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A Few Useful Mental Tools from Richard Feynman

We’ve covered the brilliant physicist Richard Feynman many times here before. He was a genius. A true genius. But there have been many geniuses — physics has been fortunate to attract some of them — and few of them are as well known as Feynman. Why is Feynman so well known? It’s likely because he had tremendous range outside of pure science, and although he won a Nobel Prize for his work in quantum mechanics, he’s probably best known for other things, primarily his wonderful ability to explain and teach.

This ability was on display in a series of non-technical lectures in 1963, memorialized in a short book called The Meaning of it All: Thoughts of a Citizen Scientist. The lectures are a wonderful example of how well Feynman’s brain worked outside of physics, talking through basic reasoning and some of the problems of his day.

Particularly useful are a series of “tricks of the trade” he gives in a section called This Unscientific Age. These tricks show Feynman taking the method of thought he learned in pure science and applying it to the more mundane topics most of us have to deal with every day. They’re wonderfully instructive. Let’s check them out.

Mental Tools from Richard Feynman

Before we start, it’s worth noting that Feynman takes pains to mention that not everything needs to be considered with scientific accuracy. So don’t waste your time unless it’s a scientific matter. So let’s start with a deep breath:

Now, that there are unscientific things is not my grief. That’s a nice word. I mean, that is not what I am worrying about, that there are unscientific things. That something is unscientific is not bad; there is nothing the matter with it. It is just unscientific. And scientific is limited, of course, to those things that we can tell about by trial and error. For example, there is the absurdity of the young these days chanting things about purple people eaters and hound dogs, something that we cannot criticize at all if we belong to the old flat foot floogie and a floy floy or the music goes down and around. Sons of mothers who sang about “come, Josephine, in my flying machine,” which sounds just about as modern as “I’d like to get you on a slow boat to China.” So in life, in gaiety, in emotion, in human pleasures and pursuits, and in literature and so on, there is no need to be scientific, there is no reason to be scientific. One must relax and enjoy life. That is not the criticism. That is not the point.

As we enter the realm of “knowable” things in a scientific sense, the first trick has to do with deciding whether someone truly knows their stuff or is mimicking:

The first one has to do with whether a man knows what he is talking about, whether what he says has some basis or not. And my trick that I use is very easy. If you ask him intelligent questions—that is, penetrating, interested, honest, frank, direct questions on the subject, and no trick questions—then he quickly gets stuck. It is like a child asking naive questions. If you ask naive but relevant questions, then almost immediately the person doesn’t know the answer, if he is an honest man. It is important to appreciate that.

And I think that I can illustrate one unscientific aspect of the world which would be probably very much better if it were more scientific. It has to do with politics. Suppose two politicians are running for president, and one goes through the farm section and is asked, “What are you going to do about the farm question?” And he knows right away— bang, bang, bang.

Now he goes to the next campaigner who comes through. “What are you going to do about the farm problem?” “Well, I don’t know. I used to be a general, and I don’t know anything about farming. But it seems to me it must be a very difficult problem, because for twelve, fifteen, twenty years people have been struggling with it, and people say that they know how to solve the farm problem. And it must be a hard problem. So the way that I intend to solve the farm problem is to gather around me a lot of people who know something about it, to look at all the experience that we have had with this problem before, to take a certain amount of time at it, and then to come to some conclusion in a reasonable way about it. Now, I can’t tell you ahead of time what conclusion, but I can give you some of the principles I’ll try to use—not to make things difficult for individual farmers, if there are any special problems we will have to have some way to take care of them,” etc., etc., etc.

That’s a wonderfully useful way to figure out whether someone is Max Planck or the chaffeur.

The second trick regards how to deal with uncertainty:

People say to me, “Well, how can you teach your children what is right and wrong if you don’t know?” Because I’m pretty sure of what’s right and wrong. I’m not absolutely sure; some experiences may change my mind. But I know what I would expect to teach them. But, of course, a child won’t learn what you teach him.

I would like to mention a somewhat technical idea, but it’s the way, you see, we have to understand how to handle uncertainty. How does something move from being almost certainly false to being almost certainly true? How does experience change? How do you handle the changes of your certainty with experience? And it’s rather complicated, technically, but I’ll give a rather simple, idealized example.

You have, we suppose, two theories about the way something is going to happen, which I will call “Theory A” and “Theory B.” Now it gets complicated. Theory A and Theory B. Before you make any observations, for some reason or other, that is, your past experiences and other observations and intuition and so on, suppose that you are very much more certain of Theory A than of Theory B—much more sure. But suppose that the thing that you are going to observe is a test. According to Theory A, nothing should happen. According to Theory B, it should turn blue. Well, you make the observation, and it turns sort of a greenish. Then you look at Theory A, and you say, “It’s very unlikely,” and you turn to Theory B, and you say, “Well, it should have turned sort of blue, but it wasn’t impossible that it should turn sort of greenish color.” So the result of this observation, then, is that Theory A is getting weaker, and Theory B is getting stronger. And if you continue to make more tests, then the odds on Theory B increase. Incidentally, it is not right to simply repeat the same test over and over and over and over, no matter how many times you look and it still looks greenish, you haven’t made up your mind yet. But if you find a whole lot of other things that distinguish Theory A from Theory B that are different, then by accumulating a large number of these, the odds on Theory B increase.

Feynman is talking about Grey Thinking here, the ability to put things on a gradient from “probably true” to “probably false” and how we deal with that uncertainty. He isn’t proposing a method of figuring out absolute, doctrinaire truth.

Another term for what he’s proposing is Bayesian updating — starting with a priori odds, based on earlier understanding, and “updating” the odds of something based on what you learn thereafter. An extremely useful tool.

Feynman’s third trick is the realization that as we investigate whether something is true or not, new evidence and new methods of experimentation should show the effect getting stronger and stronger, not weaker. He uses an excellent example here by analyzing mental telepathy:

I give an example. A professor, I think somewhere in Virginia, has done a lot of experiments for a number of years on the subject of mental telepathy, the same kind of stuff as mind reading. In his early experiments the game was to have a set of cards with various designs on them (you probably know all this, because they sold the cards and people used to play this game), and you would guess whether it’s a circle or a triangle and so on while someone else was thinking about it. You would sit and not see the card, and he would see the card and think about the card and you’d guess what it was. And in the beginning of these researches, he found very remarkable effects. He found people who would guess ten to fifteen of the cards correctly, when it should be on the average only five. More even than that. There were some who would come very close to a hundred percent in going through all the cards. Excellent mind readers.

A number of people pointed out a set of criticisms. One thing, for example, is that he didn’t count all the cases that didn’t work. And he just took the few that did, and then you can’t do statistics anymore. And then there were a large number of apparent clues by which signals inadvertently, or advertently, were being transmitted from one to the other.

Various criticisms of the techniques and the statistical methods were made by people. The technique was therefore improved. The result was that, although five cards should be the average, it averaged about six and a half cards over a large number of tests. Never did he get anything like ten or fifteen or twenty-five cards. Therefore, the phenomenon is that the first experiments are wrong. The second experiments proved that the phenomenon observed in the first experiment was nonexistent. The fact that we have six and a half instead of five on the average now brings up a new possibility, that there is such a thing as mental telepathy, but at a much lower level. It’s a different idea, because, if the thing was really there before, having improved the methods of experiment, the phenomenon would still be there. It would still be fifteen cards. Why is it down to six and a half? Because the technique improved. Now it still is that the six and a half is a little bit higher than the average of statistics, and various people criticized it more subtly and noticed a couple of other slight effects which might account for the results.

It turned out that people would get tired during the tests, according to the professor. The evidence showed that they were getting a little bit lower on the average number of agreements. Well, if you take out the cases that are low, the laws of statistics don’t work, and the average is a little higher than the five, and so on. So if the man was tired, the last two or three were thrown away. Things of this nature were improved still further. The results were that mental telepathy still exists, but this time at 5.1 on the average, and therefore all the experiments which indicated 6.5 were false. Now what about the five? . . . Well, we can go on forever, but the point is that there are always errors in experiments that are subtle and unknown. But the reason that I do not believe that the researchers in mental telepathy have led to a demonstration of its existence is that as the techniques were improved, the phenomenon got weaker. In short, the later experiments in every case disproved all the results of the former experiments. If remembered that way, then you can appreciate the situation.

This echoes Feyman’s dictum about not fooling oneself: We must refine our process for probing and experimenting if we’re to get at real truth, always watching out for little troubles. Otherwise, we torture the world so that results fit our expectations. If we carefully refine and re-test and the effect gets weaker all the time, it’s likely to not be true, or at least not to the magnitude originally hoped for.

The fourth trick is to ask the right question, which is not “Could this be the case?” but “Is this actually the case?” Many get so caught up with the former that they forget to ask the latter:

That brings me to the fourth kind of attitude toward ideas, and that is that the problem is not what is possible. That’s not the problem. The problem is what is probable, what is happening. It does no good to demonstrate again and again that you can’t disprove that this could be a flying saucer. We have to guess ahead of time whether we have to worry about the Martian invasion. We have to make a judgment about whether it is a flying saucer, whether it’s reasonable, whether it’s likely. And we do that on the basis of a lot more experience than whether it’s just possible, because the number of things that are possible is not fully appreciated by the average individual. And it is also not clear, then, to them how many things that are possible must not be happening. That it’s impossible that everything that is possible is happening. And there is too much variety, so most likely anything that you think of that is possible isn’t true. In fact that’s a general principle in physics theories: no matter what a guy thinks of, it’s almost always false. So there have been five or ten theories that have been right in the history of physics, and those are the ones we want. But that doesn’t mean that everything’s false. We’ll find out.

The fifth trick is a very, very common one, even 50 years after Feynman pointed it out. You cannot judge the probability of something happening after it’s already happened. That’s cherry-picking. You have to run the experiment forward for it to mean anything:

I now turn to another kind of principle or idea, and that is that there is no sense in calculating the probability or the chance that something happens after it happens. A lot of scientists don’t even appreciate this. In fact, the first time I got into an argument over this was when I was a graduate student at Princeton, and there was a guy in the psychology department who was running rat races. I mean, he has a T-shaped thing, and the rats go, and they go to the right, and the left, and so on. And it’s a general principle of psychologists that in these tests they arrange so that the odds that the things that happen happen by chance is small, in fact, less than one in twenty. That means that one in twenty of their laws is probably wrong. But the statistical ways of calculating the odds, like coin flipping if the rats were to go randomly right and left, are easy to work out.

This man had designed an experiment which would show something which I do not remember, if the rats always went to the right, let’s say. I can’t remember exactly. He had to do a great number of tests, because, of course, they could go to the right accidentally, so to get it down to one in twenty by odds, he had to do a number of them. And its hard to do, and he did his number. Then he found that it didn’t work. They went to the right, and they went to the left, and so on. And then he noticed, most remarkably, that they alternated, first right, then left, then right, then left. And then he ran to me, and he said, “Calculate the probability for me that they should alternate, so that I can see if it is less than one in twenty.” I said, “It probably is less than one in twenty, but it doesn’t count.”

He said, “Why?” I said, “Because it doesn’t make any sense to calculate after the event. You see, you found the peculiarity, and so you selected the peculiar case.”

For example, I had the most remarkable experience this evening. While coming in here, I saw license plate ANZ 912. Calculate for me, please, the odds that of all the license plates in the state of Washington I should happen to see ANZ 912. Well, it’s a ridiculous thing. And, in the same way, what he must do is this: The fact that the rat directions alternate suggests the possibility that rats alternate. If he wants to test this hypothesis, one in twenty, he cannot do it from the same data that gave him the clue. He must do another experiment all over again and then see if they alternate. He did, and it didn’t work.

The plural of anecdote is not data. Click To Tweet

The sixth trick is one that’s familiar to almost all of us, yet almost all of us forget about every day: The plural of anecdote is not data. We must use proper statistical sampling to know whether or not we know what we’re talking about:

The next kind of technique that’s involved is statistical sampling. I referred to that idea when I said they tried to arrange things so that they had one in twenty odds. The whole subject of statistical sampling is somewhat mathematical, and I won’t go into the details. The general idea is kind of obvious. If you want to know how many people are taller than six feet tall, then you just pick people out at random, and you see that maybe forty of them are more than six feet so you guess that maybe everybody is. Sounds stupid.

Well, it is and it isn’t. If you pick the hundred out by seeing which ones come through a low door, you’re going to get it wrong. If you pick the hundred out by looking at your friends you’ll get it wrong because they’re all in one place in the country. But if you pick out a way that as far as anybody can figure out has no connection with their height at all, then if you find forty out of a hundred, then, in a hundred million there will be more or less forty million. How much more or how much less can be worked out quite accurately. In fact, it turns out that to be more or less correct to 1 percent, you have to have 10,000 samples. People don’t realize how difficult it is to get the accuracy high. For only 1 or 2 percent you need 10,000 tries.

The last trick is to realize that many errors people make simply come from lack of information. They don’t even know they’re missing the tools they need. This can be a very tough one to guard against — it’s hard to know when you’re missing information that would change your mind — but Feynman gives the simple case of astrology to prove the point:

Now, looking at the troubles that we have with all the unscientific and peculiar things in the world, there are a number of them which cannot be associated with difficulties in how to think, I think, but are just due to some lack of information. In particular, there are believers in astrology, of which, no doubt, there are a number here. Astrologists say that there are days when it’s better to go to the dentist than other days. There are days when it’s better to fly in an airplane, for you, if you are born on such a day and such and such an hour. And it’s all calculated by very careful rules in terms of the position of the stars. If it were true it would be very interesting. Insurance people would be very interested to change the insurance rates on people if they follow the astrological rules, because they have a better chance when they are in the airplane. Tests to determine whether people who go on the day that they are not supposed to go are worse off or not have never been made by the astrologers. The question of whether it’s a good day for business or a bad day for business has never been established. Now what of it? Maybe it’s still true, yes.

On the other hand, there’s an awful lot of information that indicates that it isn’t true. Because we have a lot of knowledge about how things work, what people are, what the world is, what those stars are, what the planets are that you are looking at, what makes them go around more or less, where they’re going to be in the next 2000 years is completely known. They don’t have to look up to find out where it is. And furthermore, if you look very carefully at the different astrologers they don’t agree with each other, so what are you going to do? Disbelieve it. There’s no evidence at all for it. It’s pure nonsense.

The only way you can believe it is to have a general lack of information about the stars and the world and what the rest of the things look like. If such a phenomenon existed it would be most remarkable, in the face of all the other phenomena that exist, and unless someone can demonstrate it to you with a real experiment, with a real test, took people who believe and people who didn’t believe and made a test, and so on, then there’s no point in listening to them.

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Still Interested? Check out the (short) book: The Meaning of it All: Thoughts of a Citizen-Scientist.