Creativity

I was reading a chapter from The Element this evening that reminded me of The Medici Effect.

ACM Ubiquity had an interview with Frans Johansson, author of The Medici Effect, around the time the book came out. The title comes from the idea that it takes more than just genius to create a Leonardo da Vinci. It also takes the community of a Renaissance Florence, made possible by patrons like the Medici family.

I thought it was a great premise for a book and bought the book shortly after reading the interview. Unfortunately, the book didn’t live up to my expectations. I recommend the interview, but I’m not as enthusiastic in my recommendation of the book.

Related post:

Don’t standardize education, personalize it

There was an odd story in NA Digest a couple days ago, John Francis of QR found. When I saw that someone was found, I assumed he had lost as in lost at sea, like Jim Gray. But that wasn’t the case.

John Francis developed the QR algorithm, an algorithm for finding the eigenvalues and eigenvectors of a matrix. Some experts regard the QR algorithm as one of the 10 most important numerical algorithms of the 20th century. He developed the algorithm in 1959 but then left the numerical analysis community three years later. The NA Digest article doesn’t say whether Francis became a recluse or simply moved on to a job outside mathematics. No one in numerical analysis knew anything about him until a couple folks tracked him down recently. He is doing well. He remembers his earlier work clearly but was unaware of the impact it had had.

Related post: Simple legacy (how people often underestimate the importance of their most useful work)

In what sense did Christopher Columbus discover America? Obviously he wasn’t the first human to step foot on the New World. Columbus wasn’t even the first European. Norwegian explorer Leif Erikson seems to have arrived 500 years before Columbus. But as Stephen Mills famously stated,

There have been other people before Columbus, but when Columbus discovered the New World, it stayed discovered.

The same principle could be used to resolve debates about priorities in mathematical discoveries.There is some debate over whether John Tukey or Carl Gauss discovered the Fast Fourier Transform (FFT). But there is no doubt that after Tukey discovered it, the FFT stayed discovered. The algorithm is now used in digital signal processing applications everywhere.

Gauss and Tukey were both brilliant mathematicians. Tukey, however, also had an aptitude for creating memorable names. For example, you may have heard “software,” a term he coined.

Related posts:

Innovation versus invention
Three quotes on originality
Don’t try to be God, try to be Shakespeare

In the movie Redbelt, Chiwetel Ejiofor plays Mike Terry, a Jiu Jitsu instructor who will fight but will not compete. He will fight in a real fight if necessary, but he won’t fight in a ring because competitions have arbitrary rules. He is a skilled fighter because he is creative, and competitions take away that creativity. At one point in the movie, someone Terry if he teaches people to win. He says no, he teaches people to prevail. In his mind, you can’t “win” a fight. A fight is a problem to be solved.

Mike Terry’s distinction between fights and contests makes me think of the distinction between practical and academic problem solving. Practical problem solving does not have arbitrary constraints whereas academic problems often do: you can use this technique but not that one, you can use this reference but not that one, etc. These academic limitations serve a purpose in their context, but sometimes we can imagine these constraints are still on us after we leave the classroom.

Sometimes we’ll struggle mightily to solve a problem analytically that could be easily be solved numerically (or vice versa). Or we’ll imagine that a problem must be solved using a particular programming language even though it could be done more easily using a different language. It feels like “cheating” to go for the easier solution. But if you’re not in an academic setting, you can’t “cheat.” (Of course I’m not talking about violating ethical standards to solve a problem, only dismissing artificial restrictions. Where there is no law, there is no sin.)

There may be good reasons for pursuing the more difficult solution. For example, entertainment value. Sometimes we want to see whether we can do something the hard way. There’s nothing wrong with that, as long as we acknowledge that’s what we’re doing. But sometimes we do things the hard way for no good reason other than not having examined our self-imposed limitations. Maybe we’re trying to win rather than solve the problem.

I’m not saying entertainment value is the only reason to go down a more difficult road. Maybe you suspect there will be additional benefits if the more difficult approach succeeds. Again, that’s fine if this is a conscious decision and not a lack of creativity.

Related post: Try the simplest thing that could possibly work

Here are three ways to evaluate a person’s performance.

1. How good are they at their worst?
2. How good are they on average?
3. How good are they at their best?

Schools use the first two criteria, but the market uses the third.

Schools evaluate people at their worst

Teachers average grades to come up with semester grades, and semester grades feed into a grade point average. So in some sense schools evaluate average performance.

But in more subtle ways schools evaluate students by how good they are at their worst. To graduate, your lowest course grade in all your required courses must be passing. No amount of brilliance in one area can compensate for a failing grade in another area. Your creative writing grades are excellent, Mr. Shakespeare, but we cannot let you graduate until you pass physics.

How do you get on the honor roll? Your lowest grade has to be above a certain level. Again, what matters is how good you are at your worst.

How do you get to be valedictorian? Be good enough at every class to get an A. You have to be pretty good at everything, but you don’t have to be truly exceptional at anything.

Schools encourage perfectionism, not excellence. They encourage people to avoid mistakes, not to be creative.

Markets evaluate people at their best

Markets often evaluate people and products at their best.

If you write 100 obscure novels and one best-seller, you’re a best-selling author. If you consistently write moderately popular novels, you’re not. If you write one really good novel, you might get a Nobel prize. Imagine the Nobel committee evaluating a writer saying “Yeah, these two novels were brilliant, world-changing. But he also wrote this one novel that was mediocre. Let’s give the prize to someone whose books are consistently pretty good.”

The Ford F150 did poorly in focus groups. The average rating wasn’t good. But the people who liked it really liked it. And the F150 went on to be the most popular truck in history. All that matters in business is people who like your product enough to buy it. You don’t make any money by being everyone’s second choice.

If a company has one product that is a runaway success, the company is a success. If it has two or three runaway successes, even better. But a company can produce a few dismal failures (think Microsoft Bob or the Apple Newton) and still do quite well if their flagship products succeed.The same is true of the people behind these products. Someone can make a successful career with one big win even if they have a number of failures.

We all want others to see the best in us. There are ethical and economic reasons to look for the best in others. But years of education can incline us to look for the worst in others and in ourselves.

Related posts:

Quantity and quality
Four reasons we don’t apply the 80/20 rule
Gerald Weinberg’s law of twins

Last night I listened to the latest FLOSS Weekly podcast, an interview with the creators of Processing. I’d heard of the Processing language before, but I thought it was some sort of ETL (extract, transform, and load) tool for data processing. Instead, it’s a Java-like language for artists. Here’s the description from the processing.org site.

Processing is an open source programming language and environment for people who want to program images, animation, and interactions. It is used by students, artists, designers, researchers, and hobbyists for learning, prototyping, and production. It is created to teach fundamentals of computer programming within a visual context and to serve as a software sketchbook and professional production tool.

Show notes | audio

When I was in college, I had the pleasure of taking a couple math classes taught by Mike Starbird. One of the things he told us about problem solving was this: when you’re stuck, draw a picture. Good advice, though hardly original. But then he said something else: If you’re still stuck, draw a bigger picture.

When you draw small, you think small. It’s surprising how much your thinking opens up when you draw a bigger picture. You can draw some little diagram and think “that didn’t help.” But when you take that same unhelpful diagram and make it much larger, it may be just what you need.

Unix advocates often say Unix is great because it has all these powerful tools. And yet practically every Unix tool has been ported to Windows. So why not just run Unix tools on Windows so that you have access to both tool sets? Sounds reasonable, but hardly anyone does that. People either use Unix tools on Unix or Windows tools on Windows.

Part of the reason is compatibility. Not binary compatibility, but cultural compatibility. There’s a mental tax for shifting modes of thinking as you switch tools.

I think the reason why few people use Unix tools on Windows is a sort of negative space. Artists use the term negative space to discuss the importance of what is not in a work of art, such as the white space around a figure or the silence framing a melody.

Similarly, part of what makes an operating system culture is what is not there. You don’t have to worry about what’s not there. And not worrying about something frees up brain capacity to think about something else. Having too many options can be paralyzing. I think that even though people say they like Unix for what is there, they actually value what is not there.

The other day Nils gave an interesting answer to a question on StackOverflow regarding color theory. 

NEVER ever use pure colors. … If you have no idea what color to start with, get a classic masterpiece of painting from the net. Blur it a bit and then pick some nice colors from it. If you use some common sense it’s hard not to end with pleasant colors this way.

He gave the example of extracting this color scheme

from this painting.

Andy Hunt posted an article this morning entitled Science Failure and Cubicle Brain Death. He explains that one reason it took so long to discover that adult animals could grow new brain cells was that such growth doesn’t happen in laboratory conditions. To grow new brain cells, animals need stimulation that a sterile lab environment does not provide. People need stimulating environments too. Little things matter.

… things like the pen and paper you use, the decorations at your desk, the lighting and ceiling height of your cubicle all have a measurable effect on your cognitive processes.

Joel Spolsky talked about this in the latest StackOverflow podcast. His company often faces criticism for spending so much money on office space for developers. But as he put it, the difference between depressing and stimulating office space may amount to whether you devote 4% or 6% of your total budget to rent. The extra investment in office space allows you to recruit more competitively for top talent and makes the people you hire more productive.

Related posts:

Selective use of technology
Brain plasticity
Getting to the bottom of things

Benoit Mandelbrot makes the following observation in The Fractal Geometry of Nature.

Many creative minds overrate their most baroque works, and underrate the simple ones. When history reverses such judgments, prolific writers come to be best remembered as authors of “lemmas,” of propositions they had felt “too simple” in themselves and had to be published solely as preludes to forgotten theorems.

If you’re not familiar with lemmas and theorems, think of a musician who is famous for a short prelude written as an introduction to a longer piece nobody remembers. For example, Rossini’s four-minute William Tell Overture is far more famous than the four-hour William Tell opera it introduces.

Returning to famous mathematicians, I remember as an undergraduate hearing of Schwarz’s lemma and waiting for the corresponding theorem that never came. The same applies to Poincaré’s lemma, Zorn’s lemma, and Fatou’s lemma.

We’re all naturally proud of things we work hard for. We expect other people to value our work in proportion to the amount of effort we put into it, but the world doesn’t work that way. It can be discouraging focus on the big, complex projects we’ve worked on that haven’t been appreciated. On the other hand, it can be very encouraging to think of the potential impact of small projects and simple ideas.

Neptune was discovered in 1846. But Galileo’s notebooks describe a “star” he saw on 28 December 1612 and 2 January 1613 that we now know was Neptune. Galileo even noticed that his star was in a slightly different location for his two observations, but he chalked the difference up to observational error.

The men who discovered Neptune were not the first to see it; they were the first to realize what they were looking at.

Classroom exercises always have nice, tidy solutions. So students implicitly assume that all problems have nice, tidy solutions. If the solution isn’t working out simply, you must have made a mistake.

Outside the classroom, applications seldom have simple solutions. So after a while you get jaded and quit trying to find a simple solution. But sometimes real problems do have simple solutions, or at least simpler solutions than seemed possible.

The Extreme Programming folks have a saying “Try the simplest thing that could possibly work.” If that doesn’t work, then try the next simplest thing that could possibly work. That line of thinking has paid off a few times lately.

I’ve had a couple math problems that I first assumed had to be approximated numerically that were more easily computed exactly. And I’ve had a couple programs where I was able to debug a section of code by simply deleting it. Things don’t always work out that well, but it’s fun when they do.

In the article Neo-Amish Drop Outs, Kevin Kelly shares a quote from Donald Knuth explaining why he (Knuth) seldom reads email.

Rather than trying to stay on top of things, I am trying to get to the bottom of things.

Getting to the bottom of things — questioning assumptions, investigating causes, making connections — requires a different state of mind than staying on top of things. Deep thought is difficult when you’re frequently interrupted. It’s just as difficult when you anticipate being interrupted even if the interruption never comes.

We don’t task switch nearly as well as we think we do. We think we can switch instantly between tasks, when in reality it takes at least 15 minutes to recover our thoughts, and that’s if we were doing something relatively simple. With more complex tasks, it takes longer.

When I began to understand this a few years ago, I asked a colleague how long it takes her to recover from an interruption. She said three days. I thought she was exaggerating, but now I appreciate that it really can take a few days to get into a hard problem.