The following quote, often attributed to Einstein, is a gem:
Not everything that can be counted counts, and not everything that counts can be counted.
However, QuoteInvestigator points out that it is likely due to the sociologist William Bruce Cameron, who wrote the following in his 1963 text Informal Sociology: A Casual Introduction to Sociological Thinking.
It would be nice if all of the data which sociologists require could be enumerated because then we could run them through IBM machines and draw charts as the economists do. However, not everything that can be counted counts, and not everything that counts can be counted.
Below is a letter (not published) that I submitted to the Wall Street Journal in response to EO Wilson’s op ed piece in the April 5, 2013 edition.
April 9, 2013
I read with interest the article by E.O. Wilson, a distinguished
scientist whose work I greatly admire. Wilson addresses a problem that
concerns us all: the declining interest of young people in science.
I agree with much in Wilson’s article, e.g., that ideas play a key role,
that disciplined fantasies are the fountainhead of creativity. This
said, I take issue with the implication that mathematical semiliteracy
is an adequate preparation for a young person interested in science. What
is sufficient in one generation may not be in the next. Consider two
fundamental advances in physics: Faraday’s law of induction, which made
possible the electric generator, and Maxwell’s discovery that
electromagnetic waves propagate in a vacuum at the speed of light,
which made possible radio communication. Just thirty years apart, one
discovery was made without mathematics, while the other used the most
sophisticated mathematics of the day — and it did come from “staring at
One sees the same progression in biology. In the days of Linnaeus and
Darwin, mathematics played no role. But now whole fields of biology have
been created using mathematics. It is one thing to cut chromosomes into
pieces with enzymes. It is another to assemble the pieces into a map, a
dictionary of life. That was done with a sophisticated piece of
mathematics, the Smith-Waterman algorithm. Mathematics also plays a key
role in reconstructing the tree of life: when and how did species branch
off from their ancestors? Darwin would be pleased!
Back to Wilson’s concern — no student should be deterred from a
career in science by mathematics — but that same student should know
enough mathematics to collaborate fruitfully and to be conversant with
ideas his colleagues will use: statistical argument, model, simulation,
algorithm, etc. Better to enter the game with a full deck.
University of Utah
An article in the New York Times by Jal Mehta of the Harvard Graduate School of Education notes that the US, despite years of reform efforts, ranks low compared to other industrialized nations: for 15-year-olds in 2009, the US ranked 14th in reading, 17th in science and 25th in math, behind Belgium, Estonia, and Poland. Here is one extract from the article:
HERE’S what the old debates have overlooked: How schools are organized, and what happens in classrooms, hasn’t changed much in the century since the Progressive Era. On the whole, we still have the same teachers, in the same roles, with the same level of knowledge, in the same schools, with the same materials, and much the same level of parental support.
Call it the industrial-factory model: power resides at the top, with state and district officials setting goals, providing money and holding teachers accountable for realizing predetermined ends. While rational on its face, in practice this system does not work well because teaching is a complex activity that is hard to direct and improve from afar. The factory model is appropriate to simple work that is easy to standardize; it is ill suited to disciplines like teaching that require considerable skill and discretion.
Teaching requires a professional model, like we have in medicine, law, engineering, accounting, architecture and many other fields. In these professions, consistency of quality is created less by holding individual practitioners accountable and more by building a body of knowledge, carefully training people in that knowledge, requiring them to show expertise before they become licensed, and then using their professions’ standards to guide their work.
By these criteria, American education is a failed profession. There is no widely agreed-upon knowledge base, training is brief or nonexistent, the criteria for passing licensing exams are much lower than in other fields, and there is little continuous professional guidance. It is not surprising, then, that researchers find wide variation in teaching skills across classrooms; in the absence of a system devoted to developing consistent expertise, we have teachers essentially winging it as they go along, with predictably uneven results.
Mehta notes the disparity in research effort between teaching and other professions:
Anthony S. Bryk, president of the Carnegie Foundation for the Advancement of Teaching, has estimated that other fields spend 5 percent to 15 percent of their budgets on research and development, while in education, it is around 0.25 percent.
… In the nations that lead the international rankings — Singapore, Japan, South Korea, Finland, Canada — teachers are drawn from the top third of college graduates, rather than the bottom 60 percent as is the case in the United States. Training in these countries is more rigorous, more tied to classroom practice and more often financed by the government than in America. There are also many fewer teacher-training institutions, with much higher standards. (Finland, a perennial leader in the P.I.S.A. rankings, has eight universities that train teachers; the United States has more than 1,200.)
A fascinating 1988 interview with Isaac Asimov on learning via the internet. Very prescient. Asimov was one of my teenage heroes — I read almost everything he wrote when I was in my science fiction phase. See clip at 2:45 for comments on baseball and mathematics.
zipTimer: an iPod/iPhone app for pacing piano practice, cooking, workouts, you name it.
#5. Some months ago, I noticed the new doorman, S, reading a dog-eared book as I waited for the elevator. Curious, I asked S, who seemed be be about two-thirds of the way through, what he was reading. “Ulysses,” he replied. It was indeed a copy of James Joyce’s magnum opus. Over the next few months, we had many brief and not so brief conversations about literature. Sometimes S recommended a book to me, sometimes (less frequently) I to him. S, who came from the Midwest to do standup comedy, said that several years ago, he decided to embark on a program of purposeful reading, carefully selecting the books with which he would be spending long hours. “Rewarding,” he said. The book of the moment is The Cyberiad, by Stanislaw Lem, also one of my favorites. “Interesting for its philosophical content,” said S, as I made ready to go out into the winter’s cold.
My ideas usually come not at my desk writing but in the midst of living.
– Anais Nin
zipTimer: an iPod/iPhone app for pacing piano practice, cooking, workouts, you name it.
The Rise of the New Groupthink, by Susan Cain
Any denizen of the worlds of academia, education, or management will recognize the words quoted below from Susan Cain’s article:
SOLITUDE is out of fashion. Our companies, our schools and our culture are in thrall to an idea I call the New Groupthink, which holds that creativity and achievement come from an oddly gregarious place. Most of us now work in teams, in offices without walls, for managers who prize people skills above all. Lone geniuses are out. Collaboration is in.
As for me, I will take the advice of Steve Wozniak, aka “the other Steve:”
“Most inventors and engineers I’ve met are like me … they live in their heads. They’re almost like artists. In fact, the very best of them are artists. And artists work best alone …. I’m going to give you some advice that might be hard to take. That advice is: Work alone… Not on a committee. Not on a team.”
— Steve Wozniak
Without great solitude, no serious work is possible.
— Pablo Picasso
Thanks Steve, for that bicycle. I use it a lot. So does my son, my wife, my whole family. Each one in a different way, their own way. We’ve all traveled to new places on our bicycles. By the way, besides working really well, they are beautiful: sleek, elegant.
You inspire us.
Your time is limited, so don’t waste it living someone else’s life. Don’t be trapped by dogma — which is living with the results of other people’s thinking. Don’t let the noise of others’ opinions drown out your own inner voice. And most important, have the courage to follow your heart and intuition. They somehow already know what you truly want to become. Everything else is secondary. — Stanford Commencement Speech, 2005
Why circle and square? There is really no good reason, except that these are simple, classic shapes beloved by mathematicians, artists, and children. The circle appears everywhere: in the sky, as the face of the sun and moon; in children’s drawings as a primitive shape to which eyes, mouth, nose, ears, arms and legs are later added; in philosophy and Greek science, as the perfect form; in mathematics, as one of the principal shapes treated in Euclid’s elements; in art, as an element of composition; in music, as the circle of fifths governing harmonic movement. A good starting point for a blog whose purpose is at yet undefined. (This is an experiment).