donetimeofthewidowitgotaghost

From Adventures of Huckleberry Finn, by Mark Twain, illustration by Samuel Clemens

From American Scientist:

Perception entails not just sensing the world but also making sense of it. When you listen to orchestral music, you hear oboes, violins, timpani and so on, each playing distinct notes. But the sound waves reaching your ears do not come packaged as separate channels for the winds, the strings and the percussion section; the signal the ear detects is nothing more than air pressure changing as a function of time, p(t). In effect, the sound of the whole orchestra is condensed into a single wiggly line. Notes and chords, melodies and harmonies are all abstractions created by the interpretive brain; they are “hidden variables” to be inferred from an analysis of the signal. Vision involves a similar inferential process. The array of receptor cells in the retina of the eye is not too different from the array of light-sensitive elements in the sensor chip of a digital camera; they both record color and brightness as a function of position. But what we see when we look around the world is not a two-dimensional mosaic of discrete, colored pixels. Somehow we organize the flickering map of brightness and color into surfaces, textures, shapes and objects embedded in a three-dimensional space. … A computer program generates some meaningless, random text according to a known probability distribution, and then it removes all the word spaces from the text. The following small example is based on the probability of sequences of letters in the text of Huckleberry Finn:

donetimeofthewidowitgotaghost

Your assignment is to restore the word boundaries—to break the garbled string of letters into a sequence of plausible words. Mumford and Desolneux are looking for an algorithmic solution, but it’s also fun to try the puzzle without the aid of a computer. How does the human mind solve such problems? When I stare at the string of letters, I find that a few words pop out spontaneously, brought to my attention by some process operating just below the level of conscious awareness; then, in a more deliberate phase, I search left and right for a set of words consistent with the initial choice. In other words, I find myself employing an iterative scheme of forming and testing hypotheses, with backtracking when necessary. (For the example given above, the reading that first leapt out at me was “done time of the widow it got a ghost,” but there are many other possibilities, such as “do net i me oft hew i do wit go tag host.”) Although this exercise is somewhat artificial (since we don’t ordinarily omit word spaces in written language), segmentation is a crucial step in understanding many other kinds of signals, including speech and genetic sequences. And the problem of segmenting images into distinct objects or features is quite tricky.

“Making Sense of the World”, Brian Hayes, American Scientist