Last night I went to a concert by the Branford Marsalis Quartet. One of the things that impressed me about the quartet was how creative they are while also being squarely within a tradition. People who are not familiar with jazz may not realize how structured it is and how much it respects tradition. The spontaneous and creative aspects of jazz are more obvious than the structure. In some ways jazz is more tightly structured than classical music. To use Francis Schaeffer’s phrase, there is form and freedom, freedom within form.
Every field has its own structure, its tropes, its traditions. Someone unfamiliar with the field can be overwhelmed, not having the framework that an insider has to understand things. They may think something is completely original when in fact the original portion is small.
In college I used to browse the journals in the math library and be completely overwhelmed. I didn’t learn until later that usually very little in a journal article is original, and even the original part isn’t that original. There’s a typical structure for a paper in PDEs, for example, just as there are typical structures for romantic comedies, symphonies, or space operas. A paper in partial differential equations might look like this:
- Motivation / previous work
- Weak formulation of PDE
- Craft function spaces and PDE as operator
- A priori estimates imply operator properties
- Well posedness results
An expert knows these structures. They know what’s boilerplate, what’s new, and just how new the new part is. When I wrote something up for my PhD advisor I remember him saying “You know what I find most interesting?” and pointing to one inequality. The part he found interesting, the only part he found interesting, was not that special from my perspective. It was all hard work for me, but only one part of it stood out as slightly original to him. An expert in partial differential equations sees a PDE paper the way a professional musician listens to another or the way a chess master sees a chess board.
While a math journal article may look totally incomprehensible, an expert in that specialization might see 10% of it as somewhat new. An interesting contrast to this is the “abc conjecture.” Three and a half years ago Shinichi Mochizuki proposed a proof of this conjecture. But his approach is so entirely idiosyncratic that nobody has been able to understand it. Even after a recent conference held for the sole purpose of penetrating this proof, nobody but Mochizuki really understands it. So even though most original research is not that original, once in a while something really new comes out.
I heard of someone who had a commitment to get rid of something every Thursday. I don’t know anything about how they carried that out. It could mean throwing out or donating to charity a physical object each Thursday. Or maybe it could be handing over a responsibility or letting go of an ambition. It could be a combination, such as getting rid of an object that is a reminder of something intangible that you want to let go of.
This may mean reducing your total inventory of objects or obligations, or it could be simply turnover, making room for new things.
Getting rid of an obligation is not necessarily irresponsible, nor is letting go of an ambition necessarily lazy. Letting go of one obligation to take on another could be very responsible. Letting go of one ambition to pursue another could be a lot of work.
I was listening to a classic music station yesterday, and I heard the story of a professional pianist whose hand was injured in an accident. He then started learning trumpet and two years later he was a professional trumpeter. I didn’t catch the musician’s name.
I was not surprised that a professional in one instrument could become a professional in another, but I was surprised that he did it in only two years. It probably helped that he was no longer able to play piano; I imagine if he wanted to learn trumpet in addition to piano he would not have become so proficient so quickly.
If you go by the rule of thumb that it takes about 10 years to master anything, this professional pianist was 80% of the way to becoming a professional trumpeter before he touched a trumpet. Or to put it another way, 80% of being a professional musician who plays trumpet is becoming a professional musician.
Transferable skills are more difficult to acquire and more valuable than the context in which they’re exercised.
This is a post about letting go of something you think you need. It starts with an illustration from programming, but it’s not about programming.
Bob Martin published a dialog yesterday about the origin of structured programming, the idea that programs should not be written with
goto statements but should use less powerful, more specialized ways to transfer control. Edsgar Dijkstra championed this idea, most famously in his letter Go-to statement considered harmful. Since then there have been countless “considered harmful” articles that humorously allude to Dijkstra’s letter.
Toward the end of the dialog, Uncle Bob’s interlocutor says “Hurray for Dijkstra” for inventing the new technology of structured programming. Uncle Bob corrects him
New Technology? No, no, you misunderstand. … He didn’t invent anything. What he did was to identify something we shouldn’t do. That’s not a technology. That’s a discipline.
Huh? I thought Structured Programming made things better.
Oh, it did. But not by giving us some new tools or technologies. It made things better by taking away a damaging tool.
The money quote is the last line above: It made things better by taking away a damaging tool.
Creating new tools gets far more attention than removing old tools. How might we be better off by letting go of a tool? When our first impulse is that we need a new technology, might we need a new discipline instead?
Few people have ever been able to convince an entire profession to let go of a tool they assumed was essential. If we’re to have any impact, most of us will need to aim much, much lower. It’s enough to improve our personal productivity and possibly that of a few peers. Maybe you personally would be better off without something that is beneficial to most people.
What are some technologies you’ve found that you’re better off not using?
I don’t know how many times I’ve heard about how Mozart would compose entire musical scores in his head and only write them down once they were finished. Even authors who stress that creativity requires false starts and hard work have said that Mozart may have been an exception. But maybe he wasn’t.
In his new book How to Fly a Horse, Kevin Ashton says that the Mozart story above is a myth based on a forged letter. According to Ashton,
Mozart’s real letters—to his father, to his sister, and to others—reveal his true creative process. He was exceptionally talented, but he did not write by magic. He sketched his compositions, revised them, and sometimes got stuck. He could not work without a piano or harpsichord. He would set work aside and return to it later. … Masterpieces did not come to him complete in uninterrupted streams of imagination, nor without an instrument, nor did he write them whole and unchanged. The letter is not only forged, it is false.
From Freeman Dyson:
Economic forecasting is useful for predicting the future up to about ten years ahead. Beyond ten years the quantitative changes which the forecast accesses are usually sidetracked or made irrelevant by qualitative changes in the rules of the game. Qualitative changes are produced by human cleverness … or by human stupidity … Neither cleverness nor stupidity are predictable.
Source: Infinite in All Directions, Chapter 10, Engineers’ Dreams.
Zig Ziglar said that if you increase your confidence, you increase your competence. I think that’s generally true. Of course you could be an idiot and become a more confident idiot. In that case confidence just makes things worse . But otherwise when you have more confidence, you explore more options, and in effect become more competent.
There are some things you may need to learn not for the content itself but for the confidence boost. Maybe you need to learn them so you can confidently say you didn’t need to. Also, some things you need to learn before you can see uses for them. (More on that theme here.)
I’ve learned several things backward in the sense of learning the advanced material before the elementary. For example, I studied PDEs in graduate school before having mastered the typical undergraduate differential equation curriculum. That nagged at me. I kept thinking I might find some use for the undergrad tricks. When I had a chance to teach the undergrad course a couple times, I increased my confidence. I also convinced myself that I didn’t need that material after all.
My experience with statistics was similar. I was writing research articles in statistics before I learned some of the introductory material. Once again the opportunity to teach the introductory material increased my confidence. The material wasn’t particularly useful, but the experience of having taught it was.
Related post: Psychological encapsulation
 See Yeats’ poem The Second Coming:
The best lack all conviction, while the worst
Are full of passionate intensity.
The other day I was driving by our veterinarian’s office and saw that the marquee said something like “Prevention is less expensive than treatment.” That’s sometimes true, but certainly not always.
This evening I ran across a couple lines from Ed Catmull that are more accurate than the vet’s quote.
Do not fall for the illusion that by preventing errors, you won’t have errors to fix. The truth is, the cost of preventing errors is often far greater than the cost of fixing them.
From Creativity, Inc.
I’ve seen exhortations to think like Leonardo da Vinci or Albert Einstein, but these leave me cold. I can’t imagine thinking like either of these men. But here are a few famous people I could imagine emulating when trying to solve a problem
What would Donald Knuth do? Do a depth-first search on all technologies that might be relevant, and write a series of large, beautiful, well-written books about it all.
What would Alexander Grothendieck do? Develop a new field of mathematics that solves the problem as a trivial special case.
What would Richard Stallman do? Create a text editor so powerful that, although it doesn’t solve your problem, it does allow you to solve your problem by writing a macro and a few lines of Lisp.
What would Larry Wall do? Bang randomly on the keyboard and save the results to a file. Then write a language in which the file is a program that solves your problem.
What would you add to the list?
Sometimes you can apply math just by raiding it for vocabulary. You may not need to apply a single theorem.
This has been a surprise to me. I’m more used to creating a mathematical model so you can compute something or apply some theorem. But sometimes you can move a project along just by providing a name for a concept. A meandering discussion can snap into focus because someone has a name for an idea everyone vaguely understands.
Sometimes it may be clear that only part of a mathematical definition applies. In this case math can guide the discussion by asking whether the rest of the definition applies. “It sounds like we’ve got a widget here. A widget has to have these five properties and clearly we have the first three. Let’s think about whether the last two hold.” The answers don’t have to be positive to be useful. You might realize something important in the process of explaining why your thing is not a widget.
Sometimes a definition may not apply at all and still be useful! “This reminds me of a widget. It’s not a widget in any strict sense. But if it were, this is what we’d do next. I wonder whether we can do something like that.”
In describing writing his second book, Tom Leinster says
… I’m older and, I hope, more able to cope with stress: just as carpenters get calloused hands that make them insensitive to small abrasions, I like to imagine that academics get calloused minds that allow them not to be bothered by small stresses and strains.
Mental callouses are an interesting metaphor. Without the context above, “calloused minds” would have a negative connotation. We say people are calloused or insensitive if they are unconcerned for other people, but Leinster is writing of people unperturbed by distractions.
You could read the quote above as implying that only academics develop mental discipline, though I’m sure that’s not what was intended. Leinster is writing a personal post about the process of writing books. He’s an academic, and so he speaks of academics.
Not only do carpenters become more tolerant of minor abrasions, they also become better at avoiding them. I’m not sure that I’m becoming more tolerant of stress and distractions as I get older, but I do think I’m getting a little better at anticipating and avoiding stress and distractions.
This morning my daughter told me that she did well on a spelling test, but she got the easiest words wrong. Of course that’s not exactly true. The words that are hardest for her to spell are the ones she in fact did not spell correctly. She probably meant that she missed the words she felt should have been easy. Maybe they were short words. Children can be intimidated by long words, even though long words tend to be more regular and thus easier to spell.
Our perceptions of what is easy are often upside-down. We feel that some things should be easy even though our experience tells us otherwise.
Sometimes the trickiest parts of a subject come first, but we think that because they come first they should be easy. For example, force-body diagrams come at the beginning of an introductory physics class, but they can be hard to get right. Newton didn’t always get them right. More advanced physics, say celestial mechanics, is in some ways easier, or at least less error-prone.
“Elementary” and “easy” are not the same. Sometimes they’re opposites. Getting off the ground, so to speak, may be a lot harder than flying.
“It was a favorite theme of C. S. Lewis that only lazy people work hard. By lazily abdicating the essential work of deciding and directing, establishing values and setting goals, other people do it for us; then we find ourselves frantically, at the last minute, trying to satisfy a half dozen demands on our time, none of which is essential to our vocation, to stave off the disaster of disappointing someone.” — Eugene Peterson
Whenever you remove noise, you also remove at least some signal. Ideally you can remove a large portion of the noise and a small portion of the signal, but there’s always a trade-off between the two. Averaging things makes them more average.
Statistics has the related idea of bias-variance trade-off. An unfiltered signal has low bias but high variance. Filtering reduces the variance but introduces bias.
If you have a crackly recording, you want to remove the crackling and leave the music. If you do it well, you can remove most of the crackling effect and reveal the music, but the music signal will be slightly diminished. If you filter too aggressively, you’ll get rid of more noise, but create a dull version of the music. In the extreme, you get a single hum that’s the average of the entire recording.
This is a metaphor for life. If you only value your own opinion, you’re an idiot in the oldest sense of the word, someone in his or her own world. Your work may have a strong signal, but it also has a lot of noise. Getting even one outside opinion greatly cuts down on the noise. But it also cuts down on the signal to some extent. If you get too many opinions, the noise may be gone and the signal with it. Trying to please too many people leads to work that is offensively bland.
Related post: The cult of average
From “The Inheritance of Tools” by Scott Russell Sanders:
I had botched a great many pieces of wood before I mastered the right angle with a saw, botched even more before I learned to miter a joint. The knowledge of these things resides in my hands and eyes and the webwork of muscles, not in the tools. There are machines for sale—powered miter boxes and radial arm saws, for instance—that will enable any casual soul to cut proper angles in boards. The skill is invested in the gadget instead of the person who uses it, and this is what distinguishes a machine from a tool.
Related post: Software exoskeletons