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But ignorance exists in the map, not in the territory. If I am ignorant about a phenomenon, that is a fact about my own state of mind, not a fact about the phenomenon itself. A phenomenon can seem mysterious to some particular person. There are no phenomena which are mysterious of themselves. To worship a phenomenon because it seems so wonderfully mysterious is to worship your own ignorance.
But the deeper failure is supposing that an answer can be mysterious. If a phenomenon feels mysterious, that is a fact about our state of knowledge, not a fact about the phenomenon itself. The vitalists saw a mysterious gap in their knowledge, and postulated a mysterious stuff that plugged the gap. In doing so, they mixed up the map with the territory. All confusion and bewilderment exist in the mind, not in encapsulated substances.
Marcello and I developed a convention in our AI work: when we ran into something we didn’t understand, which was often, we would say “magic”—as in, “X magically does Y”—to remind ourselves that here was an unsolved problem, a gap in our understanding. It is far better to say “magic,” than “complexity” or “emergence”; the latter words create an illusion of understanding. Wiser to say “magic,” and leave yourself a placeholder, a reminder of work you will have to do later.
This cognitive phenomenon is usually lumped in with “confirmation bias.” However, it seems to me that the phenomenon of trying to test positive rather than negative examples, ought to be distinguished from the phenomenon of trying to preserve the belief you started with. “Positive bias” is sometimes used as a synonym for “confirmation bias,” and fits this particular flaw much better.
I have been writing for quite some time now on the notion that the strength of a hypothesis is what it can’t explain, not what it can—if you are equally good at explaining any outcome, you have zero knowledge. So to spot an explanation that isn’t helpful, it’s not enough to think of what it does explain very well—you also have to search for results it couldn’t explain, and this is the true strength of the theory.
Subjects just keep guessing red, as if they think they have some way of predicting the random sequence. Of this experiment Dawes goes on to say, “Despite feedback through a thousand trials, subjects cannot bring themselves to believe that the situation is one in which they cannot predict.”
Can even a human be that overconfident? I would suspect that something simpler is going on—that the all-blue strategy just didn’t occur to the subjects. People see a mix of mostly blue cards with some red, and suppose that the optimal betting strategy must be a mix of mostly blue cards with some red. It is a counterintuitive idea that, given incomplete information, the optimal betting strategy does not resemble a typical sequence of cards. It is a counterintuitive idea that the optimal strategy is to behave lawfully, even in an environment that has random elements. It seems like your behavior
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When your knowledge is incomplete—meaning that the world will seem to you to have an element of randomness—randomizing your actions doesn’t solve the problem. Randomizing your actions takes you further from the target, not closer. In a world already foggy, throwing away your intelligence just makes things worse.
It is a counterintuitive idea that the optimal strategy can be to think lawfully, even under conditions of uncertainty
Long ago, in the unthinkably distant past, I was a devoted Traditional Rationalist, conceiving myself skilled according to that kind, yet I knew not the Way of Bayes. When the young Eliezer was confronted with a mysterious-seeming question, the precepts of Traditional Rationality did not stop him from devising a Mysterious Answer
This I will not describe, for it would be a long tale and complicated. I was young, and a mere Traditional Rationalist who knew not the teachings of Tversky and Kahneman. I knew about Occam’s Razor, but not the conjunction fallacy. I thought I could get away with thinking complicated thoughts myself, in the literary style of the complicated thoughts I read in science books, not realizing that correct complexity is only possible when every step is pinned down overwhelmingly.
Today, one of the chief pieces of advice I give to aspiring young rationalists is “Do not attempt long chains of reasoning or complicated plans.”
But my hypothesis made no retrospective predictions. According to Traditional Science, retrospective predictions don’t count—so why bother making them? To a Bayesian, on the other hand, if a hypothesis does not today have a favorable likelihood ratio over “I don’t know,” it raises the question of why you today believe anything more complicated than “I don’t know.” But I knew not the Way of Bayes, so I was not thinking about likelihood ratios or focusing probability density. I had Made a Falsifiable Prediction; was this not the Law?
As if you could save magic from being a cognitive isomorph of magic, by calling it quantum gravity.
When I think about how my younger self very carefully followed the rules of Traditional Rationality in the course of getting the answer wrong, it sheds light on the question of why people who call themselves “rationalists” do not rule the world. You need one whole hell of a lot of rationality before it does anything but lead you into new and interesting mistakes.
The way Traditional Rationality is designed, it would have been acceptable for me to spend thirty years on my silly idea, so long as I succeeded in falsifying it eventually, and was honest with myself about what my theory predicted, and accepted the disproof when it arrived, et cetera. This is enough to let the Ratchet of Science click forward, but it’s a little harsh on the people who waste thirty years of their lives. Traditional Rationality is a walk, not a dance. It’s designed to get you to the truth eventually, and gives you all too much time to smell the flowers along the way.
The Way of Bayes is also an imprecise art, at least the way I’m holding forth upon it. These essays are still fumbling attempts to put into words lessons that would be better taught by experience. But at least there’s underlying math, plus experimental evidence from cognitive psychology on how humans actually think.
We read history but we don’t live it, we don’t experience it. If only I had personally postulated astrological mysteries and then discovered Newtonian mechanics, postulated alchemical mysteries and then discovered chemistry, postulated vitalistic mysteries and then discovered biology. I would have thought of my Mysterious Answer and said to myself: No way am I falling for that again.
There is a habit of thought which I call the logical fallacy of generalization from fictional evidence
The trouble with generalizing from fictional evidence is that it is fiction—it never actually happened. It’s not drawn from the same distribution as this, our real universe; fiction differs from reality in systematic ways. But history has happened, and should be available.
In our ancestral environment, there were no movies; what you saw with your own eyes was true. Is it any wonder that fictions we see in lifelike moving pictures have too great an impact on us? Conversely, things that really happened, we encounter as ink on paper; they happened, but we never saw them happen. We don’t remember them happening to us.
So (I thought), to feel sufficiently the force of history, I should try to approximate the thoughts of an Eliezer who had lived through history—I should try to think as if everything I read about in history books had actually happened to me. (With appropriate reweighting for the availability bias of history books—I should remember being a thousand peasants for every ruler.) I should immerse myself in history, imagine living through eras I only saw as ink on paper.
Remember how you had always thought that slavery was right and proper, and then you changed your mind. Don’t imagine how you could have predicted the change, for that is amnesia. Remember that, in fact, you did not guess. Remember how, century after century, the world changed in ways you did not guess.
If I’d said, “Huh, that does seem paradoxical. I wonder how the apparent paradox is resolved?” then I would have hit Explain, which does sometimes take a while to produce an answer.
I want to cast my brilliant flare of light so that I can read a book on the train—without anyone becoming curious. Is there a spell that stops curiosity?
Yes indeed! Whenever anyone asks “How did you do that?,” I just say “Science!”
As McDermott says, “The whole problem is getting the hearer to notice what it has been told. Not ‘understand,’ but ‘notice.’” Suppose that instead the physicist told you, “Light is made of little curvy things.” (Not true, by the way.) Would you notice any difference of anticipated experience?
Almost as soon as I started reading about AI—even before I read McDermott—I realized it would be a really good idea to always ask myself: “How would I regenerate this knowledge if it were deleted from my mind?”
If confusion threatens when you interpret a metaphor as a metaphor, try taking everything completely literally.
What should I believe? As it turns out, that question has a right answer. It has a right answer when you’re wracked with uncertainty, not just when you have a conclusive proof. There is always a correct amount of confidence to have in a statement, even when it looks like a “personal belief” and not like an expert-verified “fact.”
You are never entitled to your opinion. Ever! You are not even entitled to “I don’t know.” You are entitled to your desires, and sometimes to your choices. You might own a choice, and if you can choose your preferences, you may have the right to do so. But your beliefs are not about you; beliefs are about the world. Your beliefs should be your best available estimate of the way things are; anything else is a lie. [ . . . ]
But never forget that on any question about the way things are (or should be), and in any information situation, there is always a best estimate. You are only entitled to your best honest effort to find that best estimate; anything else is a lie.
Our culture hasn’t internalized the lessons of probability theory—that the correct answer to questions like “How sure can I be that Bob has a crush on me?” is just as logically constrained as the correct answer to a question on an algebra quiz or in a geology textbook. Our clichés are out of step with the discovery that “what beliefs should I hold?” has an objectively right answer, whether your question is “does my classmate have a crush on me?” or “do I have an immortal soul?” There really is a right way to change your mind. And it’s a precise way.
In the first volume of Rationality: From AI to Zombies, we discussed the value of “proper” beliefs. There’s nothing intrinsically wrong with expressing your support for something you care about—like a group you identify with, or a spiritual experience you find exalting. When we conflate cheers with factual beliefs, however, those misunderstood cheers can help shield an entire ideology from contamination by the evidence.
When something we care about is threatened—our world-view, our in-group, our social standing, or anything else—our thoughts and perceptions rally to their defense.4,5 Some psychologists these days go so far as to hypothesize that our ability to come up with explicit justifications for our conclusions evolved specifically to help us win arguments.6
Probability theory defines how we would ideally reason in the face of uncertainty, if we had the time, the computing power, and the self-control. Given some background knowledge (priors) and a new piece of evidence, probability theory uniquely defines the best set of new beliefs (posterior) I could adopt. Likewise, decision theory defines what action I should take based on my beliefs. For any consistent set of beliefs and preferences I could have about Bob, there is a decision-theoretic answer to how I should then act in order to satisfy my preferences.
But equally obviously it’s useful to be able to use a limited amount of evidence wisely, in the same way it’s useful to be able to use a limited amount of money wisely.
The Dartmouth-Princeton game hints at an answer. Much of our reasoning process is really rationalization—story-telling that makes our current beliefs feel more coherent and justified, without necessarily improving their accuracy. “Against Rationalization” speaks to this problem, followed by “Against Doublethink” (on self-deception) and “Seeing with Fresh Eyes” (on the challenge of recognizing evidence that doesn’t fit our expectations and assumptions).
A further problem is that humility is all too easy to profess. Dennett, in Breaking the Spell: Religion as a Natural Phenomenon, points out that while many religious assertions are very hard to believe, it is easy for people to believe that they ought to believe them. Dennett terms this “belief in belief.” What would it mean to really assume, to really believe, that three is equal to one? It’s a lot easier to believe that you should, somehow, believe that three equals one, and to make this response at the appropriate points in church. Dennett suggests that much “religious belief” should be
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“To be humble is to take specific actions in anticipation of your own errors. To confess your fallibility and then do nothing about it is not humble; it is boasting of your modesty.”
Is this too obvious to be worth mentioning? I say it is not too obvious, for many bloggers have said of Overcoming Bias: “It is impossible, no one can completely eliminate bias.” I don’t care if the one is a professional economist, it is clear that they have not yet grokked the Quantitative Way as it applies to everyday life and matters like personal self-improvement. That which I cannot eliminate may be well worth reducing
“Would you be willing to change your mind about the things you call ‘certain’ if you saw enough evidence? I mean, suppose that God himself descended from the clouds and told you that your whole religion was true except for the Virgin Birth. If that would change your mind, you can’t say you’re absolutely certain of the Virgin Birth. For technical reasons of probability theory, if it’s theoretically possible for you to change your mind about something, it can’t have a probability exactly equal to one.
As for “absolute certainty”—well, if you say that something is 99.9999% probable, it means you think you could make one million equally strong independent statements, one after the other, over the course of a solid year or so, and be wrong, on average, around once. This is incredible enough. (It’s amazing to realize we can actually get that level of confidence for “Thou shalt not win the lottery.”) So let us say nothing of probability 1.0. Once you realize you don’t need probabilities of 1.0 to get along in life, you’ll realize how absolutely ridiculous it is to think you could ever get to 1.0
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What would convince me that 2 + 2 = 3, in other words, is exactly the same kind of evidence that currently convinces me that 2 + 2 = 4: The evidential crossfire of physical observation, mental visualization, and social agreement.
Concerning the proposition that 2 + 2 = 4, we must distinguish between the map and the territory. Given the seeming absolute stability and universality of physical laws, it’s possible that never, in the whole history of the universe, has any particle exceeded the local lightspeed limit. That is, the lightspeed limit may be, not just true 99% of the time, or 99.9999% of the time, or (1 - 1/googolplex) of the time, but simply always and absolutely true.
The map is not the territory.
I cannot help but care how you think, because—as I cannot help but see the universe—each time a human being turns away from the truth, the unfolding story of humankind becomes a little darker.
Politics is the mind-killer. Arguments are soldiers. Once you know which side you’re on, you must support all arguments of that side, and attack all arguments that appear to favor the enemy side; otherwise it’s like stabbing your soldiers in the back. If you abide within that pattern, policy debates will also appear one-sided to you—the costs and drawbacks of your favored policy are enemy soldiers, to be attacked by any means necessary.
It seems quite intuitive to explain rain by water spirits; explain fire by a fire-stuff (phlogiston) escaping from burning matter; explain the soporific effect of a medication by saying that it contains a “dormitive potency.” Reality usually involves more complicated mechanisms: an evaporation and condensation cycle underlying rain, oxidizing combustion underlying fire, chemical interactions with the nervous system for soporifics. But mechanisms sound more complicated than essences; they are harder to think of, less available. So when someone kicks a vending machine, we think they have an
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To understand why people act the way they do, we must first realize that everyone sees themselves as behaving normally. Don’t ask what strange, mutant disposition they were born with, which directly corresponds to their surface behavior. Rather, ask what situations people see themselves as being in. Yes, people do have dispositions—but there are not enough heritable quirks of disposition to directly account for all the surface behaviors you see.