Algorithm

An algorithm is a certain sort of formal process that can be continued on – logically – to yield a certain sort of result whenever it is “run” or instantiated. Algorithms are not new, and were not new in Darwin’s day. Many familiar arithmetic procedures, such as long division or balancing your checkbook, are algorithms, and so are the decision procedures for playing perfect tic-tac-toe, and for putting a list of words into alphabetical order. What is relatively new – permitting us valuable hindsight on Darwin’s discovery – is the theoretical reflection by mathematicians and logicians on the nature and power of algorithms in general, a twentieth-century development which led to the birth of the computer, which has led in turn, of course, to a much deeper and more lively understanding of the powers of algorithms in general.

The term algorithm descends, via Latin (algorismus) to early English (algorisme and, mistakenly therefrom, algorithm), from the name of a Persian mathematician, Muusa al-Khowarizm, whose book on arithmetical procedures, written about 835 A.D., was translated into Latin in the twelfth century by Adelard of Bath or Robert of Chester. The idea that an algorithm is a foolproof and somehow “mechanical” procedure has been present for centuries, but it was the pioneering work of Alan Turning, Kurt Godel, and Alonzo Church in the 1930s that more or less fixed our current understanding of the term. Three key figures of algorithms will be important us to, and each is somewhat difficult to define. Each, moreover, has given rise to confusions (and anxieties) that continue to beset our thinking about Darwin’s revolutionary discovery, so we will have to revisit and reconsider these introductory characterizations several times before we are through:

[1] substrate neutrality: The procedure for long division works equally well with pencil or pen, paper or parchment, neon light or skywriting, using any symbol system you like. The power of the procedure is due to its logical structure, not the causal powers of the materials used in the instantiation, just so long as those casual powers permit the prescribed steps to be followed exactly.

[2] underlying mindlessness: Although the overall design of the procedure may be brilliant, or yield brilliant results, each constituent step as well as the transition between steps, is utterly simple. How simple? Simple enough for a dutiful idiot to perform – or for a straightforward mechanical device to perform. The standard textbook analogy notes that algorithms are recipes of sorts, designed to be followed by novice cooks. A recipe book written for great chefs might include the phrase “Poach the fish in a suitable wine until almost done,” but an algorithm for the same process might begin, “Choose a white wine that says “dry’ on the label; take a corkscrew and open the bottle; pour an inch of wine in the bottom of a pan; turn the burner under the pan on high…….” 1 a tedious breakdown of the process into dead-simple steps, requiring to wise decisions or delicate judgments or intuitions on the part of the recipe-reader

[3] guaranteed results: Whatever it is that an algorithm does, it always does it, if it is executed without misstep. And algorithm is a foolproof recipe.

It is easy to see how these features made the computer possible. Every computer program is an algorithm, ultimately composed of simple steps that can be executed with stupendous reliability by one simple mechanism or another. Electronic circuits are the usual choice, but the power of computers owes nothing (save speed) to the casual peculiarities of electrons darting about on silicon chips. The very same algorithms can be performed (even faster) by devices shunting photons in glass fibers, or (much, much slower) by teams of people using paper and pencil. …. ~ Page 50/51