Occasional reflections on Life, the World, and Mathematics

Archive for April, 2013

The Life of Julia: Another longitudinal fable

Picking up from my earlier discussion of the way cross-sectional data  get turned into (sometimes misleading) longitudinal stories, it’s been about a year since the Obama campaign unveiled The Life of Julia, a slide show that contrasted Obama’s and Romney’s policies with regard to their effects on women at different ages. Stated that way it would be pretty standard and uncontroversial, but in fact it turned into a flashpoint for the early part of the campaign. Why? Precisely because it was not a list of cross-sectional promises — What President Obama will do for children; What President Obama will do for seniors; etc. would be standard campaign web site headings — but was turned into a longitudinal story. These were not 12 different women, of different ages, who would putatively be helped by the president’s policies, but a single woman “Julia” who seems to be spending her whole life looking for government programs to scrounge from. Of course, it only seems this way because of the way this infographic interacts with our expectations of a biographical narrative, where we expect to be seeing the high points of her life, and every one of them involves government services. Creepy! It’s no wonder some critics were reminded of cradle-to-grave socialism.

Of course, the real story is cross-sectional. If Julia is 3 years old now, Obama is not really promising to provide a small business loan to her in the year 2040. And by the time she reaches retirement, she’ll probably be living on a Mars colony or hiding out from roving mutant bandits in subterranean bunkers after the nuclear climate catastrophe.

obama-julia-infographic julia full

Stephen Wolfram’s longitudinal fables

There’s lots of interesting plots on Stephen Wolfram’s analysis of Facebook data, but what jumps out to me is the way he feels compelled to turn his cross-sectional data — information about people’s interests, structure of friendship networks, relationship status, etc. as a function of age — into a longitudinal story. For example, he describes this plotrelationship-status-vs-age2

by saying “The rate of getting married starts going up in the early 20s[…] and decreases again in the late 30s, with about 70% of people by then being married.” Now, this is more or less a true statement, but it’s not really what is being illustrated here. (And it’s not just the weird anomaly, which he comments on but doesn’t try to explain, of the 10% or so of Facebook 13 year olds who describe themselves as married.) What we see is a snapshot in time — a temporal cross section, in the jargon — rather than a description of how the same people (a cohort, as demographers would put it) moves through life. To see how misleading this cross-sectional picture can be if you try to see it as a longitudinal story of individuals moving through life, think first about the right-hand side of the graph. It is broadly true, according to census data, that about 80% of this age group are married or widowed. But it is also true that 95% were once married. In fact, if they had had Facebook when they were 25 years old, their Stephen Wolfram would have found that most of them (about 75%) were already married by that age. (In fact, about 5% of the women and 3% of the men were already in a second marriage by age 25.)

So, the expansion of the “married” segment of the population as we go from left to right reflects in part the typical development of a human life, but it reflects as well the fact that we are moving back in time, to when people were simply more likely to marry. And the absence of a “divorced” category masks the fact that while the ranks of the married expand with age, individuals move in and out of that category as they progress through their lives.

Of course, the same caveat applies to the stories that Wolfram tells about his (quite fascinating) analyses of structure of friend networks by age, and of the topics that people of different ages refer to in Facebook posts. While it is surely true that the surge in discussion of school and university centred at age 18 reflects life-phase-determined variation in interests, the extreme drop in interest in salience of social media as a topic is likely to reflect a generational difference, and the steep increase in prominence of politics with age may be generational as well. (I wonder, too, whether the remarkably unchanging salience of “books” might reflect a balance between a tendency to become less involved with books with age, cancelling out a generational shift away from interest in books.)

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.)

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.

Third most popular

Being a fan of the Dvorak keyboard layout, I was intrigued to learn that there is another QWERTY competitor, called Colemak. On the official Colemak web site one learns that

Colemak is now the 3rd most popular keyboard layout for touch typing in English, after QWERTY and Dvorak.

That formulation could be effective in other contexts. For example,

Standing up is now the 3rd most popular posture for sleeping, after lying down and sitting.

Or a political version:

Congress is now the 3rd most respected branch of the US government, after the executive and the judiciary.

Not going anywhere

Is it a good thing to be “not going anywhere”? I thought about this when I read President Obama’s comment that “Planned Parenthood is not going anywhere”. As with many things in life, it depends on what the alternative is. It could mean “not going someplace good”. In Obama’s phrase, where it’s not going is presumably “away”, or into the dustbin of history. Or going downhill.

It’s another example of a self-negation, an expression that can mean two exact opposites. If Planned Parenthood is “going downhill”, we mean the future looks bleak. If it’s “all downhill from here for PP”, the future looks pretty good. The difference in metaphorical emphasis between these two is subtle. In “going downhill” we emphasise that up is good and down is bad, and don’t explicitly mention the relative difficulty of going up and down. In “all downhill from here” we think about the difficulty of going up relative to down, and ignore the question of whether it’s better to be up or down. The attention is focused on some sort of forward motion that presumably has been impeded by the uphill slog. So if PP isn’t going anywhere, it’s not going downhill. If it is going somewhere, it’s because it’s all downhill from here.

Unterwegs mit Mum

According to the NY Times, “The Guilt Trip” is a “mild-mannered dud” of a comedy, in which Seth Rogen and Barbra Streisand play son and mother on a road trip together for some not very interesting reason. But I’m amused by the German version of the title, above, which translates to “Travelling with Mum”. It has many of the classic qualities of German film titles that I catalogued in “What’s German for G.I. Joe?“: The modest wordplay of the original title has been stripped out, replaced by a straight three-word description of the plot. But then, you wouldn’t want the audience to fail to notice that the film is a foreign import, so the English “Mum” has to be in there. Except, the film American, so it really should have been “Mom”, but who knows the difference?

Of course, a really classic German film title would have played the description out longer, something like “A Totally Crazy Week in the Car Travelling Across America with Mum” (on the model of “The Unbelievable Trip in a Wacky Airplane” — “Airplane” in the original — since it helps to be sure the audience knows it’s a comedy).

Bad apples

I remember being mystified back when President Bush defended his administrations stewardship of the Iraqi penal system by saying that the torture enhanced interrogation torture (I guess it was officially, since people got prosecuted for it) at Abu Ghraib was the work of “a few bad apples”. I guess that phrase had been going around for a while, and now it’s certainly common. (For example, here is the assertion that “a few bad apples” are responsible for most complaints about doctors.)

But back in 2003 I was confused by this expression. Bush seemed to be using it to mean that the US occupation of Iraq, and the US military and antiterror policies more generally, were sound, and that the crimes were the isolated work of individuals with no broader implications. But why apples? Why not “a few bad people”? The reference is clearly to the phrase “one rotten apple spoils the barrel”. But that expression has exactly the opposite implication: Rottenness is not isolated. If you’ve found “a few bad apples”, you must expect that the rot is widespread. Now, there’s nothing compulsory about that metaphor — you may not think that one bad individual casts suspicion on the rest — but why are apples being gratuitously referred to when the desired implication is exactly the opposite? How did this adage get turned into its converse? Or is the referent actually something else?

Without a net

One linguistic phenomenon that fascinates me more than it probably should is when a word or phrase can have opposite meanings in different contexts. Like the English word cleave (e.g. Genesis 2:24 “Therefore shall a man leave his father and his mother, and shall cleave unto his wife”, as opposed to a meat cleaver.)

I recently watched Ken Burns’s controversial 15-hour documentary Jazz. One segment, focusing on Miles Davis’s turn to fusion and electronica, was titled “Tennis Without a Net”. This quotes the critic Gerald Early, who appears in the segment, but of course refers back to Robert Frost’s bon mot about free verse (“tennis with the net down”). The implication is that music is a game, whose spectators are judging above all the players’ adroitness in accomplishing inherently simple things under complicated artificial constraints. Free jazz has also been tagged with this undead witticism.

So playing “without a net” means making things too easy, too safe, since no one can say if you’ve gotten it wrong. But “performing without a net” can also mean taking exceptional risks, as in the title of the Grateful Dead’s 1990 album “Without a Net”. There the metaphor is the circus acrobat’s net, and the implication is that the band’s free improvisation is particularly risky, since they are performing live without the support of a predetermined musical structure.

And this reminds me again of Natalia Cecire’s fascinating attack on statistics as an “inherently puerile discipline”, because its highest priority is “commitment to the rules of the game”. (I should make clear, as I argued before, I disagree with Cecire’s opinion of statistics, but I find the framework she lays on it both creative and useful.) Are statisticians making their research too safe by performing with the net of mathematical methodology, or are humanists like Cecire setting themselves a too-easy task by playing with the net of rigorous quantitative analysis down?

The Long Room: An academic allegory

Richard Tames’s A Traveller’s History of Oxford describes the “Long Room” of New College, a range of first-floor latrines built over a huge cesspit. Robert Plot, first superintendent of the Ashmolean Museum rhapsodised in the late 17th century that it was

stupendous… so large and deep that it has never been emptied since the foundation of the College, which was above three hundred years since, nor is it ever likely to want it.

The book also notes that this historical appraisal was in fact erroneous, as the pit had in fact, according to College records, been emptied in 1485.

The author does not make clear whether this description is intended as an allegory of academic productivity.

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