>> Debra Carnegie: Welcome to the Microsoft February Research Visiting Speaker Series. I’m Debra
Carnegie and it’s my pleasure to introduce today’s speaker, Professor Steven Strogatz. Professor
Strogatz is really the Math teach you wished you’d had. He is the Stremen Professor of Live
Mathematics at Cornell University, a renowned teacher, and one of the worlds most highly sighted
mathematicians. He’s been a frequent guest on National Public Radio’s RadioLab. Among is honors are
MIT’s highest teaching prize, membership in the American Academy of Arts and Sciences, and a lifetime
achievement award for communication of Math to the general public awarded by the 4 major American
Mathematical Societies.
He also wrote a popular New York Times online column The Elements of Math which form the basis of
his new book The Joy of X. In the Joy of X, Professor Strogatz takes us on a tour of the greatest ideas of
Math, revealing how it connects to literature, philosophy, law, medicine, art, business, and even pop
cultures in ways we never imagined.
Please join me in giving him a warm welcome to Professor Steven Strogatz.
[applause]
>> Steven Strogatz: Thanks very much. It’s my first visit to Microsoft Research. I’m thrilled to be here.
Also it’s a nice treat to, is my microphone on?
>>: Yes.
>> Steven Strogatz: Yeah, okay. So it’s a nice treat to have an audience that I’m presuming is pretty
mathematical. Normally I don’t have that luxury. So, in fact I think what I’ll be doing here today is
maybe more a talk and a conversation. I’m hoping that if I ask rhetorical questions that, they’re not
really meant to be rhetorical, they’re serious questions for you to give opinions. That is, let’s have a bit
of a conversation about the subject of math communication.
How do you get, or how does one get ideas about math from elementary math up to let’s say graduate
school level math out to the public in a way that they would find interesting, and maybe even joyful or
beautiful? So that’s the theme here.
I suppose I should start by telling you a little bit about the genesis of this book, Joy of X which I’m
amazed to see is being sold for 10 dollars that is a pretty good deal.
[laughter]
I mean –
>> Debra Carnegie: They’re gone now, so –
>> Steven Strogatz: They’re gone? Oh –
>> Debra Carnegie: [inaudible] –
>> Steven Strogatz: The 10 dollar ones are gone. All right I take it back, ha-ha. They’re being sold for
whatever their normal price is.
[laughter]
>> Steven Strogatz: Ha-ha. Anyway so the book grew out of the column that Debra mentioned which
was The Elements of Math for the New York Times, 2 years ago. So, it’s a pretty odd thing to have a
math column in the newspaper. There really aren’t very many of those. I don’t know if I know of any.
So you maybe wondering how did that all get started? I had written some Op Ed’s for the Times over
the years. I wrote my first book for the public in 2003. At the time the literary agent who represented
the book talked to the editor of the Op Ed Page and said would you consider an Op Ed from this author
of mine? Sure, if it doesn’t hurt them to consider it they can always reject it later. So anyway I sent
something and they did publish it and I got to be friends over the years with this editor, David Shipley.
So a few years ago, actually I can remember exactly when because it was the day of my 50th birthday.
He didn’t happen to know that but I was in New York and he asked me to look him up next time I was in
the city and I did. We ended up having lunch on that day. He surprised me by say we would like me to
think about writing a series for the “Page” as he puts it, for the Opinion Page.
Would you ever have time to write a series? So I though that’s a wild idea. What would that even
mean? But as it happened I had taught all my courses in the fall semester of that year. He was asking
about the spring and I had the spring pretty open. So I said I could do it this spring.
Then the first question was, well, what would a math series be like? So he told me what he had in mind.
Which was that he himself had gone to a good college, he went to Williams. I think he was an English
Major.
He said he took math all the way up to calculus in high school. He could get good grades in it but he
never knew what he was doing. It didn’t really mean anything to him. That is it all felt kind of like, I
don’t know, he was just doing what he was told but there was no internal sense of this is a fantastic
subject or anything pleasurable.
So he said I know that you mathematicians and people who like math say it’s elegant or you use words
like beautiful or inspiring. He said I have no idea what you’re talking about. I think a lot of the readers
of the New York Times don’t know what that is. So could you convey to the rest of us what is the joy of
math or the beauty of this kind of thinking?
So that was the goal and let me tell you a few choices I made along the way. That’s where I think we
could have a conversation because you might think that some of these were bad choices or good. I’d be
interested in, seriously in, your take on this. I think it’s a really interesting issue. How do you present to
the public?
So, well, alright the first thing was how should it be organized? That is what I suggested to the editor
was I thought it should be math in the new. That is it is a newspaper and so there’s always math relating
to, let’s say the economy, or climate change, or controversies about the Census, or whatever. So maybe
tie it to something in the news.
He said, no absolutely not, don’t want that. I’d want you to start in kindergarten with what are
numbers. Then I’d want you to do addition, and then I want you to do subtraction, and so on. Just, I
was shocked at this answer because it sounded really pedantic. It also sounded like the first thing any
math professor would think of to just begin at the beginning and grind forward through the curriculum.
He said that’s exactly what I want you to do but, you know, maybe go faster. Don’t just leave us in
elementary school. Let’s try to get to something more sophisticated too. Definitely start at the
beginning so we know where we are.
Alright, so here’s what that looked at when I tried it. By the way, so this series then grew into the book.
There were 15 separate weeks in The Elements of Math and the book has 30 chapters. So there are 15
brand new chapters.
So there, well I will read it anyway. “I have a friend who gets a tremendous kick out of science, even
though he’s an artist.” Now you might notice something a little problematic with that first sentence.
Yes, you’re nodding the gentleman there. What’s the matter with that sentence?
>>: Well, you’re creating, you’re separating out arts and science and –
>> Steven Strogatz: Yes.
>>: In a demeaning way.
>> Steven Strogatz: In a demeaning way to the artist?
>>: The artist.
>> Steven Strogatz: The phrase even though is the offensive.
>>: [inaudible].
>> Steven Strogatz: Yes. Yeah, ha-ha –
[laughter]
>> Steven Strogatz: I didn’t mean it like that. This is the issue of writing for a deadline. Now, you have
your own deadlines here I’m sure with actually producing valuable products. You know, in the academic
world we don’t do much of that. We just –
[laughter]
>> Steven Strogatz: Normally don’t have deadlines. Here I had a deadline each week and that was a
new thing for me. I regret certain choices. I’m not sure how I would wanted, I thought about this
sentence, should I say I have an artist friend who gets a tremendous kick out of science? That might be
better. There’s a certain snap and it’s true that there’s bias in this way of saying it. Some people
complained in the comments but anyway that’s how it came out. It’s a true story. I do have a friend
who gets a tremendous kick out of science and he’s an artist.
“Whenever we get together all he wants to do is chat about the latest thing in evolution or quantum
mechanics. But when it comes to math, he feels at sea, and it saddens him. The strange symbols keep
him out. He says he doesn’t even know how to pronounce them.”
That’s true. I mean if he sees something with sigma or an integral he doesn’t know how to read that.
But know idea what he’s even suppose to say let alone what it means.
“In fact, his alienation runs a lot deeper. He’s not sure what mathematicians do all day, or what they
mean when they say a proof is elegant. Sometimes we joke that I just should sit him down and teach
him everything, starting with 1 + 1 = 2 and going as far as we can.”
“Crazy as it sounds, over the next several weeks I’m going to try to do something close to that. I’ll be
writing about the elements of mathematics, from pre-school to grad school, for anyone out there who’d
like to have second chance at the subject – but this time from an adult perspective. It’s not intended to
be remedial. The goal is to give you a better feeling for what math is all about and why it’s so
enthralling to those who get it.”
“So let’s begin with pre-school.”
So then the, now what happens to get out of here? Should I hit reader again? Hide reader, okay, hey
that’s pretty good that worked.
Alright so I thought as a way in I would show – by the way the series was online so I was able to link
videos. This is what the series looks like if you go to the New York Times.
So this is a clip from Sesame Street that I had always admired. My kids had watched it in this video 1, 2,
3, Count with Me. It explains why numbers are helpful. So take a look at this. Let me start at the
beginning here. Now, I wonder if I’m going to have a problem. Yeah, I had this; no I’m not having a
problems, good.
[video]
>> Steven Strogatz: Yeah, so there are 2 points that I like about that, which is first that 1 of the
characters says, “This counting thing can save a person a lot of trouble”. Which is true, right? That’s the
first lesson that kids are suppose to learn that numbers are efficient, shortcuts, instead of having to say
fish, fish, fish 6 times.
You could just have the concept of 6 but then comes this deeper point which is when they say, “Does it
work on other stuff?” “Does it work on cinnamon rolls?” Yes, does it work on spark plugs? Yes because
6 is more general than 6 fish or 6 spark plugs. 6 is abstract not to us maybe but it is, right? 6 is more
general concept than 6 specific things like 6 fish.
So in fact the concept of 6 is an abstraction from reality that you could ask philosophical questions
about. Like where is 6? 6 is not really in the world. 6 is somewhere in the world of ideas in the way that
truth and justice and good are in the world of ideas. These are platonic concepts that are transcendent
above the level of reality. They’re abstractions from reality.
Now what I like about that is that a lot of times you hear the word abstract used in a sort of insulting
way. People say I don’t like math because it’s so abstract. I like it when it’s real world. Yet a lot of the
power of math comes precisely when it is abstract. When it’s general and can apply to different things
like cinnamon rolls, spark plugs, and fish. So to me this is a really nice introduction to the idea of the
power of abstraction.
Anyway, so in this essay I tried to make this point and also connect it to this philosophical question of
are numbers invented or are they discovered? Actually in general is math, where is math in philosophy?
Is it something that we’re discovering like the facts of science or is it something that we’re inventing like
the creations we make in music and art? Do you, here you all have probably thought about this
question. Anyone want to weigh in on that? Do you have a feeling? Yes, sir.
>>: So first explicit here is a couple of concepts. One is their numeral system and the other one is a
positional system, right? So we don’t need to write like Roman numerals. So, when you define a
language I think you invent it you don’t discover it. Maybe there is some where in which case where you
can discover a language of something but it’s invented and it was refined throughout times.
>> Steven Strogatz: U-huh. So you’re saying the representational system, like in this case they actually
counted with the Hindu-Arabic system 1, 2, 3, with the symbols we’re use to. That surely was invented –
>>: Yes.
>> Steven Strogatz: We know that. What about the concept of 6? Like when they look at 6 fish, I don’t
know if that’s discovered or invented. One example that I discuss later in the piece is, suppose that
another room calls in with the same order. So, just as many penguins want just as many fish then, so
like just to cut to the chase it’s now going to be 6 plus 6 which we know to be 12.
You know, that’s not invented. Once you have the idea of 6 and once you have the idea of addition to
group rooms together there’s no logical freedom in the result. So in that sense, you can say that some
of the truths of mathematics are discovered even though you’ve invented the concepts.
Did you want to make a comment? Yes.
>>: I’d like to return the question to you. Do you think logic is invented?
>> Steven Strogatz: Ah, well that’s a good, now your –
[laughter]
>> Steven Strogatz: Yes, now that maybe questionable. Right, I’m presuming that some how logic is
given and you could say no it’s not. If that’s invented too then it’s all invented. Is that what you’re
saying as a possible argument? Yeah, that is a possible argument.
I don’t like it as; I don’t want to believe that. Of course there is alternative logic so we know that you
can, you know, consider them. The logic that is the standard logic whatever it should be called,
conventional logic seems to work pretty well in reality and so that’s the one that we use. But there’s
quantum logic and fuzzy logic.
So, yes, this is deep territory. I don’t want to spend too long on this. For the purpose of the New York
Times column I took it that we’re not going to question logic. We’re just going to use the ordinary
Aristotelian style logic. Yes.
>>: I just remember when I went I first took math in college and pianos, axinous –
>> Steven Strogatz: Yes.
>>: Starting real analysis and I go great let me, I’m doing this Weeding Advance Mathematics and
starting with things like there exists a number 1 –
>> Steven Strogatz: Yes, yes.
>>: And, and having those basic assumptions because if you don’t have those basic assumptions to start
with you can’t get all the other stuff –
>> Steven Strogatz: U-huh.
>>: So, I just found that kind of mind blowing.
>> Steven Strogatz: You liked that or didn’t like it? It sounds like you did like –
>>: I liked the structure of it but it did disappoint me that nobody could point to a purer truth of these
things of just self [indiscernible].
>> Steven Strogatz: Yes, ha-ha. That’s interesting all that. Yeah, you do have to start somewhere. I
don’t think anyone has found a way around that.
Wow, we could, this is all very interesting. I feel talking about biblical references here, right? The
beginning of Genesis and Hebrew starts with the second letter not the first letter, Breshiek. There are
interpretations, why don’t we start with the first letter if it’s the beginning of the book? So the old
rabbis say it’s because you shouldn’t ask too many questions about the beginning, just get on with your
life.
[laughter]
>> Steven Strogatz: That’s a traditional interpretation –
[laughter]
>> Steven Strogatz: That you’ll be stuck if you worry about the beginning. The letter itself is shaped like
this which sort of says, go that way.
[laughter]
>> Steven Strogatz: Go forward. I mean, anyway, that’s a one rabbinical interpretation. Okay, this is
not where I was thinking I was going, ha-ha.
[laughter]
>> Steven Strogatz: Okay, so that was the first column and then the question is would there be anyone
who would want to read stuff like that? It turned out that it got to be number 2 on the most emailed list
for that week. You can see up here in tiny, 546 comments which was a lot of comments. Most of the
comments, I tell you like a really large majority, were along the lines of thank you to the New York Times
and thank you to the author. I always had trouble with math in school or I didn’t really get it and I
appreciate having, this phrase I use, second chance at math for an adult really hit a nerve. It turns out
there’s a lot of adults who wanted a second chance. I didn’t realize that. I mean I had a feeling from my
friend that there might be people but there are a lot of people.
So what’s interesting about that, at least to me, when you look at typical pop math books they’re not
addressing that audience. Pop math books are popular or usually written for us, people who already like
math and want to just learn some other part of it. But math for the people who need it the most it’s
very hard to write for that audience. Not many people try. Anyway, so that’s who I was aiming at.
Well, let me give you an example or 2 of what I’m trying to do both in the book and in the column. The
main thing, there was a question of a choice, like for instance should there be proofs? A lot of people
have trouble with proofs and the reasoning involved in rigorous math.
Some would say you should focus on history. Like people like to read about people, tell stories about
the great mathematicians and what they discovered. I felt like, no actually I want to make people have
the mathematical experience, that is, feel what it’s like.
Why do we get a thrill from a proof or a calculation or a picture? I want them to have a little bit of that
thrill to see, because that’s I think what drives people to do math, other than practical things is the
pleasure of it.
So, here’s an example of an attempt to do that. Here’s where I get to do Power Point. No, I don’t want
to do that one. That was an attempt, oops what happened? Oh, here I am, sorry.
>>: It’s a feature.
>> Steven Strogatz: Ha-ha, feature, yeah, ha-ha. Thank you, I knew it had to be a feature. This is where
I wanted to start. So this was an attempt to discuss a problem that could come up in high school
geometry which is the area of a circle. We all learn in high school that the area of a circle is Pi r squared.
If r is the radius and I defined Pi for the readers in terms of the circumference of a circle divided by the
diameter. That was the definition of Pi after reminding them what circumference and diameter mean.
I addressed the question how do I know it’s the same number for all circles? It’s an interesting; I mean if
you’re really careful and sophisticated you would ask that. How do I know Pi is the same for a big circle
or a little circle?
I didn’t give a real proof of that I just said, you could imagine taking a circle and putting it on a
photocopier and if you scale it down you’ll shrink all distances. Suppose you shrink it by 50 percent,
you’ll shrink the diameter by 50 percent but you’ll shrink all distances by 50 percent including the
circumference. So the ratio will always be whatever this same number. I thought for that audience that
might be convincing enough.
Not a proof but, okay, but now why is the area Pi r squared if Pi is defined in terms of circumference
divided by diameter? So here’s a proof and what I liked about this proof was that it contains what I
think of is drama. That is in a typical drama, like on television or in the movies; things get worse for the
hero before they get better, right. The hero gets in trouble.
I feel like this proof begins immediately you feel like you’re in trouble. So there’s this circle. We’re
going to cut it into 4 pieces. If we could rearrange those pieces and calculate the area of the new shape
then we could calculate the area of a circle. So I take those 4 and rearrange them into this strange
looking scalloped shape here on the bottom and it looks like I made it worse. I mean how am I going to
figure out the area of this crazy thing?
Well, I don’t know but I can observe a couple of things about it. One is that this distance is the original
radius because that’s just; you know how we defined radius from the center out to the rim. Also we
defined Pi so that this whole circumference would be 2 Pi times the radius or Pi times the diameter. So
here are 2 of the curved pieces, that’s half the circumference there. So Pi r and then on the top that
would be another Pi r. So I have Pi r as the arc length here on the bottom and r for that length of that
slopey side.
As I say at the moment it doesn’t look promising. But the thought would be well what if we took more
pieces? So there’s with 8 slices and I stack them up the same way. You notice now that the curvy parts
are not quite as curvy as they were. It looks like its trying to get flat. The part that was slopey is now
standing a little more straight up. Let’s compare that one that angle of that to the next one. It’s starting
to stand more straight up. If we take 16 pieces now it’s really getting quite straight up and also pretty
darn flat.
So you can see that what I’m trying to do here is teach the reader who doesn’t know calculus that if you
go to the infinite limit things will become simpler. That is most people don’t have this intuition. The
average person thinks that infinity is mind boggling. The idea that infinity could be your friend in math
and could help you solve a problem, which of course that’s the heart of calculus is that infinity is being
domesticated and tamed and becomes your ally.
That’s what I’m trying to show them here and if I can take more and more of these slices, in fact, this
shape will converge to something very simple. It will become a rectangle.
Now we know how to find the area of something like a rectangle. It’s just the, course this bottom which
is o has been Pi r through out the whole process times this r which is now standing straight up. So Pi r
squared the area of a circle.
So I don’t know if you’ve seen that proof before. Isn’t that nice? That is a totally elementary proof that
any kid, I see a child there. Do you know about Pi? So maybe, okay, that’s a proof that I hope you could
understand. I see other younger people there too, yes, okay, ha-ha, anyway.
That’s not usually a proof that shown in school. I’m not sure why not. It’s been known for thousands of
years. It’s an ancient proof.
What is so great about it is that I think it shows the idea of elegance. That you really now see why it’s Pi
r squared and it’s just a very sweet little argument. You didn’t have to do any calculations either.
I did think that the reader, just like my friend doesn’t understand about symbols, I thought I should
avoid doing a lot of explicit symbol manipulation. That was a choice that I feel like for a lot of people the
symbols are a big hang up in math. So to the extent that I could use the power of the web and use color
pictures and, you know, make it visual that a lot of people might be less scared of that.
Anyone want to react or say anything about that example before we go on?
>>: [inaudible] point of view attempts in the last 10 – 15 years to do more of a [indiscernible]novel
approach or a comic book approach to teaching math. There was a really outstanding one that sort of
[indiscernible] Bertram Russell. I thought that was [indiscernible] a lot of people and it kind of pushes
your approach farther but to a non-electronic or non-digital audience.
>> Steven Strogatz: U-huh.
>>: Did you consider going that way?
>> Steven Strogatz: So the book that’s being mentioned was called Logicomix. Some of you might have
seen its one word Logicomix with an x at the end. Your right, it was a phenomenal book about set
theory and paradoxes of infinity. Bertram Russell was the main star but there’s Cantor and Fraga, all
these characters are in it. It was told very dramatically against a backdrop of World War I, written in
comic book style, graphic novel style.
I did not ever think of that because the offer that was given to me was to write a series on the web. I
thought the web has certain advantages as a medium. I could show that Sesame Street video or, also I
didn’t have the resource of a guy who could do the graphics like the artist who did for that Logicomix
book.
So, no I never actually thought of that. I agree that it’s really a successful approach. What they did was
remarkable. Yes, gentleman on my left.
>>: So my wife, we went to the bookstore and my wife bought a book called Draw Yourself Smart –
>> Steven Strogatz: Draw Yourself Smart.
>>: It’s about geometry –
>> Steven Strogatz: Yes.
>>: Which geometry kind of lends it’s self to that. There’s a lot of geometric problems and the learning
is very specific about, you know, please draw these pictures yourself, encouraging you do so. I thought
that was really interesting. Your comment about having a second chance at math –
>> Steven Strogatz: U-huh.
>>: I think that provided me, of my wife by buying that because I think that was an, oh yeah I might like
to learn more about that. I kind of, the book kind of looked almost graphic null. It does not look like a
math book at all.
>> Steven Strogatz: I don’t know that book that’s interesting. You say the title again, Draw –
>>: Draw Yourself Smart.
>> Steven Strogatz: That sounds interesting. Yes, did you want to make a comment?
>>: My reaction specifically to your question on using symbols. I haven’t looked through your book
although everything looks fantastic already –
>> Steven Strogatz: Well, thank you, ha-ha.
>>: Applause on that. I think there’s a big difference between making something easy and making
something accessible –
>> Steven Strogatz: Yes.
>>: So you would hope that if symbols have elegance because they encapsulate a concept after a lot of
work. So if you had something that, let’s talk about [indiscernible] limitation or concepts behind it and
then you ended up by saying here’s –
>> Steven Strogatz: That’s right.
>>: The symbol then that gives somebody an [indiscernible] to understand the elegance of it. If you just
do it without giving the symbols then you kind of you told a story but not given them the climax. Like –
>> Steven Strogatz: Yeah.
>>: [inaudible] talk on teaching they say give your audience 2 plus 2 that will give them 4, right. So if
you’re teaching it’s okay to make them work for it just engage them, engage of their senses first so have
a little apprehension of saying you didn’t want to teach them the symbols because I think the symbols
are the actual payoff –
>> Steven Strogatz: Good, I see –
>>: [inaudible]
>> Steven Strogatz: Well I think we’re in agreement about that. I do in fact show some symbols and
algebra for the same reason that you suggested. They can be the payoff just like in this trivial example
at the beginning that 6 is the payoff for the fish, fish, fish.
Also as you point out you want to really make it clear why you’ve introduced the symbol. That is that
they are your friend and a time saver, and a concise embodiment of lots of ideas. The reader has to be
ready for it. That’s what I think is often the mistake in the Pedagogy, standard Pedagogy is that we’re in
a rush to give students answers and procedures but to questions that they haven’t thought to ask.
So I want my reader to always be ready to ask the question before I give them the answer. So it does go
slowly but yeah, nothing wrong with symbols, absolutely. There’s 1 of the 6 main sections of the book is
about algebra including a pretty elaborate chapter on the quadratic formula which a lot of people think
of as ugly.
I really think it’s a magnificent formula that does a lot of work. Yes, it’s bulky looking but it’s solving all
quadratic equations in 1 stroke. So that’s a case where I did absolutely show the symbols and try to
explain what they’re about. Yes, you wanted to say something?
>>: So returning to the idea of these very simple notions that we take for granted like, what is 6? I can
see a student reader perhaps being a skeptic, healthy skeptic and saying well, what do you mean by area
of a closed figure –
>> Steven Strogatz: Yeah.
>>: Isn’t a square? You know, implicit in this it seems an assumption that well I can sort of divide into
smaller regions and I’ll get the same answer if I add up the areas of the smaller regions –
>> Steven Strogatz: U-huh.
>>: As the original. But, you know, people can ask things like, well what do you mean by area?
>> Steven Strogatz: Yep, absolutely. These are very good points. Now, in my experience very few
people who are mathematically unsophisticated will ask that question. A reader who asks the questions
that you just asked, what is area? How do I know that area is preserved when I move the pieces
around? Those are the questions that only we think of. We’re usually pretty good at math already. I
just think in practice that’s not a serious issue. But I could image there could be a very brilliant reader
who for some reason is naïve mathematically thinking of all that and they might, yes they would not be
on resonance with this series perhaps.
>>: I think part of my point is as people that are trying to convey these concepts we have to be
prepared for, be surprised by questions that are as simple as, well wait a minute you haven’t really
defined it or I don’t really have a clear, I have an intuitive notion but can you describe more properties
of [inaudible].
>> Steven Strogatz: I think maybe you and I disagree a little bit. Yes, you need to be prepared for those
but I believe empirically that is not a serious issue in practice. That I think a lot of what we do as
teachers is worry about that kind of thing and try to fend off those attacks or those serious and proper
questions that never coming in practice. In doing that we end up confusing the 98 percent of readers
who just want to understand why is it Pi r squared?
So we give, like that is, the objection to the proof that I just gave is it’s not really rigorous for the reasons
you said. We haven’t defined area. I haven’t proven invariance with respect to Euclidian motions and
stuff like that. That’s all true but nobody, like my wife or the average person who’s not into math they
don’t care about that. They don’t even know why its Pi r squared.
So, I worry that in a lot of our books we’re so careful to be right that we miss the main educational
point. So, I mean I don’t know if you would agree with what I’m saying or not. I think it’s, I try not to lie,
I have a section notes at the end where I do say what the gaps are in the proof. I think then I’ve got
myself covered.
Also it’s a real issue on the web because a lot of people are ready to criticize and do. They put these
criticisms in the comments. So, I would show each of these columns to my 4 or 5 smartest friends that
are real nit picking type of people and they would pick, pick, pick and that was a very helpful filter to go
through.
Okay, let me see what else might be fun to discuss. I do have 1 lesson that I feel like I learned through
all of this. You know, while we’re talking about Heuristics for effective teaching of this audience or not,
that I want to share with you because it didn’t occur to me. Which is what can you get away with? How
far can you stretch this audience?
Here’s a category. Let me give you 2 categories. There’s familiar and unfamiliar and there’s concrete
and abstract. The example I just gave with the area of a circle I would consider abstract. That’s it’s
about pure geometry of a circle. But it’s familiar; people have all dealt with the area of a circle.
So you can get away with familiar and abstract. The readers seem to like it or can tolerate it. You can
also get away with unfamiliar if it is sufficiently concrete.
As an example of that I would mention when I had 1 chapter about conditional probability. Which the
average person hasn’t thought much about conditional probability, but I tried to tie it to a few real
world problems, such as a woman goes in for a mammogram and she’s in a very low risk group. There’s
no history of breast cancer in her family, her age is 40, you know, she’s fairly young. Her test comes
back positive.
The question is after we give the doctor the statistics about what the incidents, what are the rates of
false positives from this test and what’s the incident for someone in her cohort and that sort of thing.
How worried should she be about this very scary result that she tests positive?
This is a real question that has been, medical students and doctors; trained people have been tested on
this. They give surprisingly wide range of answers. They can’t calculate the probability given the
information needed to calculate the probability which is kind of disturbing considering that they have to
make diagnostic recommendations about what to do. I mean not just diagnostic but what procedure
should be done or not.
Anyway the correct way to think about it involves Bays Rule which again a typical person without much
math training hasn’t thought of. So in the rest of this essay I tried to give a very concrete illustration of
Bays Rule by talking about the O.J. Simpson murder case. Again, this being familiar but, you know,
mathematically difficult, or concrete I should say.
So here’s the story, I notice you’re somewhat amused by this. This seems like an odd application, right?
But have you heard this story about Bays applied to O.J.? Let’s talk about it then for a minute.
So, just to remind you of the details of the case, so it was back in 1994 that the football star, O.J.
Simpson was accused of murdering his wife, Nichole, ex-wife I guess at that time. She was murdered by
somebody. She was found dead with her throat cut and also another person was killed at the scene, a
friend of hers, Ron Goldman. So O.J. was on, O.J. who had been a football star and TV broadcaster, and
a movie star, anyway he was on trial for having killed his ex-wife.
Now the issue here was that involves probability theory was that he had a history of beating his wife, his
ex-wife. It was known that he use to beat her up and she had called 911. The police had come. She had
photographs with her bruised face. There was really no dispute that he was a wife beater and had a
history of beating her up.
But the question was should this be admissible in the murder trial. Because it’s not, this is, well is it
germane or not, is it relevant? The prosecution argued that the jury should be told. They argued to the
judge that this was relevant because it’s known that when men murder their wives they frequently had
a history of beating them before they murdered them. That is a murder in the past is often an abuser.
But the defense said that’s, you’re getting that backwards. It’s not relevant because if you look at the
rate at which batterers’ murder their wives it’s very small. In a given year, according to the FBI Crime
Statistics in a given year a batterer will murder his wife with a probability 1 out of 2000. That is to say of
2000 women who are being battered 1 of them will be murdered by her abuser that year, on average,
which is a small number 1 out of 2000. So it proves nothing that O.J. was a batterer and shouldn’t be
admitted. It’s prejudicial, it’s irrelevant.
Anyway the judge in the case agreed with that argument and did not allow the jury to hear about O.J.’s
history. So my point here is that both the prosecution and the defense are thinking about this
incorrectly.
A gentleman back there is nodding, yeah. Because here’s how they should have looked at it and this
was pointed out in Nature Magazine by a statistician named I.J. Good. So he says, think of it this way,
the things that you need to know about Nicole, the murdered woman are first that she was previously
beaten by her husband and she was murdered by somebody. That is she’s not just a random battered
woman, she’s a battered woman whose been found dead, murdered.
So, those are pieces of prior information that we need to take into account. So the correct calculation is
to ask, suppose we, well one other piece of information I should give you is if you’re just a woman, you
know anybody not necessarily a battered wife. In the year 1994 when she was killed the murder rate in
the U.S. at that time for women was 1 per 20,000, per year.
So let me run the numbers. We can do these in our head. What you should think of is imagine 20,000
battered women and ask how many of them will be killed in that year, on average by their battering
husband or boyfriend? Answer I just told you a minute ago it’s 1 per 2,000 per year. So 10 of them will
be dead at the end of the year on average from their batterer. 1 of them will be dead from someone on
the street, you know a random, because the murder rate, assuming that their murder rate is the same as
for everybody at large, which may not be right.
But let’s just suppose that they’re not special in other respects, 1 in 20,000 will be killed at random, 10
in 20,000 will be killed by their abuser. So 11 will be found dead, 10 of which were killed by their
boyfriend or husband.
So the odds if you’re found dead and you’ve previously been battered, 10 out of 11 times it was your
husband that did it. So it’s just about a 90 percent chance just on that, that O.J. did it. Now that doesn’t
prove that O.J. did it of course because there could be other evidence. He could be, he might have an
alibi.
I mean there could be all kinds of exonerating evidence. It could also be higher than 90 percent because
his DNA might exactly match the blood at the scene. His footprint might exactly match the bloody
footprint found at the scene. In fact those things were all true.
But, so I’m not saying 90 percent is the probability he did. But just on the basis of the prior beating it
seems like it could be argued to be relevant and the judge should have, but, okay.
Anyway the point being that for the New York Times audience this could be done easily in our heads. It
was an easy calculation to walk people through and the audience loved it. This was a very popular
column. A lot of people said this was the most important column of all of them. Because, well between
mammograms and the legal system, I mean this seems like this is real life and death stuff.
This is where, and also the math is tricky and important. So my Pedagogical point here was that you
could do things that are familiar like the circle but abstract. Or you could do very concrete things like
mammograms and murder cases with unfamiliar math like Bayesian Probability. But you can’t do both.
You can’t do unfamiliar and abstract. That’s a conjecture. I found out, I was lead to this conjecture by a
column I did about differential geometry.
Let me show you that one and then I’ll stop.
[laughter]
I thought that people should learn about geometry on curved surfaces not just geometry on the plain
because why not I mean that’s where geometry has gone. So here was an attempt to do that. Let’s see,
there it is.
Yeah, Think Globally this was called. I always tried to have some kind of little catch phrase. You know,
act locally think globally, expect I mean here think globally in the sense of global geometry. So the first
example I thought of was, harmless enough and it was, which was the shortest flight path from New
York City to Rome?
You know Rome is about on the same latitude as New York. That’s a good geography question. A lot of
people assume that Rome is farther south than New York because of the nicer weather, but, no it’s not
its due east of New York.
If you’ve ever taken that flight you know that the pilot hugs the coast of Canada for awhile and then
goes south of Ireland and into Rome. I remember the first time I took the flight stupidly thinking that,
you know, this must be because we’re just trying to play it safe. We’re going to stay near Canada just in
case the engine drops off we’ll be near land. But that’s not why we’re staying near Canada, ha-ha.
It’s just if you hold up a real globe and look at it you can see that’s the shortest path, that’s effectively,
well it’s an arc of a great circle would be the correct term. But it’s the geodesic path, the analog of a
straight line on the surface of the earth. It does no additional curving other than the curving due to the
curvature of the earth. It’s not curving sideways so to speak.
Okay, so that’s the generalization of a straight line on a sphere. But I thought well, alright; let’s really do
something here because I had a video. See this was the mistake I had been told by someone that on the
web you should build the column around the visuals. So figure out what you want to show and then
write the words.
What I wanted to show was some, this video down here that one of my geometry colleagues had shown
me, which is to figure out what the shortest paths look like on a surface, can you see that thing? It’s not,
I don’t know, it’s a double holed torus, sort of a pretzel shape.
I don’t know how visible that is. It’s kind of bright, you can see? Yeah, so here’s now a movie in which a
motorcycle is going to be driving without a driver. With the handlebars locked straight a head, no
turning. This is to show that we’re just driving straight. This is to be the analog of a straight line. So this
motorcycle is just going to drive straight ahead at all times on this 2 holed torus and watch what a
straight line looks like on a 2 holed torus.
Let’s see if this will run. I might have to reload the page. Sometimes these don’t seem to run. Alright,
I’m going to risk, what would happen, is that going to work?
>>: I think so.
>> Steven Strogatz: How do I do that?
>>: Next to reader there’s a re –
>> Steven Strogatz: Oh, good, thank you. You guys are great, ha-ha.
>>: [indiscernible] as a drawing.
[laughter]
>>: You don’t have to –
>> Steven Strogatz: Excuse me.
>>: You won’t have this problem under Windows.
>> Steven Strogatz: No, I’m sure I wouldn’t, ha-ha. Do you guys seriously prefer your products? No.
[laughter]
>>: Oohh –
[video]
>> Steven Strogatz: I’m going to pause that because you get the idea. This is what a shortest path looks
like on a 2 holed torus. I thought it was great but my wife warned me. She said this is really not good,
ha-ha. This is not good and I don’t know why you like it so much but I don’t recommend it. I just said,
no, I think it’s great. She was right, the audience didn’t like it and 1 reader even wrote in a comment
saying the series has now jumped the shark.
Now, I didn’t know what that expression meant, maybe I see some of you chuckling, you know. I had to
look it up. So it refers to the old show Happy Days where the character Fonzie, you know, who dressed
in a black leather jacket and is suppose to be a greaser is water skiing, I guess in his black leather jacket,
and he jumps over a shark. The point of the example with jumping the shark is that the series had been
on for a few years, it had been successful and then it started to get like it needed something new. The
writers felt they needed to freshen it up so they started doing absurd things like having Fonzie jump the
shark.
So I was being accused of jumping the shark and it was only in like the 6th or 7th out of 15 columns and I
didn’t mean to, I didn’t think I was jumping the shark. I thought I was just doing something fun.
Anyway this is my evidence that this example was so unfamiliar and apparently so abstract that even
though it was visual it was not, it certainly wasn’t successful with that reader. In terms of how often it
got emailed around and everything it was an unpopular choice.
I don’t know, I think it’s an interesting lesson.
>>: [inaudible], ha-ha?
>> Steven Strogatz: Ha-ha, do I not feel as cool as the Fonz? I didn’t after that reaction. I was trying to
please the readers and I, I still like it though. That might be a sign of trouble. That is the things I found
interesting maybe at the wrong level. So I should probably be showing them things more like the area
of a circle or the O.J. case.
>>: Or sharks.
>> Steven Strogatz: Or sharks, ha-ha.
>>: [inaudible] shark [indiscernible].
>> Steven Strogatz: Ha-ha, very good. Alright, so I think that’s all I wanted to say. I’d be happy to take
any questions that you have. Thanks very much.
[applause]
Yes sir.
>>: Just as a teacher and kind of mathematician I lied earlier when I said I was a [indiscernible] I’m
actually a designer.
>> Steven Strogatz: Oh, you’re a designer, very good.
>>: [inaudible] designers around the same as between a mathematician and a programmer. So I think
as a lot of generations are coming up. Like, right now I’m working on a problem with the linear algebra.
So I’ll get a book. You go through all of the functions and you see all the mathematics and matrix math
and the tangents and normal’s and bi-tangents and stuff. But at the end I have to go to the code first
because my lingua franca is code when I’m looking at it. So I have to read the code then I can move back
and understand these notations that I don’t use everyday.
I know that I’m a very, well not fringe case here, ha-ha, we’re all in the same case. As kids continue to
grow, right, and they’re learning programming as something that many, many people use including
designers. Some of these math concepts are we hitting that point where some of these concepts or
computations almost need to shift to teaching it through code, because that much more of a practical
applied mathematic versed than trying to teach some of these symbols that have this rich legacy but are
becoming more and more niche just to those that are studying the [indiscernible].
>> Steven Strogatz: Well, very interesting. I don’t have a clear answer for you having only taught it;
yeah only, I mean I’m still 1 of those people teaching it the traditional way.
But I’m getting aware of the need to do more of what you’re saying. That so many people whether in
quantitative finance, or design or you know biotech need to sit behind a computer and build software or
run calculations that are being done by computers and not by people. Or by people who have
programmed, and to be teaching old style pencil and paper math without that is kind of ridiculous, now
a days.
So clearly we want to be doing more of that. But there are so few of us who are trained. That is the
math training, pretty nearly everyone say at Cornell that I’m most familiar with, I think almost no one in
the Math Department can write a program to do even the most basic thing. There are some people.
We have people who do computational algebra and they really are computing things, efficiently and. So
there are people who see it as part of their day to day work. But, I know from when the mathematicians
teach engineering students, who are big customers, that they’re very reluctant to include even
something like mat lab or mathematica, canned stuff.
Even that is a challenge because of the training that people get in pure math. In applied math it’s a little
better.
>>: As a follow up I use to have to teach, because I’m in between design and development.
>> Steven Strogatz: Yes.
>>: So I use to have to teach math to designers at the Art Institute and it’s kind of like if you like
computers and you like math you become a programmer. If you like computers and you don’t like math
then you become a web designer.
[laughter]
[inaudible] it’s kind of the crucible but a lot of times they fail for, at least in America through high school
it seems to be this filter that we’re going to force it to you and if you’re of this particular mind set –
>> Steven Strogatz: Force it math?
>>: Yes, force these concepts without telling you the story, without teaching you the mystery about
anything –
>> Steven Strogatz: Yeah.
>>: All the stuff even through calculus, if you make that cut you can learn the really cool stuff like
transferring numbers up, but if you don’t make the cut you’re going to think you have to become a
designer, right. So kind of normally have to do it is here’s what [indiscernible] this is what it looks like,
right, as a designer. Here’s the scripts, you start visualizing this. There’s the animation loops and most
of the time some of these kids, I mean, not that they literally cry but you just blow their brain because
they have been taught by high school that they were not good at math and they had computational
dispositions –
>> Steven Strogatz: Right.
>>: They just felt that they weren’t good enough.
>> Steven Strogatz: Yeah, this is a really important point for the whole educational system that we need
to be doing more of that. It’s not only, I guess I would amplify what you’re saying. That students are
sometimes learning not just their not good at math but how boring math is. That’s what really kills me.
I see my poor daughter who’s 12 learning something now called the Order of Operations, which is what
multiplying comes before adding, etcetera. Okay, we agree that we need a convention and there’s logic
to the way we do it. That’s all fine I don’t have any problem with the order of operations.
But when you look at her homework which might be on the order of 50 problems involving very long
strings of pluses and exponentiations and so on that might have, you know, 10 or 12 terms and she’s got
to do 50 of them. They don’t have parentheses in them. You know, we would never write that.
There’s no meaningful place that this would ever occur. It makes me mad because I could see how she’s
suffering through it and she thinks this is math. I tell her that’s not math. They’re not teaching you
math. They’re, and some moron who doesn’t understand math –
[laughter]
Is making this, are you taking that now, do you have Order of Pindos and stuff? This young person is
raising –
>>: I’m in Algebra 1; I’m 12 years old –
>> Steven Strogatz: Yes.
>>: Just like your daughter –
>> Steven Strogatz: Yes.
>>: Do you think that things like this applying to kids like me and my friend here whose also the same
math and age. Do you thing that would also apply to us if they could relate that to real problems in
algebra in things like how you turn the circle into a square they could do things like that. Do you think
that would change our opinion of that?
>> Steven Strogatz: I want to ask you, ha-ha. Yes, I think it might help. Because I’ve shown some of
these to my kids and they seem to like it. By the way my kids are not particularly mathematical. They
like looking at Vyhearts videos on You Tube. Some of you might know her stuff. So you ever, do you
know her?
No, okay, but they, yeah they’re more arty than mathy, my wife is very arty. I feel like these are
beautiful ideas that yes young people could enjoy and should see.
So, like another example would be you can do the Pythagorean Theorem by making pictures of triangles
and you put squares made out of crackers on the side. You can count the crackers and then you can eat
the crackers when you’re done.
It’s just fun. Or you can do math with other kinds of food. You could look at Fibonacci numbers by
getting pinecones and drawing spirals on them. So I think that makes the point that first math is fun, it’s
related to art, and it’s in the real world.
I like doing all that. I think kids like it. But, what do you think? Do you have an answer in mind when
you ask the question or did you just mean it as a question?
>>: I was just wondering your opinion.
>> Steven Strogatz: Yeah, okay. Yes, sir in the back corner.
>>: I think that you’re [indiscernible] between art and science, or art and math gears to what he was
saying. It also goes to what you’re trying to do here. Which is there really is no dichotomy between art,
science, and math.
>> Steven Strogatz: U-huh.
>>: Most artist I know, especially younger ones are emerged in some area of science and technology –
>> Steven Strogatz: U-huh.
>>: In terms of say the melding point of specific metals in order to achieve a certain affect by using
electronics, writing some software, even say formulas for paint, for pigments. They have to think about
that they’re not of matter –
>> Steven Strogatz: U-huh.
>>: So they’re at that level of a web designer versus the coder –
>> Steven Strogatz: Yeah.
>>: They can only go so far because of that sense that they’ve been shut out of mathematics.
>> Steven Strogatz: U-huh.
>>: I mean that’s the way it seems to work to me.
>> Steven Strogatz: Huh, yeah I hope I didn’t make that dichotomy sound like something I either
support or really believe in. I mean in practice they do feel like worlds that, maybe you’re right. There
maybe a world I’m not seeing that’s a younger generation or something where these –
>>: [inaudible] it’s much more common among young [indiscernible] a piece of software –
>> Steven Strogatz: U-huh.
>>: Or use some high tech equipment in [indiscernible].
>> Steven Strogatz: Yeah.
>>: They have to understand how that works because they may not understand the math behind it –
>> Steven Strogatz: U-huh.
>>: That’s what I think is a limitation. It’s like being barefoot doctor in the old Chinese sense. You know
how to do an operation but you would never be able to explain why.
>> Steven Strogatz: Yeah, what I like about the, to me it feels like emotionally the practice of art and the
practice of math have a lot in common. As I say my wife is an artist and a lot of the artistic impulse and
also the feeling of struggling and being stuck, you have an idea you’re trying to get out. It’s not working
properly, and the frustration and then the exhilaration when sometimes you make a little progress.
This to me feels very like a shared experience that artists and mathematicians can, we can relate to each
other perhaps more easily than people in other, I don’t know, like so to speak real world. I don’t know
that artists and let’s say venture capitalists have that much in common as an artist and a mathematician.
I don’t know, I don’t now venture capital people. I shouldn’t pick on them.
It just feels to me like we’re both a little bit other worldly in art and math, at least for the pure
mathematicians. Okay, let’s take some more on that side of the room. Yes, you on the far end.
>>: Yes, so I just want to get your opinion on there’s an idea floating around in engineering education at
the university level now where they’ve noticed that a lot of students drop out after the first 2 years and
they figured out it’s because they get hit in the head with 2 years of math and physics immediately –
>> Steven Strogatz: U-huh.
>>: That’s not something that they’re use to. So there’s this thought that you start them doing some
design stuff, you know the fun stuff first and once they get that then they want to learn the math and
physics to figure out why they did it the way they did it. So I just wanted to get your opinion on do you
think that would work at a high school or middle school level for math? You know, just do reverse to
give them a reason to –
>> Steven Strogatz: U-huh.
>>: To want to learn it. You know –
>> Steven Strogatz: The way you’re describing it, it sounds like it could be a good idea in that it fits with
this educational philosophy that I touched on earlier. That I feel like we give answers before students
are ready to ask questions, too often.
So when you mention that we hit them with math and physics in the first 2 years and it’s not fun and it
causes them to drop out I think it’s because we’re giving them a lot of answers and techniques to
questions that they haven’t thought of, for the most part. So it could be that by having hands on design
experiences you might, a student might start to ask those questions on his or her own.
Then, so, yeah I mean in principle it sounds like it could work but I don’t’ know. It’s an experimental
question. I guess it has to be, you say people are trying it now or they’re considering trying it?
>>: [inaudible] I know the University of Illinois my alma martyr is looking at it because they realize that
something like 40 percent of our students that enter as freshman don’t graduate in engineering .
>> Steven Strogatz: Right –
>>: So –
>> Steven Strogatz: Part of it I think, you know, a different way to look at it is not that we need to
reverse the order we just need to straighten out how we’re teaching math and physics. That is they
could still come first but they just have to be done in a better way.
So that maybe a different solution but it’s probably worth trying this thing that you’re –
>>: I think it’s also –
>> Steven Strogatz: Yes.
>>: Part of the thought is not just that we’re teaching it wrong but that it’s actually used as a filter.
>> Steven Strogatz: Literally?
>>: People teach giant 300 person survey courses and sink or swim. It’s thought that the people who
swim will be the ones that deserve to be in the [indiscernible] –
>> Steven Strogatz: Yes.
>>: In the first place. Instead of thinking, you know, maybe with a little bit more effort, smaller class
sizes, better teaching, whatever we could get people, you know, into an engineering program who
otherwise would be filtered out by hitting this giant wall.
>> Steven Strogatz: Yeah. Wow, I hear you and maybe it’s true that it is deliberately used that way. I
would hate to think that but you maybe right. Partly why I hate it is because I was almost filtered out by
that filter myself. Not exactly that one I wasn’t an engineering student but as a freshman I took the
freshman wiz kid Linear Algebra class, where every good university has such a class.
It’s for the kids who took BC calculus, got a 5. They’re sitting there. What math are they going to take
when they hit freshman year? So they give them a very rigorous linear algebra course where you’re
supposed to learn how to prove things. Usually it doesn’t include many pictures, doesn’t include
software. It’s a very abstract the way it’s presented.
So I took that course and was getting wiped out by it. It made me think after it was over okay I don’t
have the right stuff to be a pure mathematician or any kind of mathematician. That might be correct
but, ha-ha, but I did love math and just through whatever reason kept taking it. The next year I had a
complex analysis course which I could suddenly understand again. That felt like calculus except with
complex numbers but I could do that.
When I think back on what that freshman year course was I think it was what you’re saying it was the
math equivalent. The Math Department doesn’t want to be too big. We don’t want too many majors
and we’re going to filter out the people who thought they were good in math in high school but they
don’t have the right stuff.
So I think I was identified as one of those people without the right stuff. I don’t think it’s really true
there are various types of right stuff. There’s a talent for pure math. There’s a talent for seeing
connections and then becoming an applied mathematician. Or, you know there are visual people, there
are algebraic people, and there’s analysis.
I mean there’s a lot of different ways to be good at math. There’s also computing, people who are
computational. So it burns me up to think that they’re deliberately filtering people out. I don’t really
imagine that. I just think it’s laziness that it’s more efficient to have 1 professor and have a bit lecture
and it saves money, you know.
But maybe it’s more malicious than that. Yes, sir.
>>: I was surprised that you didn’t complete by reading –
>> Steven Strogatz: We should stop after maybe 1 more question?
>>: I’m surprised that you didn’t complete the O.J. Simpson calculation.
>> Steven Strogatz: We didn’t complete it?
>>: Maybe you did in the column –
>> Steven Strogatz: What else do you want –
>>: [inaudible] either. Because the question was is this evidence prejudicial –
>> Steven Strogatz: Yes.
>>: And to answer that seems you would need to know for murdered women who are in a non-abusive
relationship what fraction of them was murdered by their partners?
>> Steven Strogatz: Oh.
>>: And if that is also added to that 11 then there really are prejudicial [inaudible] –
>> Steven Strogatz: Oh, hold on let’s see this is, no ones ever made this point before. So you say
murdered women who are in non-abusive relationships –
>>: Murdered.
>> Steven Strogatz: But they may also be murdered by their partners. That is the partner until that
point had no history of abuse but because of the kinds of passions that happen, or whatever, we don’t
have to make an explanation. There’s just a statistical point –
>>: Right.
>> Steven Strogatz: That often the husband did it, that we should know what that rate is to. Oh, good
point.
>>: If it’s the same then –
>> Steven Strogatz: If it’s 9 out of 10 that the husband always did it –
[laughter]
Abuser or not then what?
>>: Then the evidence is prejudicial –
>> Steven Strogatz: Because the battery would have no barring. It’s 9 out 10 either way, ha-ha, except
that would be worth knowing that 9 out of 10 the husband did it, ha-ha.
[laughter]
Which is probably what the police think anyway.
>>: [inaudible] they knew that he was her husband. So they had the information.
>> Steven Strogatz: But the question is, is it relevant that he was a batterer or not –
>>: Right.
>> Steven Strogatz: I mean if they, you’re saying, whereas your point would be that he’s the husband or
not?
>>: No.
>> Steven Strogatz: And it might, no.
>>: No, the point is it relevant that he’s the batterer because if battery doesn’t increase the probability
–
>> Steven Strogatz: Yes.
>>: Then it shouldn’t be admitted.
>> Steven Strogatz: Yes, you’re right. So that should be included. Yeah, it seems like the FBI should
have that data. That is of how many murders were with people with no prior record of that. You’re
right, that’s a very nice, and that number should be taken into consideration. I didn’t include it. It
wasn’t in any of the articles on this. It’s an interesting point, good.
Do we have time for 1 more or should we stop with that?
>>: [inaudible].
>> Steven Strogatz: Okay. I think I took 1 from you before so I’ll let that gentleman go.
>>: So going over what you were saying –
>> Steven Strogatz: Yes.
>>: You’ve written an awesome article about the O.J. Simpson trial. Lots of people read it, very, very
intrigued. They could see how math can improve their lives and just sort of society in general. How
does this, how do people that read that take that away and then themselves become people who can
analyze the world around them using the different principles that have been demonstrated in that
article? For example, if the jury themselves had those analytical capabilities –
>> Steven Strogatz: Ha-ha.
>>: You know it would be completely different from needing to bring in other people to try to sway one
way or the other that the whole court system in that case.
>> Steven Strogatz: Let’s see if I get the question. So you’re saying, so here I’m imagining my reader,
the reader has read this column which is a little taste of math. Its 1500 words and they’re now not
suddenly statistically savvy. They’re just the same reader they were except they read this column.
Yeah, now maybe they know a little bit.
Now I do have footnotes that say if you want to learn more about either the legal system or conditional
probability here are different references. Maybe if some small fraction of them are interested enough
to go do that, but even if they did then you’re saying that, so what? So –
>>: Can I clarify?
>> Steven Strogatz: Yes, please.
>>: So where opportunities that we can do as a society to make all of these concepts in general more
accessible this is just the beginning but what do you think the next steps are in general to make these
concepts more accessible to –
>> Steven Strogatz: Yeah, what are the next steps for the society to make these concepts more
accessible?
>>: We should all buy his book.
>> Steven Strogatz: Well, I didn’t want to say that.
[laughter]
I don’t think that would help so much, ha-ha. I mean what I guess I’m hoping with the book that’s a
question I have maybe a better answer is that people will be more open to teaching themselves more
and getting more sophisticated across the board about quantitative reasoning or math in general. Partly
it’s the informed citizen re-argument to be able to think about the issues that face us. Partially it’s just
the pure hedonism argument that your life is richer and better the more things you know and
understand whether it’s music, or art, or math, or anything else.
But in some system, at the societal level what is there to do? I don’t know when do you, people are out
of school you could hope that the media, I’m not sure what to say. I don’t really; I’m kind of just
foundering with your question.
I guess I can only imagine that people will have to take it on themselves. First they have to get curious,
then they have to find the resources to learn which there’s a lot of good stuff on the web and there are
a lot of books being written and people that they could talk to.
I think the first step has to be the spark of curiosity. So if I can spark a little curiosity I hope that people
can help themselves. I haven’t really thought about your question. It’s really important.
Okay, thanks a lot everybody.
[applause]