Judea Pearl explains why correlation isn't causation. Conditioning on observed values can create or destroy correlations entirely, as shown in the coin-and-bell thought experiment. Observational studies about driver sleepiness and autonomous driving hit hard limits without controlled experiments.
What is correlation? What is it? So probability of something happening is something, but then there's a bunch of things happening and sometimes they happen together, sometimes not. They're independent or not. So how do you think about correlation of things?
Correlation occurs when two things vary together over a very long time as one way of measuring it, or when you have a bunch of variables that they were very cohesively, then we call, we have a correlation here. And usually when we think about correlation, we really think causally. Things cannot be correlated unless there is a reason for them to vary together. Why should they vary together? If they don't see each other, why should they vary together?
So underlying it somewhere is causation.
Yes. Hidden in our intuition there is a notion of causation because we cannot grasp any other logic except causation.
And how does conditional probability differ from causation? So what is conditional probability?
Conditional probability, how things vary when one of them stays the same. Now staying the same means that I have chosen to look only at those incidents where the guy has the same value as previous one. It's my choice as an experimenter. So things that are not correlated before could become correlated. Like for instance, if I have two coins which are uncorrelated and I choose only those flippings experiments in which a bell rings and bell rings when at least one of them is a tail, okay? Then suddenly I see correlation between the two coins because I only look at the cases where the bell rang, you see, is my design. With my ignorance, essentially with my audacity to ignore certain incidents, I suddenly create a correlation where it doesn't exist physically.
Right? So that's. You just outlined one of the flaws of observing the world and, and trying to infer something fundamental about the world from looking at the correlation.
I don't look at it as a flaw. The world works like that, which. But the flaws comes if we try to impose causal logic on correlation, it doesn't work too well.
I mean, but that's exactly what we do. That's what that has been. The majority of science, the majority of.
Naive science, statisticians know it. Statisticians know that if you condition on a third variable, then you can destroy or create correlations among two other variables, right? They know it, it's in the data, right? There's nothing surprising. That's why they all dismiss the Simpson paradox. Ah, we know it. He don't know anything about it.
Well, there's, there's disciplines like psychology where all the variables are hard to, to account for. And so oftentimes there's a leap between correlation to causation. You're, you're impulsive.
Leap. Who, who is trying to get causation from correlation?
Not, not. You're not proving causation, but you're sort of discussing it. Implying, sort of hypothesizing with our ability.
Which discipline you have in mind. I'll tell you if they are obsolete or if they are outdated or they're about to get outdated.
Yes.
Yeah, tell me, which one do you have?
Oh, psychology, you know, semi. No, no, I was thinking of applied psychologists studying, for example, we work with human behavior and semi autonomous vehicles, how people behave and you have to conduct these studies of people driving cars.
Everything starts with a question. What is a research question?
What is the research question? The research question. Do people fall asleep when the car is driving itself?
Do they fall asleep or do they tend to fall asleep more frequently? More frequently than the car not driving.
Not driving itself.
That's a good question. Okay.
And so you measure, you put people in the car because it's real world. You can't conduct an experiment where you control everything.
Why can't you? You could turn the automatic module on.
And off because it's on road, public. I mean there's, you have, it's, there's aspects to it that's unethical because it's testing on public roads. So you can only use vehicle. You. They have to. The people, the drivers themselves have to make that choice themselves. And so they regulate that. And so you just observe when they drive it autonomously and when they don't. And then.
But maybe they turn it off when they were very tired.
Yeah, that kind of thing. But you, you don't know those. There you go.
So that you have now uncontrolled experiment.
Uncontrolled experiment.
We call it observational study.
Yeah.
And we form the correlation detected. We have to infer causal relationship whether it was the automatic piece that caused him to fall asleep. Oh, okay.
So.
So that is a issue that is about 120 years old. Yeah, I should only go 100 years old. Okay. And. Oh, maybe it's. No, actually I should say it's 2,000 years old because we have this experiment by Daniel about the Babylonian king that wanted the exile. The people from Israel that were taken in exile to Babylon to serve the king. He wanted to serve them king's food, which was meat. And Daniel as a good Jew couldn't eat non kosher food, so he asked them to eat vegetarian food. But the king overseers said, I'm sorry, but if the king see that your performance falls below that of other kids, you know he's going to kill me. Daniel said, let's make an experiment. Let's take four of us from Jerusalem, okay? Give us vegetarian food. Let's take the other guys that to eat the king's food. And about a week's time we'll test our performance and you know the answer. Of course he did the experiment. And they were so much better than the others. And the kings nominated them to super position in his case. So it was a first experiment. Yes. So there was a very simple. It's also the same research questions. We want to know if vegetarian food assist or obstruct your mental ability. And okay, so that the question is very old one. Even Democritus said, if I could discover one cause of things, I would rather discuss one cause and be a king of Persia. Okay. That the task of discovering causes was in the mind of ancient people from many, many years ago. But the mathematics of doing that was only developed in the 1920s. So science has left us often. Okay. Science has not provided us with the mathematics to capture the idea of X causes Y and Y does not cause X. Because all the equation of physics are symmetrical algebraic. The equality sign goes both ways.
