kitchen table math, the sequel: a mathematician on math and writing

Wednesday, March 9, 2011

a mathematician on math and writing

re: math & writing:
In both math and writing, the core idea that you are trying to express exists somewhere in the aether. In both math and writing, you start out staring at the blank page, trying to figure out how to summon the idea, make it yours, and commit it to the page. In both math and writing, you make false starts (unless you are very lucky) and work hard (unless you are very lucky) to express the idea with precision and clarity. In both math and writing, your familiarity with the idea that you are trying to express and your prior practice at expressing ideas can sometimes give you a head start in knowing in which direction to start.

Math is writing. Most of math is persuasive writing; math is an exquisitely structured argument.

(I am a professional mathematician.)
I love this.

This passage captures what writing is for me.

This one does, too:
Writing is easy. All you do is stare at a blank sheet of paper until drops of blood form on your forehead.
Gene Fowler


SteveH said...

I don't feel this way. In writing, you can quit at most any time. Good writing might seem like it takes the effort of math or computer science, but it's OK if a few bugs remain. If you get across the main ideas with just the right words, the result can be powerful.

In math, however, there is a level of exactness that is not found in writing. The result can fail no matter how much you work on a problem. The result might not be usable. I could try to find correlations between the two, but what is the goal of this comparison?

"With math, the experience is more like discovering something that's always existed and finally decided to stop playing hard-to-get."

This isn't how I feel either. My specialty is geometric modeling. I have a large toolbox of mathematical techniques that I use to find new solutions to problems. You might say that I'm like a carpenter. I could come up with a number of analogies.

Is the issue whether mathematical museums come close to ever getting students to be more successful in math? The museum might engage and motivate kids to learn, but how large is that effect? Getting excited about fractals, codebreaking, or huge lightning cages won't fix the big gap in fractions you might have. Is the Museum of Science in Boston more than just a fun place to go?

I also think of comments by Feynman about how a poet might see a rainbow and how a physicist might see a rainbow. There is no less poetry in what the physicist sees. But the poet can't see what the scientist sees. I just read a book about how science diverged from philosophy and poetry at the beginning of the 19th century. It talked about people like Humphry Davy and Samuel Coleridge. It was interesting to read about the philosophical difficulties both sides had with the split.

Anonymous said...

And that's the difference between mathematics and engineering. Engineering, as Steve explains, is like carpentry.

If Catherine writes about the parts of the brain, and I read it and end up thinking that the amygdala controls motor functions, then what she wrote was wrong. (Even if she fully understands the amygdala and thought that she wrote about what it really does.) If my understanding of the amygdala is just a little bit off, then what she wrote is less wrong. (Not to be picking on Catherine or her exposition about the amygdala.) Similarly, I can write a theorem that is very incorrect and for which counter-examples exist and justify my so-called theorem with a proof with a horrible, gaping hole. That would be very wrong. Or I might just leave one "obvious" hypothesis out of my theorem, and while it is technically wrong, the addition of a simple clarification (maybe the intersection must be over a finite number of sets and not an arbitrary number or over a countable number and not an arbitrary number -- whatever) can fix it up for the purposes for which it is intended. I can revise my theorem and fix it so that it represents the truth that I am trying to capture.

SteveH said...

Mathematicians are known to do applications and engineers are known to create new math. However, I never wonder whether or how much writing and math are the same. Maybe that's a writer's thing to do. Or not...

My writing and math seem much different, but are they? I'm getting done with the analysis and design phase of a large project and can write up lots of things that sound awfully good and convincing. However, I can't wave my hands with the low level math. It's not clear that all of the pieces will work and work correctly together no matter how much I think or write about the problem.

Maybe this is true with large writing projects; that you don't know what you are doing until you are done. A common saying for new computer programs is that it takes three times to get it right, and I'm not talking about rev 2.0 and rev 3.0. I'm talking about potentially major rewrites. The project I'm working on is (unfortunately) going way too far in the preliminary thinking stage when some key parts have not been proven. I'm big on prototypes. How many writers start from the beginning and go to the end and how many write everything at one level and then refine it? I find that for a lot of my technical writing I get a general outline and then go from the start to the end, restarting many times in the process.

For many complex projects, there is no way to understand something before you do it. I remember doing a test of this years ago for just a very simple function; pass in some variables and return the results. The code was no more than 50-75 lines of code. I tried to write and rewrite it on paper until I was sure it was correct. By the time I implemented it and tied it to the rest of the program, it changed substantially.

If I could generalize a common process, I would say that it's good to get into the details as early as possible, either in a real prototype of a program, or in a real writing project. It seems that you can spend your life working on writing outlines or code UML charts and never get closer to a good result. It's too easy to avoid details if you stay on a higher plane.

Perhaps that's why I like to start to writing exactly what I want to say right from the start, restarting if necessary. Perhaps that's why I like using prototypes for programs where I am actually writing real code as soon as possible. In both cases, I don't start doing this without some preliminary analysis and organization, but I find that too much analysis doesn't help. It is also psychologically helpful to actually get going and have something real to look at.

OK. I did think about it.

Katharine Beals said...

For me, computer programming is like writing. It's like expository writing in that you're trying to figure out the most perspicuous, efficient way of organizing things. And it's like creative writing in that you're creating a cast of characters and events (functions, procedures and/or objects) and assigning them names, properties, and roles; along with a top function that organizes all these characters and events into some sort of plot.

Independent George said...

Computer programming is like writing an instruction manual for an 8-year-old with OCD.