science and society – Page 9 – Common Infirmities

Dawkins’ faulty taxonomy

Science enthusiast Richard Dawkins is always good for a laugh, even if the laughter sometimes curdles at his anti-Catholic and anti-Muslim bigotry, and his inclination to minimise the the significance of child rape when it serves the interests of the former. He has recently published on Twitter the comment

All the world’s Muslims have fewer Nobel Prizes than Trinity College, Cambridge. They did great things in the Middle Ages, though.

There are all kinds of comments one could make about this, and many have, but what I find most striking is the utter failure of logic in the area that is closest to his area of purported expertise, which is not religion or sociology, but taxonomy. To a statistician, this comparison seems risible. Not only are Muslim and Member of Trinity College not comparable categories (I hope Professor Dawkins won’t get the vapours when I mention that they are not even mutually exclusive), but even if they were, Dawkins seems to be suggesting that the difference in NPF (Nobel Prize Frequency) between the devotees of Muhammed and of the Cambridge Trinity are due to negative selection by Islam, whereas another observer might suspect that there is some form of positive selection by Trinity College.

To put it baldly, you don’t need a Nobel Prize to get a post at Trinity College, but it doesn’t hurt. For example the most recent Trinity College Nobel Prize went to Venkatraman Ramakrishnan, who had a nearly 30-year scientific career before joining Trinity College.

A more valid comparison would ask, why does Trinity College, Cambridge boast so many more nobel laureates (32) than the comparably sized Trinity College, Oxford. (2, by my count from this list). Is it the vitiating effect of Oxford’s high-church Anglicanism? Or is it that Dawkins cherry-picked one of the wealthiest, most exclusive academic institutions, one most concentrated on exactly the sorts of subjects that attract Nobel prizes? Why have Scandinavian authors received so many Nobel Prizes in Literature? Religion? Climate? Reindeer?

I leave the resolution of these questions to the skeptical reader. Those who are interested in a more amusing version of Dawkinsian taxonomy can have a look at Borges’s essay “John Wilkins’ Analytical Language“. Borges describes an imaginary ancient Chinese encyclopedia, Celestial Emporium of Benevolent Knowledge that divides up all animals into the following categories:

Continue reading “Dawkins’ faulty taxonomy”

Research impact and road construction

I’ve been interested in the turn of government funders of scientific research in several countries — in particular, US, UK, and Canada — to target research spending likely to have high economic benefit. I’ve commented here on Canadian developments, and satirised UK impact obsession here (though I actually think the UK bureaucracy has done a fairly good job at diverting the ill-informed government rhetorical pressure into less harmful directions). Lawrence Krauss, writing in Slate, has pulled together some of these recent developments with some interesting commentary.

One interesting analogy has recently occurred to me: Scientific research is a public good, like roads. I’m no expert on transportation policy, but my impression is that when transportation plans are laid, when they decide to invest the necessary capital in widening this highway, or paving that cowpath, the political decision-makers don’t devote a lot of energy to questioning whether it’s really productive for people to be travelling along this route, whether people going from A to B (and back) is actually going to provide economic benefits. The arguments usually stop at the evidence that people are travelling that route, that the current roads are congested, and so on. Experience has shown that efficient transportation infrastructure promotes economic growth and general public welfare, and government should provide people with the means to get where they want to go reasonably quickly and safely, without needing to micromanage exactly why everyone wants to go wherever it is they want to go.

Similarly, experience shows that thriving scientific research promotes economic growth, and public welfare, and we should invest in making it thrive. Where should we invest? We should look where the traffic is going, and not ask why it is going there.

This is not quite as straightforward as the road-building problem, because we do want to distinguish between high-quality research and low-quality research, but even a certain amount of boring, non-paradigm-breaking, grey-skies research can play an important part in keeping the scientific enterprise healthy. Making this distinction is the job of peer-review, and maybe it needs to be done differently, but I would contend that trying to slather on another layer of “impact” evaluation is not going to make the process or the research more productive.

Impact à la canadienne

I’ve mocked the sometimes risible implications of the British obsession with tying academic research one-for-one with “impact” on industry or society. It’s not absurd to want to ask the question, I would argue, but expecting to be able to get answers about impact on the fine grain that is needed for steering funding decisions leads, I suggest, is a fool’s errand. There is also a (not very) hidden political agenda behind impact: Research that elucidates the origin of the Himalayas or the inner workings of modern religious movements, let us say, has no impact unless the BBC makes a documentary about it. Research that helps one bank increase its market share over another bank by better confusing its customers is rewarded for its impact, because definable (and potentially grateful) people have made money from it.

Nonetheless, the British establishment is not so crass as to suppose that helping to make money is the only possible utility of research. The UK research councils are at pains to point to the multiple “pathways to impact”, through changing public understanding, government policy, health benefits, education. For some purposes, even something as useless as influencing the progress of science can be counted as impact, though it fail to swell the bank account of even the smallest party donor.

To see the full unfolding of impact’s crassness potential, we need to look to Canada. John MacDougal, director of Canada’s National Research Council (NRC), announced his agency’s new focus on impact by saying,

Scientific discovery is not valuable unless it has commercial value.

No hedging there about social impact, contributing to public understanding, government policy, etc. Science minister Gary Goodyear said that

We want business-driven, industry-relevant research and development.

This is not quite as outrageous as astronomer Phil Plait makes it seem, when he contends that “the Canadian government and the NRC have literally sold out science”. And he goes on to say that NRC “will only perform research that has ‘social or economic gain’.” An article quotes Goodyear saying

the government isn’t abandoning basic science, just shifting its focus to commercializing discoveries. “The day is past when a researcher could hit a home run simply by publishing a paper on some new discovery,” he said. “The home run is when somebody utilizes the knowledge that was discovered for social or economic gain.”

Continue reading “Impact à la canadienne”

More scary maths

I was just working through the sheet music for “As Time Goes By”. I don’t remember ever having heard the intro — it was left out when the song appeared in Casablanca, and seems never to have been performed since. It begins with the lines

This day and age we’re living in gives cause for apprehension,

With speed and new invention, and things like the third dimension.

Yet, we grow a trifle weary with Mister Einstein’s theory,

So we must get down to earth, at times relax, relieve the tension.

“Third dimension” — pretty scary! (Those interested in the influence of geometric ideas on early 20th century literature, in particular the work of Franz Kafka, could look at this paper. Though typically the anxiety about dimensions started at four.)

http://www.youtube.com/watch?v=8EsTZiXYJJY

I’ve commented earlier on suggestions that math education should be confined to the rudiments to spare children from math anxiety, and the use of math anxiety by unscrupulous politicians to distract attention from their policies.

Who needs math?

According to a study by sociologist Michael Handel, summarised here by Jordan Weissman, 75% of American workers never use any mathematics more complicated than fractions in their work. (It goes without saying that most partake of recreational calculus, at least on weekends…) Writing in the NY Times last year, Andrew Hacker argued that most schoolchildren are wasting their time learning mathematics: They’ll never understand it, and they won’t be any the worse off for it. As for scientists, the great entomologist E. O. Wilson has recently taken to the pages of the Wall Street Journal to argue that

exceptional mathematical fluency is required in only a few disciplines, such as particle physics, astrophysics and information theory.

For that matter, even Albert Einstein famously remarked to a schoolgirl correspondent

Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.

But that was after he’d mostly decamped from physics for sagecraft.

Wilson goes on to portray mathematical biologists as technicians, armed with useful tools and useless ideas. And if you need them, you just hire them. (It’s not like they have anything important to do with their time.) So what’s going on? Are mathematicians scamming the public, teaching algebra and other unnecessaries to justify their existence? I would suggest that there are several important issues that these wise men are ignoring or underplaying:

It may be true (as Hacker argues) that only a tiny techno-elite actually needs to know how a computer works, or how to compute the trajectory of a spacecraft, or how to program a Bayesian network. But when they’re 11 years old you don’t know who will have the interest or aptitude to join that elite. If you start sieving the children out early because they don’t seem like a likely candidate for that track — and let’s be honest, a lot of the tracking is going to be based on parental status and educational attainment — most of them will have no way to change tracks later on, because of the cumulative nature of mathematical understanding. Worth noting, in this context, is Handel’s observation (cited above) that skilled blue collar jobs are actually slightly more likely to require “advanced maths” (algebra and beyond) than skilled white collar jobs. So you can’t decide who needs the advanced maths based on the kinds of work they’re going into. Those without the education are simply more likely to be stuck at the lower rungs of whatever trade or profession they go into. (On the other hand, a larger fraction of white collar workers are in Handel’s “upper” (skilled) category, so an average blue collar worker probably needs less maths than an average white collar worker.)
Mathematics is a language. And what is discussed in that language is, as Hacker recognises, crucial to the fate of everyone in the world. Those who have not learned at least the rudiments of the language are excluded from the conversation. I am reminded of a friend who dismissed the value of learning to speak French, with the argument that “Everyone in France speaks English.” Now, France might have been a bad choice for his claim, but even if it were true, it puts you at a significant disadvantage to be surrounded by people who speak your language, while you can’t decipher their language to understand what it is they’re saying to each other.
Think about that Einstein quote: Everyone finds mathematics difficult when they’re pushing beyond their current knowledge. If we’re going to drop mathematics training when it becomes challenging, we might as well stop counting when we run out of fingers and toesies.
I would suggest that Wilson may be using more sophisticated mathematics in his work than he is aware. To paraphrase J M Keynes, practical biologists who believe their work to be quite exempt from any need for mathematics, are usually the slaves of some defunct mathematician. Modern biologists of bench and field are often quite attached to some mathematical and statistical machinery that happens to be some years old, and seemed impossibly abstruse when it first seeped in from the pure mathematics or theoretical statistics world. Many of the attempts to apply mathematical techniques in biology (or sociology or economics or whatever) will prove more clever than enlightening, but some will stick, and become part of the basic toolkit that the biologists who think they don’t need any sophisticated math do use. Wilson’s arrogant posture really reflects the fact that there are far more trained mathematicians who are intellectually flexible enough to try and figure out what the biologists are doing, and what the connections might be to their own field, than trained biologists willing to work in the other direction.

What’s the Matter with Economics?

One of the most politically important economics results of recent years has been the paper by Reinhart and Rogoff on the link between high sovereign debt and low GDP growth. This work is something I’d been following for a while, as R&R’s book was one that I’d admired greatly. Their work claimed to show a strong negative correlation between sovereign debt/GDP ratio and ensuing GDP growth, and was reported as saying that 90% debt/GDP ratio marks a cliff that an economy falls off, killing future growth. This was seized upon by proponents of austerity as proof that budget cuts can’t wait.

As reported here and here by Paul Krugman, and here and here by Matt Yglesias, it now turns out that the result isn’t just theoretically misguided, it’s bogus. Economists who struggled to reproduce the results finally isolated a whole raft of errors and dubious hidden assumptions that completely undermine the conclusion. Only the most blatantly ridiculous fault was an error in their Excel spreadsheet formula that caused them to exclude important sections of the data from their computation. You’d think that this couldn’t get any worse, but instead of apologising abjectly, R&R have tried to argue that none of this was really essential to their real point, whatever that was.

My main thoughts:

Do economists really do their analysis with Excel? I find this kind of shocking, like if I found out that some surgeons like to make their incisions with flint knives, or if airline pilots were calculating their flightpaths with slide rules. Once you accept that premise, it’s not surprising that they made a blunder like this. I’m not a snob about technology. Spreadsheets are great for doing payrolls, and for getting a look at tables of numbers, and doing some quick calculations. But they’re so opaque, they’re not appropriate to academic work, and they’re so inflexible that it’s inconceivable to me that someone who analyses data on a more or less regular basis would choose to use them. Continue reading “What’s the Matter with Economics?”

Are you demographic?

As a sometime demographer myself, I am fascinated by the prominence of “demographics” as an explanatory concept in the recent presidential election, now already slipping away into hazy memory. Recent political journalism would barely stand without this conceptual crutch, as here and here and here. A bit more nuance here. Some pushback from the NY Times here.

The crassest expression of this concept came in an article yesterday by (formerly?) respected conservative journalist Michael Barone, explaining why he was no longer confident that Mitt Romney would win the election by a large margin. Recall that several days before the election, despite the contrary evidence of what tens of thousands of voters were actually telling pollsters, he predicted 315 electoral votes for Romney, saying “Fundamentals usually prevail in American elections. That’s bad news for Barack Obama.” In retrospect, he says,

I was wrong because the outcome of the election was not determined, as I thought it would be, by fundamentals…. I think fundamentals were trumped by mechanics and, to a lesser extent, by demographics.

Continue reading “Are you demographic?”

The Silver standard

Who speaks for statistics?

Ace forensic psephologist Nate Silver has attracted quite a bit of attention lately, with his 4+-year-old blog devoted to his statistical model that is intended to provide a synoptic view of the entire range of public data to produce a single probabilistic prediction of the outcome. Now, there are some clear criticisms that could be made of his approach, and of his results — in particular, the obvious failure of his successive predictions to be martingales, as they would have to be if they were appropriately using all current information — but he has been remarkably clear and open about his procedures and principles, and his reasoning on matters large and small seems generally sound, if not necessarily compelling. It’s funny that his conclusions should arouse any controversy at all, given that they are hardly different (as Silver himself is quick to acknowledge) from the conclusions one would draw from a simplistic combination of poll results. His main contribution is in giving careful answers to the obvious critiques that could be proposed: What’s a reasonable estimate for the difference between state poll results and the actual election result? How correlated are polling errors? What’s the best way to average polls of varying qualities done over multiple days? And so on. In the end, the answer doesn’t differ much from what anyone with number sense would come up with in a few hours, but you don’t know that for sure until you do it. And Silver’s reputation derives from the sense and good care that he takes in posing these questions and resolving them.

(The failure of the martingale property is actually evidence of his honesty in following the model that he set up back in the spring. He clearly would have been capable of recognising the trends that other people can see in the predictions, and introducing an ad hoc correction. He didn’t do that.) Continue reading “The Silver standard”

Math anxiety turns political

In a recent interview, vice presidential candidate Paul Ryan was asked about the problem with his party’s proposed “budget” (if we may loosely use that word for a set of proposals that refrain from actually saying how much money will be raised, or how it will be spent), and suggesting that it would “take me too long to go through all the math”. He actually spent a couple of minutes avoiding wasting time by going through all the math. And in an interview the following day he further expatiated on his mathless mission of mercy: “I like Chris [Wallace, the interviewer]. I didn’t want to get into all of the math on this because everyone would start changing the channel.”

Sure, you may think you want to know how I’m going to be covering the pension and health care you think the government has promised you (“federal government legacy costs”, as his running mate might term them), but trust me, the answer involves MATH! MATH, I TELL YOU! Imagine Jack Nicholson at the end of A Few Good Men yelling, “You want the math? You can’t handle the math!” Paul Ryan is a selfless soul who has descended into the pit of reckoning, done battle for your sake with the math demons, and returned with a golden budget for all our sakes. Surely we cannot be so cruel (and so self-destructive) as to demand details of the horrors he encountered there. Maybe Obama has done okay protecting us from bin Laden and alQaeda, but only Paul Ryan is going to be able to save us from Euclid and alGebra. Continue reading “Math anxiety turns political”