Double Reading Rainbow (All Across The Sky)
January Edition:
In Pursuit of the Traveling Salesman
&
The Best of All Possible Worlds:
Mathematics and Destiny
By Becky Ferreira
January should be one of the most depressing months of the year. But the resetting of the annual clock is traditionally both a reflective and a hopeful time, even when it’s tarnished by this bullcrud. People have an excuse to make big goals and start again with a clean slate.
My resolution this year is to review science and mathematics books monthly, pegged to a theme. I’m hoping I’ll at least get to March with it, which is, I think, a relatively long lifespan for a New Years resolution. In the spirit of January, the month that inspires people to grab life by the life-balls, the theme is optimization. The books are In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William Cook and The Best of All Possible Worlds: Mathematics and Destiny by Ivar Ekeland. Spreading the math love, 2012-style.
In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William Cook
The best way to write a science history is through the lens of a longstanding problem. Not only does it familiarize the reader with the fundamentals of a relevant logic dilemma, but we get to embark on a guided tour through past centuries to see brilliant minds grapple with it. Both books I’m reviewing this month do this, but In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is based on a much more modern conundrum: the traveling salesman problem. The TSP is worth your while to learn about – it’s an unsolved Clay Institute Prize Problem, which means whoever figures it out has a $1,000,000 check coming to them. Yeah, that’s right. Get out your calculators.
It also happens to be an easy problem for laypeople to understand: “in its general form, we are given a collection of cities and the distance to travel between each pair of them. The problem is to find the shortest route to visit each city and return to the starting point.” It’s a deceptively simple premise. As Cook explains in the book’s preface, were we to use the 22 cities named in Geoff Mack’s song, “I’ve Been Everywhere,” we would end up with 51,090,942,171,709,440,000 possible routes.
Modern supercomputers can calculate all these routes if given a few days, but raising the number of cities to 50, 100 or more and you’re staring infinity in the face. And that’s exactly what makes this problem such a “white whale of mathematics.” To quote Cook, “Is the general problem easy, hard or impossible? The short answer is that nobody knows. This is both the mystery and attraction of this famous challenge in computational mathematics. And much more than a struggling salesman is at stake. The TSP is the focal point of a larger debate on the nature of complexity and possible limits to human knowledge.”
Indeed, while the traveling salesman is a great visual metaphor for this problem, it can’t do an adequate job of communicating how revolutionary an algorithmic solution would be. The question isn’t what fields would be affected by solving it, but what fields wouldn’t? As Cook explains, unlocking it would be a huge leap for finding earthlike planets, mapping genomes, manufacturing computer chips, organizing mass transportation and countless other applications. This is an indicator of how much I’ve been playing the new Legend of Zelda game Skyward Sword, but if we were to unlock the TSP, it would be like Link unlocking the Triforce. As Cook describes the roots of its history, the outlier fields of math it now drives, and the scope of its applicability if conquered, its impossible not to feel gratified that something simple enough for a layperson to understand is all that stands between us and a dramatically more efficient society. Math FTW.
There is no point to a science history in which the author is not completely in love with the subject matter. That’s why so many haphazard science and math teachers cripple their students’ understanding of the joy that can come from understanding reality. Cook has an obvious passion for the TSP that shines through on every page, and makes this book a very engaging read. Not only that, but In Pursuit is surprisingly beautiful, featuring colour images of graphs, historical documents, maps and other oddities in the TSP’s history and future, liberally sprinkled throughout. A picture of Cook’s friend and fellow TSP enthusiast Vašek Chvátal on page 133 confirms what I’ve always suspected: the nerd stereotype for mathematicians is only half right. They’re also the most serious badasses out there. Looking at you, Ian Malcolm. And with that…
The Best of All Possible Worlds: Mathematics and Destiny by Ivar Ekeland
My discovery that this book existed was the most exciting thing that has ever happened to anyone anywhere. Ivar Ekeland is the chaos theorist that Ian Malcolm of Jurassic Park is based on. Ian Malcolm is my favorite fictional character, and Ekeland advised Michael Crichton on how to create him and Jeff Goldblum on how to play him. That in itself is a Becky dream, but there’s more. The title of the book is a partial quote from Leibniz; the full quote being, “we are living in the best of all possible worlds.” Voltaire was so infuriated by this quote that he wrote Candide, his masterpiece, as a giant middle finger to it. Voltaire is my favorite historical figure, and his beef with Leibniz has fascinated me since I was 13, because I started nerdefyin’ real young (I’d explain the portmanteau “nerdefiance” but I’m trying to be better about explanabrags). So finding this book is obviously the most exciting thing that has ever happened to anyone. Life finds a way.
Even with expectations as loaded as mine were, The Best of All Possible Worlds measured up. I think it might become my Bible? We’ll see. Anyway, the titular conundrum is as old as the written word: “the optimist believes this is the best of all possible worlds, and the pessimist fears this might be the case.” The problem itself goes back millennia, during which time it’s been explained away by religion and mythology (unsatisfactorily, despite Zeus’s valiant attempts). But from 1600-1800, scientists actively tried to solve the problem through math. Ekeland focuses on that story, casting the dilemma as an optimization problem.
Galileo’s breakthrough measuring time with pendulums and roulettes led to the idea that we might be living in a “perfect” cosmos, as it ushered in the discovery of the laws of motion. Ekeland combines mathematical conclusions, historical backdrops and a slew of beautiful quotes from Renaissance treatises to emphasize how revolutionary and beautiful these laws were (and are). Many scientists, Galileo included, felt they had happened upon the true language of God. Take that, tongues, Latin and Aramaic – turns out God be mad fluent in math.
Researchers made it their goal to decode this heavenly language to find an underlying meaning behind the universe. The 1687 publication of Newton’s Mathematical Principles of Natural Phenomenon popularized this idea, though Newton himself thought that science could only uncover how God worked, and not why. The French mathematician Pierre Louis Maupertius was much more hopeful. His life’s work was proving that religion and science were intended to join forces in proving this is the optimal, God-created universe. His contribution was the least action principle, which states that in all natural phenomena, there is a quantity called the “action” that is minimized. Ekeland goes into fascinating detail about the controversy this principle caused, and the groundwork it laid for mathematical optimization.
The last few chapters take a more sociological look at the “best of all possible worlds” problem. They were revelatory to me, for an obvious reason: Jurassic Park – the book more so than the movie – primed me. There’s a toned down version of Crichton’s Ian Malcolm here (or rather I should say that Malcolm’s a cockier, exaggerated version of Ekeland), as the book’s overarching philosophy is exposed. It’s an elegant, depressing but empowering conclusion. I won’t debase it in summary, but basically: if the universe humbles you significantly more than humanity does, you should read this book.
I love Ian Malcolm because he’s unapologetically committed to the truth. He takes the unpopular, pessimistic side of the Jurassic Park debate, but it’s not because he’s a pessimist himself. He’s advocating awareness, not despair. He believes scientific discovery can only be as good as the society that inherits it. It’s not inherently pessimistic to think that’s true: sometimes it’s just the math.
My resolution this year is to review science and mathematics books monthly, pegged to a theme. I’m hoping I’ll at least get to March with it, which is, I think, a relatively long lifespan for a New Years resolution. In the spirit of January, the month that inspires people to grab life by the life-balls, the theme is optimization. The books are In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William Cook and The Best of All Possible Worlds: Mathematics and Destiny by Ivar Ekeland. Spreading the math love, 2012-style.
In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation by William Cook
The best way to write a science history is through the lens of a longstanding problem. Not only does it familiarize the reader with the fundamentals of a relevant logic dilemma, but we get to embark on a guided tour through past centuries to see brilliant minds grapple with it. Both books I’m reviewing this month do this, but In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation is based on a much more modern conundrum: the traveling salesman problem. The TSP is worth your while to learn about – it’s an unsolved Clay Institute Prize Problem, which means whoever figures it out has a $1,000,000 check coming to them. Yeah, that’s right. Get out your calculators.
It also happens to be an easy problem for laypeople to understand: “in its general form, we are given a collection of cities and the distance to travel between each pair of them. The problem is to find the shortest route to visit each city and return to the starting point.” It’s a deceptively simple premise. As Cook explains in the book’s preface, were we to use the 22 cities named in Geoff Mack’s song, “I’ve Been Everywhere,” we would end up with 51,090,942,171,709,440,000 possible routes.
Modern supercomputers can calculate all these routes if given a few days, but raising the number of cities to 50, 100 or more and you’re staring infinity in the face. And that’s exactly what makes this problem such a “white whale of mathematics.” To quote Cook, “Is the general problem easy, hard or impossible? The short answer is that nobody knows. This is both the mystery and attraction of this famous challenge in computational mathematics. And much more than a struggling salesman is at stake. The TSP is the focal point of a larger debate on the nature of complexity and possible limits to human knowledge.”
Indeed, while the traveling salesman is a great visual metaphor for this problem, it can’t do an adequate job of communicating how revolutionary an algorithmic solution would be. The question isn’t what fields would be affected by solving it, but what fields wouldn’t? As Cook explains, unlocking it would be a huge leap for finding earthlike planets, mapping genomes, manufacturing computer chips, organizing mass transportation and countless other applications. This is an indicator of how much I’ve been playing the new Legend of Zelda game Skyward Sword, but if we were to unlock the TSP, it would be like Link unlocking the Triforce. As Cook describes the roots of its history, the outlier fields of math it now drives, and the scope of its applicability if conquered, its impossible not to feel gratified that something simple enough for a layperson to understand is all that stands between us and a dramatically more efficient society. Math FTW.
There is no point to a science history in which the author is not completely in love with the subject matter. That’s why so many haphazard science and math teachers cripple their students’ understanding of the joy that can come from understanding reality. Cook has an obvious passion for the TSP that shines through on every page, and makes this book a very engaging read. Not only that, but In Pursuit is surprisingly beautiful, featuring colour images of graphs, historical documents, maps and other oddities in the TSP’s history and future, liberally sprinkled throughout. A picture of Cook’s friend and fellow TSP enthusiast Vašek Chvátal on page 133 confirms what I’ve always suspected: the nerd stereotype for mathematicians is only half right. They’re also the most serious badasses out there. Looking at you, Ian Malcolm. And with that…
The Best of All Possible Worlds: Mathematics and Destiny by Ivar Ekeland
My discovery that this book existed was the most exciting thing that has ever happened to anyone anywhere. Ivar Ekeland is the chaos theorist that Ian Malcolm of Jurassic Park is based on. Ian Malcolm is my favorite fictional character, and Ekeland advised Michael Crichton on how to create him and Jeff Goldblum on how to play him. That in itself is a Becky dream, but there’s more. The title of the book is a partial quote from Leibniz; the full quote being, “we are living in the best of all possible worlds.” Voltaire was so infuriated by this quote that he wrote Candide, his masterpiece, as a giant middle finger to it. Voltaire is my favorite historical figure, and his beef with Leibniz has fascinated me since I was 13, because I started nerdefyin’ real young (I’d explain the portmanteau “nerdefiance” but I’m trying to be better about explanabrags). So finding this book is obviously the most exciting thing that has ever happened to anyone. Life finds a way.
Even with expectations as loaded as mine were, The Best of All Possible Worlds measured up. I think it might become my Bible? We’ll see. Anyway, the titular conundrum is as old as the written word: “the optimist believes this is the best of all possible worlds, and the pessimist fears this might be the case.” The problem itself goes back millennia, during which time it’s been explained away by religion and mythology (unsatisfactorily, despite Zeus’s valiant attempts). But from 1600-1800, scientists actively tried to solve the problem through math. Ekeland focuses on that story, casting the dilemma as an optimization problem.
Galileo’s breakthrough measuring time with pendulums and roulettes led to the idea that we might be living in a “perfect” cosmos, as it ushered in the discovery of the laws of motion. Ekeland combines mathematical conclusions, historical backdrops and a slew of beautiful quotes from Renaissance treatises to emphasize how revolutionary and beautiful these laws were (and are). Many scientists, Galileo included, felt they had happened upon the true language of God. Take that, tongues, Latin and Aramaic – turns out God be mad fluent in math.
Researchers made it their goal to decode this heavenly language to find an underlying meaning behind the universe. The 1687 publication of Newton’s Mathematical Principles of Natural Phenomenon popularized this idea, though Newton himself thought that science could only uncover how God worked, and not why. The French mathematician Pierre Louis Maupertius was much more hopeful. His life’s work was proving that religion and science were intended to join forces in proving this is the optimal, God-created universe. His contribution was the least action principle, which states that in all natural phenomena, there is a quantity called the “action” that is minimized. Ekeland goes into fascinating detail about the controversy this principle caused, and the groundwork it laid for mathematical optimization.
The last few chapters take a more sociological look at the “best of all possible worlds” problem. They were revelatory to me, for an obvious reason: Jurassic Park – the book more so than the movie – primed me. There’s a toned down version of Crichton’s Ian Malcolm here (or rather I should say that Malcolm’s a cockier, exaggerated version of Ekeland), as the book’s overarching philosophy is exposed. It’s an elegant, depressing but empowering conclusion. I won’t debase it in summary, but basically: if the universe humbles you significantly more than humanity does, you should read this book.
I love Ian Malcolm because he’s unapologetically committed to the truth. He takes the unpopular, pessimistic side of the Jurassic Park debate, but it’s not because he’s a pessimist himself. He’s advocating awareness, not despair. He believes scientific discovery can only be as good as the society that inherits it. It’s not inherently pessimistic to think that’s true: sometimes it’s just the math.
