Updated on Thu, 01 Jun 2017 06:17:23 GMT, tagged with ‘tech’—‘math’.
I’m happy to announce the publication of a fun, potentially even useful, library I worked on over September 2016. (This post started as a “Work In Progress”-kind of post, but apologizing was more painful than just finishing it and shipping it!)
Mudder.js is a JavaScript library that lets you create lexicographically-evenly-spaced strings. So for example, you can ask for the ten strings that lexicographically sort between two input strings, and you'll get just that, ten short-as-possible evenly-spaced sorted strings.
As a fun bonus, it simplifies converting between JavaScript numbers and their stringy representations in arbitrary bases (non-base-ten) and using arbitrary symbols.
Fun § First things first. We can specify a base-214 number system that uses the 214 Kangxi radicals used by the Chinese to organize Chinese characters, i.e., 0 through 20 is 一丨丶丿乙亅二亠人儿入八冂冖冫几凵刀力勹匕. Example: one billion is 疋亠鼠尢 in this number system, while one-billion-plus-one is 疋亠鼠尸. Another example: Confucius’ name is written 孔子 and consists of the radicals 子乚子, which in this Kangxi number system is 8170—maybe that has some cosmic significance?
var kangxi = `一丨丶丿乙亅二亠人儿入八冂冖冫几凵刀力勹匕匚匸十卜卩厂厶又口囗土士
夂夊夕大女子宀寸小尢尸屮山川工己巾干幺广廴廾弋弓彐彡彳心戈戶手支攴
文斗斤方无日曰月木欠止歹殳毋比毛氏气水火爪父爻爿片牙牛犬玄玉瓜瓦甘
生用田疋疒癶白皮皿目矛矢石示禸禾穴立竹米糸缶网羊羽老而耒耳聿肉臣自
至臼舌舛舟艮色艸虍虫血行衣襾見角言谷豆豕豸貝赤走足身車辛辰辵邑酉釆
里金長門阜隶隹雨青非面革韋韭音頁風飛食首香馬骨高髟鬥鬯鬲鬼魚鳥鹵鹿
麥麻黃黍黑黹黽鼎鼓鼠鼻齊齒龍龜龠`.replace(/\s/g, '');
var rad = new mudder.SymbolTable(kangxi);
console.log('Confucius: ', rad.stringToNumber('子乚子'));
console.log('Billion:', rad.numberToString(1e9));The above code snippet should be live, thanks to the Klipse plugin—feel free to edit the code and instantaneously see the result!
Business § This numerology actually was an unexpected stepping stone to a more serious use. In NoSQL databases like CouchDB or Redis, entries are indexed by stringy keys and I needed a way to reliably insert, delete, and reorder entries to maintain an external ordering without knowing ahead of time how many entries or how they would be ordered. Mudder.js makes it easy to ask for three strings that are lexicographically between, say, 'anhui' and 'azazel', using only the 26 lower-case letters:
console.log(mudder.alphabet.mudder('anhui', 'azazel', 3))
// [ 'aq', 'at', 'aw' ]With Mudder.js, I can always call mudder (i.e., “midder”) to get one or more strings lexicographically between any two stringy keys. Feel free to edit the code above—the results should update instantaneously thanks to the magical Klipse plugin.
(I’ve been referring to “lexicographic” ordering, which is a common (though not the only!) sort order on strings, that is, a way of saying whether a string is “less than”, “equal to”, or “greater than” another. Java’s String.compareTo docs are reasonably clear.)
Most of the complete details are in the literate source, which is actually very verbose 🙄. As usual, the literate methodology—of explaining in prose what I was doing and then showing code that did it—helped a lot, by enormously decreased the activation energy to refactoring bad code. It’s more painful to contort one’s prose explanations to positively spin bad design than just to refactor and make it more cogent.
Near the end though, I tapered off with the literate code because I needed to get on with Real Life and use the library. I didn’t publish the library for this reason, but I’m happy to complete several tests, fix several bugs, and write up the API documentation to publish it now.
JavaScript stack § I also switched from using ES2015 modules, Rollup, and Babel (imitating D3v4, e.g., d3-array) to using simple Node.js require/module.exports modules, Browserify, and Google Closure Compiler. Not only do the former require much ceremony to set up, they also make me do manual dead-code elimination (by carefully specifying with items in a module to import). I am very pleased with using much simpler tools (Node.js modules and Browserify) and just leaning on the powerful Google Closure Compiler to do dead-code elimination for me—as a bonus, it also handles minification and transpilation to ES5. The Dat Project repos influenced me to try this simpler approach—they still don’t do the Google Closure Compiler, that part I got from my ClojureScript background 💪.
Klipse § Perhaps I can note here that I might have had a small role to play in introducing to Klipse’s Yehonathan Sharvit (@viebel) the role he could play in giving voice once again to Alan Kay’s expectation of interactive computing. In “A new way of blogging about javascript”, @viebel quotes an interview where Kay uses Wikipedia to illustrate how unambitious our vision for learning and interacting with computers is:
go to the article on Logo, can you write and execute Logo programs? Are there examples? No. The Wikipedia people didn’t even imagine that, in spite of the fact that they’re on a computer.
Kay’s own presentations, of course created and executed in Smalltalk VM, provided me with a visceral feeling of this disappointing lack of vision. For him, it’s obvious that we should illustrate our thinking right there, with examples in the same medium as the prose that expresses it. No, it does not make any sense to have to install a program, switch to a command-line, or open a new browser tab to try a programming language, or verify a numerical fact, or test an optical illusion as Kay does here.
I see immediately-interactive code is the sister to literate programming. In the last couple of projects (e.g., Ebisu) I’ve worked out a very opinionated, personalized workflow for the latter. In this webpage, I’m happy to acknowledge the fantastic work Klipse has done in making interactive JavaScript blogs dead-simple. Kudos, Klipse!
(That said, the Klipse plugin does weigh in at 1.1 MB minified (225 kB minified+gzipped). In case its download was blocked, the much smaller Mudder.js has been loaded into this window, and should be available in your browser’s JavaScript Console.)
(Banner credit: self, with Gimp’s Flame effect.)
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