Interview with James D. Stein | Sound Authors Radio

December 11, 2008

Dr. Kent: Welcome back to Sound Authors. We’ve all been glued to the TV set watching Michael Phelps and all the rest and it makes us think about numbers. He won by one hundredth of a second; I don’t even know how fast that is. With the physics and all of that, of swimming, of volleyball, we’re all thinking about how mass explains the world. So my next guest on the show hopefully can give us some enlightenment about that. His name is James D. Stein and he’s the author of How Math Explains the World: A Guide to the Power of Numbers from Car Repair to Modern Physics. Welcome to the show.

James D. Stein: Thank you very much Dr. Kent, thanks for inviting me on this show. Incidentally, in the time that Michael Phelps, the one one hundredths of a second, a radio program can travel from Chicago to Los Angeles at that.

Dr. Kent: Can you give us some enlightenment about how they could possibly get one hundredth of a second faster?

James D. Stein: Its always amazed me that there are certain activities which it seems like the winners win by very small amounts and of course what they do is in the old days when they had mechanical stop watches I can remember that with the mechanical stopwatches you saw hands go around and they stopped time to within about 1/5 or 1/10 of a second. But nowadays the timing is electronic and actually what NBC did was they showed you the underwater view and at the moment that Phelps’ finger touched the end wall, it registered on the sensor system and the other swimmer who came next, I think he was ###, touched a very small amount later, but you could actually see it because its interesting that your eye can actually pick up the difference of 1/100 of a second. Of course because their all within the same second, the same machine, it was easy to see that Phelps touched first and it registered on the machine.

Dr. Kent: So do you watch the Olympics and find yourself calculating through mathematical situations? Do you see the math in the Olympics?

James D. Stein: I certainly see it but I must admit where I find that it’s most interesting and where it’s actually discussed with some extent in my book is the way that the scoring in events like gymnastics is so difficult. The same happens virtually in any sport that is subject to scoring by human beings rather than the electronic scoring of races. It turns out that the problem of deciding who won the gymnastic event is very similar to the problem of deciding who wins an election and one of the great results of mathematics in the 20th century is something known as Harold’s Impossibility Theorem in which he showed that there was no perfect way of implementing a democracy and that’s very similar with the problem of deciding who won an Olympic gymnastics performance.

If you take a look at a contested election in which you have three people, it’s very difficult to decide who should be the winner in case one person doesn’t win a clear majority of the votes. One of the ways this happens and one of the ways that we decided was the person who gets the most first place votes but there are lots of people lots of areas where the elections are decided by taking the top two contenders and having them run off. And you can get different results depending upon which way you decide the election.

I happened to see for the Olympic high beam, what they did was they had a tie breaking procedure between the Chinese girl who ended up winning and Nastia Luiken who ended up finishing second and they actually had the same number of votes initially. They both had exactly the same score, but there was a very complicated tie breaking procedure, which ended up with the Chinese girl winning it. Had they adopted a different equally sensible tie breaking procedure, Luiken would have won.

Dr. Kent: So there is a lot of subjectivity every day of our lives.

James D. Stein: Yes, it occurs with some frequency. What mathematics does, mathematics is perfect with regard to the things that it discusses, the computation it makes et cetera, but when it comes to solving problems that actually exist in the real world math turns out practically like any other endeavor and it has its limitations. That was my motivation in writing the book. There are three very important results which show the limitations of what we can know about the universe and these results were discovered in the late 20th century. One of them which I just talked about was the impossibility theorem of Kenneth Arrow which showed that you can’t come up with a perfect method for implementing a democracy, a perfect method for electing people when you have more than two candidates. That’s actually impacted our lives in several different ways. It impacted us during the 2000 election for instance.

One of the things which also affects our lives is it turns out that we can’t measure everything precisely in the universe. We can’t know everything about the universe. This was the Heisenberg Uncertainty Principle and it turns out that has fantastic ramifications. If you look at much of the electronic equipment that has been invented over the past 75 years; the computers, the lasers, the magnetic implements and imagers, they all depend on quantum mechanics which in essence tells us that there are limitations to what we can know. And finally, mathematics itself is not impervious to its inability to know things.

One of the key results in mathematics in the 20th century was known as Riddell’s Incompleteness Theorem; it’s a theorem about the limitations of logic by the Austrian mathematician (Kirk Ridell) and he showed that there are mathematical truths which logic is incapable of proving.

Dr. Kent: The way you speak is so similar to the actor on television on the show Numbers, and I’m sure you get all the time students and others that say, “Oh, that’s just like on that show Numbers.” What’s your opinion of the math on that show?

James D. Stein: Well I’ve only seen a few shows of it. I think anything that brings a higher level of awareness of mathematics is good because quite frankly mathematics you can go through you could go through months of the newspaper and never see an article about mathematics. So for there to be a hit show about mathematics is I think wonderful. My only objection to the show and there’s a Cal Tech mathematician who acts as advisor so in some respects in fact in many respects the show is pretty accurate when it talks about mathematics. But I think in order to add to the drama of the show, the things that mathematics can do are probably in the real world not as impressive as the things that go on in the show.

I think there is a tendency on the part of the people who haven’t really studied mathematics to think that there’s sort of this mystical or magical aspect to mathematics. For instance, when you talk about the television show Numbers, there are lots of mystical disciplines which rely to some extent upon numbers and relationships between mathematical quantities. In fact the original numerical mystics were the partheganons.

The parthagerists, the guy who invented the theorem about the right triangle, he was very much into the sense that numbers explained everything. It turned out that he found out that there were limitations to what the arithmetic of the Greeks could do. I think that if people were more educated about mathematics they would be able to realize that this is a tremendously useful tool but its not a mystical or magical tool and it’s a tool that they can acquire a facility with beyond the arithmetic of balancing their checkbook and whatever else they might use arithmetic for on a daily basis.

Dr. Kent: I’m intrigued by a couple of things. One is the book itself; How Math Explains the World. It’s a fun topic now and I got to say Numbers is part of the reason that I’m so intrigued by it but I grew up loving math so there’s two issues there. One is maybe you could give us an example or two of how math explains the world in your book and the second part is how is math taught in schools today? When I was a kid I had wonderful math teachers and I spent a lot of time on it. Is it the same these days?

James D. Stein: First of all let me say that I’ve had several radio interviews. I’ve had a bunch but you are the first talk show host who has said “I loved math when I was growing up.” Most of them had bad experiences with it so Dr. Kent, you are unique. But one of the examples in the book, in fact the one that I lead off with is one of the dilemmas that we constantly face. Why doesn’t the garage have our car ready when they say they were going to? It turns out that it’s a very competent scheduling that a garage has to do; it’s a very complicated problem.

If you look at what mathematicians would call a problem; paying the monthly bills. When you finally decide to pay your monthly bills you have a stack of envelopes, you got your checkbook, you write out a check, you put it in the envelope, you put a stamp on it and you continue doing this and you can see the stack of envelopes dwindling and you can get a sense of when the job is going to be done. If you look at what a car garage has to do during repairs.

Let’s say that they have four different cars in the shop and they have a bunch of mechanics and each car needs different things to be done to it. So you start constructing a hypothetical schedule and you get close to the end and all of a sudden you realize all of those four cars in the shop need the hydraulic lift at exactly the same time. This is obviously a bad schedule; you’ve run into a bottle neck. So you tear up the schedule and start again. Even when you get the schedule completed you can look at the schedule and say if I’d only changed the spark plugs on the Chevy I could have been through a half an hour sooner. That’s what makes scheduling an extremely difficult problem.

Mathematics looks at all sorts of problems from the very simple ones to the very difficult ones and it assesses how difficult the problem is, whether or not they’re going to be able to solve it and what the best way to do it is. One of the things that has always fascinated me is that in the 20th century it turns out the difficulty of solving the mathematical problem turns out in many aspects to be an asset to us. That’s exactly how the password on your bank account and ATM machines is protected because it’s related to a mathematical problem factoring a very large number that’s a product of two prime numbers. These turn out to be immensely difficult problems. They put a computer network on factoring such a problem and it turned out that the computer network took nine months to do it.

That gives you a lot of faith that your bank account is secure. It’s nice to know that this is a really difficult problem and this is one of the things that mathematics tells us. In fact it was the reason that they adopted this method of password security on ATM machines and computer various accounts that we use passwords on. That takes care of your first question. As far as teaching mathematics today, I think that mathematics has always to some extent become a hard sell the older you get. Younger kids almost always find mathematics intriguing. Because it’s not just a fact that they’re given, its something they can explore and see for themselves. They can see that two plus four equals six and five times four equals twenty and that the facts in the multiplication table are true and they can perform more complicated tasks. But as they get older they do not stay so interested in it.

There are people of course who do get interested in it and math teachers today are every bit as dedicated as the ones who you had whom you enjoyed when you were younger. I was lucky that I had some great mathematics teachers too, starting with my father but I think part of the problem today is that there is so much in the way of competition for someone’s time, especially students. I remember when I was growing up what you did was you had school, then you played baseball and at the end of the day you went home and did your homework.

Now you have school, you have soccer practice, you got to make sure that you have your Facebook entries up to date; you have to IM and text all your friends et cetera. It’s a more complicated process growing up today and as a result, that time has to come from somewhere and sadly it tends to come from school because kids are reluctant to give up their enjoyable time.

Dr. Kent: Well, it’s been a real honor speaking you; I could speak with you all day about how math explains the world. That’s the title of James D. Stein’s book, A Guide to the Power of Numbers from Car Repair to Modern Physics. It’s put out by Smithsonian Books and that’s part of Harper Collins. It’s been a real honor chatting.

James D. Stein: Thank you very much Dr. Kent. I enjoyed it too.

Dr. Kent: My next guest on the show is a musician. Her name is Carol Ann and she plays with Red Molly. I’m going to play a song from Red Molly called The Mind of a Soldier, and then we’re going to chat with her about that. Come on back.

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