December 15, 2013

MIT: "Even when test scores go up, some cognitive abilities don’t"

The trendy Common Core in K-12 education is intended to teach "critical thinking skills" rather than rote memorization of stale facts. This sounds much like the old fluid v. crystallized distinction in IQ research. But can even effective schools improve fluid IQ?

From an MIT press release:
Even when test scores go up, some cognitive abilities don’t 
MIT neuroscientists find even high-performing schools don’t influence their students’ abstract reasoning. 
Anne Trafton, MIT News Office 
December 11, 2013 
To evaluate school quality, states require students to take standardized tests; in many cases, passing those tests is necessary to receive a high-school diploma. 
These high-stakes tests have also been shown to predict students’ future educational attainment and adult employment and income. 
Such tests are designed to measure the knowledge and skills that students have acquired in school — what psychologists call “crystallized intelligence.” 
However, schools whose students have the highest gains on test scores do not produce similar gains in “fluid intelligence” — the ability to analyze abstract problems and think logically — according to a new study from MIT neuroscientists working with education researchers at Harvard University and Brown University. 
In a study of nearly 1,400 eighth-graders in the Boston public school system, the researchers found that some schools have successfully raised their students’ scores on the Massachusetts Comprehensive Assessment System (MCAS). 
However, those schools had almost no effect on students’ performance on tests of fluid intelligence skills, such as working memory capacity, speed of information processing, and ability to solve abstract problems. 
“Our original question was this: If you have a school that’s effectively helping kids from lower socioeconomic environments by moving up their scores and improving their chances to go to college, then are those changes accompanied by gains in additional cognitive skills?” says John Gabrieli, the Grover M. Hermann Professor of Health Sciences and Technology, professor of brain and cognitive sciences, and senior author of a forthcoming Psychological Science paper describing the findings. 
Instead, the researchers found that educational practices designed to raise knowledge and boost test scores do not improve fluid intelligence. “It doesn’t seem like you get these skills for free in the way that you might hope, just by doing a lot of studying and being a good student,” says Gabrieli, who is also a member of MIT’s McGovern Institute for Brain Research.

If you are effectively teaching kids the right things, they don't need as much fluid IQ.
This study grew out of a larger effort to find measures beyond standardized tests that can predict long-term success for students. “As we started that study, it struck us that there’s been surprisingly little evaluation of different kinds of cognitive abilities and how they relate to educational outcomes,” Gabrieli says. 

Actually, there has been, but the answers never turn out welcome, so findings get forgotten.
The data for the Psychological Science study came from students attending traditional, charter, and exam schools in Boston. Some of those schools have had great success improving their students’ MCAS scores — a boost that studies have found also translates to better performance on the SAT and Advanced Placement tests. 
The researchers calculated how much of the variation in MCAS scores was due to the school that students attended. For MCAS scores in English, schools accounted for 24 percent of the variation, and they accounted for 34 percent of the math MCAS variation. However, the schools accounted for very little of the variation in fluid cognitive skills — less than 3 percent for all three skills combined. 

Civilization, when properly functioning, is a device for minimizing the amount of fluid intelligence you need to function. You don't need to turn military history into a superb epic oral poem like The Iliad anymore: you just write it down. Nowadays, you don't have to go the library to read it. You can look it up on the Internet.

A huge problem with educational reform efforts is that they are typically designed by people who have high confidence in their own fluid intelligence relative to the average. Combine that with the contradictory dogma that students must all have equally high fluid intelligence -- Jefferson wouldn't have written it into the Declaration of Independence if it weren't true -- and you wind up with remarkably little critical thinking about education fads like critical thinking.

In contrast, the military tends to assume that everybody is an idiot who will find a way to screw up massively and probably get himself and large numbers of people around him killed, so it's best to break things down into simple steps so soldiers can rely upon crystallized intelligence rather than fluid intelligence.

But the notion that the public schools can learn anything from the military has been out of fashion for just under 50 years. The people who took control of education 45 years ago may talk all the time about critical thinking skills, but they sure don't like critical thinking about themselves and their ideas.
In one example of a test of fluid reasoning, students were asked to choose which of six pictures completed the missing pieces of a puzzle — a task requiring integration of information such as shape, pattern, and orientation. 
“It’s not always clear what dimensions you have to pay attention to get the problem correct. That’s why we call it fluid, because it’s the application of reasoning skills in novel contexts,” says Amy Finn, an MIT postdoc and lead author of the paper. 
Even stronger evidence came from a comparison of about 200 students who had entered a lottery for admittance to a handful of Boston’s oversubscribed charter schools, many of which achieve strong improvement in MCAS scores. The researchers found that students who were randomly selected to attend high-performing charter schools did significantly better on the math MCAS than those who were not chosen, but there was no corresponding increase in fluid intelligence scores. 
However, the researchers say their study is not about comparing charter schools and district schools. Rather, the study showed that while schools of both types varied in their impact on test scores, they did not vary in their impact on fluid cognitive skills. 

“What’s nice about this study is it seems to narrow down the possibilities of what educational interventions are achieving,” says Daniel Willingham, a professor of psychology at the University of Virginia who was not part of the research team. “We’re usually primarily concerned with outcomes in schools, but the underlying mechanisms are also important.” 
The researchers plan to continue tracking these students, who are now in 10th grade, to see how their academic performance and other life outcomes evolve. They have also begun to participate in a new study of high school seniors to track how their standardized test scores and cognitive abilities influence their rates of college attendance and graduation. 
Gabrieli notes that the study should not be interpreted as critical of schools that are improving their students’ MCAS scores. “It’s valuable to push up the crystallized abilities, because if you can do more math, if you can read a paragraph and answer comprehension questions, all those things are positive,” he says. 

Right.
He hopes that the findings will encourage educational policymakers to consider adding practices that enhance cognitive skills. Although many studies have shown that students’ fluid cognitive skills predict their academic performance, such skills are seldom explicitly taught. 
“Schools can improve crystallized abilities, and now it might be a priority to see if there are some methods for enhancing the fluid ones as well,” Gabrieli says.

You know, there is a literature on this subject going back generations.
Some studies have found that educational programs that focus on improving memory, attention, executive function, and inductive reasoning can boost fluid intelligence, but there is still much disagreement over what programs are consistently effective, 
The research was a collaboration with the Center for Education Policy Research at Harvard University, Transforming Education, and Brown University, and was funded by the Bill and Melinda Gates Foundation and the National Institutes of Health.

By the way, this somehow reminds me of the famous video "A Private Universe" shot at the graduation ceremony at that other college in Cambridge, MA, where cap-and-gowned newly minted Harvard graduates answer the question "Why is it colder in winter" with winning self-confidence, eloquently explaining that it's because the Earth's orbit isn't a perfect circle as in the discredited Ptolemaic model; instead, as the Copernican revolution emphasized in displacing humanity from the center of the universe, the earth's orbit is an ellipse, which means we are farther from the sun in winter, ergo, it's colder. Meanwhile, the working class students at a local public high school stumble with deer-in-the-headlights expressions through their implausible-sounding explanation that it's colder in winter because the earth is ... further ... from the sun?
(Here's the real reason.)

In other words, much of what you acquire at Harvard isn't fluid or even crystallized intelligence, but attitude.

A friend of mine remarks that going to Harvard was kind of depressing since half of the cabdrivers in Cambridge wanted to hear how their favorite professors were still doing. "Has old Grosvenor finally given in and gotten a hearing aid, or is he still as deaf as when I took Intro?" But he discovered over a long career in corporate law that the farther he got from Cambridge, MA, the more people seemed to be impressed with his diploma. East of Suez, he found himself treated like a demigod whenever he dropped it into conversation.

It was a huge help in business negotiations in Asia. Whenever he found himself losing dominance, he'd excuse himself to go the the men's room, stare in the mirror, and buck himself up with the thought, "Never forget -- I am a Harvard Man! Now, get back in there and fleece these swine!"

57 comments:

countenance said...

Possible explanations to describe the results and some of the apparent contradictions in this MIT study:

1. The MCAS is getting regressively easier by the year

2. The MCAS is not a g-loaded test

3. Using rote to teach to the test in order to goose up scores

4. Cheating, a la Atlanta Public Schools

You wrote:

A friend of mine remarks that going to Harvard was kind of depressing since half of the cabdrivers in Cambridge wanted to hear how their favorite professors were still doing.

Which doesn't say much for the value of a Harvard degree in Boston itself, does it?

carol said...

you just right it down.

Of course, intelligence and grammar/usage skills don't necessarily go together.

Anonymous said...

In other words, much of what you acquire at Harvard isn't fluid or even crystallized intelligence, but attitude.

Harvard types tend to be very verbally dexterous.

Anonymous said...

"A huge problem with educational reform efforts is that they are typically designed by people who have high confidence in their own fluid intelligence relative to the average... In contrast, the military tends to assume that everybody is an idiot who will find a way to screw up massively and probably get himself and large numbers of people around him killed, so it's best to break things down into simple steps...
But the notion that the public schools can learn anything from the military has been out of fashion for just under 50 years."

I don't know how things were in schools 50 yrs ago, but I think we can understand why they would want to emphasize fluid intelligence today. It's because of the rapid change in science and technology. When technology moved a lot slower, people could learn skills and rely on them for a long time, even a lifetime at work.

But consider all the changes and advances in science and technology in just the last 10 yrs.
Skills learned today--especially in computers--may be obsolete in 5 yrs. So, to succeed in the new economy, it's not enough for one to be able to learn things slowly and step-by-step. Rather, one has to learn how to stay several steps ahead of the learning curve.
Of course, the real problem is relatively few people have such abilities, and such can't really be taught. Some people have it, many don't.

Anonymous said...

Probably the only cultural adaptation that could actually help improve "critical thinking skills" would be teaching the old staples - logic and related subjects like grammar, rhetoric, geometry, etc. We "know" that they "work". That is they tend to correspond with physical reality and have practical value and applications. I put those words in quotes though because in reality we don't actually know exactly why they work. These are still contentious issues and open questions in philosophy.

Of course these are exactly the subjects that have been deemphasized over the past century.

Glossy said...

"But can even effective schools improve fluid IQ?"

Yes. Drumming anti-drug propaganda into their little heads will, on average, make their fluid IQ higher in adulthood than it would have been otherwise. There was a study not long ago that showed that pot use decreased IQ by 8 points on average.

Civilization, when properly functioning, is a device for minimizing the amount of fluid intelligence you need to function.

This is essentially an endorsement of statist economics. Laissez-faire economics requires more fluid intelligence from participants. Statist economics makes a lot of sense in ethnically-homogeneous societies and in diverse societies where the main ethnic groups have roughly equal amounts of ability and altruism. It doesn't make sense in America, which I'm sure Steve understands.

"But he discovered over a long career in corporate law that the farther he got from Cambridge, MA, the more people seemed to be impressed with his diploma."

I didn't go to Harvard or anywhere like it, but I would guess that the most common reaction received by grads is jealous hostility. People really, really hate learning that they're dumber than you are. They hate this much more than learning that they're poorer than you are, for example. In comparison, athletic prowess elicits very little jealousy. One can brag about that all one wants.

Anonymous said...

That "Private Universe" video is quite shocking. Seriously? These Harvard dumbfucks have never heard an expression "low winter sun"? Never heard that Summer months are not the same in the Northern and Southern hemispheres??? And these are our "well-rounded" competition winners? OMG, we are doomed.

Anonymous said...

Dang, I wished they'd shown one of the two people who got it right. Now we'll never know! Anyway, it's odd that a single piece of common knowledge (summer in America = winter in Australia) doesn't occur to anyone to disprove their theory, or that there's this thing called a "lunar eclipse" that is distinct from Luna's waxing and waning.

Ironically, it's science books that show the solar system at an angle who are at fault.

Anonymous said...

Steve, could you please correct the two typos:
"you just right it down"
"get back in their"

Anonymous said...

"Steve, could you please correct the two typos"

Needs more crystal than fluid spelling.

Anonymous said...

In the age of Kanye West and Smiley Circus, I think most boys and girls are into cocknitive ability than cognitive ability.

Dave Pinsen said...

"Civilization, when properly functioning, is a device for minimizing the amount of fluid intelligence you need to function."

"This is essentially an endorsement of statist economics. Laissez-faire economics requires more fluid intelligence from participants."

No, not really. I would have tweaked Sailer's quote to say "institutions" instead of "civilization", but civilization is essentially the aggregate of its institutions, so the same principal applies. Laissez-faire economies still have large institutions, and like the military, most of them are designed to minimize the need for fluid intelligence at most levels.

We don't have a state-run hamburger restaurant monopoly, we have Burger King, McDonald's, Wendy's, etc. But all of them are set up to minimize the need for fluid intelligence from their workers. That goes from the cash registers that calculate change to the manuals that lay out all the procedures for franchise owners. They are, like Herman Wouk's old line about the US Navy, systems designed by geniuses to be run by idiots.

Sure, some of the guys that start biotech startups, etc., need a lot of fluid intelligence. But these are a tiny minority of the workers in our economy.

DPG said...

The common source of error between the two questions, cause of seasons and cause of lunar cycle, is viewing the problem in 2 dimensions rather than 3. I wonder how much of that is due to being taught on 2 dimensional chalkboards. As computers become more ubiquitous in education, will we become better at thinking in 3 dimensions?

Glossy said...

Dave Pinsen,

Let's compare the statist and the laissez-faire approach to healthcare and retirement. In the statist setup everyone is covered by government-run insurance and everyone gets a state pension. In the laissez-faire set-up you have to shop and invest, i.e. to make choices. That requires more fluid intelligence.

I'm sure that as European societies become more diverse through immigration, they will become more laissez-faire, more economically American. The statist = civilized equation stops working if there are large groups of free-riders.

Dave Pinsen said...

"The common source of error between the two questions, cause of seasons and cause of lunar cycle, is viewing the problem in 2 dimensions rather than 3. I wonder how much of that is due to being taught on 2 dimensional chalkboards."

You can easily illustrate the tilt of the earth relative to the plane of its orbit on a chalk board. Just draw a circle to represent the earth and have little lines coming out of the poles at angles to illustrate the tilt.

Frankly, I'm surprised by the ignorance of the Harvard grads, considering that many of them have probably traveled to at least the tropics on vacation. That the sun sets later on St. Bart's than in Cambridge in December should have been a clue.

Anonymous said...

-Fluid intelligence doesn't do much good if you have nothing to think about.

-They inadvertently proved their own point by demonstrating that crystallized knowledge is important by innocently rediscovering what people outside the coastal elites have known for hundreds of years. As in actually knowing stuff is at least as important as reinventing the wheel every time every time you see a problem in order to solve it.

Anonymous said...

Right after I heard of this Harvard fiasco I visited a nephew's 3rd grade class and there, taped to the windows was the correct explanation of the seasons, being taught that day. Seems to me that that is where I learned it also. So those Harvard folks probably couldn't even remember this pure knowledge, which, perhaps not coincidentally, has no political overtones.
Robert Hume

Dutch reader said...

I wonder how the persons who are so shocked at students' lack of knowledge about astronomy, or about scientific subjects in general, would do at explaining, for example, the principles of, voice assimilation in speech, the proximate causes of the outbreak of the First World War, or the circle of fifths in Western music.

Assistant Village Idiot said...

Also, swine don't have fleece. I can show you Romanian peasants who knew that.

Cail Corishev said...

"It doesn’t seem like you get these skills for free in the way that you might hope, just by doing a lot of studying and being a good student,” says Gabrieli.

In other shocking news, putting your dishes on a high shelf so you have to reach up for them all the time won't make you taller, and standing next to an ugly girl won't make you prettier.

Chief Seattle said...

I don't know if the Harvard video is faked, or the participants were carefully selected, or if it was just the coked up eighties, but it doesn't ring true to me. First of all, that's basic science that inevitably gets tested on at some point, and Harvard students are good at tests. Second, a minute of thought recalls that the seasons are opposite in the Southern hemisphere, and that could not be explained if the change was due to distance from the sun.

Anonymous said...

@ Dutch reader:
Don't be a fool! The change of seasons is the most basic stuff there is. In a sane world, anyone graduating from high school should be able to realize that that the "close-far from the Sun" is an obviously wrong explanation because it's always summer in the equatorial areas. This stuff is not an "astronomy"!



Anonymous said...

"swine don't have fleece."

Humans don't either. And yet they are fleeced by others all the time.

DPG said...

"You can easily illustrate the tilt of the earth relative to the plane of its orbit on a chalk board. Just draw a circle to represent the earth and have little lines coming out of the poles at angles to illustrate the tilt."

Yes, but in order to explain seasonality, you have to show the tilt AND the Earth's relative position to the Sun. For example, if the northern hemisphere were always tilted towards the Sun, it would be summer all the time, right? All of the kids tend to be viewing it in 2 dimensions of X and Y, determining the location of the Earth along its elliptical orbit. You need to add in Z to show the tilt of the Earth: sometimes it's tilted towards the sun, at other times away.

Likewise, the kids are caught up thinking of the moon's orbit in 2D. However, because the moon's orbit is in 3D, it does not necessarily pass behind the shadow of the Earth. They end up confusing a new moon and a lunar eclipse because they're not taking into account the tilt of the moon's orbit.

Anonymous said...

Does it really matter WHY its colder in winter?

Anyhoo, I can't remember the reason I was taught in elementary school. But i do know that when its winter in the USA its summer in Australia, which leads me to believe its about the tilt of the earth and the amount of sunlight hitting various spots at different times.

If I'm wrong - so what?

Difference Maker said...

I chortle at those Harvardian fools; I knew the reason in second grade. But then, I don't compare disfavorably in test scores so there is no reason for me to treat them apart.

I have high confidence and verbal ability, I should take the pearls from these swine!

Alas, with sleep deprivation, it was not yet to be

Anonymous said...

I wonder how the persons who are so shocked at students' lack of knowledge about astronomy, or about scientific subjects in general, would do at explaining, for example, the principles of, voice assimilation in speech, the proximate causes of the outbreak of the First World War, or the circle of fifths in Western music.

Speaking solely for myself, I wouldn't do very well at all. But then:

1) I wasn't taught those things in my mediocre grade school.
2) The average Harvard grad would probably only know, at most, one of those three things, based on which field of study they chose. I do not find it particularly surprising when people know things about subjects they are interested enough in to choose to study.
3) I wouldn't confidently assume that I did know the answer to those things, and then proceed to spew out nonsense that could easily be disproven by other facts I know, such as the fact that the seasons are reversed in the Southern hemisphere.
4) There is no doubt in my mind that these people, with their sub-grade-school level of knowledge, would have no problem whatsoever in lecturing people about topics like global warming, and would naturally assume that anyone who disagrees with them is completely ignorant about science.

Anonymous said...

Instead, the researchers found that educational practices designed to raise knowledge and boost test scores do not improve fluid intelligence.

If memory serves correctly, there was a fellow named Pavlov who broke new ground in that field.

Foreign Expert said...

I didn't understand the ecliptic until I was about 40. I was shocked to learn that the ancient greeks had identified it.

BTW, in 1989, when I taught Curriculum & Instruction (at the grad level) we used a textbook that advocated teaching "thinking skills" across the curriculum. Nothing new.

Anonymous said...

First of all, that's basic science that inevitably gets tested on at some point, and Harvard students are good at tests.

Basic science does not "inevitably get tested" at any modern American university. Most students graduating from even top universities are scientifically illiterate and ignorant of most basic facts. I would not be at all surprised if a majority of Ivy League grads couldn't recite Newton's three laws.

The students in the video probably learned the cause of seasons in elementary school and later forgot. That wouldn't be unusual. Like many students, I was taught the basic system of classifying clouds around 4th or 5th grade. I've since completely forgotten it. The point being, you cannot expect even highly intelligent people to know everything they've ever been taught, especially if it's something they learned as children.

Second, a minute of thought recalls that the seasons are opposite in the Southern hemisphere, and that could not be explained if the change was due to distance from the sun.

Those of us who have never lived in the southern hemisphere (most Americans, and most humans generally) rarely think of that. In fact, I would bet money that a majority of Americans are unaware that the seasons are reversed in the south. At any rate, that's a non-trivial inference even for a Harvard grad.

David Davenport said...

1238You need to add in Z to show the tilt of the Earth: sometimes it's tilted towards the sun, at other times away.

Are you saying that Earth's tilt angle relative to the ecliptic plane changes during Earth's orbit around the Sun?

Think: If the northern hemisphere is tilted away from the Sun, the southern hemisphere must be simultaneously tilted closer to the Sun.

Bonus question: During what month is all of planet Earth closest to the Sun?

peterike said...

So those Harvard folks probably couldn't even remember this pure knowledge, which, perhaps not coincidentally, has no political overtones.

No political overtones? Are you kidding? The earth is tilted in such a way so that Europeans can have snow during Christmas because WHITE PRIVILEGE.

RageWithTheMachine said...

Apparently the Nude Socialist has some critical thoughts:

http://www.newscientist.com/article/dn24745-nature-more-than-nurture-determines-exam-success.html#.Uq50NXVDuDA

Steve Sailer said...

In general, modern Americans aren't particularly well-informed about the length of the day at different times of the year.

I used to be a day-length obsessive because I could use the knowledge to exploit golf courses' twilight fee structures. Golf courses charge lower rates to tee off in the afternoon when you probably can't finish 18 holes. But they used to only change the hours for twilight rates two or three times per year, so there were periods when you can save a lot of money and finish comfortably before dark. Teeing off at 2:30 pm for $50 (instead of paying $100 to tee off at 10:00 am) is a great deal in late April or in late September? But, I noticed that my golfing friends, usually MBA-types, always found my explanations of this fascinating phenomena less than galvanizing and were quite happy to take my word for it and let me arrange the tee-times.

In this century, golf courses change their twilight hours more often to prevent guys like me from taking advantage, but it took decades for this change to come about.

Anonymous said...

Whereas today random Harvard students can't name the capital of Canada (except for Canadian students)

Anonymous said...

The earth is tilted in such a way so that Europeans can have snow during Christmas because WHITE PRIVILEGE.

Reminded me of my single Christmas in Sydney. Boy, that was weird! Even their evergreens are strange. There is no Christmas in Australia as far as I am concerned :-)

Harry Baldwin said...

Anonymous said...If I'm wrong - so what?

If "So what?" is an acceptable answer to you, then you can dispense with most knowledge.

Steve Sailer said...

"swine don't have fleece."

Clearly, Harvard's Ag program has declined sadly.

Steve Sailer said...

Seriously, I don't think people know that much about where the sun is now that farming is a niche occupation. Try asking people:

In the middle of the day, is the sun:

A. North
B. South
C. East
D. West

It's the kind of thing gardener hobbyists would get instantly, but it's probably fading in the general public.

The rise of GPS directions means that knowing which direction the sun is isn't useful in navigating streets anymore, so why bother?

Maybe Conan Doyle was right in having Sherlock Holmes not know anything about astronomy because he didn't need to know anything to solve crimes and it would just take up space in his brain. The older view was that astronomy was the fundamental science that provides the framework and testing ground for the other sciences, but maybe, who cares?

Jack Amok said...

Let's compare the statist and the laissez-faire approach to healthcare and retirement. In the statist setup everyone is covered by government-run insurance and everyone gets a state pension. In the laissez-faire set-up you have to shop and invest, i.e. to make choices. That requires more fluid intelligence

Or, a group of lower fluid IQ folks could voluntarily rely on someone else to pick for them. If he proves untrustworthy and rips them off, they can just hang him.

It takes all kinds to make a world. If you design a society where only the smartest 20% can succeed, soon or later one of the guys in the 20% is going to figure out how to mobilize the other 80% as his goon squad and take over.

Society needs institutions - preferably voluntary civic institutions - to avoid a totalitarian dictatorship.

Anonymous said...

I suppose those Harvard students have never noticed that in the southern hemisphere they have winter while we have summer and vice versa.

Anonymous said...

Fleece these swine?

Was your Harvard friend taught about mixed metaphors?

Anonymous said...

Funny you should mention golf. I play every Wednesday at a local muni course where the deal is all you can play after 4 o'clock for 10 bucks. Some midsummer evenings we can get all 18 holes in.

BB753 said...

Jack Amok
If you design a society where only the smartest 20% can succeed, soon or later one of the guys in the 20% is going to figure out how to mobilize the other 80% as his goon squad and take over.
That´s te story of Leftism in a nutshell, from Julius Caesar down to these days, where a small group of upper class people (Liberals) have figured out how to use the rabble to pillage and control society to their profit.

Florida resident said...

A remarkable mathematician of 20th century V.I.A. said about invention of calculus by Leibniz:
"He invented the notations using which, those who do not understand calculus, can teach it to those, who will never understand calculus".
That elitist statement by V.I.A. had the aim to promote intuition (i.e. fluid intelligence) required to understand Newton's approach to calculus as to the theory of (possibly infinite) power series.
In particular, Newton understood that the formula
(1+x)^a = 1
+ x
+ a*x
+ [a*(a-1)/2!]*x^2
+ [a*(a-1)*(a-2)/3!]*x^3
+ [a*(a-1)*(a-2)*(a-3)/4!]*x^4
+ … ,
known to his predecessor Vieta
for positive integer “a” only,
is actually valid for any “a”,
be it positive or negative,
integer or fractional,
rational or irrational,
real or complex.
It is this generalization, which is called
“Newton’s binomial formula”.
Meanwhile its variant
with positive integer “a”,
when the series is finite,
should be called
“Vieta’s formula”.
Sure, Leibniz’s notations for derivatives
allow to get “Newton’s binomial formula” using acquired knowledge, i.e. "crystallized intelligence",
but not in such an elegant manner.
***
At the same time V.I.A. spoke quite harshly about bad personal qualities of Isaac Newton.
***
With invariable respect of Mr. Sailer,
F.r.

NOTA said...

Markets let you condense all kinds of information about how hard it is to get, say, copper vs aluminum into a ratio of prices. Lacking prices, you need to understand the alternative uses for each metal, the recent difficulties mining them, which countries have nationalized their copper mines lately, etc.

Anonymous said...

Does this mean that folks that get good grades and ace the SATs so that they get into Harvard will not necessarily be the most creative?

But how else to tell? Most every test, if known in advance, can be gamed. Perhaps trustworthy interviews? But likely they would be criticized as non-objective and biased toward fellow ethnics.

Hopeless: the ambitious succeed in getting into Harvard. The only hope for the truly creative is to get into a lesser college and work hard in a field where real achievement speaks for itself.
That won't get you into high class law schools; so society will just have to suffer with less than the best there.

But will probably get you into a good research institution; if thats what you really want.
Robert Hume

NOTA said...

I suspect the big hurdle here for people who have never thought this through before is realizing they need to think it through before answering. If you spend a couple minutes thinking about it, it's not so hard to see that the "further from the sun" explanation can't be right (though I think it does have an effect on seasons, just not as big a effect as the tilt of the axis). But it's easy to self-confidently charge ahead with all that stuff you know that ain't so. I wonder if Harvardites are even any more susceptible to this than other people--it's not like working out the answer requires a sky-high IQ.

Another example like this is "what causes the phases of the moon?" It's not all that complicated to work out the answer, and you can illustrate it to a child with a ball, a dark room, and a single lamp, but I suspect almost nobody you ask will answer correctly at first. I saw an illustration of this at a planetarium some years ago, and realized I'd never even considered how phases of the moon worked, and that if someone had asked me, I'd probably have given them a wrong half-remembered, half-guesses answer without even thinking about it. (Hint: the Earth's shadow has nothing to do with it.)

Anonymous said...

I've always thought fluid intelligence isn't intelligence per se, but a personality trait better known as 'drive.' I've known a lot of people with serious smarts, but they weren't problem solvers. Why? They were lazy and didn't want to apply themselves. Problem solving is hard work.

Also, once you've worked an eight-hour day at your job, the sad fact is even plenty of smart people just zone out in front of the TV because they're tired. It's not because they're mentally incapable.

BurplesonAFB said...

Steve, I had previously been assured that somewheres out East of Suez, the best was like the worst.

Anonymous said...


http://www.youtube.com/watch?v=woqK9z5f7yg

Rocking classic. Nah, doesn't quite work.

Florida resident said...

Mr. Sailer !
Can you kindly correct the typo in Newton's binomial formula in my previous post. One should drop the term "x" without any coefficient, so that correct expression is
(1+x)^a = 1 +
+ a*x +
+ [a*(a-1)/2!]*x^2 +
+ [a*(a-1)*(a-2)/3!]*x^3 +
+ [a*(a-1)*(a-2)*(a-3)/4!]*x^4 +
+ … .

Thomas O. Meehan said...

Rutgers grows in stature the farther away you are as well. Far more respected in the UK than in New Jersey certainly.

David Davenport said...

Why Earth is Closest to Sun in Dead of Winter

by Mary Lou Whitehorne, Special to SPACE.com | January 02, 2007 09:00am ET


It's winter in the Northern Hemisphere and we're at our closest point to the Sun. Closest? Yes, you read that right. Closest. For northerners, the winter solstice has just passed. But the truth is, on January 3, 2007, Earth reaches perihelion, its closest point to the Sun in its yearly orbit around our star.
( Only a little bit closer. --DD )


At first glance, it makes no sense. If Earth is closest to the Sun in January, shouldn't it be summer? Maybe, if you live in the Southern Hemisphere. So what does this mean?

Earth's orbit is not a perfect circle. It is elliptical, or slightly oval-shaped. This means there is one point in the orbit where Earth is closest to the Sun, and another where Earth is farthest from the Sun. The closest point occurs in early January, and the far point happens in early July (July 7, 2007). If this is the mechanism that causes seasons, it makes some sense for the Southern Hemisphere. But, as an explanation for the Northern Hemisphere, it fails miserably.


In fact, Earth's elliptical orbit has nothing to do with seasons. The reason for seasons was explained in last month's column, and it has to do with the tilt of Earth's axis. ....

Difference Maker said...

Those of us who have never lived in the southern hemisphere (most Americans, and most humans generally) rarely think of that. In fact, I would bet money that a majority of Americans are unaware that the seasons are reversed in the south. At any rate, that's a non-trivial inference even for a Harvard grad.

Non trivial?

I would say that's a fairly dramatic divorce from the real world, evidence of a lack of curiosity and attention span. And bad memory

Of course, I know all about getting by on IQ with reduced attention span, but at least I had a good one, I noticed those things. When we learn that Santa Claus visits the southern hemisphere in summertime it is something quite memorable.

How can we expect any understanding of matters from those who cannot model even a simple axis tilt in their heads? We can hardly entrust the leadership of a great nation to those living in a fairyland

Then again, my test scores are quite favorable, so I suppose I can only pat myself on the back

Difference Maker said...

I've always thought fluid intelligence isn't intelligence per se, but a personality trait better known as 'drive.' I've known a lot of people with serious smarts, but they weren't problem solvers. Why? They were lazy and didn't want to apply themselves. Problem solving is hard work.


They are closely related. I just don't feel like lecturing right now. Like you say, it is hard work

But at least you have an idea of it

Anonymous said...

Let's compare the statist and the laissez-faire approach to healthcare and retirement. In the statist setup everyone is covered by government-run insurance and everyone gets a state pension. In the laissez-faire set-up you have to shop and invest, i.e. to make choices. That requires more fluid intelligence.

Crystallized intelligence isn't really a set of rote algorithms that have been memorized, it's more about having a body of knowledge that you can then apply your ability to reason to. Having more crystallized intelligence favors people who make economic decisions, because knowing something about the world and about markets helps.

The military does not really cultivate having high levels of crystallized intelligence, as such, but on giving them the right information to bolster their low levels of crystallized intelligence (you can analogize this to trying to present fluid IQ problems in a way solvable for the average low fluid IQ person).

A situation where other people do things for you is obviously one where you have to reason and rely on your intelligence less about that thing... but perhaps this frees you up to reason more and more usefully on other things, which are much more tractable to an individual, rather than messing up trying to find margins on problems where you have little information that you can use to make an optimal choice (health events being mostly random, a health market being janked so the public information has little relationship to what medical providers work off, etc).