The Odds of Life’s Oddities, with Mathematician John Allen Paulos

March 21, 2016

John Allen Paulos is an award winning mathematician and best selling author. A professor in mathematics at Temple University, he has written for The Guardian, CFI’s Committee for Skeptical Inquiry, and his monthly column for, “Who’s Counting?” His new book is called A Numerate Life: A Mathematician Explores the Vagaries of Life, His Own and Probably Yours.

Paulos uses basic mathematic principles to lend a fresh perspective to everyday life, and the results can be fascinating. He sheds light on everything from the mathematical science behind romantic crushes to the astronomical consequences of the butterfly effect. Some of the harsher mathematical realities can be troubling, like the inevitable probability of becoming more jaded as we age. But Paulos’s mathematical message also has plenty to take solace in, like knowing that dimensional geography suggests that every single one of us is far more peculiar than we may be willing to admit. That’s right, you are not the only weirdo you know; in reality we’re all a bunch of weirdos.

This is point of inquiry for Monday, March 21st, 2016. 

Welcome to Point of Inquiry, a production of the Center for Inquiry. 

I’m your host, Lindsay Beyerstein, and my guest today is John Allen. Paola’s a mathematician and author of several beloved books, including Innumeracy, Irreligion, and a mathematician reads the newspaper. He’s here today to talk about his new memoir and Numerate Life. A mathematician explores the vagaries of life, his own and probably yours. He argues that well-chosen mathematical concepts can lend fresh insights into the coincidences and incongruities that shape our biographies. 

John, welcome to the program. 

It’s a pleasure to be here. 

So you’re a fan of biography as a drama, but you also think that biographies, maybe not a very good tool for getting to know a person. 

Why do you think that are partly for reasons that arise in everyday life. 

And I’m told often. Oh, of such and such has is MSDS is that she’s this she’s that other people say this as always. Everybody knows that. And then I meet the person in question her. There’s nothing like the description that is painted of them. And in general, I mean, biographies rely on human reporting. Self reporting or reporting in others is notoriously unreliable. Memories are unreliable. There’s all kinds of contingencies and imponderables and an incommensurable values and attitudes. So I have basic kind of mathematical mindset that doesn’t seem to apply. I mean, if you read a poll about Bernie Sanders and Hillary Clinton in Iowa ION and the sample size was three or four, you’d kind of laugh. Yet people tend to take as gospel a biography which relies on three or four people, sometimes only one. And people have very different narratives, even a story of adultery that say saying take an example. Is it told from the point of view of the person who, quote unquote, has been cheated upon or from the point of view of the quote unquote, cheater, or from the point of view of the outside lover or from the point of view, some sort of neutral observer began to get very different accounts of the same thing. Not because people necessarily are purposely lying, but memories are unreliable. People can have an idea of themselves, a grand narrative that they try to maintain and they’re in denial about certain things. I mean, imagine to take an extreme case of Kim Kardashian and write a biography of Stephen Hawking could be funny maybe, or the other way around. Stephen Hawking writing a biography of Kim Kardashian. So I’m dubious of biographies. And part of what I do in the book is, you know, it’s in part a memoir kind of closet, a memoir. I take it events from my life and describe them little vignettes. And so in that sense as a memoir. And then I use them as jumping off points to discuss ideas, mathematical ideas, probability, logic, dynamics, philosophy, sometimes cognitive psychology, to talk about notions that are relevant to telling you of any life story. 

In honor of the recent passing of David Bowie, you talk about your mathematical argument for why everybody is a weirdo, OK? 

It is strings from saying that my father used to say make a lot, and that is that there are two kinds of people in the world. Those are very strange and those one doesn’t know very well. And once you come into closer contact with almost everybody, they turn out to be strange alone. A lot of dimensions. In any case, I illustrate that in the following way. Imagine you’ve got a straight line, 10 inches long. You chop off a half inch at either end the extreme ends and the interior, the interior nine inches are, let’s call them normal. And these half inch on either end is, let’s say, for lack of a better term, abnormal. 

And this could be any trait. This could be liking for a liquor, assure any injury to vote Republican. 

There any dimension at all. Of which there are countless. Many, but they’re not. Think of a square and that’s 10 inches by 10 inches. Imagine the outside gets within a half an inch of the edge. The interior part now is nine tenths, nine inches. So nine times nine is 81 square inches. The edge is no longer. The edges are constitute 19 percent of the area of a square. And if you do it with a Q 10 by 10 by 10 inch Q and look at the half inch along each of the surfaces, the interior is nine inches by nine inches by nine inches. And you multiply that to get seven hundred and thirty approximately. So twenty seven percent of the area is on near the surface, very near the surface. You can do that with a four dimensional hypercube, five, 10, 20. But how many dimensions can characterize a person? Hundreds and hundreds. If you have so-called hypercube with that many dimensions, almost all the volume will be around the edge. The interior will be completely empty, are essentially empty. And if you think of persons being the. Fine by the hundreds and hundreds of dimensions and characteristics that are possible. We’re all on the edge. We’re all extremely strange and in at least this geometric slash statistical sense. And it’s not surprising. I mean, I give examples like one that comes to mind was asked in graduate school at the time. And there was this fellow student who always wore suit and tie and was very on the surface, at least for now. Conservative never said anything to class. And one day and I was in downtown Madison and I saw him around the corner of a building and he was giggling. And I noticed that people were walking by and trying to pick up what I later found was a ten dollar bill that he had somehow attached to the sidewalk. He selected or something and they couldn’t pick it up. And he would sit there and look at them and giggle and an excellent prayer. 

And it just struck me as what a strange he had a hidden life. Yeah. And I mean, Larry, you know, every day you come across examples like this as a doctor, did you ever ask him so if you start giving money to the sidewalk? I think I probably should, but I was a little afraid of him because even this doctor in Montana, you can lose your day. I mean, it’s just that was a crazy story. It’s a crazy story. Like, why would you throw away his life like that? 

Yeah. For listeners at home who may not have heard about this story. There was this doctor is a really high up in emergency medicine at Mount Sinai Hospital. And he was accused by a patient of sexually assaulting her and treating him. He was really famous for health care reform and read a book on the doctor patient relationship. 

All right. 

He was internationally known and it’s looking like he’s actually guilty. I mean, the woman I was amazed he drugged her before he assaulted her and she still had the presence of mind to take her hospital gown with her as evidence to prove what happened, to prove what she was alleging. And then another victim came forward, a couple from an incident months earlier. So it’s not looking good for this guy. 

Yeah, it is. It is like jarring when you discover that and. Yeah. 

I mean, when I say almost everybody strange, I don’t mean everybody is a sexual predator or a molester, but they’re strange in a variety of ways. On most dimensions, most people are somewhat normal, but there are so many dimensions along which we can vary. There there’s always a good number one way at the extreme ends. 

But does that sort of depiction assume that all these different things are independent of each other, all these different variables and not connected somehow that there’s no there’s no connection between the magnitude of voting Republican and wearing a tie and. 

Right. That they’ve done that. They’re not all independent. But there are enough independent ones and they’re not completely dependent, the ones that are not independent. I mean, you can refine the model, but it’s more suggestive and metaphorical than anything. But it is a way to picture humanity on this multi-dimensional hyper hypercube and realize that we’re we’re all kind of marginal in the literal sense of the word. We’re always for all kinds of weird. 

Yeah. As a journalist, I feel like I that everybody is like that and it’s just my job to ask the right questions, to draw out what’s actually interesting. 

Right? Yes. I think that people generally try to hide the fact that they select ten dollar real suicide. Would spoil the joke otherwise that anywhere. Tell me why. One thing I do in the book is introduce mathematical metaphors that I think shed some light on the whole notion of biography and even the telling of a biography. The writing of a biography is not all that different from technique that she the latest statistics, which is finding the surface of best fit that goes through some multi dimensional space. And in the fundamental case, what’s the best line that goes through a set of data points? You don’t want too many points far off the line. You want to the line, that is to say, a line of best fit. You can define it technically. 

So assigning somebody the narrative of the tragic hero, let’s say, is really a process of finding a line that fits the data out their life. Right. That would be a way of finding a line of best fit through all the data points of their possibly messy life. 

Right. Exactly. And that’s what biographies do. There’s a kind of narrative that they try to shoehorn everything into them. But I don’t like that. There are all kinds of points far off the surface of the spread. And in a way, that’s often what makes people interesting, not so much the standard story which everybody knows, but the deviations from it. I mean, it’s kind of interesting that somebody so accomplished could yet do this. Sure. Somebody so reprehensible could yet do this. Good. So as a result, I mean, biography’s, I think, tend to be more boring than they have to be. 

Does mathematics give us any lessons for understanding those kinds of incongruities like this? You this heroic doctor who is allegedly and probably a sexual abuser. Does it have any sort of insights as to how? If you were writing the biography of his life, you might reconcile those two into it, something that was a coherent narrative? 

Not really. I mean, mathematics sheds light, but in a very ugly sort of way. And now I also write mathematics, statistics in particular. But all mathematics is kind of an imperialist discipline that can invade any other discipline and take over. Never, nevertheless. I don’t want to be totally reductionist about mathematics and think that the only thing is I mean, I think we do need other sorts of understanding, human understanding. 

Can you talk about what Bayesian analysis adds to our understanding of crushes and romantic crush? 

What happens? You have some interaction with a person that’s generally brief. You know, a certain smile or a certain way of handling a set of papers or rolling their eyes at some blowhard and you become smitten. 

And that that’s a good thing. I think questions are good things, whether they’re personal questions or scientific conscious. But they’re as you go on, you gather more information and you realize that that was to use a technical term that was very proud of very you use there and which is a way of upgrading your knowledge when you received more information than your estimate varies. And that does have to be negative. It’s just deeper and fairer. And that’s what basically all of you to do initially have a very small sample. So that’s a statistical sense because of the sample of behaviors like maybe two minutes interaction, if that. 

And so your challenge just the crusher is to figure out whether, like this one charming incident is representative of this person that you think you’re in love with. 

That’s. That’s right. Or even less longer. But after all, reality and everyday life such then and the your estimate changes don’t necessarily become negative, but they become fuller. Deeper. All right, Lombard. I mean, Daniel Kahneman in his book Thinking Fast, Thinking Slow, talks about these two methods of thinking. One is immediate and emotional and visceral. And that’s where the cash comes in and the other is considered an abstract. And it comes in in later and it is much slower. The first is immediate. The other is slow. Logic is slow. Feelings are fast. And I think that’s part of the appeal for many people. Donald Trump in some sense, have a crush on him. But I’d like to think that when they come to their senses, they crush will evaporate. 

He’s kind of an interesting guy because he’s such an overwhelming narcissist, obviously is a very strong sense of himself. And his overarching narrative points in the book that you talk about is how illusory even Essene the idea of a consistent self really is. 

Yeah, yeah, I wore a number of passages, a number of sections in the book where I kind of invoke an almost cross a Buddhist attitude towards life. I mean, I think that the notion of self is a kind of a chimera. It’s natural to think of oneself. I mean, the notion develops from Murano commotion and gradually you develop this complex of neurons in neuronal structures that is the eye or that is other people. But is there any thing if you drill down far enough that’s really there or we notion of self just as nominal is the notion of New York Yankees and the new New York Yankees. They are not the New York Yankees of Babe Ruth, Babe Ruth time. I mean, they have the same name. And until recently, they had the same stadium. But nobody says. What’s the essence of the New York Yankees? It’s that kind of identity that I think is our identity. And it’s not something you can put that much weight on. 

But, yeah, like the philosopher David Hume said, you know, he sort of tried to introspect and find himself and all he could find were a series of ideas and impressions was nothing that he could access. Underlying it, right. 

Exactly. I mean, no. I was really, in that sense, a Buddhist. In fact, I cite him and Brutus in the book is having similar mentalities. I mean, I’m not a Buddhist. They’re all kind of my thing, all kinds of nonsense associated with with Buddhism, but particularly inside the kind of chimerical nature of the self. I do by and I think it’s supported by neuroscience and will more and more become clearer, I think. 

Do you think that the experience of writing a memoir changed you? I mean, the sort of systematically reflecting on and trying to capture all your past selves in some kind of narrative? 

Yeah, I did. Right. You are necessarily introspective when you write a book, a memoir, and you’re generally older. I mean, is part of the section I wrote on Growing Jaded as you get older records of one sort or another, the best movie ever seen. I remember as a kid I go to movies, not the best movie other thing I’ve ever seen, maybe three or four movies writer. Oh, that’s the best. Now, you don’t come across the best movie very often at all. But then not just that. The first experience with the first sexual experience, the first this or that, and these peak moments become ever more rare. 

And I mean, you can illustrate that not just because you’ve done it more times and there’s more in the back catalog to compare it to. 

Oh, yeah. And I mean, really, the one kind of idea metaphor I use is imagine flipping a coin a thousand times and keep track of the number of threads. Let’s say you do it. You get five hundred and seven. Hej. That’s a record since you know you’ve never done it before. But let’s say you flip the coin another thousand times. This time gets 193 heads. That’s not a record. You do it another thousand times. You get 500 run hedge bets on a record. A few more times finally get five hundred and eleven heads. That’s a new record. But it occurred five or six times later. And the next new record is going to occur after 20 iterations of this process of flipping a coin a thousand times and the frequency of new records becomes less and less. In fact, you flip a coin a million times. The number of new records will be around 40. So on any dimension. Records, extreme experiences are extremely intensive experiences as they have when you’re a teenager or a young adult, necessarily become less frequent. And it’s just there is some mathematical reason to become that partially exchange. Means. I mean, the only way, as I mentioned the book, any way you can keep on scoring records is with your your size. Every year your your ears exceed the record of size of the year before. But it’s not a particularly exciting record. 

Do you think that’s the bias that may. I’m always fascinated by it. You know, every year you can see, you know, ancient Greece, the 1950s, anything that is currently regarded as being a golden age or something, you can find text for people. We’re talking about the good old days as being something else, something earlier. Or do you think this this bias explains why people tend to posit a good old days? It’s like, oh, yeah, you know, back in the 1970s, every movie was good, but maybe you just hadn’t seen as many movies from Appio until the 1970s as you have now. 

I think that’s part of the reason for the soldier, for the good old days that people feel no matter what their age, because, you know, the older you are, they’re the better. The good old days appear in, at least in part because of these more frequent first best seller records. I mean, I talk about. Back and forth between the personal and the abstract and in numerous life, but it was dissipated by my receiving several awards in the last few years from the mathematical societies, from the Association for the Advancement of Science and so on. And I’ve won these communication awards. But I mean, the downside to winning a lifetime achievement awards, achievement awards of that sort. They are sort of a mark that you’re you’re no exception. But yeah, I’d rather please and flatter to receive them. But I said to myself, no. Very upsetting to get good. 

In the course of writing the memoir, did you have occasion to sort of go back and check on something and find something was really different than the way you remembered it or that other people were saying, oh, no, that’s totally not what happened? 

Yeah, that is the case. Particularly strong when I looked through all photographs. They found some old photographs of my grandfather. My sister had and I had no memories of this letter. And the other thing and you look at the pictures and that could have been the case. And I mean, you tell yourself stories and then you don’t remember reality anymore. You remember the story. And just as well, you tell the various names for the game where you whispered to the person next year who was suppose the person next to them telephone or whatever. And at the end of the line, the story that comes out of the last person’s mouth is nothing like the story that went into the second person’s mouth. 

But this is just you telling the story to yourself even that it’s getting destroyed. 

Yeah, but you’re telling me I did. The sequence of people is yourself. 

So as a result, I mean, each time you’re not remembering necessarily reality, but the previous version of the story and every time you recall it, it may change a little bit. I mean, you like to think that you have photographs of what happened, but you generally try to make your memories consistent with the present program, memories of your life, which is probably fairly recent. And so you kind of massage the memories if they don’t quite fit until they do. 

You think that social media and, you know, sort of social media timelines and the ubiquity of digital photos are going to change how people’s autobiographical memories develop over the course of their lives? If you have some concrete reminders to go back to, I think about my grandmother who had, you know, maybe one picture of herself for her entire preadolescent as compared to my cousin, who has 12000 pictures from Deeyah. She was traveling around. 

Yeah, I think the so-called quantified life wouldn’t make it harder to do that in the memory to fit a narrative. But there are people really want to change their life story no matter how many factors you have. And nobody how many tweets. I mean, you can test them in a certain way. I mean, I think about prudery would say, you know, spend too much time on. Is that it? It’s one kind of alive. And, you know, it’s evanescent. It’s kind of bubbling with contemporary energy. And to me, it sounds the kind of problem that accounts for a small world phenomena whereby there are clusters where you are more likely to connect not just intuitively any social network to connect to people, but nearby in some sense of the word. 

Began with a certain admixture of people in distant clusters. So if you know somebody in there, in a couple of people in a foreign country, you’re not that unusual, unrelated to almost everybody in that foreign country. And it gives rise to the view that the six degrees of separation phenomena, depending on the network you’re talking about, could be less than six. I mean, there was a mathematician, Paul Oceans, of pretty literally peripatetic. He traveled around the world doing math of various people and he wrote all kinds of junk papers. And you said they have a number of one. If you wrote a paper with Paul Ocean and Arrows, number two, if you wrote a paper with so many wrote a paper with Folliard Ocean Shore. 

So this is the six degrees of Kevin Bacon for mathematicians, right? 

Yeah. It’s exactly the same Kevin Bacon for movies. Are those four for mathematics? Happily, my Irish number is four. But it’s it’s an interesting. 

I mean, the small world phenomenon ideas are characteristic of the networks where there’s clustering and some connection, distant connection with distant people or wherever the knowledge of the network are. So in that sense, I like Twitter because I’m connected to all sorts of people and followers here, there and everywhere. And I follow people here, there. 

And they’re going to share your Twitter handle so our listeners can follow to assist. 

John Allen Paulos at John Allen tells L-A. Ian is PKU Ellis. You’re welcome to follow me. I look forward to that. 

That’s great. We’re at point of inquiry where you’re at point of inquiry. Yeah. 

All right, Feierstein, I know that whether there’s anything that you can. I mean, it’s kind of cliché knowledge, right. But if you can do and at least this minimal contact with almost anybody is pretty amazing. 

I was just on Facebook yesterday checking my messages and suddenly I was in contact with a kid in a Muslim countries like first year university student, the only person he knows who’s atheist. And he’s just kind of befriending people on on Facebook because he doesn’t know who else to talk to. And it was just kind of a nice experience to be able to be somebody who could be an atheist conversation partner for someone who can’t talk about it with anybody else in his life. 

Yeah, no, I I’ve had a similar experience, as it happens, with people from Muslim countries who can’t talk. I mean, especially if there is a Bangladesh or there’s a famine and they’re going to go wrong and form a little reading group. 

Now they get arrested. Nothing worse than that. Yeah. 

So they say there’s different ideas that said, some light, like I even card tricks, which are somewhat mathematical. Are that gratifies structure of a person’s life. And why people, despite very varied backgrounds in this food additives, kind of after awhile develop similar attitudes, similar certainly similar aches and pains are because as they get older, I mean, no matter what career path, they become similar in one sense or another, which I discuss that I relate that. 

You mean just as in terms of the sort of biological and social processes of aging? We are guthman bread. 

And I talk about the Kruskal trick, which is a nice trade card trick in its own right. What you do is you say you have a deck of cards and you tell somebody you pick a number. It’s say it’s only cards eight to 10. Once you turn and have to pick a number that says that, pick three and say, you going to turn over the cards or that one at a time. Whenever a third card is that, say, for five, that becomes your new number. And I’ll keep turning the cards over until I get to the fifth card after that one. Whatever that card is, let’s say it’s an eight. You look at the eight card after red. 

And if you’re doing it at the same time silently as the person to whom you’re explaining, the trick will almost always end up on the same card, because despite jumping around and having different numbers at first, sooner or later you’re going to end up on the same card with different V a different paths. But they’re on you’re going to go in lock step. So you can surprise somebody at the end and say, I’m make sure that. Sure. Your secret number now. And you’re almost always right. You can do that even with with words. You can take a passage of Reviver. Let’s say they pick a word from the first few lines and contin number of letters in it. And then if you’ve got six letters in the sixth word after that, it gets an F word after that has three letters. Go ahead. Three words to go to the next one that has five letters. Go ahead and write an appropriately artful choice of passage. You can always get the person to land on a particular word of your choice so you can establish a religious hope. And it always ends up on devel or something. And it’s just another example of the Chris Mooney trick. It’s a U.S. case. And it’s very, very easy. It’s just fun to to go back and forth, as I said, between games, puzzles, mathematics stuff, eBay and the personal in the course of writing the memoir. 

Did you ever sort of think about, you know, sort of coincidences that changed the whole course of your life where you think if that hadn’t happened, I would be somewhere entirely different today? 

Yes, of course. I mean that I talk about how and some like the extended picnicking and sense I was responsible for George Bush’s election in the year 2000. And how so? Well, as you remember, there was no go ahead half a million more votes than Bush nationwide. 

Florida was essentially tie. There were six million votes. And the reference to preen and the official reference was a couple hundred. I mean, if you flip a coin six million times, the difference between the number of heads and tails would likely be bigger. But in any case, there was the issue of hanging chads and machine ballots and butterfly ballots, the military ballots and and anomalies and counting. And so I wrote Not Dead during the recount process in Florida, which was going to decide the whole election, a method for New York Times. I wish I said the electoral apparatus in Florida is so gross as to be incapable of measuring the tiny differences, if any, between Bush and Gore. It’s somewhat analogous to measuring bacteria with a yardstick. And I said there really is no fact of the matter is the margin of error is greater than the margin of victory anyway. The recount was going on and the Florida Supreme Court voted to continue the recount and a couple of disputed counties. But the chief justice that we will argue, the Florida Supreme Court said I just read this. We found that by a giant mathematician, John Allen Paulos, and he says there’s no fact of the matter. It’s just margin of error is greater in the margin of victory. So I’m stopping the. Well, we can’t because continually. Will just lead to merry little gray litigation, more of appropriation, more divisiveness. And he stopped it. And eventually, after a lot of convoluted legal wrangling, it went to the U.S. Supreme Court. And the rest is history. And George Bush was elected or perhaps more accurately, she’d like to do it over again. 

Would you still have written the piece? 

No, no, I want that. I mean, I have to admit that I was a little bit flattered to have been mentioned, but I was horrified at the way in which the put my op ed. I mean, if you just look at those countries, there’s conflicting episode’s conclusions you can come to. They stay recounted the whole state. Gore would have won and that would have changed. Yeah. That would have changed the course of history. I doubt if the Iraq war would have taken place. The environmental legislation would have been much stronger, much sooner. And for me, it’s I talk about the butterfly effect and so-called non-linear dynamics, Tiny’s of differences cascading into huge differences over time. So in that sense, I was the butterfly. I mean, there are lots of intermediate butterflies, mainly Jeb Bush, his brother. I, I mean, you can’t really blame the butterflies. They can’t be heard. Yeah. But nevertheless, I always had this twinge of guilt, which is not unwarranted. But nevertheless, I sometimes feel that way. 

Well, thank you so much. That’s all the time we have. Thank you so much for coming on the program. 

Thank you very, very much. 

Lindsay Beyerstein

Lindsay Beyerstein

Lindsay Beyerstein is an award-winning investigative journalist and In These Times staff writer who writes the blog Duly Noted. Her stories have appeared in Newsweek, Salon, Slate, The NationMs. Magazine, and other publications. Her photographs have been published in the Wall Street Journal and the New York Times’ City Room. She also blogs at The Hillman Blog (, a publication of the Sidney Hillman Foundation, a non-profit that honors journalism in the public interest.