Ken’s Blog

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?

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.

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.

Our culture’s usual view of technology is of a continually upward spiral of capability. Over time cars go faster, planes fly higher, and computers become ever more powerful. But a curious epiphenomenon of all this change is the creation of “temporary technologies: — innovations that end up getting left behind.

When the CD came out, people started to see the LP record as an outdated technology. The LP, of course, had in an earlier era replaced the cylindrical recording. But now we realize that it was the very concept of a musical recording as a physical object that was the temporary technology. In another few years, children will find it incomprehensible that we ever associated musical recording with a physical artifact.

Radio as a medium for narrative fiction was in its time the embodiment of all that was new and modern. But when television came along, radio become the exemplar of everything that was old and quaint.

I’m sure this exact phenomenon has repeated itself throughout all of recorded history. Just as it happened to image morphing and tape recorders, to kinescopes and mimeograph machines, It’s going go happen to the SmartPhone, to Twitter, and to Facebook. I think it has already happened to flash mobs. History is littered with the detritus of abandoned technologies.

In a way this is sad, but it’s also somewhat poetic and redemptive. Technology is, after all the creation of humans. And like humans, it has only a very circumscribed claim on immortality — the creation of progeny (of one sort or another). Thomas Edison may be dead, and his cylindrical recording apparatus long fallen out of favor, but in the centuries to come we will probably still have recorded music, in one form or another.

Around four thousand years ago humans started working out how to express their verbal thoughts in written language. As far as I know, there is not, as yet, any good way to know the details of how this transition played out. Parts of it were quite gradual — as in the slow transformation of markings that started as notations on traded goods up and down the Yangtze River by merchants and traders with no verbal language in common.

But other parts of it might have been quite abrupt, occurring over just a few generations, or perhaps springing from the mind and hand of a single exceptional individual. When those abrupt transitions happened, some people must have suddenly realized the ability of the written word to fold time and space itself. For the first time an individual could send their thoughts across vast distances, could learn from the words of one already dead, or conversely, could speak to generations yet unborn.

I wonder whether there was a sense of dislocation, like that experienced by the first generation to encounter the telephone, or to see reality move upon a flickering movie screen, or to hold a long distance phone conversation from a mountaintop.

It’s a shame we can’t see what it felt like to witness the beginning of the written word — the greatest leap into virtual reality in all of human history.

The wonderful talks at this morning’s papers session got my mind racing in so many directions at once that it was becoming difficult to concentrate. This is the two-edged sword of an experience like SIGGRAPH. By the time the afternoon comes my head is so filled with things to think about, it’s hard to focus on the talk that is right in front of me. It’s like being served a fabulous banquet many times a day. After each meal you wish you had time just to savor — and to digest.

By the last afternoon session I had completely given up trying to focus. Instead, I was sitting with my laptop writing a computer program to work out some new ideas suggested by the morning’s talks. I can’t quite figure out whether, strictly speaking, that is the best use of time, but it sure is a fun way to spend a day!

Today I am happily ensconced attending technical talks on the first day of the annual SIGGRAPH computer graphics conference in Vancouver, along with several thousand other like-minded people. There is nothing else quite like this event — the sheer number of great ideas, the combination of advanced mathematical and computational techniques in service of passionate artistic goals. I love the vast diversity to be found here. Some of the presented work aims for perfect realism, while other work creates artistic tools for far more impressionistic results.

What it all has in common is a perfect confluence of aesthetic expressiveness as a goal and top-notch mathematical engineering as a means. Talks are filled with technical terms like Principal Component Analysis, Single Value Decomposition and Hidden Markov Models, while the images one sees are of rays of light streaming through clouds, ocean waves at sunset, gracefully dancing figures, mysterious forests filled with dappled trees, and digital artworks that look like the marble sculptures, evocative pencil sketches, soft watercolors and sombre oil paintings of old masters.

It’s a bit of an arcane world — this use of shared mathematical language and computational expertise to describe the creation of things of aesthetic beauty — and it is a wonderful world, filled with passionate true believers.

Best of all, this year it is in the beautiful city of Vancouver, where the mountains meet the ocean, and the world itself seems made to inspire art.

Transitions between two ways of thinking can be complicated. For example, there are things you need to do when trying to introduce people to reasoning in four dimensions that would be unnecessary if you were talking to people who were already comfortable with four dimensional reasoning.

In that sense, the discussion about “how to enable people to think in four dimensions” reminds me of other discussions I’ve had recently about transitions. For example, this question about the (possible) transition to a world in which cars drive themselves.

The general reasoning here, which seems plausible to me, is that as computers become ever more powerful, computer driven cars will eventually become so much safer than human driven cars that the huge death toll caused by driver accidents will come to seem socially unacceptable, and eventually illegal — kind of like what has been happening with smoking in the workplace.

But the transition between a world with only human drivers and a world with only robot drivers is rather complicated. During this transition, robot drivers will need to correctly model and react to what those crazy human drivers are doing. And this can be far more difficult to compute than simply making rational decisions in a world that has only rationally acting robot cars.

Analogously, I suspect that even if we do manage to figure out how to transition people to reasoning in four dimensions, a lot of that effort will consist of relating everything back to the three dimensional reasoning people already understand (even if that isn’t the best way to think in four dimensions). I don’t really see any way out of this — we’re probably just going to have to do this the hard way.

I realized after posting the 4D Pong game yesterday, and watching peoples’ reactions, that the tricky concept is hypervolume — the equivalent of volume, but in one higher dimension.

The problem is that we have no direct experience of navigating in that very rich space. It’s deceptively simple — go up/down, left/right, in/out, and also one other dimension, but that extra dimension is one for which we simply have no intuition, since we don’t live there.

Something as simple as playing Pong — moving a box around in a hypercube and bouncing off its hyper-walls (ie: cubes, which serve the same function as the square walls on a 3D cube) — is already stretching beyond what makes sense to most people on any intuitive level, even if they get what’s going on intellectually.

I’m starting now to think about what might be good scaffolding experiences, even simpler than something like Pong, by which one could gradually “level up” to having the intuition required to navigate with ease through a hypervolume.

Well ok, here’s what I have so far. It’s clearly a work in progress, and it’s already really clear that trying to play Pong in four dimensions is hard.

Try it for yourself, by clicking on the image below: