...an idea is no more an even relatively constant thing than is a feeling or emotion or volitional process. There exist only changing and transient ideational processes; there are no permanent ideas that return again and disappear again.
-- Wilhelm Wundt An Introduction to Psychology
Complexity and Likeablity
Wilhelm Wundt is famous for his many contributions to psychology. I have been interested in one particular contribution of his for many years now: the Wundt Curve. The Wundt Curve is a Bell-like curve laying on the x and y axes of Complexity and Likeability. The Wundt Curve shows how we like things to be more complex to a point (the apex of the curve) at which point any more complexity results in a decrease in likeability. The Wundt Curve plays nicely both into Clojure and the Run-Length encoding problem - # 12 in 99 Lisp Problems.
Clojure
First, since I would prefer not to incure the wrath of Rich Hickey, I must clearly state that the complexity I spoke of in the previous paragraph is not the complexity Rich spoke of in his seminal presentation Simple Made Easy. In fact, just to make things clear I won't use the word complexity anymore - suffice to say that we are talking about novelty here and not something consisting of interwoven parts.
I love Clojure. It is simply beautiful. For the other Comp Sci students like me that learned assembly and C rather than Lisp, it certainly has novelty in syntax, but over time, the Clojure student realizes that this novelty sits nicely in a spot that is very likeable. Beyond the syntax, the budding Clojurist realizes that the language is filled with beautiful data structures, ubiquitous interfaces (protocols) and a simple power that is both novel and very likeable indeed.
Information Theory
The Wundt curve always makes me think of Information Theory, of entropy and bits and data compression. Run length encoding is a simple form of lossless compression where the encoder reduces the size of an input sequence by representing repeating input elements as a tuple of the element and the count of the "run", for example we can encode the following input sequence [:a :a :a :a :b :b :b :c :c] as [(4 :a) (3 :b) (2 :c)] reducing our input by 33%.
Problem 12 in the 99 Lisp Problems concerns writing a run-length decoder. A very simple way to write this in Clojure is:
(defn rl-decode [xs]
(->> xs
(map #(if (coll? %) (let [n (first %) x (second %)] (repeat n x)) %))
flatten
))First we thread our input collection xs into map with an anonymous function that either (a) returns the element unchanged or if the element is itself a collection (b) takes the first element as the count and the second element as the item to be repeated and does just that. Finally, thread that output to flatten, which could probably be replaced with better use of mapcat.
In any case, this is an elegent simple concise solution to an elegant simple concise problem. Huzzah.