Continuing from yesterday…

Today I discovered my first eccescopic creature. I was attempting to peer into the future, when she unexpectedly hopped right onto my hand. I was able to identify this little gal as a kwalado.

Kwalados are expert climbers. They are also extremely gentle creatures, and rather shy. If you hold your hand very still, they will use their long prehensile toes to clamber up your fingers (see photo).

They also have an unnerving but oddly charming tendency to stare deeply into your eyes. I understand they are quite soulful, and fall all too easily into fits of sadness. Fortunately, all kwalados, being mathemalians, love perfect numbers. If you name any three perfect numbers, they will cheer right up.

I’m very sorry about the quality of the photo. The kwalado is a bit difficult to see, since like all eccescopic creatures it dwells in the future. I’m going to try some image enhancement techniques. With any luck, tomorrow I will be able to show you a better picture.

Sketching the future

Today I began some experiments in using old-style media in my research. Ironically, I’m doing this to sketch out ideas for futuristic augmented reality.

In particular, my procedure is to take an image captured from my computer’s camera, print it out on plain white paper, then overlay a fresh sheet of white paper over the printed image.

I then place this sandwich atop an old-fashioned light box. This is quite literally the first time the light box has been used in about ten years — it’s amazing that it still turns on.

Using a #2 pencil, I then sketch lines and figures on the clean top sheet to represent augmented reality concepts. Then I digitize my pencil drawing, and go back to the computer to digitally overlay the drawing onto the captured photo.

I could do all of this in the computer, but it’s just so freeing to be able to use an actual #2 pencil on paper for sketching visual ideas. A pencil is still a far better tool than any digital tablet yet invented.

In any case, when the world for which I’m designing these ideas comes about, digital tablets will all go away anyway. People will be able to go back to sketching with good old paper and pencil like any sane artist would prefer to do — except that the results will be instantly digitized, with all the advantages of computer enhancement but none of the disadvantages.

So you might say that by using tools from the past, I’m getting a jump on the future.

Science and emotion

Following on yesterday’s post on the connections between research and philosophy, there is, more generally, an interesting relationship between science and emotion. Science tries to understand what is, in some approximation of objective truth. Yet to conduct science, you need to be motivated. Without passion the mind does not create. In fact, studies of people suffering from severe anhedonia (the inability to feel pleasure) have shown that such people can have difficulty solving even the simplest of problems. In humans at least, emotion is a precondition for a well functioning intellect.

And so we have what appears to be a contradiction (but in fact is not): To pursue objective truth, we start with emotion. Perhaps people go into different fields of science not because of intellectual proclivities, but because we each feel an emotional connection with certain truths. Some people are drawn to chaos and randomness, and so they choose fields that study inherently chaotic systems, such as meteorology or oceanography. Others are drawn to perfection and harmony, and so they study crystallography or number theory.

In each case, the research itself must be done honestly and without bias, but the excitement that leads to insight and discovery is fed by a pre-existing emotional resonance.

Philosophy of noise

I was in a conversation yesterday in which the subject came up of how science interacts with the prevailing metaphysics of society. For example, the 1st century B.C. poem On the Nature of Things by Lucretius was rediscovered fifteen hundred years later, an event which injected Epicurean philosophy into European thought, leading to various modern, essentially atheist, views that the universe is directed of the movement of atoms — not by the will of gods.

At first blush, it would seem that my own research on procedural texturing and modeling has been similarly Epicurean, since it builds up the world around us from a set of essentially random primitives. But that’s not quite right. In fact the core idea of my approach to procedural modeling is that any observable signal can be perceptually modeled by some appropriate noise-based function — as long as it is a noise-based function that imparts the same subjective impression as the original signal.

This is very freeing. For example, to model the shape and movement of a cloud or fire, we don’t need to compute the actual Navier-Stokes equations for turbulent flow. We only need to understand how people perceive clouds and fire as sets of somewhat noisy signals.

So really, my texture work isn’t so much an expression of atheism as it is of phenomenalism, in that the true nature of the world outside of humans simply doesn’t matter, apart from its effect on our own human perception.

Crowds in finite worlds, continued

I implemented a little simulation in which I placed little circles, representing people in a crowd, into a finite square world, and programmed each person to try to keep their distance from all the others.

I made ten worlds in total. In the first world I placed one person, in the second world two people, and so on up to ten people.

Each little square world is a torus (just like the Asteroids game), so when a person goes off to the right, they come back on the left. Similarly, when a person goes up off the top, they come back on the bottom.

To make it easier to see patterns, I’m showing a 4×4 arrangement of each world. So in each of the ten images below, there are actually 16 little worlds, in a 4×4 tiling. I didn’t draw any edges between tiles. Because each tile is really a little toroidal patch, it doesn’t matter where you draw the edges between neighboring tiles — people can wander continuously between tiles, and each person lives simultaneously on all 16 tiles.

As you can see from the images below, the world containing nine people is the most visually interesting. While most of the others look quite geometric and regular, the crowd of nine people has a very natural quality, like an actual milling crowd.

I find that very intriguing.

Crowds in finite worlds

Suppose you were standing in a finite world that was just big enough to fit, say, ten people comfortably, or twenty people. How would you all arrange yourselves so that everyone was comfortable, with nobody scrunched up against anyone else?

It’s easy to think about something like this if the finite world is a sphere. That’s pretty much the situation represented by my applet Little creatures in a little world.

But it’s not so obvious what happens if the world is toroidal — like the world of an Asteroids game. Since the finite world itself is featureless and without boundaries, any interesting pattern that emerges is going to depend mainly on the number of people all trying to maintain their personal space.

More tomorrow.

Finite worlds I have loved

We are used to a finite world being a sphere, but we also have experience of a finite world being other shapes, even if most of us don’t think about it that way.

For example, the classic video game Asteroids was on a torus. That’s the same topology as a donut, which might seem odd, since the screen is flat. But in Asteroids, if you fly off the screen to the right, you show up again on the left side of the screen. Similarly, if you fly up, you appear again at the bottom of the screen. If you think about it, this is exactly what happens if you walk around a donut.

You can see that it’s more like a donut than like a sphere if you think about two characters standing side-by-side going around the world and coming back to where they each started. On a sphere, their paths will cross along the way. On a torus (such as the world of Asteroids) their paths will never cross.

In the early Charlie Kaufman film Human Nature, there is a scene with Tim Robbins in the afterlife where his character tries to leave by a door to the left, only to find himself walking back into the same room via an identical door on the right. At that point the character realizes he is trapped in a tiny self-contained universe.

This idea was blatantly ripped off two years later in Matrix: Revolutions, when Neo runs along a set of train tracks only to find himself arriving back at the same station from the other direction. The sad sad thing is that this was the only actual clever moment in the entire film.

Finite worlds

Our Earth is, topologically, a finite world. If you go far enough in any one direction, in a “straight” line, you are actually traveling in a great circle around the globe, so you will sooner or later end up back where you started.

For most people this is a theoretical concept. It is rare that anyone has occasion to go completely around the world, so the finiteness of the Earth is in many ways disconnected from our everyday experience of life.

But suppose we lived in a universe that was truly finite, at a scale small enough for it to matter on a human level. Suppose that any time you walked, say, a mile in any direction, you found yourself back where you started. What would that be like?

Things become even more radically different as the scale gets smaller. Imagine a world that repeated on such a small scale that if you looked out into the distance, you could see the back of your own head. Where if you shone a laser beam, it would come back from the other direction. In such a world, guns would be worse than useless — if you shot off a firearm, the most likely outcome would be suicide. Now we are getting to the sorts of questions that M.C. Escher was clearly thinking about.

How would living in such a world change the way we think about things? It would certainly change the way we think about city planning and architecture, but would it also transform our aesthetics, our mathematics, our music and art?

Games that generate stories, continued

In response to my post yesterday on games as generators of narratives, Sharon pointed out that she never thought of Monopoly as a story, and she noted the absence of characters. To clarify: When you play Monopoly (or chess, for that matter), you are the protagonist. The wonderful thing about narrative games is the opportunity for you to take responsibility for the adventure, rather than merely passively watching it from the outside.

If one were to create a romantic comedy game or a hero’s journey game, I would think that each player would take on a key role — perhaps hero or heroine, villain or mentor, best friend or hand of fate.

It would be interesting to personify aspects of a story that are essential but not usually personified. For example, in a hero’s journey game, a player could choose to play the journey itself. This would have the interesting benefit of illuminating the structure of such stories, so that players were aware of them.

After all, when Elizabeth Magie created The Landlord’s Game in 1903 (the game that evolved into Monopoly), her explicit ethical goal was to teach children how unfair rights for property owners lead to the impoverishment of tenants.

Alas, that’s not the lesson most children end up taking away from Monopoly. Instead, most players are happy to end up with everybody else’s money and property. Come to think of it, maybe it’s a good thing it wasn’t called The Genocide Game.

Games that generate stories

Today my friend Athomas and I were discussing a favorite topic of ours — the fact that traditional games such as Monopoly and chess create a dramatic structure that is like a linear narrative (but is not a linear narrative) through their well constructed rules of game play. The natural progression from early play to mid-game to final battle comes entirely out of the well-crafted “physics” of the game, not through post-facto act of imposed coercion and narrowing of player choices (as in some computer games).

I raised the question of whether one could target a specific well-understood genre of narrative, such as the hero’s journey, or the romantic comedy (genres that have a very clear and definitive structure, well understood by authors and intuitively recognized by audiences), and create a game that invokes in its players an equivalent emotional arc and meta-narrative.

It would be particularly cool if this could be done without computers — simply through such relatively traditional means as moving pieces on a physical board, rolling dice and the choosing of chance cards.

More to follow.