The End of Average: Jagged Brain

The End of Average  talks about the “jaggedness principle,” which is the notion that what seem to be homogenous qualities, like intelligence or physical size, turn out to be quite heterogenous or  “jagged” when broken down into their parts. For instance, measuring one part of a person’s body provides no clue whatsoever to their other dimensions (which would explain why off-the-rack clothes never fit properly). We are all variable in every possible way, all the time.  Another classic example is intellectual performance:

[James] Cattell administered a battery of physical and mental tests to hundreds of incoming freshmen at Columbia University across several years, measuring things such as their reaction time to sound, their ability to name colors, their ability to judge when ten seconds passed, and the number of letters in a series they could recall. He was convinced he would discover strong correlations between these abilities—but, instead, he found the exact opposite. There was virtually no correlation at all. Mental abilities were decidedly jagged.

For a devout believer in ranking, there was worse to come. Cattell also measured the correlation between students’ grades in college courses and their performance on these mental tests and discovered very weak correlations between them. And not only that—even the correlations between students’ grades in different classes were low. In fact the only meaningful correlation Cattell found at all was between students’ grades in Latin classes and their grades in Greek classes.

—Todd Rose, The End of Average: How We Succeed in a World That Values Sameness

As it turns out, even standardized IQ tests reveal the variability in people’s talents, at least until it all gets boiled down into a single number. When IQ subtests are broken out, jaggedness rears its ugly head, and it turns out the everyone has a unique collection of strengths and weaknesses. Trying to characterize people’s abilities with a single score, such as IQ or GPA, gives us the wrong answer because their shining talents get obscured by their mediocrities. No one expects an artist to be good at math or an astronaut to be a talented singer (Chris Hadfield notwithstanding), but we somehow expect students to be good at everything and dock marks when they are not. Is that fair?

Todd Rose proposes a system of higher education where students pursue the competencies they desire for their chosen career, and receive certificates for each subject area they master. So, instead of a single degree and a single GPA, you get a portfolio of proven abilities tailored to your interests and ambitions. This must be music to the ears of every student who wondered why they had to learn algebra to become an English teacher. It might also take some of the guesswork out of hiring motivated employees. When students are simply following a required course of study, it’s hard to know what they are really jazzed about. An à la carte education makes a lot of sense, especially if it can be extended as required without signing up for a whole degree program. Rose points to MOOCs and the Khan Academy as examples of this new paradigm of education. The Internet makes self-paced, self-directed education viable for almost anyone in a wide variety of fields. This is a good time to chart your own course, and learn what you need to know.

The End of Average: Take All the Time You Need

When I was in public school, classmates would often remark on my good grades and said I must be way smarter than them. Instead of taking it as a compliment, these sorts of comments made me uncomfortable. I refused to believe that I was mentally superior, but always said that it just was a matter of paying attention and doing the homework. Later on when my IQ was measured and I read a bit about IQ testing, I had to admit that some people seem to have more brainpower than others. But now I am reading a book, The End of Average, that takes me right back to my conviction that most people are capable of anything they set their minds to. It seems that the key ingredient is time. Every brain takes its own time for each particular task, but they can all get there in the end.

[Benjamin] Bloom and his colleague randombly assigned students to two groups. All students were taught a subject they had not learned before, such as probability theory. The first group—the “fixed-pace group”—was taught the material in the traditional manner: in a classroom during fixed periods of instruction. The second group—the “self-paced” group—was taught the same material and given the same total amount of instruction time, but they were provided with a tutor who allowed them to move through the material at their own pace, sometimes going fast, sometimes slow, taking as much or as little time as they needed to learn each new concept.

When Bloom compared the performance of students in each group, the results were astounding. Students in the traditional classroom performed exactly like you would expect if you believed in the notion that faster equals smarter: by the end of the course, roughtly 20 percent achieved mastery of the material (which Bloom defined as scoring 85 percent or higher on a final exam), a similarly small percentage did very poorly, while the majority of students scored somewhere in the middle. In contrast, more than 90 percent of the self-paced students achieved mastery.

Bloom showed that when students were allowed a little flexibility in the pace of their learning, the vast majority of students ended up performing extremely well. Bloom’s data also revealed that students’ individual pace varied depending on exactly what they were learning. One student might breeze through material on fractions, for instance, but grind through material on decimals; another student might fly through decimals, but take extra time for fractions. There was no such thing as a “fast” learner or a “slow” learner. These two insights—that speed does not equal ability, and that there are no universally fast or slow learners—had actually been recognized several decades before Bloom’s pioneering study, and have been replicated many times since, using different students and different content, but always producing similar results. Equating learning speed with learning ability is irrefutably wrong.

Of course, the conclusion that logically follows from this is both obvious and terrible: by demanding that our students learn at one fixed pace, we are artifically impairing the ability of many to learn and succeed. What one person can learn, most people can learn if they are allowed to adjust their pacing. Yet the architecture of our education is simply not designed to accommodate such individuality, and it therefore fails to nurture the potential and talent of all its students.

—Todd Rose, The End of Average: How We Succeed in a World That Values Sameness

Reading this filled me with great sadness for my friends and all the other people who thought they were not smart and hated school and learning as a result. The fact is they simply did not fit the assembly-line model of standardized schooling, and indeed neither did I. I instinctively shied away from certain subjects, like English and Social Studies, where I knew I would be “slow,” and so I came away looking “smart,” when in fact I was only smart in subjects that my brain could take in during the time allotted. If I had taken those other classes, I likely would have resembled Lucy Ricardo in the chocolate factory, unable to keep up with the speeding conveyor belt of information. I was lucky to escape those GPA-destroying courses, but not everyone is. To think of the opportunities, and worse, the self-confidence, that is denied to most students because they are not allowed to learn in their own time, is truly tragic. Changes are being made, such as eliminating grades and grade levels in elementary school, but if students at every level are not allowed to take their time, most of them will be left behind. That’s simply not good enough if we want to build a smarter society for the future.

The shared solitude of writing and reading

Writing is saying to no one and to everyone the things it is not possible to say to someone. Or rather writing is saying to the no one who may eventually be the reader those things one has no someone to whom to say them. Matters that are so subtle, so personal, so obscure that I ordinarily can’t imagine saying them to the people to whom I’m closest. Every once in a while I try to say them aloud and find that what turns to mush in my mouth or falls short of their ears can be written down for total strangers. Said to total strangers in the silence of writing that is recuperated and heard in the solitude of reading. Is it the shared solitude of writing, is it that separately we all reside in a place deeper than society, even the society of two? Is it that the tongue fails where the fingers succeed, in telling truths so lengthy and nuanced that they are almost impossible aloud?

—Rebecca Solnit, “The Faraway Nearby” (via Brain Pickings)

The Labours of Hercules: Classical Criminals

‘What I understand you to mean is, that in physical appearance I do not resemble a Hercules?’

Dr Burton’s eyes swept over Hercule Poirot, over his small neat person attired in striped trousers, correct black jacket and natty bow tie, swept up from his patent leather shoes to his egg-shaped head and the immense moustache that adorned his upper lip.

‘Frankly, Poirot,’ said Dr Burton, ‘you don’t! I gather,’ he added, ‘that you’ve never had much time to study the Classics?’

‘That is so.’

‘Pity. Pity. You’ve missed a lot. Everyone should be made to study the Classics if I had my way.’

Poirot shrugged his shoulders.

Eh bien, I have got on very well without them.’

‘Got on! Got on! It’s not a question of getting on. That’s the wrong view altogether. The Classics aren’t a ladder leading to quick success like a modern correspondence course! It’s not a man’s working hours that are important—it’s his leisure hours. That’s the mistake we all make. Take yourself now, you’re getting on, you’ll be wanting to get out of things, to take things easy—what are you going to do with your leisure hours?’

Poirot was ready with his reply.

‘I am going to attend—seriously—to the cultivation of vegetable marrows.’

…But seriously, Poirot, what a hobby! Compare that to’—his voice sank to an appreciative purr—’an easy chair in front of a wood fire in a long, low room lined with books—must be a long room—not a square one. Books all round one. A glass of port—and a book open in your hand. Time rolls back as you read:’ he quoted sonorously:

‘”Μὴτ ὃ αὐτε xυβερνὴτης ἐνὶ οὶνοπι πόντῳ
νῆα θοὴν ιθύνει ἐρεχθομένην ὰνέμοισι

He translated:

‘”By skill again, the pilot on the wine-dark sea straightens
The swift ship buffered by the winds.”

Of course you can never get the spirit of the original.’

For the moment, in his enthusiasm, he had forgotten Poirot. And Poirot, watching him, felt suddenly a doubt—an uncomfortable twinge. Was there, here, something that he had missed? Some richness of the spirit? Sadness crept over him. Yes, he should have become acquainted with the Classics … long ago … Now, alas, it was too late …

Hercule Poirot was plunged head first into a bewildering sea of classical lore with particular reference to ‘Hercules, a celebrated hero who, after death, was ranked among the gods, and received divine honours.’

So far, so good—but thereafter it was far from plain sailing. For two hours Poirot read diligently, making notes, frowning, consulting his slips of paper and his other books of reference. Finally he sank back in his chair and shook his head. His mood of the previous evening was dispelled. What people!

Take this Hercules—this hero! Hero, indeed! What was he but a large muscular creature of low intelligence and criminal tendencies! Poirot was reminded of one Adolfe Durand, a butcher, who had been tried at Lyon in 1895—a creature of oxlike strength who had killed several children. The defense had been epilepsy—from which he undoubtedly suffered—though whether grand mal or petit mal had been an argument of several days’ discussion. This ancient Hercules probably suffered from grand mal. No, Poirot shook his head, if that was the Greeks’ idea of a hero, then measured by modern standards it certainly would not do. The whole classical pattern shocked him. These gods and goddesses—they seemed to have as many different aliases as a modern criminal. Indeed they seemed to be definitely criminal types. Drinking, debauchery, incest, rape, loot, homicide and chicanery—enough to keep a juge d’Instruction constantly busy. No decent family life. No order, no method. Even in their crimes no order or method!

‘Hercules, indeed!’ said Hercule Poirot, rising to his feet, disillusioned.

He looked round him with approval. A square room, with good square modern furniture—even a piece of good modern sculpture representing one cube place on another cube and above it a geometrical arrangement of copper wire. And in the midst of this shining and orderly room, himself. He looked at himself in the glass. Here, then, was a modern Hercules—very distinct from that unpleasant sketch of a naked figure with bulging muscles, brandishing a club. Instead, a small compact figure attired in correct urban wear with a moustache—such a moustache as Hercules never dreamed of cultivating—a moustache magnificent yet sophisticated.

Yet there was between this Hercule Poirot and the Hercules of Classical lore one point of resemblance. Both of them, undoubtedly, had been instrumental in ridding the world of certain pests … Each of them could be described as a benefactor of the Society he lived in …

—Agatha Christie, The Labours of Hercules

Below Stairs: Continuing Education

It was when my youngest son was going to grammar school and my eldest was preparing for the university that I realised we had nothing in common to talk about except the weather. They would come home and discuss history, astronomy, French, and all those kind of things, some of which meant nothing to me. I’d never tried to keep up with the Joneses, but I determined to have a shot at keeping up with the boys.

First of all I thought about taking a correspondence course. But apart from the expense, you’re on your own doing a correspondence course; if you don’t feel like working there’s no one to urge you on, you’re not in rivalry with anyone and it doesn’t matter how long you take.

Then one of my boy’s history masters told me about a course of lectures given by Professor Bruce, Extra-Mural Professor from Oxford. They weren’t expensive, I think it was only a shilling a time, or cheaper if you took the whole lot, twenty-four of them. I took the lot.

It was fascinating to me this course of lectures. He must have been a brilliant teacher because the lessons were in the evening from half past seven to half past nine, with a break in between for a cup of coffee, but often with the discussion that used to go on afterwards it was eleven o’clock before I got away, and eleven thirty before I got home. My husband used to say, ‘I don’t know what kind of education you’re getting that keeps you out till half past eleven.’

But it was a real eye-opener for me, I’d always thought history was a dry thing, a succession of dates and things like that.

Then I started going to evening classes in philosophy, history, and literature. The only thing that really beat me was this metaphysical philosophy. You know when you first start anything, you want to be all high-hat. You don’t want to go to the same things that everyone else goes to, you want to come out with some high-falutin’ name, so I signed on for metaphysical philosophy.

I never knew what it was about. All I could understand was it was something to do with being a hedonist, or some such thing. After six evenings I decided that it wasn’t for me. But that was the only subject where I didn’t stick the course out.

Where has it all taken me? Well, I passed my  ‘O’ levels at the age of fifty-eight, and I’m now taking the Advance levels which I hope to get before I’m sixty. People say to me, ‘I can’t understand you doing it.’

I think it springs from the beginnings. All life is bound up together, isn’t it? I liked school, I won a scholarship which I couldn’t afford to take; I went into domestic service….

When I got married, I had the boys and became a mother pure and simple. Then when they were off my hands it came out again.

People say, ‘I supposed you got bored with life’, but it wasn’t as sudden as that. The seeds are in you and although it may take ten, twenty, or forty years, eventually you can do what you wanted to do at the beginning….

So, despite what it may sound like, I’m not embittered about having had to go into domestic service. I do often wonder what would have happened if I could have realised my ambition and been a teacher, but I’m happy now, and as my knowledge increases and my reading widens, I look forward to a happy future.

—Margaret Powell, Below Stairs

Emerson: Enchanted Library

In a library we are surrounded by many hundreds of dear friends, but they are imprisoned by an enchanter in these paper and leathern boxes; and though they know us, and have been waiting two, ten, or twenty centuries for us,—some of them,—and are eager to give us a sign, and unbosom themselves, it is the law of their limbo that they must not speak until spoken to; and as the enchanter has dressed them, like battalions of infantry, in coat and jacket of one cut, by the thousand and ten thousand, your chance of hitting on the right one is to be computed by the arithmetical rule of Permutation and Combination,—not a choice out of three caskets, but out of half a million caskets all alike. But it happens in our experience, that in this lottery there are at least fifty or a hundred blanks to a prize. It seems, then, as if some charitable soul, after losing a great deal of time among the false books, and alighting upon a few true ones which made him happy and wise, would do a right act in naming those which have been bridges or ships to carry him safely over dark morasses and barren oceans, into the heart of sacred cities, into palaces and temples. This would be best done by those great masters of books who from time to time appear,—the Fabricii, the Seldens, Magliabecchis, Scaligers, Mirandolas, Bayles, Johnsons, whose eyes sweep the whole horizon of learning. But private readers, reading purely for love of the book, would serve us by leaving each the shortest note of what he found.

—Ralph Waldo Emerson, “Books” in Society and Solitude: Twelve Chapters

And so we have the book blog. 🙂

Polyglot: Knowledge is Boring

I wonder about those who learn a language for practical reasons rather than for itself. It is boring to know. The only thing of interest is learning.

…An exciting game, a coquettish hide-and-seek, a magnificent flirt with the spirit of humanity. Never do we read so fluently and with such keen eyes as in a hardly known, new language. We grow young by it, we become children, babbling babies and we seem to start a new life. This is the elixir of my life.

…Sometimes I think of it with a certain joy that I can even learn Chinese at my ancient age and that I can recall the bygone pleasure of childhood when I first uttered in the superstitious, old language “mother,” and I fall asleep with this word: “milk.”

—Dezső Kosztolányi from the story “I read in Portuguese” in Our Strong Fortress, Language, quoted in Kató Lomb, Polyglot: How I Learn Languages [Download PDF]

Polyglot: Why it’s better to learn languages from books

I see another difficulty in practicing a language with others. An uninteresting partner is uninteresting in a foreign language as well.

I have written about how much I suffered in Japan because everyone wanted to practice their English with me and I couldn’t attain with the greatest effort to get answers in Japanese to my questions asked in Japanese. In the end, someone took pity on me and recommended a certain Mr. Matsumoto, who understood my sorrow and showed willingness to converse with me in Japanese in the afternoons.

Mr. Matsumoto proved to be a Buddhist monk. He was indeed ready to talk in Japanese, but unfortunately his only topic was Buddhism; specifically, that 11 of its 12 branches held completely false views. Only the branch that he followed was the true one. While he was explaining to me what the sole correct interpretation of the Lotus Sutra was for the third hour, I slipped away.

—Kató Lomb, Polyglot: How I Learn Languages [Download PDF]

Through the wonders of Twitter, YouTube and Wikipedia, I just discovered Kató Lomb (1909-2003), a Hungarian translator and interpreter who worked in 16 (sixteen) languages. Though her training was in chemistry, the Depression forced her to seek alternative employment, and she decided to try teaching English. (80 years later that is still a viable alternative for unemployed graduates!) Then came Russian (which was handy when the Soviets took over Hungary), French, and so on, and so forth. Each time she had some immediate incentive to learn a language (usually economic), and so she racked up language after language. She denied having any particular gift for languages, and in fact did poorly in language classes as a child. What she did have was motivation, and a method that made learning interesting. Her key to learning was to seek out texts that were interesting enough to stick with through the rough patches. She did most of her learning by reading novels. Wanting to know what happened in the end was a great spur to keep slogging through unknown words. Though she did make some use of grammars and dictionaries, and even formal classes, the bulk of her learning came from reading books. It’s the only way she was able to learn so many languages so quickly and so fluently. She felt that traditional teaching methods that focus on grammar, vocabulary lists, and boring exercises were ineffective and slow. It’s hard to argue with that given her results!

Though I am only part way through Polyglot, I definitely recommend it to anyone interested in languages. As if to illustrate her point, she also tells some very funny stories, so it is quite an entertaining read as well. Bonne lecture!