Being useful

Chuck Bearden posted this quote from Steve Holmes on his blog the other day:

Usefulness comes not from pursuing it, but from patiently gathering enough of a reservoir of material so that one has the quirky bit of knowledge … that turns out to be the key to unlocking the problem which someone offers.

Holmes was speaking specifically of theology. I edited out some of the particulars of his quote to emphasize that his idea applies more generally.

Obviously usefulness can come from pursuing it. But there’s a special pleasure in applying some “quirky bit of knowledge” that you acquired for its own sake. It can feel like simply walking up to a gate and unlocking it after unsuccessful attempts to storm the gate by force.

Avoiding difficult problems

The day after President Kennedy challenged America to land a man on the moon,

… the National Space Agency didn’t suit up an astronaut. Instead their first goal was to hit the moon — literally. And just over three years later, NASA successfully smashed Ranger 7 into the moon … It took fifteen ever-evolving iterations before the July 16, 1969, gentle moon landing …

Great scientists, creative thinkers, and problem solvers do not solve hard problems head-on. When they are faced with a daunting question, they immediately and prudently admit defeat. They realize there is no sense in wasting energy vainly grappling with complexity when, instead, they can productively grapple with smaller cases that will teach them how to deal with the complexity to come.

From The 5 Elements of Effective Thinking.

Some may wonder whether this contradicts my earlier post about how quickly people give up thinking about problems. Doesn’t the quote above say we should “prudently admit defeat”? There’s no contradiction. The quote advocates retreat, not surrender. One way to be able to think about a hard problem for a long time is to find simpler versions of the problem that you can solve. Or first, to find simpler problems that you cannot solve. As George Polya said

If you can’t solve a problem, then there is an easier problem that you can’t solve; find it.

Bracket the original problem between the simplest version of the problem you cannot solve and the fullest version of the problem you can solve. Then try to move your brackets.

How long can you think about a problem?

The main difficulty I’ve seen in tutoring math is that many students panic if they don’t see what to do within five seconds of reading a problem, maybe two seconds for some. A good high school math student may be able to stare at a problem for fifteen seconds without panicking. I suppose students have been trained implicitly to expect to see the next step immediately. Years of rote drill will do that to you.

A good undergraduate math student can think about a problem for a few minutes before getting nervous. A grad student may be able to think about a problem for an hour at a time. Before Andrew Wiles proved Fermat’s Last Theorem, he thought about the problem for seven years.

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Complex for whom?

From Out of the Tar Pit:

… the type of complexity we are discussing in this paper is that which makes large systems hard to understand. It is this that causes us to expend huge resources in creating and maintaining such systems. This type of complexity has nothing to do with complexity theory — the branch of computer science which studies the resources consumed by a machine executing a program. The two are completely unrelated — it is a straightforward matter to write a small program in a few lines which is incredibly simple (in our sense) and yet is of the highest complexity class (in the complexity theory sense).

More posts on complexity

Work or rest

According a recent biography of Henri Poincaré,

Poincaré … worked regularly from 10 to 12 in the morning and from 5 till 7 in the late afternoon. He found that working longer seldom achieved anything …

Poincaré made tremendous contributions to math and physics. His two-hour work sessions must have been sprints, working with an intensity that could not be sustained much longer.

I expect most of us would accomplish more if we worked harder when we worked, rested more, and cut out half-work.

Update: To be clear, the quote above refers to Poincaré’s most intellectually demanding work. Poincaré carried on his administrative duties outside the four hours of concentration mentioned above.

Pushing an idea

From The 5 Elements of Effective Thinking:

Calculus may hold a world’s record for how far an idea can be pushed. Leibniz published the first article on calculus in 1684, an essay that was a mere 6 pages long. Newton and Leibniz would surely be astounded to learn that today’s introductory calculus textbook contains over 1,300 pages. A calculus textbook introduces two fundamental ideas, and the remaining 1,294 pages consists of examples, variations, and applications—all arising from following the consequences of just two fundamental idea.

Design for outcomes

Designing a device to save lives is not enough. People may not use it, or may not use it correctly. Or be unable to maintain it. Or …

I’ve seen analogous problems with statistical methods. People will not necessarily adopt a new statistical method just because it is better. And if they do use it, they may use it wrongly, just like medical devices.

(“Better” in the previous paragraph is a loaded term. Statistical methods are evaluated by many criteria: power, robustness, bias, etc. When someone says his new method is better, he means better by the criteria he cares most about. But even when there is agreement on statistical criteria, a superior statistical method may be rejected for non-statistical reasons.)

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Bicycle skills

A while back I wrote about learning things just-in-case or just-in-time. Some things you learn in case you need them in the future, and some things you learn as needed.

How do you decide whether something is worth learning ahead of time, or whether it is best to learn if and when you need it? This is a common dilemma, especially in technology. There’s no easy answer. You have to decide what is best in your circumstances. But here’s a suggestion: Learn real-time skills and bicycle skills in advance.

A real-time skill is something you need for live performance. If you’re going to speak French, you have to memorize a large number words before you need them in conversation. Looking up every word in a English-French dictionary as needed might work in the privacy of your study, but it would be infuriatingly slow in a face-to-face conversation. Some skills that we don’t think of as being real-time become real-time when you have to use them while interacting with other people.

More subtle than real-time skills are what I’m calling bicycle skills. Suppose you own a bicycle but haven’t learned to ride it. Each day you need to go to a store half a mile away. Each day you face the decision whether to walk or learn to ride the bicycle. It takes less time to just walk to the store than to learn to ride the bicycle and ride to the store. If you always do what is fastest that day, you’ll walk every day. I’m thinking of a bicycle skill as anything that doesn’t take too long to learn, quickly repays time invested, but will never happen without deliberate effort.

When you’re under pressure, you don’t learn bicycle skills. You don’t make long-term investments, even if the “long-term” is 30 minutes away. I’ll just walk, thank you.

What are bicycle skills you need to learn, things that would save time in the long run but haven’t been worthwhile in the short term?

The cult of average

Shawn Achor comments on “the cult of the average” in science.

So one of the very first things we teach people in economics and statistics and business and psychology is how, in a statistically valid way, do we eliminate the weirdos. How do we eliminate the outliers so we can find the line of best fit? Which is fantastic if I’m trying to find out how many Advil the average person should be taking — two. But if I’m interested in potential, if I’m interested in your potential, or for happiness or productivity or energy or creativity, what we’re doing is we’re creating the cult of the average with science. … If we study what is merely average, we will remain merely average.

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tl;dr

The slang “tl;dr” stands for “too long; didn’t read.” The context is often either a bad joke or a shallow understanding.

What bothers me most about tl;dr is the mindset it implies, scanning everything but reading nothing. I find myself slipping into that mode sometimes. Skimming is a vital skill, but it can become so habitual that it crowds out reflective reading.

When I realize everything I’m reading is short and new, when my patience has atrophied to the point that I get annoyed at long tweets, I’ll read something long and old to restore my concentration and perspective.

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