Category Archives: Science

Mathematical Proof for Diversity

Last week, Lisa and I joined some friends for a lecture put on by the Santa Fe Institute. SFI is known for its quirkiness, and this was the first of their lectures I had attended, so I didn’t know quite what to expect. The speaker was Scott Page, who is at SFI but also at Michigan. He is a computational economist, using methods like agent-based modeling to study economics and how they impact societies.

Page spoke about diversity and how it plays a role in problem solving and prediction. However, he approached the topic from a mathematical perspective. He began with some anecdotes which “demonstrate” that diversity is good for problem solving, predicting, etc. He told of one story, in particular, from an old English fair in which people were trying to guess the weight of a steer. The average guess was withing 1 pound of the right answer! These kinds of observations are what has led to the formal study of diversity and the role it plays in groups.

The short answer is that diversity often helps. If all of the people in a group are “smart” relative to a problem (that is, they know something about the topic; they are not completely ignorant about it, like a non-mechanic trying to fix a car), then it is better to have a diverse group, including what Page called the “pinhead”, rather than a whole bunch of people who are all the very best, but are all similar. Invariably, in computer models, the diverse group always solves problems better than the “better” group. This is because they have more tools at their disposal, as the pinhead has some tools the genius does not have. By working together, they can solve a wider range of problems than if the group only had geniuses.

Related to this is the predictive quality, and there is actually a mathematical equation relating the error a crowd makes in predictions to the diversity of the crowd. If the diversity is greater, the average prediction of the crowd has a smaller error. This has been demonstrated by looking at expert predictions for, for example, sports (NFL, NBA) drafts, comparing each expert’s pick with the average guess. In almost all cases, each individual expert had more error in their predictions than did the average prediction.

I asked Page about cases where diversity hurts and he pointed out that irreversible processes, such as cooking, are cases were diversity hurts. If I throw chili peppers into the soup, it doesn’t matter what tools you have, you can’t undo what I did. If my peppers ruined the soup, it is ruined no matter how many people are helping. The military, he pointed out, is an interesting case: you want diversity in planning, to come up with the best plan, but you don’t in operations, as you want people to follow the plan already made up. They need to be more single-minded in operations.

Thus, the two adages: “Two heads are better than one” and “Too many cooks spoil the stew” are both right. It is only now, though, that math and science can begin to tell us under which conditions one or the other applies. This is fascinating stuff!

Radiation Effects in Solids

My first book is out! Ok, not exactly. But, I am a co-editor of the “hot new release” (seriously, that is what Amazon is calling it) Radiation Effects in Solids, edited by myself, Kurt Sickafus and Eugene Kotomin. I’m also co-author, with Art Voter, of one of the chapters on Accelerated Molecular Dynamics Methods.

This book grew out of a summer school that Kurt Sickafus held in 2005, I believe, in Erice, Italy. He brought together many experts on radiation effects in solids who gave lectures to the next generation of researchers in the field. The timing couldn’t have been better, as the United States, along with a number of other countries, is reexamining nuclear energy as a crucial component of the nation’s energy portfolio. Since the Carter administration, no new nuclear reactors have been built in the US and, correspondingly, the expertise in areas such as nuclear materials has diminished.

Battlestar Galactica

My wife, Lisa, had heard about Battlestar Galactica from some friends and was intrigued. So, she rented the first season or two from NetFlix and started getting into it. Eventually, she got me to watch too.

Now, normally, I’m not a SciFi fan. I tend to like fantasy better. Science people seem to come in two camps: those that like SciFi because of its basis on science and those that hate it because of the liberties and non-sensical science that are often included. I fall in the second camp. I don’t mind fantasy because the rules are just made up and don’t pretend to be based on anything real. But, SciFi has the pretext of being based on science so I have a problem with Star Trek when everything seems to be solved by a “tachyon field.”

BG is different. It is SciFi and some things are obviously pushing things (the jumping of the ships, the fact that it is so hard to tell Cylons apart from humans when they have to be based on different chemistry, etc). But, it is more of a political drama with the SciFi as a vehicle. And, I have to admit, it is really good. I’m completely captivated as well. We are eagerly awaiting the start of the second half of season three.

I highly recommend the series to anyone who just likes a good story.

Great Physicists

Over Thanksgiving vacation, I finished reading Great Physicists bt William H. Cropper. In this book, Cropper introduces us to 30 of the greatest physicists of all time, starting with Galileo and ending with Stephen Hawking. Even though many of these physicists made seminal contributions to multiple fields of physics, Cropper groups the scientists into nine sections, defined by sub-fields of physics. This presentation also lets him present the scientists in a rough chronological order that mirrors the development of physics. These sections include mechanics, statistical mechanics, quantum mechanics, and nuclear physics, among others.Each chapter introduces one scientist, describes their early history, goes into their contributions to physics, and ends with the tale of each scientist’s later years. Cropper’s description of the contributions of these scientists does not skimp on the math. While complex integrals are not presented, the seminal equations along with their meaning are described. Their importance for physics are also discussed.I found this book to be marvelously interesting. Cropper does a great job with each scientist, not only describing the importance of his or her work, but putting it in the context of the development of physics as well as the state of the world during that scientist’s life. He describes how these scientists interacted, including the feuds amongst them. He also goes into the unique challenges each scientist encountered in growing up, trying to do their work, and in their later years.

I learned a great deal in reading this book. First, I was a bit dismayed by how much of my physics I have lost since school. While in the middle of graduate school I may have been more familiar with the science presented in this book, now, as I don’t use most of it on a daily basis, I am not as crisp with most of it as I would like. For that alone, this book is a nice primer or refresher of the basics of physics, covering all of the key fields.

As interesting are the lives of these men and women. Most of them were very unique personalities and most also went through a great deal in their pursuit of science. Many were very dedicated, almost obsessed, people. Many had some kind of mental issue, often in the form of depression. I was particularly captivated by the lives of Gibbs and Boltzmann, two of the most interesting but more unknown of the figures presented in this book.

I was struck, in reading this book, by how little most of us know of these great figures who have transformed our lives more than probably any other set of people. Not only did the people presented here radically transform our view of the world, from the development of Newtonian physics and the view of the world as a sophisticated clock to quantum mechanics and its revelation of the world as indeterminate and “fuzzy”, but their work led to the incredible technological advances science has afforded us. In my view, these people deserve greater recognition by society. They should be our celebrities, our rock stars.

I highly recommend this book to anyone who is considering any kind of life in science, especially students in the midst of studying science. The amazing work of the people Cropper presents is an inspiration. The achievements of these physicists are also daunting as they seem so incredible, especially considering the state of science at the time they were made and the world conditions they were made in. The science that these people developed was amazing, and is difficult to understand even with the advantage of the further development and testing we now enjoy.

More treatments such as this book would be welcome for other fields. The format was great, with each chapter not overly long, but giving enough detail to give a basic understanding of each scientist. I would be interested in such an approach for historical figures, including say explorers of the US west or pirates, or mathematicians, etc.

European Tour Part 3: England

The third leg of my trip to Europe took me to England, specifically Cambridge and London. My colleague had done a postdoc in Cambridge and wanted to see it again, so he arranged for us to give a talk at the school. We spent some time wandering around the city. Unfortunately, most of the colleges were closed as it was the week students were returning. So, we didn’t get to see, for example, the statue of Newton in Trinity College.

I’m currently reading “Great Physicists” and it is amazing the scientific history that happened at Cambridge. Many of the great scientists of all time spent cosiderable portions of their careers at Cambridge. It was amazing to walk around the same streets that they had strolled around, even if we didn’t get to go in. Everywhere I turned there were old buildings that must have been there since the time of Newton. What little I could see of the colleges was spectacular: huge green yards, magnificent chapels, and incredible buildings. We went into King’s Chapel as it was open. The grandeur of the chapel was amazing. And even more amazing was the fact that there was more imagery associated with the English royalty than with Christianity: the roses, the lions and greyhounds, and the portices. I definitely have to return when I can see the colleges themselves.

Just to give some idea of the historic significance of Cambridge, Kurt and I went to a bar called, I believe, the Eagle’s Nest. It is famous because they had uncovered a bunch of writing on the ceiling written American pilots during WWII. However, it is also the place where Watson and Crickk had their “eureka” moment on the structure of DNA. Pretty damn cool.
After Cambridge, we went to London to meet with some collaborators at Imperial College and Loughborough University. So, we spent most of the rest of the week working. But, our host, Robin, did take us to down town London in the evening. We spent a night of touring the sites as well as hitting a few pubs.

This always annoys Robin, but I don’t find British beers as flavorful as their American counterparts. For example, American IPAs are much better, to me, than British bitters. Even though the Brits invented the IPA, it seems that the Americans perfected them, at least for my palette. I don’t find that British bitters are all that, well, bitter. They don’t have much hoppy flavor.

Anyways, we hit China town for a great dinner one night. And another evening, Robin treated us to BBQ, which was very good. And that was the end of the trip. It was pretty uneventful returning to the US. There was a small snafu with the planes. When we got to Gatwick, our flight had been cancelled. Fortunately, we were able to get on other (but separate) flights. In the end, that was fine as I some how got upgraded to business class. So no complaints.