The compartmented mind

I'm always surprised to find scientists whose work I respect having religious beliefs. It seems, from an essay by Carl Zimmer in today's New York Times, that mathematical biologist Martin Nowak of Harvard University may be one such scientist believer. As Zimmer quotes Nowak,

Like mathematics, many theological statements do not need scientific confirmation. Once you have the proof of Fermat’s Last Theorem, it’s not like we have to wait for the scientists to tell us if it’s right.

Nowak has done lots of great work on the logic of social behavior and cooperation in biology, not only among humans, but among may other organisms. It's brilliant work, and I've written about this field in the past. If you think we humans are really special because of our ability to cooperate, think again; single-celled bacteria manage many of the same tricks (which I think really brings home the point that some social phenomena have much more to do with the logic of collective organization than with the "specialness" of individual human beings).

Still, I find Nowak's comment on theology quite striking, and really hard to understand. (And obviously, I don't know the complete context in which he said it.) Does he believe that principles of religious belief can be established with the same kind of mathematical certainty as Fermat's last theorem, or any other mathematical theorem? His argument seems to have a devious logic.

Mathematical certainty is of a different order from anything requiring empirical confirmation; I believe in Pythagoras' Theorem in plane geometry because of mathematical proof, not empirical facts (that it works in practice merely shows how well plane geometry fits our world of ordinary experience). Quite reasonably, therefore, Nowak argues that scientists don't go demanding empirical evidence for mathematical assertions, the truth of which has been established by logic (if one already accepts the beginning assumptions). But then comes the punchline -- so why should scientists demand evidence for religious assertations?

Well the problem, obviously, is that religious beliefs aren't established by any appeal to logic, but are taken on faith. They aren't like mathematics, and so the comparison is just irrelevant. It seems as if Nowak is implying that some theological statements can be proven by pure logic, but which ones? I'd love to see some examples.

All this brings to mind a fascinating novel I just read, A Certain Ambiguity, by Gaurav Suri and Hartosh Singh Bal (I have a short review of it forthcoming in New Scientist). In the novel, an Indian mathematician Vijay Sanhi gets arrested in New Jersey under archaic laws against "blasphemy," when he publically doubts the truths of Christianity. He must defend himself before a Judge who is himself a committed Christian. Sahni tries to argue to the judge that religious certainty never approaches the same level as mathematical certainty, and illustrates the nature of mathematical reasoning by showing how geometric truths (such as the Pythagorean theorem) can be established from a handful of "self evident" axioms and pure logic.

To this demonstration, the Judge quickly responds that the same is true in Christianity:

I start with the "simple fact" that everything in the Universe must be created by something; it cannot come into being out of nothing. ... ; hence, the first something must have been created by a being that was always there, a being that could create something from nothing, and a being that lived before time started. Humans have just given that being a name; we call Him God.

To which Sanhi replies:

The problem is I do not believe your underlying "simple fact" that everything in the universe must have been created by something... Everywhere I look, life is full of cycles.. Or I could equally well claim that the "first thing" always existed... You assumption that everything must have a cause of creation applies to the world of sense experience. In this realm I will agree with you that your "simple fact" of causality is self-evident. But you have extended the "simple fact" beyond the world of sense experience to something that is supposed to transcend it. You have applied an experiential notion beyond all possible experience, as well as beyond the limits for which there are any guarantees that our sensory perceptions are reliable. So, yes, Judge, I disbelieve your underlying simple fact, and hence I disbelieve your conclusion that God exists.

Curiously, the Zimmer article also quotes another well-known scientist believer, biologist Francis Collins, director of the National Human Genome Research Institute. But Collins and Nowak seem to disagree with one another. While Collins claims that "Selfless altruism presents a major challenge for the evolutionist," a point I've argued against in The Social Atom, and in this blog, and elsewhere, Nowak seems to think there's no big problem. “The current theory," he says, "can certainly explain a population where some people act extremely altruistically."

But so what. People disagree, and people are all over the board on this religion versus science argument, and what it comes down to, it seems to me, is a point made very well by Sam Harris in The End of Faith -- that those motivated by religion and faith seem to have marked off a special corner of life in which the ordinary laws of thinking and evidence just aren't supposed to apply. For those persuaded by religious faith, the world seems to fall into two disjoint parts -- one in which the search for evidence and application of reason is the only known method for gaining sure knowledge, and the other in which the need for evidence is wilfully suspended:

Tell a devout Christian that his wife is cheating on him, or that frozen yogurt can make a man invisible, and he is likely to require as much evidence as anyone else, and to be persuaded only to the extent that you give it. Tell him that the book he keeps by his bed was written by an invisible deity who will punish him with fire for eternity if he fails to accept its every incredible claim, and he seems to require no evidence whatsoever.

bin Loggin'

No real time to post today as I'm past deadline and trying to fathom and write about a long paper on the "hybrid analysis" of genetic regulatory networks. Don't worry - -I won't say another word on the topic.

But...for amusement, have a look at George Mason economist Bryan Caplan's grim reckoning of the political process and why we idiot citizens get what we deserve, as summarized in today's New York Times opinion piece of Nicolas Kristof. The gist:

This book, by Bryan Caplan, an economist at George Mason University, does a remarkably thorough job of insulting the American voter. The cover portrays the electorate as a flock of sheep.

“Democracies frequently adopt and maintain policies harmful for most people,” Professor Caplan notes. There are various explanations for this — the power of special interests, public ignorance of details, and so on. But Mr. Caplan argues that those accounts fall short.

“This book develops an alternative story of how democracy fails,” he writes. “The central idea is that voters are worse than ignorant; they are, in a word, irrational — and vote accordingly.”

I haven't yet read Caplan's book, The Myth of the Rational Voter: Why Democracies Choose Bad Policies, but I'm going to order a copy as he seems to explore fertile territory -- how our biological "thinking instincts" tend to lead us into bad decisions, whether because we weigh up risks incorrectly, or vote for people because they seem strong and "presidential". In their short review of the book, Publisher's Weekly says the book explores "how social science's 'misguided insistence that every model be a 'story without fools'" has led it to a very poor understanding of human systems. I can certainly agree with that.

Maybe nothing brings the point home more clearly, as Tim Grieve at Salon.com notes, than that 41 percent of Americans still think Saddam Hussein helped pull off 9/11, or that 11 percent actually think we've caught bin Laden (or "bin Loggin'", as a man in Pennsylvania apparently pronounced the name to Grieve).

Politicians and quantum "flip-flops"

One update (below)

As the campaign for the U.S. Presidential election gains momentum, we're once again subjected to the irritating spectacle of candidates responding to simple questions with paragraphs of vacuous waffle, and mouthing totally contradictory opinions to different groups. It's tempting, and maybe partially correct, to suspect they're all just slippery and mealy-mouthed weasels. But here's another idea: maybe the way they act has its origins in a deeper problem inherent in the mathematics of democracy and public opinion. There's good reason to believe that a candidate can appeal to more people by holding several contradictory views all at once.

The French philosopher, the Marquis de Condorcet, once proved a truly surprising theorem about public opinion. As individuals, people tend to be logically consistent in their opinions or preferences. If I prefer Obama over Clinton, and Clinton over Romney, then I'll also prefer Obama over Romney. If A outranks B, and B outranks C, then A should outrank C. Most of our thinking conforms to this basic rule of logic, at least most of the time.

But just because individual preferences follow such logic, this doesn't imply that groups do as well. Within a population of people, Condorcet proved, it is entirely possible for a majority to prefer A over B, a majority to prefer B over C, and a majority also to prefer C over A - making a cycle of collective preference, so that's its impossible to say which of A, B or C the people really prefer. (For example, take three voters who, respectively, rank three policy alternatives in the following orders: A > B > C, C > A > B, and B > C > A. It is easy to see that two out of three will prefer A over B, B over C, and yet also C over A.)

Nearly a decade ago, physicist David Meyer of the University of California at San Diego, and political scientist Thad Brown of the University of Missouri, suggested that this peculiar logic of popular opinion might well have something to do with the slippery views of politicians. Think of a candidate who just tries to mouth opinions that match up as closely as possible with the majority view. Quite possibly those opinions will necessarily involve some contradictions and apparently irrational cycles of preference. If so, then candidates and their advisors face a real choice between a strategy that respects ordinary logic, with the candidate promoting the kinds of consistent preferences than an individual might hold, and another in which the candidate abandons the need for consistency and uses more flexible and slippery tactics to appeal to as many voters as possible.

I'm guessing that almost all candidates follow the latter strategy, and those who don't tend to fall out of the polls very quickly. I recall being excited some years ago at the early Presidential candidacy of Governor of Arizona Bruce Babbit, who seemed to speak entirely sensibly about the importance of things like education, public health, investment in the nation's infrastructure, etc. He was so sensible and intelligent that his polling number quickly fell into the single digits and he dropped out of the race in about three weeks.

I suspect that experienced politicians may get drawn into adopting strategic contradictions more or less unconsciously, as they study polls and the results of focus groups and try to say things that put them in touch with the voters. "This," as Meyer and Brown put it, "is why it’s so hard for us as voters to discern exactly for what they stand."

The naive view of political strategy might hold that if most peoples' views fall into three sets, A, B, and C, which you might visualize in some "policy space," then the politician does best by "triangulating" -- setting out a position that falls at the center of those views. This way he or she appeals at least a little to everyone. But if cycles exist among the voting public, then a better bet may be to occupy not one point in policy space, but to spread out over a region and, roughly speaking, be as inconsistent as the voters.

Maybe there's a kind of perverse quantum logic to flip-flopping: just as quantum particles don't exist at any one point, but act as quantum waves and spread out through space, politicians defy the logic of individual thinking, and benefit by having fuzzy and ill-defined views.

Update

Just after I posted this, I remembered another interesting point relevant to this problem of Condorcet cycles in public opinion. The importance of the matter depends, of course, on the actual likelihood that public opinion really does show such cycles. Condorcet proved that it can. But in reality, does this happen very often?

Some physicists, Matteo Marsili and Giacomo Rafaelli, looked into this a few years ago. Their idea was to assume that individuals in a big population rank a series of alternatives, A, B, C, ... and so on in a random order. Each person has his or her own ranking, determined at random. Then they asked -- what is the chance, mathematically, that you'll find cycles in the group preferences when these people vote on the various alternatives in pairs? They vote on A versus B, A versus C, B versus C and so on. How likely is it that their voting shows a cycle? Their results showed that as the number of alternatives gets reasonable large, the chance of not having cycles dwindles rapidly to zero.

So if peoples' preferences were random, cycles are almost a guarantee. Of course, preferences aren't random, but treating them as such is at least crude approximation. And it suggests that the trouble presented by cycles, and the waffling strategies they make effective, may indeed be real.

On caveat, however -- Marsili and Rafaelli also showed that the tendency of people to conform with the views of others may play a powerful role in preventing Condorcet cycles and making the public's collective views more "rational" than they would otherwise be.

Fat spreads

Just about any kind of human behavior or characteristic can spread between people more or less mechanically, like a virus. This is hardly news anymore; it's been found in most crime, in decisions to buy cellphones or have children, in suicides, you name it. Now a new study reported in the New York Times demonstrates the case for obesity as well. Fat spreads. (A possible mechanism, the researchers suggest, is that people with obese friends revise their views on what is an acceptable body type.)

The NYT article touches on an extremely delicate topic. If obesity is a serious health problem, akin to a disease, then it looks as if it's a disease that spreads. So should people drop their fat friends? That's clearly a reprehensible take on the matter; one could easily reverse the perspective and say that thinness and health spreads too, so that befriending the fat is an act for public health. Not to mention that lots of recent psychology shows that we judge our well being in relative terms, comparing ourselves to those around us. So having fatter friends is probably good for our self esteem, and that surely feeds into health as well.

But I'm betting that more than a few people will draw some weird and anti-social conclusions from this...

Curiously, and it seems accidently, Dick Cavett also talks about obesity in an opinion piece, also in the New York Times. He makes a very good point that advertisers seem to have taken note of the rapidly increasing size of the American person, and put obese people all over television:

This disturbs me in ways I haven’t fully figured out, and in a few that I have. The obese man on the orange bench, the fat pharmacist in the drug store commercial and all of the other heavily larded folks being used to sell products distresses me. Mostly because the message in all this is that its O.K. to be fat.

Of course, advertising isn't the primary cause of U.S. obesity, which seems clearly linked to changes in food technology that have made high-calorie junk food readily available in a convenient format and extremely cheap. Oh yeah, and government subsidies for snack foods and soft drinks, manufactured out of corn syrup and soybean oil. I saw a study recently, don't recall where, showing that junk food in pure calorie-to-cost ratio is the cheapest food there is in the typical supermarket; so the incentive is there for anyone with limited funds to buy it.

A sensible government would take steps to change matter. Will our government be sensible? Don't hold your breath.

Comments anyone?

Idiot me...I just realized today, inspired by a helpful email from one reader (thanks Todd), that I've inadvertently been hindering people from commenting on my posts. I was not accepting comments from "anonymous" and, as I didn't realize, that meant only those with Blogger accounts were able to comment. I had assumed anyone could.

I've changed the setting now so anyone can comment...

Deliberation difficulties

Getting back to group polarization and the problems of deliberation. Following on from the original essay in my New York Times column, I posted again on the topic a few weeks ago, exploring recent experiments by Cass Sunstein of the University of Chicago and colleagues on the phenomenon of group polarization. They found -- and a wealth of other evidence also supports this view -- that when people are brought together into discussion, the group often ends up coming to a consensus that is more extreme than the original views of the people making it up. You can read this paper here; it's due out soon on the California Law Review.

In an earlier paper in the Yale Law Journal, Deliberative Trouble? Why Groups Go to Extremes, Sunstein mentions, for example, a classic study in the 1960s that found what is called "the risky shift." The experiments had graduate students in management respond to questions involving attitudes toward risk. After answering, the students then engaged in open deliberation on the questions. The experiment found that the students in their deliberations almost always moved toward expressing more aggressive attitudes towards taking risks, stronger than they had privately.

By the way, if you have some time, read the Sunstein paper which talks about a number of similar examples. It's both illuminating and a great deal of fun to read.

But there is obviously a lot more to what happens in deliberation that a tendency toward polarization. The Sunstein et al. experiments show that groups of people who are relatively similar in their views to begin with -- say, a group of Democrats, or a group of Republicans -- after deliberation, come to a greater consensus (as well as becoming more extreme and, one might say, convinced in the rightness of their views). But what if people aren't similar? What if Democrats and Republicans try to discuss the issues together?

In a comment to that post, John Savage wrote that...

I’m unsure why you cite the Sunstein study as a test of the hypothesis that “deliberation days” would help to break down differences, when the experiment actually involved intentionally segregating liberals and conservatives, with the unremarkable result that both groups became more extreme.

At the end, you come to an optimistic conclusion from a centrist point of view: that somehow bringing liberals and conservatives together in a common forum would quickly break down their differences. As a political blogger, I just find this intuitively wrong.... two groups of “extremists” on opposite sides would probably not moderate each other’s views by talking to each other, no matter how many “links” you tried to provide between them.

Indeed, I didn't mean to imply that the Sunstein et al. study supports the idea that deliberation days would break down differences. What it offers is more of a cautionary lesson -- that if you're going to have deliberation days, you'd better try to get lots of diversity in your groups, because if you don't, you may well make the polarization even bigger. Logically speaking, the study doesn't say *anything* about what you're likely to see in groups where you *do* have lots of diversity and polarization. It just doesn't address that situation at all.

Since then I've been wondering about this. Cass in an email offered some views on what tends to happen in groups that do have great diversity, say both staunch Republicans and Democrats. As we all know from wandering in the poltical regions of the blogosphere, you tend to find persisting if not heightened polarization. Cass suggests that this tends to be the outcome whenever people clearly recognize and identify themselves with some group, such as a political party. The "identity differences" make it difficult for either group really to listen and take the points of the other side seriously.

I've come across some other fascinating work that also touches on this point. For example, in a nice paper entitled Modeling Cultural Cognition, Dan M. Kahan, Donald Braman, and James Grimmelmann (of Yale, George Washington and New York Law Schools respectively) argue that people who strongly hold different opinions -- on an issue such as gun control, for example -- often do so largely for powerful cultural reasons that make them relatively impervious to persuasion. As they put it, "culture is prior to facts in individual cognition."

The idea is that for a number of fairly basic psychological mechanisms, people tend to hold the same beliefs as most people in their own cultural group (Republicans, economists, academic physicists, etc.). And these views do not easily get swayed in the light of new evidence. Rather, "the beliefs so formed operate as an evidentiary filter, inducing individuals to dismiss any contrary evidence as unreliable, particularly when that evidence is proffered by individuals of an opposing cultural affiliation."

Now I think we can all relate to that observation. I can present all the new climate studies I want, published in Nature, Science, wherever, to my determined climate-skeptic friends, and even if they listen politely (rolling their eyes occasionally), I know they just don't accept it. It doesn't sink in as new, legitimate information. And from my side, no new "study" on climate change written up by anyone from the American Enterprise Institute is likely to change my mind (see, I couldn't even help but put quotes around the word "study"!).

A more important question, of course, is how it might be possible to design strategies to get past these entrenched cultural differences that make it virtually impossible for people to come to agreement, even in the context of full information. You need to devise strategies for deliberation so that people can take on new information without having their cultural certainty threatened (at least not too rapidly). Seems like a tall order.

But I did hear recently of some researchers in Belgium, coming out of ecology, I think, who were devising just this sort of strategy, and using it, apparently effectively, in practice, bringing together business people with environmental activists to work together on land use issues, for example. I'll post on this soon if I can find out more about it. What I remember of the idea is that they bring the polarized parties together and first have them discuss all those things on which they AGREE, which usually are quite a lot. They establish common ground, and at least a little bit of trust, and then gradually take small steps away from that.

Irritating details

The advantage of science over ideology is that science (when it's done well) aims to learn and accept the facts, however uncomfortable they may be. You may want the universe to be infinite, or finite, finite with sharp edges or finite but unbounded (like the surface of a sphere), or something else entirely different, but ultimately your desires won't change anything. Really good scientists have the ability to question their own preconceptions, and adjust their beliefs in the light of new facts. As Nietzsche once said, it's not so hard to have the courage of one's convictions; much more difficult is to have the courage to question one's own convictions.

I noticed today that the NYT's David Brooks cited a recent paper from MIT economists Xavier Gabaix and Augustin Landier on the matter of CEO pay in the U.S. However much I find Brooks' views frequently irritating, and while I strongly suspect he cites this work because it supports his natural affinity for hard-boiled capitalism, this particular citation does seems wholly appropriate -- for Gabaix's work, at least what I know of it, is based strongly on careful science.

What the paper claims is that the six-fold rise in CEO pay over the past two decades cannot easily be attributed to a culture of runaway greed or any other insidious evolution of corporate management. Rather, it seems that relatively straightforward economic factors -- essentially the competition between firms for good decision makers -- may well explain the rise. Over the same two decades, the authors point out, the size (capitalization) of the largest U.S. firms has also gone up by a factor of six. CEO's make so much more now, the argument goes, not because of stock options, or managerial "skimming" of corporate profits, but because their actions influence enormously larger sums of money -- and small but real differences in their abilities count for a lot.

This is very much traditional "neoclassical" economics, but their argument, in more detail, seems strongly plausible. They assume that firms compete for CEO talent, and that talent naturally becomes increasingly important in larger firms with more assets at stake. Mathematically, this leads to the prediction that larger firms should have more highly paid executives, which is empirically true. (CEO pay rises in a regular way as firm size (capitalization, earnings, number of employees) raised to the 1/3rd power.) It also predicts that CEO pay on average across the largest firms should rise in direct proportion to the average size of those firms -- not actually a startling conclusion, when you begin thinking this way.

But there's one other interesting thing in this work. Gabaix and Landier use their theory, and the data on compensation, to make an estimate on the distribution of talent among CEOs. What they find is that over the top CEOs, say the top 1,000, the variation in talent is almost zero. Taking the very best CEO and replacing him or her with the 1,000th best, would tend to decrease a firm's earnings by only 0.04% -- less than one part in 1,000. BUT -- because the largest firms are so large, and have so many assets, this tiny change can have major monetary consequences. So it makes sense, from a strictly economic point of view, for CEO number 1 to make a lot more than CEO number 1,000 even though their skills are essentially equal.

Of course, none of this says anything about the kinds of effects that gross economic inequality, stirred up by such enormous pay differences, may have on the larger community. That's another story. But what is clearly so nice about this work, at least in my opinion, is that it offers such a natural and non-conspiratorial explanation by making a direct appeal to real data. We could do with more of that.