W for a World
The Thirteenth Floor, Columbia Pictures, 1999
From The Atlantic:
Gefter: If snakes aren’t snakes and trains aren’t trains, what are they?
Hoffman: Snakes and trains, like the particles of physics, have no objective, observer-independent features. The snake I see is a description created by my sensory system to inform me of the fitness consequences of my actions. Evolution shapes acceptable solutions, not optimal ones. A snake is an acceptable solution to the problem of telling me how to act in a situation. My snakes and trains are my mental representations; your snakes and trains are your mental representations.
Gefter: How did you first become interested in these ideas?
Hoffman: As a teenager, I was very interested in the question “Are we machines?” My reading of the science suggested that we are. But my dad was a minister, and at church they were saying we’re not. So I decided I needed to figure it out for myself. It’s sort of an important personal question—if I’m a machine, I would like to find that out! And if I’m not, I’d like to know, what is that special magic beyond the machine? So eventually in the 1980s I went to the artificial-intelligence lab at MIT and worked on machine perception. The field of vision research was enjoying a newfound success in developing mathematical models for specific visual abilities. I noticed that they seemed to share a common mathematical structure, so I thought it might be possible to write down a formal structure for observation that encompassed all of them, perhaps all possible modes of observation. I was inspired in part by Alan Turing. When he invented the Turing machine, he was trying to come up with a notion of computation, and instead of putting bells and whistles on it, he said, Let’s get the simplest, most pared down mathematical description that could possibly work. And that simple formalism is the foundation for the science of computation. So I wondered, could I provide a similarly simple formal foundation for the science of observation?
Gefter: A mathematical model of consciousness.
Hoffman: That’s right. My intuition was, there are conscious experiences. I have pains, tastes, smells, all my sensory experiences, moods, emotions and so forth. So I’m just going to say: One part of this consciousness structure is a set of all possible experiences. When I’m having an experience, based on that experience I may want to change what I’m doing. So I need to have a collection of possible actions I can take and a decision strategy that, given my experiences, allows me to change how I’m acting. That’s the basic idea of the whole thing. I have a space X of experiences, a space G of actions, and an algorithm D that lets me choose a new action given my experiences. Then I posited a W for a world, which is also a probability space. Somehow the world affects my perceptions, so there’s a perception map P from the world to my experiences, and when I act, I change the world, so there’s a map A from the space of actions to the world. That’s the entire structure. Six elements. The claim is: This is the structure of consciousness. I put that out there so people have something to shoot at.
Gefter: But if there’s a W, are you saying there is an external world?
Hoffman: Here’s the striking thing about that. I can pull the W out of the model and stick a conscious agent in its place and get a circuit of conscious agents. In fact, you can have whole networks of arbitrary complexity. And that’s the world.
