This post looks at how to partition complexity between definitions and theorems, and why it’s useful to be able to partition things more than one way. Quadratic equations Imagine the following dialog in an algebra class. “Quadratic equations always have two roots.” “But what about (x − 5)² = 0. That just has one root, […]
The other day I ran across a Rick Beato video entitled “The most complex pop song of all time.” I thought the song would be something by a cerebral group like Rush, but instead it’s “Never Gonna Let You Go” by Sérgio Mendes. The song made it to #4 on the weekly pop charts in […]
The other day I ran across the biochemical pathways poster from Roche. This is the first of two posters. Both posters are about 26 square feet in area. Below is a close up of about one square foot in the middle of the first poster. I’d seen this before, I think while I was working […]
Iterating simple rules can lead to complex behavior. Many examples of this are photogenic, and so they’re good for popular articles. It’s fun to look at fractals and such. I’ve written several articles like that here, such as the post that included the image below. But there’s something in popular articles on complexity that bothers […]
Physicist Lev Landau used to play a mental game with Soviet license plates [1]. The plates had the form of two digits, a dash, two more digits, and some letters. Rules of the game His game was to apply high school math operators to the numbers on both side of the dash so that the […]
This post is a riff on a line from Mathematics without Apologies, the book I quoted yesterday. In an all too familiar trade-off, the result of striving for ultimate simplicity is intolerable complexity; to eliminate too-long proofs we find ourselves “hopelessly lost” among the too-long definitions. [emphasis added] It’s as if there’s some sort of […]
Dan Sullivan coined an interesting term: The Ceiling of Complexity™. (Sullivan has a habit of trademarking™ everything™ he™ says™. I dislike the gratuitous trademarking, but I like the phrase “ceiling of complexity.”) The idea behind ceiling of complexity is that every project you complete creates residual responsibilities and expectations. This residual may be small, maybe […]
I’ve started to read through Michael Fogus’ list of recommended technical papers and ran across this gem from Out of the Tar Pit: Complexity breeds complexity. There are a whole set of secondary causes of complexity. This covers all complexity introduced as a result of not being able to clearly understand a system. Duplication is […]
Here are a dozen previous posts on simplicity and complexity. Obscuring complexity Three quotes on simplicity Complexity and unity A little simplicity goes a long way Simple legacy Simplicity in old age Software that gets used Conservation of complexity Confusing familiar with simple Four mechanical devices Rewarding complexity Stupidity scales
Sometime around 1994, my office mate introduced me to HTML by saying it was 10 times simpler than LaTeX. At the time I thought he was right. Now I’m not so sure. Maybe he was right in 1994 when the expectations for HTML were very low. It is easier to bang out a simple, ugly […]
