Field of Science

John Nash's nighttime chalkboard scribblings

From physicist Peter Woit's blog comes a link to a PDF document containing a transcript of the bizarre scribblings that John Nash used to leave at night on the blackboards of the math department at Princeton when he was at the peak of his illness in the 70s. Often he used to haunt the hallways at night and by morning the chalkboards used to be covered with these bizarre writings. 

Reading them is like reading some inexplicable combination of Hunter S Thompson, Thomas Pynchon and Salman Rushdie. It is very tempting to read patterns into the creations of a mind that was as creative as brilliant as Nash's. However some of the words ring far more true than Nash's disturbed mind intended them to. Take a look at this.

On the ethics of that "chocolate sting" study

By now many people must have heard of the so-called "chocolate sting" carried out by scientist and journalist John Bohannon. In a nutshell, what Bohannon did was to carry out a fake study on a very small sample of people that purported to investigate the effects of a chocolate-laced diet on weight. The study was actually perfectly done except for the statistics which were nicely massaged to conform to what's called 'p-hacking', the selective cherry-picking of results to correspond to statistical significance.

Bohannon and his colleagues then published the "study". Perhaps to nobody's surprise, both journalists and popular magazines jumped on it and proclaimed a new era of chocolate-enabled weight loss. Bohannon has written an article about his sting on the website iO9 which is now all over the Internet. The message from the article is that the gullibility of both journalists and the lay public is well and alive when it comes to swallowing incredulous health-related results. The result was especially depressing because one would think that even uninformed people would be skeptical about the supposedly beneficial effects of chocolate on weight.

Personally when I read about the sting and people's reactions to it I was immediately reminded of the Sokal hoax. Granted that the Sokal hoax did not perform experiments on human beings, but it too relied on deception and a sting operation to reveal the dirty truth. In that case the truth pertained to the tendency of people who called themselves "postmodernists" to dress up nonsensical notions in pseudoscientific language and try to present them as serious theories. Sokal wrote a deliberately nonsensical article and sent it to 'Social Text', the leading postmodernist journal. To his surprise it was enthusiastically published and touted as a novel insight into science and human nature. The emperor had been disrobed.

Bohannon's hoax applies to a different field but it is essentially in the same spirit. The goal of the hoax is to show that the emperor of uncritical thinking and statistical ignorance has no clothes. And the one thing the hoax managed to demonstrate is that emperors of this kind are running all over the place, and in fact each one of us has a bit of them rooted in our own thinking.

The study has drawn mixed reactions. For instance Ben Goldacre, slayer of bad science and medical studies, has praised the sting and said that it "deserves a prize" while Seth Mnookin, another slayer of bad science and campaigner against anti-vaxxers, has condemned it and called it "reprehensible". The most common reason why people are condemning the study is because they see no value coming out of it and because they see it as unethical: Bohannon did not seek approval from anything like an institutional review board (IRB) or inform his subjects about the goals of the study and get their approval (although he did lay out the general outline).

I myself got into a lively debate about the study on Twitter with two longstanding members of the science blogging community - Aatish Bhatia who blogs at Wired and Bethany Brookshire who blogs under the name Scicurious. Aatish and Bethany's concerns about the study were the same as those of Mnookin and others: the authors did not get their subjects' consent and approval from an IRB, and the value of the study was marginal at best. The thinking was, there have been several exposes of bad science and journalism in the past few years, so what exactly does this ethically dubious work demonstrate?

Here are my responses to these objections: First of all I agree with Aatish and Bethany that strictly speaking the study is not ethical. But then so aren't hundreds of other studies, especially in areas like psychology where detailed disclosure of the study goals themselves might change people's psychology and thwart those goals. Even the Sokal hoax with its explicit deception of journal editors and thousands of readers was not strictly ethical, and yet it is now regarded as a landmark critique of pseudoscience. In some cases, as long as no harm is being explicitly done to human subjects, it is only by withholding all the details that one can do a truly blinded and clean study. Bohannon's project was as much a psychology project as a nutrition project. In fact strictly speaking even most medical trials are unethical in the sense that they are run some time after the purported drug has shown a beneficial effect relative to the controls. If complete consent to every detail was a required condition for scientific experiments involving human beings, then most research projects in psychology and medicine would be deemed 'unethical.'

My bigger point though is that a discussion of ethics cannot be divorced from consequences, and any assessment of the ethical nature of research has to be done relative to the potential benefits and costs of the research. Viewed through this lens, the Bohannon study acquires a more interesting tinge. The most important benefit of the project would be an inculcation of a sense of skepticism and caution in the laypeople, journalists and magazines which were fooled. Aatish and Bethany are skeptical that such a sense would be ingrained in the victims. At the very least I agree that one would have to do a follow-up study to find out whether people have indeed become more enlightened and cautious and whether a sizable fraction of those who were fooled are now aware of the hoax.

But personally I am more hopeful. While P T Barnum's observation that a sucker is born every minute does ring true, it is also true that people often remember to be circumspect only after they have been shamed or embarrassed into doing so. Sometimes it's only a jolt of reality that can awaken people to reality. Granted that the jolt may be exaggerated, simplistic or disingenuous - in that sense Bohannan's work is what I would call the Michael Moore style of research - but it can lead to results that may not be acquired by a gentler approach. It's not the best approach, should be used sparingly and can be easily seen as cynical, but I would be surprised if it does not work. I would be surprised if at least a few of the magazines which fell hook line and sinker for Bohannon's ruse didn't think twice next time before enthusiastically publishing such results. Even if a few of them turn more skeptical I think the study would have had considerable value.

Another reasonable objection raised was that the ploy might cause people to become too skeptical and lead to a mistrust of even legitimate science from next time onwards. This is a valid point, but my response to it is to ask the question: would we rather err on the side of safety or on the side of caution (ideally we would rather not err at all, but that's a different story)? Aatish's answer was that we should try to err on the side of minimizing harm. I agree with this, but in my view harm is of different kinds. Aatish was presumably talking about the harm done to people's psyche that might cause them to mistrust honest science and journalism, but I believe that the harm done from ignorance of the scientific method and statistics is even greater, that it can lead to an equal or greater erosion of trust in science and rationality. If I were indeed to pick between the sides of overt skepticism and overt gullibility, even with my reservations I would pick the side of overt skepticism.

Ultimately my feeling about this study is that it's the kind of bitter medicine that should be administered occasionally for the health of a rational society. Strictly speaking it's not ethical, but its ethics should be balanced against its consequences. Its liberal use would indeed lead to a jaundiced populace that trusts nothing, but using it once in a while might actually cause a statistically significant increase in that skepticism that we all sorely need. And that's a good thing.

John Nash's work makes as good a case as any for the value of curiosity-driven research

What's the mark of a true genius? A Nobel Prize based on work that someone did in their PhD thesis at age 22? The fact that their theories are used in a stunning variety of disciplines, from economics to biology to government welfare? Or that their college professor signs off on their graduate school recommendation letter with a single line - "This man is a genius"?

To me, none of these facts mark out John Forbes Nash as an authentic genius as the fact that the work for which he won the Nobel Prize was, intellectually speaking, not even regarded as the most important piece of work he did, not even by himself. His most important work was instead a highly counterintuitive theorem in topology which he attacked with startling creativity and fearlessness, two qualities that he was becoming known for before his illness cut his career short. 

In contrast, he himself called his famous equilibrium "trivial", a piece of research he did because of his interest in games and pure math. In fact he almost stopped working on game theory after transitioning from Princeton to MIT as an instructor, saving his time for "real" math such as number theory and topology. In showcasing this multifaceted intellect Nash joins a rarefied tradition of brilliance that features only a handful of stars including John von Neumann, Hans Bethe, Linus Pauling and Albert Einstein. And speaking of real geniuses, even the reigning mathematical genius of the twentieth century - von Neumann - immediately recognized Nash's mathematical contribution by exclaiming "Oh that's trivial you know; it's just a fixed point theorem". Now granted that it would take any other mathematician at least a few days to figure out what von Neumann could figure out in a second, but von Neumann's instant grasp of the problem demonstrates that Nash's math itself was not exactly on par with the solution of Fermat's last theorem.

For me, what stands out especially about the Nash equilibrium was that Nash solved it mainly as an interesting problem in mathematics and not as a problem with potential applications in economics. He was first and foremost a pure mathematician and any applications were to him of secondary importance. The relevance of equilibria in games for economics had been made clear by von Neumann and Oskar Morgenstern in their landmark work introducing game theory to the world. But they had only considered so-called "zero-sum" games where one person's win is another's loss. Nash significantly extended their work by making it applicable to the real world where losses and wins are usually distributed in a complex manner across multiple parties. He identified a set of conditions where party A has nothing to gain by varying their strategy as long as party B keeps theirs fixed and vice versa, and his real interest and genius in doing this was to apply a purely mathematical theorem called the fixed point theorem to the problem. His paper on the proof of this set of conditions was one of the shortest papers ever to win the Nobel Prize, and it was an absolutely first-rate example of using ideas from one field to fertilize discoveries in another unrelated field. 

And then Nash moved on to other things, mainly regarding his contribution as something that would fetch him a quick PhD at age 22 and allow him to work on more important problems like the Riemann hypothesis. Thus, his solution of the Nash equilibrium, as relevant as it was for economics, was not seen by him as an applied problem but simply as an interesting problem in mathematics.

As economics writer John Cassidy describes it, fifty years later the Nash equilibrium was everywhere, and its reach had far exceeded Nash's wildest imagination.
"These days, political scientists, evolutionary biologists, and even government regulators are obliged to grasp best-response equilibria and other aspects of game theory. Whenever a government agency is considering a new rule—a set of capital requirements for banks, say, or an environmental regulation—one of the first questions it needs to ask is whether obeying the rules leads to a Nash equilibrium. If it doesn’t, the new policy measure is likely to prove a failure, because those affected will seek a way around it.
John Nash, in writing his seminal 1951 article, “Non-Cooperative Games,” which was published in The Annals of Mathematics, surely didn’t predict any of this. He was then a brilliant young mathematician who saw some interesting theoretical problems in a new field and solved them. But one thing led to another, and it was he, rather than von Neumann, who ended up as an intellectual celebrity, the subject of a Hollywood movie. Life, as Nash discovered in tragic fashion, often involves the unexpected. Thanks to his work, though, we know it is possible to impose at least some order on the chaos."
The message of Nash's life is that it was pure curiosity-driven work in mathematics, not economics, that led to his great contribution to economics, biology and a host of other disciplines for which it was not originally designed. This is how curiosity-driven research works; you sustain bright people and give them the freedom to pick their own problems. And then you watch the solutions to those problems sprout wondrous branches in novel and unexpected terrain. That kind of research simply does not work if you ask people to produce results for the next quarter or papers for tenure.

Nash is certainly not the first one to have benefited from this freedom, but he may very well be among the dwindling few who would be able to work unfettered if the current disdain and lethargy for basic science continues. The John Nashes of the next twenty years may have acute constraints imposed on their creativity, and while this would undoubtedly curb their creativity, the real losers in this zero-sum game would be all of us. You don't need mathematics to prove this fact. It's something Nash would have noted with more than a touch of irony. R.I.P.

Placebos can be really complicated

A review of Freeman Dyson's "Dreams of Earth and Sky"

Freeman Dyson is one of the most brilliant and wide-ranging thinkers of his time; the rare example of a truly outstanding scientist who is also a truly eloquent writer. This volume gathers together book reviews that he has written for the New York Review of books since 2004. The essays cover a range of topics as diverse as Dyson's interests and knowledge - from biotech to philosophy to theoretical physics.

Book reviews in the New York Review of Books are more than just simple descriptive reviews: they are also opportunities for authors to hold forth on their own views of the world. Thus Dyson's reviews are all accompanied by substantial personal commentary.

Every review benefits from his own vast experience with research as well as his unique friendship with many of science's best known personalities like Richard Feynman, Hans Bethe, Robert Oppenheimer and Edward Teller. Thus for instance Dyson adds his own touching reminiscences of Feynman and Oppenheimer in reviewing Jim Ottaviani's "Feynman" and Ray Monk's biography of Oppenheimer. Also in a review of Daniel Kahneman's "Thinking Fast and Slow", he uses his own unique experience as a statistician doing bomber studies during World War 2 to display the frailties of human thinking and bureaucracy.

In other cases Dyson uses specific books to inform us of his own original views on topics like biotechnology or cosmology. For instance in a review of Brian Greene's "The Elegant Universe" he speculates whether it might be impossible to detect a graviton particle using existing technology. In the first review titled "Our Biotech Future" he predicts that the domestication of biotechnology will be as significant a feature of the 21st century as computer technology was of the 20th.

Dyson also reveals himself to be no shrinking violet when it comes to controversy, although he does so with thoughtful and unfailing courtesy. His views on global warming have become well known, and his criticism of the field is balanced and moderate. And in reviewing Margaret Wertheim's book on scientific cranks "Physics on the Fringe", he also asks us not to dismiss all such cranks since some of them may turn out to have groundbreaking ideas.

You don't need to agree with all of Dyson's views in order to find them stimulating and thought-provoking, since that's what science is supposed to be about in its best tradition (as Dyson himself has said, "I would rather be wrong than uninteresting"). Even for readers who may have read these reviews the volume provides a ready reference of Dyson's views in one place as well as a glimpse into interesting literature worth reading. For those who have never read them they provide a window into one of the most original, literate and sensitive minds of its time.

The difference between popular chemistry and popular physics

This is from Half Price Books in Redmond, WA which I visited over the weekend. In this world popular physics books are popular physics books. Meanwhile, popular chemistry books are just textbooks.

Of course, as I have noted earlier, the problem is not with Half Price Books or with any other bookstore where this will be a familiar scenario. It's really with the lack of popular chemistry literature compared to popular physics fare, much of which also happens to be repetitive and marginally different from the rest. The great challenge of chemistry is to make the essential but (often deceptively) mundane exciting and memorable.

In a nutshell, the belief is that physics and biology seem to deal with the biggest of big ideas - quantum reality, the origin of the universe, black holes, human evolution - that are largely divorced from everyday experience while chemistry deals with small ideas that are all around us. But the smallness or bigness of ideas has nothing to do with their inherent excitement; witness the glory and importance of the Krebs cycle for instance. In addition, the origin of life is chemistry's signature "big idea". Plus, a conglomeration of small ideas in chemistry - like the evolution of methods for the refinement of various metals or the revolution engineered by polymers - underlies the foundation of civilization itself.

All I can do is point to my list of top 10 favorite chemistry books. Fortunately the occasional chemical splash continues to provide rays of light.

Heisenberg and Dirac in the age of NIH funding

The men who engineered the quantum revolution had some hard tasks cut out in front of them. But as the brilliant Philip Anderson says in his sparkling collection of essays "More and Different", at least they did not have to deal with the exigencies of NIH/NSF funding crunches, tenure pressures, media sensationalism, instant approbation or reprobation from social media, and the dog-eat-dog culture of peer review that has come to plague the upper echelons of science. Tis was a simpler time, and here's what would have happened to poor Werner and his fellow physicists had they tried to practice their trade would be funny if it weren't painful.