TITLE: Mathematical Formulas, The Great Gatsby, and Small Programs AUTHOR: Eugene Wallingford DATE: October 30, 2012 4:22 PM DESC: ----- BODY: ... or: Why Less Code is Better In Don't Kill Math, Evan Miller defends analytic methods in the sciences against Bret Victor's "visions for computer-assisted creativity and scientific understanding". (You can see some of my reactions to Victor's vision in a piece I wrote about his StrangeLoop talk.) Miller writes:
For the practicing scientist, the chief virtue of analytic methods can be summed up in a single word: clarity. An equation describing a quantity of interest conveys what is important in determining that quantity and what is not at all important.He goes on to look at examples such as the universal law of gravitation and shows that a single formula gives even a person with "minimal education in physics" an economical distillation of what matters. The clarity provided by a good analytic solution affords the reader two more crucial benefits: confident understanding and memorable insights. Poet Peter Turchi describes a related phenomenon in fiction writing, in his essay You and I Know, Order is Everything. A story can pull us forward by omitting details and thus creating in the reader a desire to learn more. Referring to a particularly strategic paragraph, he writes:
That first sentence created a desire to know certain information: What is this significant event? ... We still don't have an answer, but the context for the question is becoming increasingly clear -- so while we're eager to have those initial questions answered, we're content to wait a little longer, because we're getting what seems to be important information. By the third paragraph, ... we think we've got a clue; but by that time the focus of the narrative is no longer the simple fact of what's going on, but the [larger setting of the story]. The story has shifted our attention from a minor mystery to a more significant one. On some level or another nearly every successful story works this way, leading us from one mystery to another, like stepping stones across a river.In a good story, eventually...
... we recognize that the narrator was telling us more than we could understand, withholding information but also drawing our attention to the very thing we should be looking at.In two very different contexts, we see the same forces at play. The quality of a description follows from the balance it strikes between what is in the description and what is left out. To me, this is another example of how a liberal education can benefit students majoring in both the sciences and the humanities [ 1 | 2 ]. We can learn about many common themes and patterns of life from both traditions. Neither is primary. A student can encounter the idea first in the sciences, or first in the humanities, whichever interests the student more. But apprehending a beautiful pattern in multiple domains of discourse can reinforce the idea and make it more salient in the preferred domain. This also broadens our imaginations, allowing us to see more patterns and more subtlety in the patterns we already know. So: a good description, a good story, depends in some part on the clarity attendant in how it conveys what is important and what is not important. What are the implications of this pattern for programming? A computer program is, after all a description: an executable description of a domain or phenomenon. I think this pattern gives us insight into why less code is usually better than more code. Given two functionally equivalent programs of different lengths, we generally prefer the shorter program because it contains only what matters. The excess code found in the longer program obscures from the reader what is essential. Furthermore, as with Miller's concise formulas, a short program offers its reader the gift of more confident understanding and the opportunity for memorable insights. What is not in a program can tell us a lot, too. One of the hallmarks of expert programmers is their ability to see the negative space in a design and program and learn from it. My students, who are generally novice programmers, struggle with this. They are still learning what matters and how to write descriptions at all, let alone concise one. They are still learning how to focus their programming tools, and on what. -----