite simple really,” the teacher said. “One does not need to go through a door, when one may merely go around it.”

“Around it?” Josh said. “But … oh wait, I get it. You’re talking about using one of those extra dimensions of yours to take Jenny back in.”

“Precisely,” said Mr. Symarian. “but more than two will be going.” He smiled at Josh. “A path through the higher dimensions can be rather complex. We shall require a path finder.”

I’m probably going to do a higher quality run, but meanwhile here is a preliminary result of my little walking guys in action.

The photo below shows the basic set-up of the stop-action zoetrope. On the top left is a rotating stage. This stage is made of paper taped on top of foam core. Glued under the foam core is a little round spindle (you can’t see it in this shot) a little less than an inch in diameter.

On the bottom left of the photo is a support platform with a round hole in it just big enough to fit the spindle. When the stage is placed on the platform, it can rotate freely, but it can’t jiggle.

To the right you can see the little walking guys. This time we printed them out as one solid part on the 3D printer, so they would all be in the right position.

Unfortunately, one of the little guys — who was standing on one foot — broke off at the ankle after the part came out of the 3D printer. I super glued him back on, but he ended up tilting to one side. In the animation you can see this as a kind of wave going around the circle, as the tilted guy shows up in different positions.

Notice the radial lines on the rotating stage. These tell me how much to rotate the stage between successive animation frames. After photographing each frame, I rotate the stage by 1/11 of a circle. Over the course of one 12 frame animation cycle, each of the little guys has advanced 12/11 of a circle — ending up roughly in the position of the guy ahead of him.

The effect is as though each of the guys has walked forward a little ways around the circle. When you loop the animation, it looks as though all the little guys are marching continuously around the track.

The resulting animation below isn’t as good quality as what I’d like to end up with, but I thought I might as well show preliminary results. Because it’s an animated gif, the file is a bit large — almost 1MB. So if you have a slow connection, this might take a while to load:

And yes, the arms are swinging. 🙂

Jenny was torn. On the one hand she wanted to go back into the room, to rescue her grandmother from this strange force that was holding her. On the other hand, she wasn’t sure that it was the right thing to do. There were clearly things about this that she didn’t understand. What if her grandmother Amelia was actually in the right place? Although it seemed completely alien — incomprehensible — perhaps there was another way of existing, a way of being outside of time, that was also ok.

She looked at her friends. None of them could possibly understand what she was feeling. None of them had ever been outside of time. For them, things were easy. One thing happens, and then another, and then something else. It’s all so simple when things happen in order. But what if things aren’t that simple?

But they were her friends — and the ones she trusted the most. There was no getting around it — she would have to talk with them about this, even though the things she was talking about would probably sound crazy.

Jenny took a deep breath. This wasn’t going to be easy.

We’re still doing production on the little walking guy. But meanwhile my collaborator Eva Schindling and I managed to build a nice little working zoetrope of a tumbling hypercube.

For those of you who don’t know, a hypercube is something like a cube, only with four dimensions instead of three. As a cube is to a square, a hypercube is to a cube. I made a java applet some years back that lets you play with them.

Of course we don’t live in four dimensions, so it’s hard to get a feeling for what happens when you rotate four dimensional things. Eva and I thought that it would be cool, rather than looking at 4D things rotating on a computer screen, to create an animated sculpture of a rotating hypercube. That way you could look around it from all directions (at least, all 3D directions) as it does its weird 4D rotation.

Because a hypercube has four dimensions instead of three, it can rotate in some pretty fancy ways. A simple rotation only requires two dimensions. Since a hypercube has four dimensions, it can rotate one way in two of its dimensions, while rotating a different way in the other two dimensions.

In our zoetrope, we made our little hypercube tumble around a circular track (a movement that uses two dimensions), while also rotating a different way in the remaining two dimensions.

Now, this is not going to look very intuitive to us poor 3D humans. In fact, it looks as strange to us as, say, a rotating cube would look to a Flatland creature that lives its entire life in a two dimensional world.

Such a 2D creature couldn’t really see a cube — but it could see the shadow a cube makes if its silhouette is projected into the two dimensional world of Flatland:

To the Flatland creature staring at the shadow, it wouldn’t look like something rotating so much as something becoming distorted in all sorts of weird ways.

And that’s pretty much what happens when you try to make sense of a rotating hypercube. As things rotate out of our little 3D world, they look like they are changing size and shape, rather than rotating.

But see for yourself: