Causality

We have a built-in notion that some events cause other events. When one event consistently proceeds another event, we say that the first event caused the second. For instance, when I drop a stone in a pond, ripples propagate outward from where the stone hit with the pond. If we label the stone falling into the water as event A and the ripples as event B, then I can say that I believe A caused B. How do I come to this conclusion?

I could drop the stone in the pond a hundred times, and observe ripples each time. I could observe the pond without dropping the stone and observe that the surface is calm. After enough of these observations, I could come to the conclusion that these events are highly correlated; A seems to always be followed by B, and B is always proceeded by A. But how do I make that leap from correlation to causation? It could be that each time I drop the stone in the pond, I’m angering the pond gods who express their anger by shaking the waters. But even then, I’m still causing the ripples, albeit more indirectly than I assumed, aren’t I? Perhaps it’s a chemical reaction with the stone which is causing the ripples. I have only been dropping in granite rocks, maybe if I dropped in bits of concrete there would be no ripples. But even then, my action of dropping the stone still caused the ripples, even if the precise mechanism of ripple formation eludes me.

The question of how the ripples formed seems important. Every time I have ever dropped a stone stone in the pond, ripples have formed, so far without exception. Even if I don’t know exactly how they formed, I have gained useful knowledge that can be used to make predictions about the future. How certain am I that the next time I drop a stone into the pond, ripples will form? If I have never done the test, I am totally uncertain. If I have done the test a million times, then my confidence approaches 100%. What does it matter if I don’t know exactly how the ripples formed? I can construct a useful model in my head that simply says A causes B. What more to causality is there?

It could be the case that A doesn’t always cause B. My model of A to B causality would have to be amended. I’ve been running all of these experiments in the April. What if, in December, when the pond is frozen over, I try to repeat my experiment. I would find that dropping a stone into the pond does not cause ripples. I have to modify my model of causality based on the observations. On model could be: A causes B if and only if the month is April. If we think of April as an event C, then the statement becomes A and C together cause B.

That sounds silly to us, April has nothing to do with ripples. April is only strongly correlated with warmer temperatures when the pond is thawed, whereas December is strongly correlated with the pond being frozen. But based on our observations, April being the cause of ripples agrees with experimental observation as much as dropping the stone in. From our limited observation and our hypothetically limited prior knowledge, “April causes ripples” is just as true as “dropping a stone into a pond causes ripples”.

This nonintuitive result illustrates a fundamental limitation in our ability to give causal relationships between events. We are born and move about and have experiences of the world. As we make observations, our minds build up models of the external world based on correlations between events. But all of our experiences are based on a finite number of experiences. We can not drop a stone into a pond an infinite number of times, so although we can use inductive reasoning to conclude that the statement “A causes B” is very likely true, we can never be 100% certain. And even if we were able to perform the experiment an infinite number of times, we would be unable to perform all the possible variations on the experiment: dropping all types of stones, having different people drop stones, drop the stones from all possible heights… There may be some situations where the model you’ve become so certain of — “A causes B” — fails.

Once you’ve constructed a model of causality which explains 100% of previous observations, you are forced to make an important decision. Do you believe that this model can be used to predict future events because A actually causes B, or do you believe that the model can be used to predict future events not because A causes B but because the two have always been correlated and will probably continue to be correlated? This is an important distinction. There is a school of thought in the philosophy of mind called occasionalism which suggests as a solution to the mind-body problem that events which occur in the mind actually don’t causally influence what happens in the body and vice versa; they just happen to be extremely correlated. The thing that binds them together so that every time I think to lift up my arm, my arm actually is lifted up, could be God or something unexplained. But my thinking “lift up my arm” does not actually ever cause my arm to be lifted up, these two events are just correlated. Likewise, when we study a lot of observations and come up with physical laws which explain correlations between events, occasionalism posits that the laws don’t mean that events causally influence each other. It just means that they are correlated and connected by something unknown. There is no real way to scientifically separate out these two beliefs about causality, so we all must make a choice. For myself, I believe that physical laws actually represent causal relations between events, simply because it doesn’t require the existence of supernatural forces binding events together in causal chains.

How do we construct these models of causation from our existing experiences? I would love to know, as this is a central question in cognitive science, neuroscience, philosophy of mind, and artificial intelligence. The only way we will come closer to a solution is by thinking about it, and that’s what I intend to do.