The Drunkard's Walk: How Randomness Rules Our Lives | Leonard Mlodinow | Talks at Google

Good afternoon, everyone. Welcome to another Authors at Google event. Today we are hearing from Len Lodenov, who will be talking to us about the Drunkard's how Randomness Rules Our Lives. Len is a physicist whose work has spanned everything from writing children's books to writing books on the history of physics, to working as a writer on Star Trek the Next Generation. So we're all very excited to hear what he has to say about randomness and how it influences our daily lives. At the end of the talk, we'll have some time for questions and answers, and we have a mic set up in the front, and we'll also circulate a mic in the back. So just be sure to use the microphone. For our friends at YouTube, our virtual audience, and without further ado, I'd like to welcome Len. Thank you.

Thanks.

Hi, everybody. I'm Leonard Mlodinov, and the book is called the Drunkard's Walk, and it's about the role of randomness in life and how and why we often understand, misinterpret the role, and draw improper conclusions from the world around us. I won't go there yet. Some years ago, a man won millions in the Spanish National Lottery with a ticket that ended in the numbers 48. The man did not attribute this winning to luck. He had a theory and he was very proud of it. His theory is what drove him to pick the numbers 48. What was his theory? I dreamt of the number seven for seven nights in a row, he said, and seven times seven is 48. That works for some of us. And that's the point of the book. We all look at the world around us and take in a lot of data every day. And we filter and we interpret the data based on our intuition and sometimes our multiplication tables, and we come up with certain results. And some of us make errors that aren't quite as noticeable as the error that the Spanish man made. But we do make errors. And when we deal with questions that involve uncertainty or randomness, we often misinterpret what happens in the world around us. So now, this slide, this is a picture of a drunkard's walk. A drunkard's walk. A lot of you may know, if not all of you, is another name for the random walk, which is a mathematical term for basically a random meandering. And that is what's pictured here. And the reason I chose Drunkard's Walk as the title of the book is that I feel that it's a good metaphor for what happens to us in our work in our personal life, in our everyday lives, we all, of course, have our own directions and our own goals. But we're also in contact on a daily basis with unpredictable and uncontrollable events that have a very great effect on the direction that we take. And what the Drunkard's Walk illustrates is that even if we have no direction, we'll still get somewhere. This is the beginning of the Drunkard's Walk, for instance, and all these turns are made at random, and that's the end. So if you only saw the beginning and the end here, you might consider that whatever this represents, that this person got from here to here on purpose. But we all can see in this case, that the person just got there at random. And that effect, even when we have no particular direction, can still take us from point A to point B and we don't always realize it. So today I'm going to talk about two things. I can only touch a little bit of the things that I talk about in the book. And I picked two categories to talk about. One is some of the confusions and illusions of randomness that happen in everyday life that I can illustrate here. And after that, I'm going to talk about a few of the psychological reasons that we make these mistakes and that we misinterpret randomness. The first illusion I'd like to talk about I call the illusion of causality. Again, if you look at the Drunkard's Walk, you think. You might think if you see someone from the starting point and then you see them at the end point, that they got there for good reason. And we know in this case that they didn't, that it was purely random. This sort of thing happens a lot in our everyday life. Randomness has a great effect on certain processes that happen in life. We often draw improper conclusions about the causality that underlies what's happened. I have just three examples here that I picked more or less at random. There are so many in the world. But the first one represents sports. Right now, we have the NBA championships going on. We have World Series games. We have a lot of different sports in which we have championship series, usually seven games. And we tend to believe at the end of the series that the best team won, or at least the best team for that period of time won the game. And the question then is, is that really true? Similarly, this is an article here about the best high schools. We gather data about schools, and we think that the data gives us an accurate and fair portrait of the high school or college that it's talking about. And we rarely question how accurate a representation that is. And the third example I chose is from Fortune magazine, an article about the greatest money manager of our time. That's quite a claim. And they're talking about a fellow named Bill Miller who ran a mutual fund called the Legg Mason Fund, who still runs it. And his claim to fame is that his fund beat the Standard and Poor's index for 15 years in a row. So let's take that last article and let's look at it a little more closely. When his fund started having its long winning streak, many, many in the media started writing about it and quoting the odds of something like that happening if at random. Now I think that's a good thing to do because in science we often when we're looking at an effect, we do an experiment and we compare what we observe to what we think we might have observed by chance alone. And if that we observe is much different, we assume that there's a real effect behind it. So I think it makes sense to say Bill Miller was really talented because to do this by chance alone would be really rare. In this case, the quotes ran from 1 in 150,000 after the 13th year to one article I saw said 1 in 4 billion. Something that you probably would be surprised if it ever occurred with mutual fund managers. It was called the greatest fund feed in the past 40 years and many other things. So what I'd like to do is say, let's see what the real chances are of accomplishing a feat like that at random. It seems like a very great feat and a very unlikely feat at its face value, because to beat the standard imports 15 times in a row at random certainly is something that wouldn't happen every day. If you model competition with a standard in Poor's as a with a coin toss with a probability of 50% of success each year, then you can model what the chance of one person having that success would be. And if you do that for Bill Miller For 15 years, you end up with the probability of one over two to the 15th, which is about one in 32,000. And that is a very small chance indeed. And you might conclude that if someone accomplishes that, that it couldn't be at random, but now they have to look a little bit deeper. And what is really happening here? What's really happening is that you don't have one person flipping the coin every year for 15 years. You have thousands of them. There's five or 6,000 mutual fund managers today, and there's about 1,000, according to one of these articles, managers of comparable mutual funds. And since the people who write those articles are far more knowledgeable than I about these things, I'll use the number 1000 as a number of comparable mutual fund managers. Now, the question we have to ask is, when we're trying to see if we're surprised by such a feat, not what are the chances that a particular coin flipper or mutual fund manager will accomplish this, but what are the chances that one of those thousand did it? Because whether it's Bill Miller or Barry Diller sitting next to him, whoever it is would get the headlines and would be the person we anoint as a genius. So if we want to know how rare such an event is, we have to take into account all of them. And when we do that, we get a new probability which is much higher than this. It's about 3%. So, whoops. Yep, about 3%. Sorry, I thought I hit it twice. I don't want to give away the next thing. And you may be, since you're here at Google and you're really smart, you probably have an idea what the next thing is. The next point is that we still haven't really modeled the process correctly because these are the chances that one in a thousand of them starting in 1991 would achieve 15 good years in a row, right? But guess what? If they did in 1990, we would have made just as much hoopla about it. We wouldn't say, oh, he started his streak in 1990. That's really nothing. That's easy. Would have made the same headlines if it was 1990 to 2005 that it makes, if it's 1991 to 2006. So how do we really understand this? What we have to do is take a longer period and say, what are the chances if they flip these coins every year over a longer period that there'll be some 15 year period where one of them will beat the standard in Poor's. I took as my period a 40 year period because the article mentioned 40 years as modern mutual funds. And that might sound like a long period, but it's not really that long considering that the streak was 15 years. It's not even. You can't even fit three streaks back to back in that. So I did a simple calculation of the odds that someone among these thousand mutual fund managers over the period of 40 years would have a streak of 15 years of beating the Standard Poor's in a row by chance alone. And when you do that, it comes out to being about three out of four. So one way of looking at this is this doesn't prove that Bill Miller's streak was random, but it does show that if someone didn't have a streak like this in the last 40 years, then these guys aren't doing much for their money, are they? Because you could just do it at random and have a streak like this. So I think what the article should have said, if it was maybe a little bit more insightful, would have been expected. 15 year run finally occurs. Bill Miller lucky BENEFICIARY so this is one example of how if we look at something intuitively, we might be misled. Whereas if we look at it using the mathematics of randomness, we find that there's a different reality behind it. Another example that people often talk about is what they call the law of small numbers. I call it the illusion of small numbers because it's false. And when you call something the law, I find when I tell people about the law of small numbers, it's, I get into these discussions about how could it be a law if it's wrong? And it is not a law. It's a sarcastic term invented by a psychologist because people misinterpret what's called the law of large numbers and they apply it to small numbers. The law of large numbers, you may know, says that if there's an underlying probability or potential for something, then in a large number of observations, you will tend to that probability or potentiality will tend to be reflected accurately. So if you have a 50% chance of getting heads when you flip a coin, if you flip three coins or four coins, you might not see two heads. But if you flip 40 million, there's a high probability that you'll see about 50% heads. The thing is that in real life we don't really get to observe CEOs for 40 million years or sports teams playing 40 million games. So the question is, is it right to use this law in interpreting everyday life and do we use it? And the answer is it's not right to use it. But our intuitions do lead us to use it. So let's look at an example. Suppose a CEO has a 60% probability of success in any year, or that Google has a 60% probability of success in any given year. Whatever you call success and for whatever reasons, one could conclude, let's say that you have a certain probability. The question is, will your results reflect this probability? So let's look at a five year period, which is more than most CEOs would be given, and let's see if in a five year period what the chances are of having three good years. Because three out of five good years would be 60%, which would reflect exactly the underlying probability. So when you do that calculation, you find that the chances are only one in three that someone with a 60% probability of success would have three out of five good years. That means the chances are two out of three that your number of good years will not reflect your success. In fact, the chances are about one in 10 that you'll have either five good years or five bad years in a row, even though your underlying ability is 60%. The Fortune 500, for instance, that means that about 50 of those companies, if they had this probability of success despite that, would have five good or bad years in a row and be rewarded or punished accordingly. This is just what we tend to do. We look at companies and say that company had five bad years in a row, they must stink. Or they had five good years in a row and they must be perfect. And we assume that that reflects what's really going on. So the question is, if you want to see how to apply this to life, how long must you observe to get an accurate picture? So for this now I turn to sports because it's kind of fun. And suppose that the two sports teams that are competing in the championship series are somewhat closely matched. I'm saying 55 to 45, meaning that in a large number, a million head to head competitions, one team or in a million parallel worlds maybe is better to say, because that's more likely than having them play a million times in a row. If we take Stephen Hawking and develop our theory of a million parallel worlds, we would find that in 55% of them the superior team would win. But what happens in our real world? Well, we normally decide who's better in a best of seven game series. I'm not sure how they came to that. I don't think it was statistically. I think it's a balance of people's patience and ad revenues. And the question is, what is the probability that the inferior team will win in a series like this? It's 40%. So a seven game series doesn't tell you very much. There's a 40% chance that the lesser team will win. So let's ask ourselves, we want to reduce this. We want, let's say, a 25% chance that the lesser team will win. How many games do you think we have to play well? 45. So they're starting to get a little bit high here in terms of I think viewers patience or probably team's patience. And it would certainly cost a lot to put on a series like that. But I asked one more question because being a scientist, I say how many games? If we really want to turn sports into a science, which I'm sure very few people actually do, but if we wanted to, how many games would we have to play to get what we call in science statistical significance. Now that means that there's a 5% or less chance that the inferior team will win. We certainly demand that or better when we decide what medicines to take or what medicines work. But what about in sports? How many games do you think you would need? 269. So to really decide something in sports, you'd have to play about two baseball seasons or several basketball seasons of just two teams head to head every day. Obviously we're not going to do that, and I'm not suggesting that we do, but I am suggesting that we be careful about drawing conclusions from our little seven game series. The last illusion or confusion of probability that I want to talk about relates to what we call conditional probability. This is something that actually affects a lot of people in a very deep way because it's related to medical testing. So let me introduce it with an example. Suppose the probability of a false positive on a mammogram is about 10%. False positive means that you don't really have a tumor, but the test says you do. So if you have a positive test, what are the chances that you have a tumor? Are they 90% or 9%? So I say there's a 10% chance that the tumor is positive, but there's no tumor. If it's positive, what are the chances that there's a tumor? It sounds like 90%. But if you know conditional probability, you know that you actually can't answer the question with that data. You need more data. What you need to know is the incidence of the cancer, that in this case about 1% of women around the age 40 really have breast cancer. And you also have to know about false negatives, which I'm going to ignore for this. It doesn't really change anything. We're going to assume that if you actually have cancer, the test will come out positive. So this information, in addition to the question and the other information was given to some doctors in a couple studies. And in one study the Doctors chose a 90% and another study it was open ended and they guessed it to be around 75%. So the woman comes to them, has a mammogram, it's positive the false positive rate is 10%. And they say there's a 75% chance that you have cancer. It sounds absurd, but it happens. It actually happened to me, not with a mammogram, but with another test. And I have to say that doctors could really use better education in this area because the answer is actually 9%. And a lot of people are getting scared and making unwise decisions based on a misunderstanding of how this works. Now, that's easy to misunderstand because in English it sounds like this. I don't know if you can read this, but the fraction of all those tested who tested positive but aren't is not the same as the fraction of all those who tested positive but aren't. So if you were to read that in a book and that's all you had, you would kind of scratch your head and probably say it must be 75%. So let me just. This is a case where mathematics or pictures really help. So let's do that. Here's 100 women, okay? The N's represent women who do not have cancer. And since there are no false negatives, they get a negative test. The Fs represent 10 women, actually 9.9, but a little bit close enough to say 10 here, which is 10% of the negative women who get the false positive test. And the p represents the one out of 100 who actually has the disease. So you have 100 women, incidence is 1%. So one actually has the disease of the other 99. The false positive rate is 10%. So 9.9 of them, or let's say 10, gets a positive test even though they don't have the disease. So that's the setup. And now what happens is that's why this is called conditional probability. You now have a condition which is, you know, some more information. You know that you have a positive test. So now all the ends up here are irrelevant. You can send them off and all you have to look at are the people who had a positive test. And as you'll see here, there's one out of 11. So even though the false positive rate in the whole population is small, the false positive rate is much higher than the actual incidence rate. And if that happens and you have a positive test, then despite having the positive test, there's a very high chance that you do not have the disease. So if a doctor ever tells you in a medical test that these are the false positive ratings and doesn't tell you anymore, then the doctor has told you nothing at all. You have no idea what the result of a positive test means it could be anything from 0 to 1. Because if no one ever gets a disease, then whatever the false positive rate is, if you get a false positive, you're sure not to have the disease. So it could be even. Your chance of having the disease could be zero. Even with a false positive rate, we're one in a billion. So that's something to keep in mind when you do medical tests. All right, I'm going to end with the second part of the talk, which is about some of the reasons that we make these errors. One of the reasons I wrote this book, I started out actually looking at writing a book on entropy. And then I thought, randomness in life is more interesting. And around that time, the 2002 Nobel Prize in Economics was given out. And what was interesting was that it was given out to. To two people, but one of whom I want to talk about, who is a psychologist, Daniel Kahneman. And together with another psychologist, Amos Tversky, who had died before then, they investigated how we make decisions when confronted with uncertain situations and how we evaluate probability and randomness. And their ideas were so important in economics that they got the Nobel Prize. And I realized that we all make these kinds of decisions and misjudgments when we look at the world around us. And that was a very interesting application of probability and statistics. One of the illusions that people have that cause us to have a hard time grasping the role of randomness is called the illusion of control. People tend on a deep gut level to feel that they can control the world, the world around them. I don't mean, if you ask somebody, can I control a coin flip? That they'll tell you, yes, I can control the coin flip. Some of them will, probably not many working here, although maybe you aspire to do that. But on a more. On a deeper unconscious level, people really do feel that way. And so here's just one experiment that showed that this was done at Yale University. So those are some Yale students on your left, and on your right are some coins which represent coins very, very accurately, I think. And the experiment was this. The students were put in a room with an experimenter. And that usually happens in psychology experiments. They were lied to. So if you ever do a psychology experiment, don't believe a thing that the experimenter tells you. In this case, they were told that the experimenter was going to flip a coin, and they were, 30 times. And after each coin flip, they were to make a guess as to whether the coin would flip heads or tails. Then the experimenter would Tell them whether they got it right or wrong. And this would go on for 30 times. In reality, the sequence of right and wrong was predetermined. It was identical for every student, every subject. And the experimenter would just say right, wrong, according to that predetermined sequence. And every once in a while show the coin if it matched, just to show that they weren't cheating. It worked very well. And afterwards, the experimenters were interested in investigating the students attitude toward their ability to either control or foresee the future. Either control the coin flip or foresee the future and predict how it would come out. And of course they knew that they couldn't ask that question directly. So they asked them a number of questions which were meant to. To more subtly investigate their attitudes. And when I say more subtly, I don't mean a lot more subtly. I mean just a very little bit more subtly. For instance, would your performance be hampered by distraction and would your performance improve with practice? Very little deviation from the direct question, but it works. So even though the question was not, that was somewhat thinly disguised, 25% of them thought their performance would be hampered by distraction and 40% thought it would improve with practice. So obviously on some gut level, people have a feeling that they can control or be in control of these coin flips. Now this study seems amazing to me, but I talk about many studies in the book and there are really many, many studies done in a variety of venues that all show the same thing. And psychologists also have their ideas about the reason, which is that if we don't feel that we can control our environment and we feel helpless, that's depressing, basically. And there have even been studies of people in nursing homes, some of whom have no control over their environment where everything is done for them. Others who can rearrange or can have the furniture rearranged and take care of their own room. And they found that those in the latter group tend to live longer. So it's a very important thing for us is being able to control our environment. And it's very deeply seated, even if we intellectually know that we can't. The second illusion I want to mention is called the expectation bias. This is Bill Miller again of the earlier example, who by the way is by all accounts a very smart and nice man. And I don't mean to criticize him at all. I just mean to call him a lucky man. And the reason I show him here is that it's very hard when someone is smart and in a high position and highly paid and having success. It's very hard to believe that maybe that success is random, not just in mutual funds, but in whatever your endeavor is, both big and small. And so I talk about a lot of studies that discuss how these expectations affect our assessment of the world around us. And I'm just going to mention a couple here of the fun ones or the more fun ones. And since I like to drink a little wine now and then, I pick some wine studies to talk about. So I go to wine tastings and I participate in identifying the scent of green pepper or freshly tanned leather parsley old shoes in wines. And we agree, we disagree, and we all evaluate wine and have a lot of fun. The experts rate wines, and those ratings are taken very seriously. I don't remember the exact number, but every point on the wine rating is worth X dollars in sales price that they can charge for the bottle of wine. And so the question is, this is a very good area to investigate the effect of expectations. And they've had a lot of fun with this in the wine area. One thing they did is they took wine experts and they lined up a series of wines and asked them to write out their characteristics. And they were all red wines. And they all wrote out nice characteristics of red wines. Except being psychologists who were doing this, one of the wines, they weren't really told the truth. One of the wines was a white wine dyed to look red. And these experts also attributed to it the qualities of red wine, tannins and so forth. Another study that I have up there concerns some white wines. And white wines dyed to look were judged to be sweeter than the identical white wine, which is also in the lineup, which was not dyed. One of my favorite and a very recent study was done at Caltech concerned a number of students. So these were not. They're not wine experts unless you're talking Boone's Farm, but they certainly can enjoy wine. And they were tasting wines which were labeled by price. And unbeknownst to them, a couple of the wines were identical and just labeled with a different price. For instance, one pair of wines appeared in the lineup labeled $90 in one case and $10 in the other. And it actually was a $90 bottle. Well, what happened when they rated them? They didn't like it very much when it was a $10 bottle. They loved it when it was a $90 bottle. Well, okay, you might say, fair enough. What does that really prove? Everyone is going to say it's a $10 bottle. If I really like it that much, I must be a moron. I better not like it. But the trick here is that these students weren't sitting in front of a table leisurely tasting wines. They were lying on an MRI machine and having their brains imaged. And the experimenters were watching as they tasted the wines. And it's true that the pleasure center of their brain actually lit up more when they tasted the $90 bottle of wine. So if you want to have a good time with a friend, buy a $10 bottle of wine, put a $90 label, and you'll all really love it. The other experiment I have here involves Coke and Pepsi. And just briefly, they took some people who had a definite preference, Coke or Pepsi, and then they gave them the Coke and the Pepsi, and they said, which do you really like better? And this surprised me. 30% of them admitted they were wrong, and they actually chose the wrong one. But in this case, the sneaky experimenters had put Coke in a Pepsi bottle and Pepsi in the Coke bottle. So actually, 70% of the people were picking the wrong one, but they thought it was the right one. So finally, I'm going to talk about an experiment that we did. Before I started talking, I divided you into two groups. You may remember, it wasn't very long ago. And you each read and answered two questions. And the second question was, for both groups, how many countries are there in Africa? Okay, Group one and group two. Oh, can I get the results, Cliff? Just. Oh, do you have them written down or. Okay, well, then wait just one minute. So these are a few of the groups I've said I've given this to before. And you can see quite a difference in the mean estimate from group one and group two. So now, what was it here, Cliff?

So for group one, we had 64.68.

Group one said about 65, and group two about 30. About 30. So we got a similar result here at Google with all you ultra smart people. And the question is, why is that? I'm sorry? Well, the actual answer, I don't know, because we may want to take the mean of the two groups, and then you may come out smarter. The answer is about. Well, according to my Google search, it was 54. I counted the individual countries, and on another website, I found it stated to be 54. And so I'm thinking that that's probably an accurate number. And the difference between the two groups was this. Group one was asked before they estimated. They were asked, are there more than 180 countries in Africa? And group two was asked, are there more than five countries in Africa? So this is kind of an Absurd question. And you may. I don't know what you were thinking when you were answering it. You must be thinking this is an absurd question. But what it did was the point of this is this is called the anchoring bias. That your powers of estimation and thinking about probabilities and frequencies and sizes are all very fragile and very easily influenced by minor things and random things that happen around you and be careful before you trust them. And this problem is another reason that it's sometimes hard to understand randomness, because randomness involves understanding frequencies and numbers of events. There have been many studies on how this influences things and a few of them are the civil awards are affected by the amount that you demand. Civil lawsuits, bail amounts are affected by how much the prosecution requests, et cetera. My kids allowance is affected by how much I offer them, is affected by how much they ask for. Right. And they know that, so they ask for a lot. So just to end, I'm going to end with a couple of quotes. The first quote is by Bertrand Russell. We all start from naive realism, the doctrine that things are what they seem. We think that grass is green, that stones are hard and that snow is cold. But physics assures us that the greenness of grass, the hardness of stones and the coldness of snow are not the greenness, hardness and coldness that we know in our experience, but something very different. And he's talking about physics, but I believe that this applies to the mathematics of randomness as well. The mathematics of randomness shows us that the conclusions that we draw about what we observe going on in the world are not necessarily what's really going on in the world and that they can that what's really going on underneath that can be very different. Now I don't mean by this that ability doesn't matter, hard work doesn't matter, that you shouldn't try, that you don't tend to go in the direction that you're aiming. But what I mean is that what you achieve is a combination. And you always have to remember this of both how much you try and randomness. So if you fail at something, if you submit a manuscript for publication like J.K. rowling did, and it's rejected nine times, does that mean that it's not going to be one of the best selling or the best selling book in the world, do those nine rejections mean that the book sucks? No, they don't. If your project at Google doesn't quite pan out, it doesn't mean that you screwed it up. There are a lot of other unpredictable or Uncontrolling events that can intervene. On the other hand, if you have a great success, does that mean that you're a person of destiny? That you should be arrogant and think that other people aren't as good? Do you think that the person who's your boss necessarily is your boss because they are better than you? Not necessarily. So don't get a big head either. And there are many positive lessons of this. One of the positive lessons is get a lav at bat. Take your opportunities, follow your opportunities. Just because you failed several times doesn't mean you won't succeed next time. And there are ways to use this in your favor. So I'd like to end with one succinct quote from another computer guy from an earlier age from IBM, Thomas Watson. And he said, if you want to succeed, double your failure rate. Thank you.

Thank you very much. We have time for a few questions. We have a mic up in the front and we have a traveling mic in the back. So let me know if you need use of the mic to ask some questions.

Just a small comment. People always bring up coin tosses as random events, but I'm sure you're aware of Diaconus work that you can actually. Sorry, there. I'm sure you're aware of Diaconus work that you can actually more or less predictably toss coins.

I'm sure I'm aware of.

Percy Diaconus has. So I always just find it amusing that people bring up coin tosses as random events where if you have enough information, they're very predictable. But that was all.

Well, a coin toss is a example of what people call a Bernoulli process. And so it's very useful. But it's not the only way you can have a random event.

I have a question slightly related to the talk about randomness in the Drunkard's Walk. Can you tell us what it was like to write for Star Trek the Next Generation?

Sure. A random question. I'll give you a random answer just to show you how things at random things can affect your life. I had written for MacGyver and this was back in the 80s. And then we had a long writer's strike, which was extremely hard to endure and I thought was a horrible thing and financially ruinous thing, which went on for about six months. And in the end it turned out to be one of the best things that ever happened in my career. Because it was during the writers strike that the producers of Star the Next Generation, who had nothing else to do, decided to read a pile of old scripts that people had sent them, including one of my MacGyver stories. And I was hired the day after the strike ended to work on Star Trek. So it's just an example of. I find that in my life many times something that seems bad and you think was horrible turns out to have been really good later. And sometimes good things turn out to be have been not so good. But anyway, it was fun writing for Star Trek and the nice thing was that people paid a lot of attention and they don't always do that for good reason to TV shows.

So I've always had trouble with statistics. And so the basic question is how do you know when you've done the counting right? I always, you know, how do you come up with the stuff that you walk through today? It all looks so final when you present it. But I still can't judge when it's right until you draw the pretty pictures that helped.

Read the Drunkard's Walk and you'll have a revelation about. I don't know how else to answer that. You have to understand how randomness works. And you never know in science. I think if you're doing things right because you always think you are or you always do it until you decide that you've done it right. But the best that you can do is think about it and learn the principles and be aware that your intuition often works against you.

Hi, I had a question about some of the examples you showed today. The basic assumption there, I think, is that the basic assumption there is that we have independence between the different events and they are identically controlled in which, let's say, for example, the standards and poor like beating it in 15 years in a row.

Yeah, well, what we were doing was, I was saying let's compare. So I don't want to, you know, I mean, you could debate whether the stock market truly is a random walk or how close it is to a random walk. And that's a debate that goes on. And some people say that you cannot predict and it's totally random. And some say that it. There is some small ability, I don't know people, a lot of people who say now that you have a huge ability to time the market. But what I was talking about was saying let's compare it to a random process. So let's assume that someone is doing it at random and see if they're doing any better. And what I found was that they don't seem to be doing any better than you could do if it were random. And it's easy to form a Mutual fund that's random because you just take, if you take the Standard in Poor's and you throw a dart or you flip a coin and pick a few or take out a few stocks and then you have a random chance, a 50% chance of beating it or not beating it. Right. But a lot less effort and a lot less of a cost burden than on a mutual fund unless it's an index fund. But I wasn't saying that the, you know, I was comparing to actual coin tosses where it is independent.

So I'm sure you're aware that Bill Miller finally had a bad year, and.

Not only a bad year, but apparently a bit of a run on the fund, which is actually an interesting point because one of the. I talk about several different examples of CEOs and Sherry Lansing in Hollywood and other people who I think were attributed with great genius qualities based on luck. And one of the characteristics I think of someone for which that's being done is that their genius can change overnight. Right. And that certainly happened to Bill Miller because he was really riding high and now there's a bit of a run on his fund. He's just as smart a guy as he was before. But your luck can change, I think, much faster than your mental abilities.

I thought it was ironic that he said, well before the 15 year run, I also had my worst year ever. So he was essentially predicting another 15 year run.

Oh, he was. Good for him. I wish him all the luck in the world.

I have a question for you. What would you say to people who think that like, since the chance of life forming on Earth and humans evolving and everything is like such a small chance, that it couldn't have been random chance?

Well, things with small probability certainly can and do occur. And this is a discrete probability situation. But I would say that the simplest answer to that is that, well, part A and A, part B, part A is we don't really know exactly how small that chance is. And part B is there's a hell of a lot of stars out there in our galaxy, hundreds of billions and hundreds of billions of galaxies. And, and so just because there's a very small chance of life evolving doesn't mean it's not going to happen somewhere. So it doesn't really surprise me.

Are there any other questions?

All right.

Well, we'll actually have some time with Len at the end. If you have some other questions, you can go up and talk to him in person. And once again, on behalf of the authors at Google Team, we wanted to thank you for coming thank you very much.

Thank you.