Explain a Change, not an Absolute Outcome
Accepting a Relevant Factor
To explain a system is to come up with a model of how it produces some output. The first thing we need in a causal model is the set of causes, i.e., the factors that are relevant to the output.
For example, if we want to explain what causes a light bulb to glow, we have to mention that the electricity flow is a relevant factor. Otherwise, if we omit it from our model and the electricity happens to be off, we might flick on the light switch but find that the bulb doesn’t glow. Ditto for the wire connecting the bulb to the switch, the filament in the bulb, and of course the light switch itself. All of these can affect the output, namely the glowing of the bulb, and should be included in our model. We can, however, omit things like the color of the wire, the shape of the switch, and the name of the person flicking on the switch. These things don’t really affect our output variable as long as the relevant factors are present.
Hypothesis: If you want to claim some factor is relevant, you need to show it changing along with the output.
Otherwise, that factor could be irrelevant to the output without your realizing it. In the future, that factor could change without affecting the output at all.
For example, we saw that changing the light switch changed the glowing of the bulb. We could say that it was a relevant factor. However, if all the bulbs you see are transparent, you can’t say that transparency is a relevant factor. You haven’t observed a change in output along with a change in transparency. It could be that a colored bulb would also work.
Test:
A scientist who studies vision and the brain has made a curious discovery about portrait painting. Artists almost always place one eye of their subject at the horizontal center of the picture.
Dr. Christopher Tyler took photos of 170 famous portraits from the past five centuries and marked the midpoint along the horizontal top of the picture.
Then he drew a straight vertical line that divided each painting at its horizontal center. To his astonishment. one eye or the other almost always fell on or near the horizontal center. In talking to art experts, Tyler found that none knew of any rule for placing an eye at the horizontal center. He concluded that artists must be doing it unconsciously as the result of some intuitive sense of the aesthetic appeal of this arrangement.
– A Beginner’s Guide to Scientific Method by Stephen S. Carey, page 49
Dr. Tyler noticed that a bunch of famous portraits had an eye near the horizontal center. So, this obviously means that an eye near the horizontal center is a relevant factor for “aesthetic appeal”. Right?
What is the change you’re explaining? The output variable here is the “aesthetic appeal” (however that is defined). He’s claiming that an eye near the horizontal center is a relevant factor. But you haven’t observed a change in the output along with a change in that factor! You need to show that placing the eye elsewhere leads to a change in “aesthetic appeal”. One easy way would have been to look at less-famous or even amateur-drawn portraits, which presumably have less “aesthetic appeal”, and show that they tend to place the eye off-center. A more controlled experiment would have been to shift the very same famous paintings so that the eyes are off-center and check if people who haven’t seen them before rate them any less. Otherwise, what if placing the eye anywhere within reason leads to pretty much the same result? In fact, assuming that you place both eyes in the frame, what are the odds that neither will be near the center?
Test:
A number of multinational companies have been accused of subjecting workers in developing countries to poor working conditions. … [I]n developing countries, workers endure terrible working conditions. Hours are long. Wages are pitiful.
– The Undercover Economist, Tim Harford, page 222
The output variable here (or dependent variable, as some call it) is the awfulness of the working conditions in third-world factories. Obviously, the multinational companies are relevant factors.
What change are you explaining, though? Have you observed a lack of awful working conditions there along with a lack of multinational companies?
But … [w]orkers go [to the multinational companies] voluntarily, which means - hard as it is to believe - that whatever their alternatives are, they are worse.
They stay there, too; turnover rates of multinational-owned factories are low, because conditions and pay, while bad, are better than those in factories run by local firms.
– The Undercover Economist, Tim Harford, page 222
Even when it’s a factory run by a local firm and not an MNC, we get much the same outcome: poor pay and working conditions. So, we haven’t observed a lack of poor working conditions along with a lack of MNCs and can’t say that MNCs are relevant factors for those poor conditions.
A Test of your Explanation Skills
Alright. If you think you’ve understood this concept, test yourself on this example from Harry Potter and the Methods of Rationality:
“This is a game based on a famous experiment called the 2-4-6 task, and this is how it works. I have a rule - known to me, but not to you - which fits some triplets of three numbers, but not others. 2-4-6 is one example of a triplet which fits the rule. In fact… let me write down the rule, just so you know it’s a fixed rule, and fold it up and give it to you. Please don’t look, since I infer from earlier that you can read upside-down.”
The boy said “paper” and “mechanical pencil” to his pouch, and she shut her eyes tightly while he wrote.
“There,” said the boy, and he was holding a tightly folded piece of paper. “Put this in your pocket,” and she did.
“Now the way this game works,” said the boy, “is that you give me a triplet of three numbers, and I’ll tell you ‘Yes’ if the three numbers are an instance of the rule, and ‘No’ if they’re not. I am Nature, the rule is one of my laws, and you are investigating me.
You already know that 2-4-6 gets a ‘Yes’. When you’ve performed all the further experimental tests you want - asked me as many triplets as you feel necessary - you stop and guess the rule, and then you can unfold the sheet of paper and see how you did. Do you understand the game?"
“Of course I do,” said Hermione.
“Go.”
“4-6-8” said Hermione.
“Yes,” said the boy.
“10-12-14”, said Hermione.
“Yes,” said the boy.
Hermione tried to cast her mind a little further afield, since it seemed like she’d already done all the testing she needed, and yet it couldn’t be that easy, could it?
“1-3-5.”
“Yes.”
“Minus 3, minus 1, plus 1.”
“Yes.”
Hermione couldn’t think of anything else to do. “The rule is that the numbers have to increase by two each time.”
“Now suppose I tell you,” said the boy, “that this test is harder than it looks, and that only 20% of grownups get it right.”
Hermione frowned. What had she missed? Then, suddenly, she thought of a test she still needed to do.
“2-5-8!” she said triumphantly.
“Yes.”
“10-20-30!”
“Yes.”
“The real answer is that the numbers have to go up by the same amount each time. It doesn’t have to be 2.”
“Very well,” said the boy, “take the paper out and see how you did.”
Hermione took the paper out of her pocket and unfolded it.
Three real numbers in increasing order, lowest to highest.
What was the fundamental mistake Hermione made?
She tried to explain an absolute outcome, not a change. At no point did she get a negative answer. It was always “yes”. But we just saw that, to claim that something is a relevant factor, you need to show it changing along with the output. So, she shouldn’t have jumped to the conclusion that “the numbers have to go up by the same amount each time” because she had never seen that factor being toggled to give a change in the output.
A good test would have been to try with a case where the numbers didn’t go up by the same amount each time, such as “2-5-9”. Now, if it turned out to be “no”, she could say with some confidence that the factor of “the numbers had to go up by the same amount” was potentially relevant or, at least, not yet shown to be irrelevant. If the answer was “yes”, then her proposed relevant factor would be shown to be irrelevant! The numbers needn’t have gone up by the same amount.
Eliezer Yudkowsky calls this positive bias. I believe it’s more general, but in any case, this test should tell you in advance if you might be making a mistake in your explanation: are you trying to explain a change or an absolute outcome?
Examples of People Explaining Absolute Outcomes
What other explanations can we dismiss right out of the gate, based on this test? (Not saying they will be wrong, just that the available evidence won’t justify narrowing it down to them.)
Example:
It is well known that panes of stained glass in old European churches are thicker at the bottom because glass is a slow-moving liquid that flows downward over centuries.
– The Nature of Glass Remains Anything but Clear, The New York Times
That explains why the bottoms of old window panes show more distortion.
Does it explain it, though? What is the change over time that you’re explaining? Was the bottom not so thick a few centuries ago?
Well known, but wrong. Medieval stained glass makers were simply unable to make perfectly flat panes, and the windows were just as unevenly thick when new.
– The Nature of Glass Remains Anything but Clear, The New York Times
So, it turns out that there wasn’t any change to explain! We should have asked for the initial thickness of the bottom pane before announcing that the thickness was caused by the “downward flow” of the “slow-moving liquid” glass.
Example:
Carl Sagan once told a parable of someone who comes to us and claims: “There is a dragon in my garage.” Fascinating! We reply that we wish to see this dragon - let us set out at once for the garage! “But wait,” the claimant says to us, “it is an invisible dragon.”
– Belief in Belief, Eliezer Yudkowsky
On what basis will you reject that claim?
What change was that person explaining when he said there was a dragon in his garage? He didn’t see anything different from usual in his garage. Nor did he hear, smell, or taste anything different. All he had was the absolute outcome of “normal garage”. So, he shouldn’t have claimed a dragon as a relevant factor in his model of his garage.
If, on the other hand, he had seen a jet of flame and heard a roar, then that change in outcome would require us to come up with some factors that explained it (though an invisible dragon would still be a stretch of a relevant factor for many reasons). Needless to say, the same problem appears in many other supernatural explanations.
This illustrates an important point. If you get a different result from the default outcome, such as flames in your garage as opposed to the default lack of flames, then you have automatically got a change and can use that to narrow down some relevant factors. However, if you get the same result as the default outcome, namely a complete lack of flames, you cannot claim to have found any relevant factors.
Example: Next, consider this quote about the Fifth Column argument by California Governor Earl Warren in 1942:
From Robyn Dawes’s Rational Choice in an Uncertain World:
In fact, this post-hoc fitting of evidence to hypothesis was involved in a most grievous chapter in United States history: the internment of Japanese-Americans at the beginning of the Second World War. When California governor Earl Warren testified before a congressional hearing in San Francisco on February 21, 1942, a questioner pointed out that there had been no sabotage or any other type of espionage by the Japanese-Americans up to that time. Warren responded, “I take the view that this lack [of subversive activity] is the most ominous sign in our whole situation. It convinces me more than perhaps any other factor that the sabotage we are to get, the Fifth Column activities are to get, are timed just like Pearl Harbor was timed . . . I believe we are just being lulled into a false sense of security.”
…
Warren seems to be arguing that, given that we see no sabotage, this confirms that a Fifth Column exists. You could argue that a Fifth Column might delay its sabotage. But the likelihood is still higher that the absence of a Fifth Column would perform an absence of sabotage.
– Absence of Evidence Is Evidence of Absence, Eliezer Yudkowsky
What change was Warren explaining? All he saw, for the sake of our example here, was no sabotage last year and no sabotage this year. That doesn’t justify saying that a Fifth Column was active. If he had seen more sabotage than last year, then we could talk about it and possibly attribute it to a “Fifth Column”. In fact, even if he had seen less sabotage than last year, that could be a sign. But, given that the default outcome is to have no sabotage, we simply have no evidence to justify the existence of a Fifth Column.
Example: Take this quote from a nurse who worked with patients about to die:
For many years I worked in palliative care. My patients were those who had gone home to die. Some incredibly special times were shared. I was with them for the last three to twelve weeks of their lives.
…
When questioned about any regrets they had or anything they would do differently, common themes surfaced again and again. Here are the most common five: …
– Regrets of the Dying, Bronnie Ware
She goes on to list those five regrets. Paul Graham wrote an essay based on this:
The alarming thing is, the mistakes that produce these regrets are all errors of omission. You forget your dreams, ignore your family, suppress your feelings, neglect your friends, and forget to be happy. Errors of omission are a particularly dangerous type of mistake, because you make them by default.
– The Top of My Todo List, Paul Graham
Implicit in the essay (and explicit on the website) was that inverting these mistakes could somehow decrease the number of regrets at the end. The by-now-famous nurse’s website says, “We all want to know we have truly lived our best life. No one wants regrets. No one has to have them. There is choice in creating the life your heart calls you to. The Top Five Regrets of the Dying has already helped so many to find the courage they needed to create the life their heart wanted. It can help you too.”
Did you spot anything fishy?
What was the change they were trying to explain? Sure, people who forgot their dreams and ignored their family had regrets. Men had different regrets from women. But was there anybody who had no regrets? Or at least fewer regrets than the others? If so, you could have looked at how his life differed from that of the others and found out the relevant factors for “regret-free living”. But the blog post at least didn’t seem to mention any such cases. How are we to know that it is even possible to reduce or eliminate regrets?
But surely if you avoid the mistakes that have caused regret in the past, you will have fewer regrets? Maybe. Maybe not. That’s something you have to show empirically. It could be that doing less of one makes you end up with more regrets of another kind. Until you have a changed outcome, you’re not justified in calling something a relevant factor for fewer regrets when dying.
Example:
Once upon a time, there was an instructor who taught physics students. One day the instructor called them into the classroom and showed them a wide, square plate of metal, next to a hot radiator. The students each put their hand on the plate and found the side next to the radiator cool, and the distant side warm. And the instructor said, Why do you think this happens? Some students guessed convection of air currents, and others guessed strange metals in the plate. They devised many creative explanations, none stooping so low as to say “I don’t know” or “This seems impossible.”
And the answer was that before the students entered the room, the instructor turned the plate around.
– Fake Explanations, Eliezer Yudkowsky
How could the students have noticed the flaw in their explanations?
Given that their standard model didn’t seem to apply, since the nearer end wasn’t warmer, they had two options: either say that this went against their standard model and thus something was fishy or try to come up with a new model for this strange new plate. They chose the latter option.
Now, they had to get relevant factors from scratch.
If their hypothesis had been solely about distance, i.e., that distance was a relevant factor for temperature, then yes, the evidence would have backed them up because clearly we saw a change in the temperature along with a change in the distance. That met at least one of the conditions for showing that something was a relevant factor. A model that tried to predict the temperature at different spots would probably have had to take into account the distance from the radiator.
However, the students brought in another factor into their hypothesis. They said that the time spent in front of the radiator was a relevant factor for the temperature of a spot on the plate. I’m inferring this from the fact that some talked about “convection of air currents”, which happens over time. To show that time spent is a relevant factor, you need to at least show a change in the temperature of the spot as more time is spent in front of the radiator. But, here, they saw only an absolute outcome - the final temperature of the distant end being warm. They didn’t see the initial temperature.
They should have asked to see the plate as it was a minute ago. Then, they could have checked if the extra minute was accompanied by any change in temperature. Only then could they have said that the time spent in front of the radiator may be a relevant factor for a change in temperature (either an increase or a decrease).
Ok. To avoid accepting irrelevant factors, we must explain a change, not an absolute outcome. But is a change enough to accept something as a relevant factor? What other conditions must the factor satisfy? We’ll see that in the next post.
Notes
The relevant factors may hide some subtleties. If the filament is broken, the bulb may not glow even if all relevant factors are apparently present. So, there’s quite a bit hidden behind the phrase “filament in the bulb”. I won’t say that it has to be a “working filament”, since that’s a result-based description that tells you nothing in advance, but bulb manufacturers know the necessary features. Similarly, there are some factors that we don’t even mention because they’re so common. I didn’t mention the very relevant factor of being outside water, without which the bulb won’t work despite all the electricity and wiring.
Finally, relevant factors just tell you which factors are important to the output, not how they affect the output. It’s one thing to know that the accelerator will change your car’s speed; it’s another to know that pressing it for 15 seconds will make you go from 0 to 60 mph. All these details come with a detailed model. Right now, we’re just looking at the inputs, not the model that produces the output from the inputs. Also, we are concerned with the simplified output variable of glowing vs not glowing, not the exact brightness.
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