Making Mistakes

1. Making Mistakes

He who says “Better to go without belief forever than believe a lie!” merely shows his own preponderant private horror of becoming a dupe. . . . It is like a general informing his soldiers that it is better to keep out of battle forever than to risk a single wound. Not so are victories either over enemies or over nature gained. Our errors are surely not such awfully solemn things. In a world where we are so certain to incur them in spite of all our caution, a certain lightness of heart seems healthier than this excessive nervousness on their behalf. —W ILLIAM J AMES, “The Will to Believe”

If you’ve made up your mind to test a theory, or you want to explain some idea, you should always decide to publish it whichever way it comes out. If we only publish results of a certain kind, we can make the argument look good. We must publish both kinds of results. —Richard Feynman, “Surely You’re Joking, Mr. Feynman!”

Scientists often ask me why philosophers devote so much of their effort to teaching and learning the history of their field. Chemists typically get by with only a rudimentary knowledge of the history of chemistry, picked up along the way, and many molecular biologists, it seems, are not even curious about what happened in biology before about 1950. My answer is that the history of philosophy is in large measure the history of very smart people making very tempting mistakes, and if you don’t know the history, you are doomed to making the same darn mistakes all over again. That’s why we teach the history of the field to our students, and scientists who blithely ignore philosophy do so at their own risk. There is no such thing as philosophy-free science, just science that has been conducted without any consideration of its underlying philosophical assumptions. The smartest or luckiest of the scientists sometimes manage to avoid the pitfalls quite adroitly (perhaps they are “natural born philosophers”—or are as smart as they think they are), but they are the rare exceptions. Not that professional philosophers don’t make—and even defend—the old mistakes too. If the questions weren’t hard, they wouldn’t be worth working on.

Sometimes you don’t just want to risk making mistakes; you actually want to make them—if only to give you something clear and detailed to fix. Making mistakes is the key to making progress. Of course there are times when it is really important not to make any mistakes—ask any surgeon or airline pilot. But it is less widely appreciated that there are also times when making mistakes is the only way to go. Many of the students who arrive at very competitive universities pride themselves in not making mistakes—after all, that’s how they’ve come so much farther than their classmates, or so they have been led to believe. I often find that I have to encourage them to cultivate the habit of making mistakes, the best learning opportunities of all. They get “writer’s block” and waste hours forlornly wandering back and forth on the starting line. “Blurt it out!” I urge them. Then they have something on the page to work with.

We philosophers are mistake specialists. (I know, it sounds like a bad joke, but hear me out.) While other disciplines specialize in getting the right answers to their defining questions, we philosophers specialize in all the ways there are of getting things so mixed up, so deeply wrong, that nobody is even sure what the right questions are, let alone the answers. Asking the wrong questions risks setting any inquiry off on the wrong foot. Whenever that happens, this is a job for philosophers! Philosophy—in every field of inquiry—is what you have to do until you figure out what questions you should have been asking in the first place. Some people hate it when that happens. They would rather take their questions off the rack, all nicely tailored and pressed and cleaned and ready to answer. Those who feel that way can do physics or mathematics or history or biology. There’s plenty of work for everybody. We philosophers have a taste for working on the questions that need to be straightened out before they can be answered. It’s not for everyone. But try it, you might like it.

In the course of this book I am going to jump vigorously on what I claim are other people’s mistakes, but I want to assure you that I am an experienced mistake-maker myself. I’ve made some dillies, and hope to make a lot more. One of my goals in this book is to help you make good mistakes, the kind that light the way for everybody.

First the theory, and then the practice. Mistakes are not just opportunities for learning; they are, in an important sense, the only opportunity for learning or making something truly new. Before there can be learning, there must be learners. There are only two non-miraculous ways for learners to come into existence: they must either evolve or be designed and built by learners that evolved. Biological evolution proceeds by a grand, inexorable process of trial and error—and without the errors the trials wouldn’t accomplish anything. As Gore Vidal once said, “It is not enough to succeed. Others must fail.” Trials can be either blind or foresighted. You, who know a lot, but not the answer to the question at hand, can take leaps—foresighted leaps. You can look before you leap, and hence be somewhat guided from the outset by what you already know. You need not be guessing at random, but don’t look down your nose at random guesses; among its wonderful products is . . . you!

Evolution is one of the central themes of this book, as of all my books, for the simple reason that it is the central, enabling process not only of life but also of knowledge and learning and understanding. If you attempt to make sense of the world of ideas and meanings, free will and morality, art and science and even philosophy itself without a sound and quite detailed knowledge of evolution, you have one hand tied behind your back. Later, we will look at some tools designed to help you think about some of the more challenging questions of evolution, but here we need to lay a foundation. For evolution, which knows nothing, the steps into novelty are blindly taken by mutations, which are random copying “errors” in DNA. Most of these typographical errors are of no consequence, since nothing reads them! They are as inconsequential as the rough drafts you didn’t, or don’t, hand in to the teacher for grading. The DNA of a species is rather like a recipe for building a new body, and most of the DNA is never actually consulted in the building process. (It is often called “junk DNA” for just that reason.) In the DNA sequences that do get read and acted upon during development, the vast majority of mutations are harmful; many, in fact, are swiftly fatal. Since the majority of “expressed” mutations are deleterious, the process of natural selection actually works to keep the mutation rate very low. Each of you has very, very good copying machinery in your cells. For instance, you have roughly a trillion cells in your body, and each cell has either a perfect or an almost perfect copy of your genome, over three billion symbols long, the recipe for you that first came into existence when your parents’ egg and sperm joined forces. Fortunately, the copying machinery does not achieve perfect success, for if it did, evolution would eventually grind to a halt, its sources of novelty dried up. Those tiny blemishes, those “imperfections” in the process, are the source of all the wonderful design and complexity in the living world. (I can’t resist adding: if anything deserves to be called Original Sin, these copying mistakes do.)

The chief trick to making good mistakes is not to hide them—especially not from yourself. Instead of turning away in denial when you make a mistake, you should become a connoisseur of your own mistakes, turning them over in your mind as if they were works of art, which in a way they are. The fundamental reaction to any mistake ought to be this: “Well, I won’t do that again!” Natural selection doesn’t actually think the thought; it just wipes out the goofers before they can reproduce; natural selection won’t do that again, at least not as often. Animals that can learn—learn not to make that noise, touch that wire, eat that food—have something with a similar selective force in their brains. (B. F. Skinner and the behaviorists understood the need for this and called it “reinforcement” learning; that response is not reinforced and suffers “extinction.”) We human beings carry matters to a much more swift and efficient level. We can actually think the thought, reflecting on what we have just done: “Well, I won’t do that again!” And when we reflect, we confront directly the problem that must be solved by any mistake-maker: what, exactly, is that? What was it about what I just did that got me into all this trouble? The trick is to take advantage of the particular details of the mess you’ve made, so that your next attempt will be informed by it and not just another blind stab in the dark.

We have all heard the forlorn refrain “Well, it seemed like a good idea at the time!” This phrase has come to stand for the rueful reflection of an idiot, a sign of stupidity, but in fact we should appreciate it as a pillar of wisdom. Any being, any agent, who can truly say, “Well, it seemed like a good idea at the time!” is standing on the threshold of brilliance. We human beings pride ourselves on our intelligence, and one of its hallmarks is that we can remember our previous thinking, and reflect on it—on how it seemed, on why it was tempting in the first place, and then about what went wrong. I know of no evidence to suggest that any other species on the planet can actually think this thought. If they could, they would be almost as smart as we are.

So when you make a mistake, you should learn to take a deep breath, grit your teeth, and then examine your own recollections of the mistake as ruthlessly and as dispassionately as you can manage. It’s not easy. The natural human reaction to making a mistake is embarrassment and anger (we are never angrier than when we are angry at ourselves), and you have to work hard to overcome these emotional reactions. Try to acquire the weird practice of savoring your mistakes, delighting in uncovering the strange quirks that led you astray. Then, once you have sucked out all the goodness to be gained from having made them, you can cheerfully set them behind you, and go on to the next big opportunity. But that is not enough: you should actively seek out opportunities to make grand mistakes, just so you can then recover from them.

At its simplest, this is a technique we all learned in grade school. Recall how strange and forbidding long division seemed at first: You were confronted by two imponderably large numbers, and you had to figure out how to start. Does the divisor go into the dividend six or seven or eight times? Who knew? You didn’t have to know; you just had to take a stab at it, whichever number you liked, and check out the result. I remember being almost shocked when I was told I should start by just “making a guess.” Wasn’t this mathematics? You weren’t supposed to play guessing games in such a serious business, were you? But eventually I appreciated, as we all do, the beauty of the tactic. If the chosen number turned out to be too small, you increased it and started over; if too large, you decreased it. The good thing about long division was that it always worked, even if you were maximally stupid in making your first choice, in which case it just took a little longer.

This general technique of making a more-or-less educated guess, working out its implications, and using the result to make a correction for the next phase has found many applications. A key element of this tactic is making a mistake that is clear and precise enough to have definite implications. Before GPS came along, navigators used to determine their position at sea by first making a guess about where they were (they made a guess about exactly what their latitude and longitude were), and then calculating exactly how high in the sky the sun would appear to be if that were—by an incredible coincidence—their actual position. When they used this method, they didn’t expect to hit the nail on the head. They didn’t have to. Instead they then measured the actual elevation angle of the sun (exactly) and compared the two values. With a little more trivial calculation, this told them how big a correction, and in what direction, to make to their initial guess.[1] In such a method it is useful to make a pretty good guess the first time, but it doesn’t matter that it is bound to be mistaken; the important thing is to make the mistake, in glorious detail, so there is something serious to correct. (A GPS device uses the same guess-and-fix-it strategy to locate itself relative to the overhead satellites.)

The more complex a problem you’re facing, of course, the more difficult the analysis is. This is known to researchers in artificial intelligence (AI) as the problem of “credit assignment” (it could as well be called blame assignment). Figuring out what to credit and what to blame is one of the knottiest problems in AI, and it is also a problem faced by natural selection. Every organism on the earth dies sooner or later after one complicated life story or another. How on earth could natural selection see through the fog of all these details in order to figure out what positive factors to “reward” with offspring and what negative factors to “punish” with childless death? Can it really be that some of our ancestors’ siblings died childless because their eyelids were the wrong shape? If not, how could the process of natural selection explain why our eyelids came to have the excellent shapes they have? Part of the answer is familiar: following the old adage “If it ain’t broke, don’t fix it,” leave almost all your old, conservative design solutions in place and take your risks with a safety net in place. Natural selection automatically conserves whatever has worked up to now, and fearlessly explores innovations large and small; the large ones almost always lead immediately to death. A terrible waste, but nobody’s counting. Our eyelids were mostly designed by natural selection long before there were human beings or even primates or even mammals. They’ve had more than a hundred million years to reach the shape they are today, with only a few minor touch-ups in the last six million years, since we shared a common ancestor with the chimpanzees and the bonobos. Another part of the answer is that natural selection works with large numbers of cases, where even minuscule advantages show up statistically and can be automatically accumulated. (Other parts of the answer are technicalities beyond this elementary discussion.)

Here is a technique that card magicians—at least the best of them—exploit with amazing results. (I don’t expect to incur the wrath of the magicians for revealing this trick to you, since this is not a particular trick but a deep general principle.) A good card magician knows many tricks that depend on luck—they don’t always work, or even often work. There are some effects—they can hardly be called tricks—that might work only once in a thousand times! Here is what you do: You start by telling the audience you are going to perform a trick, and without telling them what trick you are doing, you go for the one-in-a-thousand effect. It almost never works, of course, so you glide seamlessly into a second try—for an effect that works about one time in a hundred, perhaps—and when it too fails (as it almost always will), you slide gracefully into effect number 3, which works only about one time in ten, so you’d better be ready with effect number 4, which works half the time (let’s say). If all else fails (and by this time, usually one of the earlier safety nets will have kept you out of this worst case), you have a failsafe effect, which won’t impress the crowd very much but at least it’s a surefire trick. In the course of a whole performance, you will be very unlucky indeed if you always have to rely on your final safety net, and whenever you achieve one of the higher-flying effects, the audience will be stupefied. “Impossible! How on earth could you have known which was my card?” Aha! You didn’t know, but you had a cute way of taking a hopeful stab in the dark that paid off. By hiding all the “mistake” cases from view—the trials that didn’t pan out—you create a “miracle.”

Evolution works the same way: all the dumb mistakes tend to be invisible, so all we see is a stupendous string of triumphs. For instance, the vast majority—way over 90 percent—of all the creatures that have ever lived died childless, but not a single one of your ancestors suffered that fate. Talk about a line of charmed lives!

One big difference between the discipline of science and the discipline of stage magic is that while magicians conceal their false starts from the audience as best they can, in science you make your mistakes in public. You show them off so that everybody can learn from them. This way, you get the benefit of everybody else’s experience, and not just your own idiosyncratic path through the space of mistakes. (The physicist Wolfgang Pauli famously expressed his contempt for the work of a colleague as “not even wrong.” A clear falsehood shared with critics is better than vague mush.) This, by the way, is another reason why we humans are so much smarter than every other species. It is not so much that our brains are bigger or more powerful, or even that we have the knack of reflecting on our own past errors, but that we share the benefits that our individual brains have won by their individual histories of trial and error.[2]

I am amazed at how many really smart people don’t understand that you can make big mistakes in public and emerge none the worse for it. I know distinguished researchers who will go to preposterous lengths to avoid having to acknowledge that they were wrong about something. They have never noticed, apparently, that the earth does not swallow people up when they say, “Oops, you’re right. I guess I made a mistake.” Actually, people love it when somebody admits to making a mistake. All kinds of people love pointing out mistakes. Generous-spirited people appreciate your giving them the opportunity to help, and acknowledging it when they succeed in helping you; mean-spirited people enjoy showing you up. Let them! Either way we all win.

Of course, in general, people do not enjoy correcting the stupid mistakes of others. You have to have something worth correcting, something original to be right or wrong about, something that requires constructing the sort of pyramid of risky thinking we saw in the card magician’s tricks. Carefully building on the works of others, you can get yourself cantilevered out on a limb of your own. And then there’s a surprise bonus: if you are one of the big risk-takers, people will get a kick out of correcting your occasional stupid mistakes, which show that you’re not so special, you’re a regular bungler like the rest of us. I know extremely careful philosophers who have never—apparently—made a mistake in their work. They tend not to get a whole lot accomplished, but what little they produce is pristine, if not venturesome. Their specialty is pointing out the mistakes of others, and this can be a valuable service, but nobody excuses their minor errors with a friendly chuckle. It is fair to say, unfortunately, that their best work often gets overshadowed and neglected, drowned out by the passing bandwagons driven by bolder thinkers. In chapter 76 we’ll see that the generally good practice of making bold mistakes has other unfortunate side effects as well. Meta-advice: don’t take any advice too seriously!

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[1] This doesn’t give navigators their actual position, a point on the globe, but it does give them a line. They are somewhere on that line of position (LOP). Wait a few hours until the sun has moved on quite a bit. Then choose a point on your LOP, any point, and calculate how high the sun would be now if that point were exactly the right choice. Make the observation, compare the results, apply the correction, and get another LOP. Where it crosses your first LOP is the point where you are. The sun will have changed not only its height but also its compass bearing during those hours so the lines will cross at a pretty good angle. In practice, you are usually moving during those few hours, so you advance your first LOP in the direction you are moving by calculating your speed and drawing an advanced LOP parallel to the original LOP. In real life everything has a bit of slop in it, so you try to get three different LOPs. If they all intersect in exactly the same point, you’re either incredibly good or incredibly lucky, but more commonly they form a small triangle, called a cocked hat. You consider yourself in the middle of the cocked hat, and that’s your new calculated position.

[2] That is the ideal, but we don’t always live up to it, human nature being what it is. One of the recognized but unsolved problems with current scientific practice is that negative results—experiments that didn’t uncover what they were designed to uncover—are not published often enough. This flaw in the system is famously explored and deplored in Feynman’s “Cargo Cult Lecture,” a commencement address he gave at Caltech in 1974, reprinted in Feynman, 1985.