thinking

Name: Tyler
Location: Mountain View, California, United States

thinking := [life, games, movies, philosophy, math, coding, pizza, &c.]

Monday, March 12, 2007

the subjective nature of causality

I would like to argue that the idea of something "causing" another thing is not an intrinsic property of the universe -- rather, it is a subjective property which is somewhat artificially assigned to the world by our own minds. It is a "useful fiction", much like the idea of a center of gravity in physics. So I do not mean to say that causality is nothing, but rather that it is an idea we use to simplify our understanding of the world, and which does not inherently exist outside our interpretations.

This is why: we feel that event x causes event y when
1. y would have not happened without x, and
2. we feel that "x almost didn't happen".
Both of these statements are purposefully vague, because the idea of causality is itself vague. The first point means that, if we imagine the world exactly the same, except that x did not happen, then it seems to us that y would also have (most likely) not happened. The second point means that, along the chain of events leading up to y, x was somehow among the least predictable. If the second point holds for several events as a possible cause (I'll give an example in a second), then we often feel that each of these events was also a cause of the ultimate event y.

In a moment I will argue that these points are dependent in a fundamental way on the ignorance of the one making the causality judgement, because if we "knew everything" then it would be hard (perhaps impossible) to imagine a world in which everything else was the same except that x didn't happen, and, further, it would be truly impossible to distinguish some event x which more "almost didn't happen" than any other past event. (I am assuming a deterministic world here -- and that is a matter for a different posting!)

Here are a couple examples to help get our mind around this intuitive "definition" of causality:
Example 1. Suppose someone named Boberta shoots an apple. In this very straightforward scenario, we might say that the bullet rather speedily touring the apple's interior is a cause of the apple's demise. But what is the "real reason" the apple was destroyed? I think most people would be more satisfied with saying that "Boberta shot the apple" is more of a "real" cause. Why is this a better answer? By the second point above, it is easier to imagine that Boberta didn't shoot the apple than it is to imagine that Boberta did shoot the apple yet the bullet did not destroy it. (Let's think of the shooting as being at very close range, so that aim is not a question.) Out of those two events, it would be less surprising if Boberta never shot the gun than if Boberta did shoot the gun and the bullet did not destroy the apple. This illustrates how the second point is important for our idea of causality. (By the way, if you are wondering why Boberta shot the apple, it's because the apple killed Boberta's father. It was a bad apple.)

Example 2. Now let us suppose that both Alfonzo and Boberta, with a merciless thirst for applejuice, simultaneous shoot the apple. In this case it intuitively feels as if either "Alfonzo shot the apple" or "Boberta shot the apple" alone are each not quite the cause of the apple's demise. In some sense, we feel a bit cheating if we do not mention both shootings. This is meant to illustrate the importance of point one -- if only one of these events didn't happen, the apple would still be maimed. Only when we imagine both shootings not taking place do we imagine the apple remaining, at least for a short while, peacefully intact.

So far I have offered some defense of my definition of causality. Now let me proffer the notion that "x caused y" is inevitably a subjective idea. This follows because our ability to imagine a slightly different world, in which either x did not happen and all else remained the same, or further our ability to estimate the probability with which x almost didn't happen, could never exist in the presence of a perfect knowledge of the world. That is, our ignorance is an integral part of our causality judgement.

Example 3. This one is a little more far-fetched in order to really capture ignorance as an almost essential property of someone in the situation. We've all seen The Matrix, our pop culture modern version of Plato's allegory of the cave. Suppose that in the future we are running a highly complex simulation of an entire world on a vast system of computers. This world is completely deterministic. And the creators of this simulated world have set it up so that at some point in time, the simulated planet of all these simulated people will be hit by a (simulated) comet, leading to the deaths of many (simulated) people. The question is: what is the cause of all these deaths? Within the simulated world, as far as these people ever know, the comet has caused this disaster. Certainly if the comet were not present (or had missed the planet), it would not have happened (point one of causality). And, for most people, it seems very easy to imagine a world in which a particular comet did not exist, or at least whose trajectory was a little bit different (point two of causality). Now let us recall that we know the entire world to be a simulation. In this example, we could also pretend that the entire simulation was set up by a rather sadistic fellow who enjoyed the idea of a planet being devastated by a comet. Now that we know more about the world, we can give a better-informed "real cause" of the destruction to be this programmer's decision to set up the simulated world in such a way.

The point of this example is to illustrate the role of ignorance in causality. No one in the simulated world could ever possibly know about the sadistic programmer unless someone in the real, non-simulated world decided to somehow interfere (and for the sake of the thought experiment we may suppose this does not happen). Hence within the simulated world, there is simply no way to ever know a better "cause" of the comet hit beyond the mere laws of physics within that world.

As far as we may ever know, we might as well be these simulated people, never knowing the complete story, but filling in those gaps in our minds by guessing at the small differences in which the world may evolve, and basing our causal links on our own internal model of many possibilities and our own idea of their probabilities. Yet these possibilities and probabilities could never exist with complete knowledge of the world, for there is but one world; no other possibilities, and no question of probability.

By the way, I suspect there's a lot of pre-existing philosophical work discussing similar ideas, and I'd love to hear about them! Also, thanks to my friend Lara for some useful brainstorming while thinking about this, and Rebecca for reminding me of Plato's somewhat-Matrixy allegory :)