How to Make Mistakes

How Things Are, J. Brockman and K. Matson, eds., William Morrow and Company, New York, 1995. pp. 137-144.

Daniel C. Dennett
Making mistakes is the key to making progress. There are times, of course, when it is 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 secret of success. What I have in mind is not just the familiar wisdom of nothing ventured, nothing gained. While that maxim encourages a healthy attitude towards risk, it doesn't point to the positive benefits of not just risking mistakes, but actually of making them. Instead of shunning mistakes, I claim, you should cultivate the habit of making them. 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. You should seek out opportunities to make grand mistakes, just so you can then recover from them.
First the theory, and then the practice. Mistakes are not just golden opportunities for learning; they are, in an important sense, the only opportunity for learning something truly new. Before there can be learning, there must be learners. These learners must either have evolved themselves or have been 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. This is true wherever there is a design process, no matter how clever or stupid the designer. Whatever the question or design problem is, if you don't already know the answer (because someone else figured it out already and you peeked, or because God told you), the only way to come up with the answer is to take some creative leaps in the dark and be informed by the results. You, who know a lot--but just not the answer to the question at hand--can take leaps somewhat guided from the outset by what you already know; you may not be just guessing at random.
For evolution, which knows nothing, the leaps into novelty are blindly taken by mutations, which are copying "errors" in the DNA. Most of these are fatal errors, in fact. Since the vast majority of mutations are harmful, the process of natural selection actually works to keep the mutation rate very low. Fortunately for us, it does not achieve perfect success, for if it did, evolution would eventually grind to a halt, its sources of novelty dried up. That tiny blemish, that "imperfection" in the process, is the source of all the wonderful design and complexity in the living world.
The fundamental reaction to any mistake ought to be this: "Well, I won't do that again!" Natural selection takes care of this "thought" by just wiping out the goofers before they can reproduce. Something with a similar selective force--the behaviorists called it "negative reinforcement"--must operate in the brain of any animal that can learn not to make that noise, touch that wire, or eat that food. 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. 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 be just another blind stab in the dark. In which direction should the next attempt be launched, given that this attempt failed?
At its simplest, this is a technique we 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 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 came to appreciate 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. Navigators, for instance, determine their position at sea by first making a guess about where they are. They make a guess about exactly--to the nearest mile--what their latitude and longitude are, and then work out how high in the sky the sun would appear to be if that were (by an incredible coincidence) their actual position. Then they measure the actual elevation angle of the sun, and compare the two values. With a little more trivial calculation, this tells them how big a correction, and in what direction, to make to their initial guess. It is useful to make a 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 you have something serious to correct.
The more complex the problem, of course, the more difficult the analysis is. This is known to researchers in Artificial Intelligence as the problem of "credit assignment" (it could as well be called blame assignment). Many AI programs are designed to "learn," to adjust themselves when they detect that their performance has gone awry, but figuring out which features of the program to credit and which to blame is one of the knottiest problems in AI. It is also a major problem--or at least a source of doubt and confusion--in evolutionary theory. Every organism on 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 discern the huge complex of positive and negative factors and "reward" the good and "punish" the bad? 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 nifty shape that they do?
One technique for easing the credit assignment problem is to build mistake-opportunities into a "hierarchy"--a sort of pyramid of levels, with a safety net at each step. By and large, don't mess with the parts that are already working well, and take your risks opportunistically. That is, plan your project so that at each step you can check for error and take a remedial path. Then you can be bold in execution, ready to take advantage of unlikely success and ready to cope gracefully with likely failure. This is a technique that stage 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! But 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. When it too fails (as it almost always will) you slide into effect #3, which only works about one time in ten, so you'd better be ready with effect #4 which works half the time (let's say), and 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 that 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 the "error" cases from view, 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, over 90% 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!
The main difference between science and stage magic is that in science you make your mistakes in public. You show them off, so that everybody can learn from them--not just yourself. This way, you get the benefit of everybody else's experience, and not just your own idiosyncratic path through the space of mistakes. This, by the way, is what makes us so much smarter than every other species. It is not so much that our brains are bigger or more powerful, but that we share the benefits that our individual brains have won by their individual histories of trial and error.
The secret is knowing when and how to make mistakes, so that nobody gets hurt and everybody can learn from the experience. It is amazing to me how many really smart people don't understand this. I know distinguished researchers who will go to preposterous lengths to avoid having to acknowledge that they were wrong about something--even something quite trivial. What they have never noticed, apparently, is that the earth does not swallow people up when they say, "Oops, you're right. I guess I made a mistake." You will find that people love pointing out your mistakes. If they are generous-spirited, they will appreciate you more for giving them the opportunity to help, and acknowledging it when they succeed, and if they are mean-spirited they will enjoy showing you up. Either way, you--and we all--win.
Of course people do not enjoy correcting the stupid mistakes of others. You have to have something bold and interesting to say, something original to be right or wrong about, and that requires building the sort of pyramid of risky thinking we saw in the card magician's tricks. And then there's a surprise bonus: if you are one of the big risk-takers, people will even get a kick out of correcting your stupid mistakes, which show that you're not so special, you're a regular bungler like the rest of us. I know philosophers who have never--apparently--made a mistake in their work. Their specialty is pointing out the mistakes of others, and this can be a valuable service, but nobody excuses theirerrors with a friendly chuckle.
We don't usually have to risk life and limb in order to learn from our mistakes, but we do have to keep track, and actually attend to them. The key to that is first, not to try to hide your mistakes. If you hide them, you may, like the magician, enhance your reputation, but this is a short-range solution that will come to haunt you in the long run. Second, you must learn not to deny to yourself that you have made them or try to forget them. That is not easy. The natural human reaction to mistake is embarrassment and anger, 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 forget them, and go on to the next big opportunity.
You are going to make lots of mistakes in your life, and some of them, unless you truly do lead a charmed life, will really hurt--yourself and others. Here are some ways of making the best of it, since the more you learn from the relatively painless mistakes, the less likely you are to commit the awful variety.