Twenty Questions - Computers, Scientific Method, and Situation Puzzles

Computers, Scientific Method, and Situation Puzzles

The game suggests that the information (as measured by Shannon's entropy statistic) required to identify an arbitrary object is at most 20 bits. The game is often used as an example when teaching people about information theory. Mathematically, if each question is structured to eliminate half the objects, 20 questions will allow the questioner to distinguish between 220 or 1,048,576 objects. Accordingly, the most effective strategy for Twenty Questions is to ask questions that will split the field of remaining possibilities roughly in half each time. The process is analogous to a binary search algorithm in computer science or successive approximation ADC in analog-to-digital signal conversion.

In 1901 Charles Sanders Peirce discussed factors in the economy of research that govern the selection of a hypothesis for trial — (1) cheapness, (2) intrinsic value (instinctive naturalness and reasoned likelihood), and (3) relation (caution, breadth, and incomplexity) to other projects (other hypotheses and inquiries). He discussed the potential of Twenty Questions to single one subject out from among 220 and, pointing to skillful caution, said,

Thus twenty skillful hypotheses will ascertain what two hundred thousand stupid ones might fail to do. The secret of the business lies in the caution which breaks a hypothesis up into its smallest logical components, and only risks one of them at a time.

He elaborated on how, if that principle had been followed in the investigation of light, its investigators would have saved themselves from half a century of work. Note that testing the smallest logical components of a hypothesis one at a time does not mean asking about, say, 1,048,576 subjects one at a time. Instead it means extracting aspects of a guess or hypothesis, and asking, for example, "did an animal do this?" before asking "did a horse do this?".

That aspect of scientific method resembles also a situation puzzle in facing (unlike Twenty Questions) a puzzling scenario at the start. Both games involve asking yes/no questions, but Twenty Questions places a greater premium on efficiency of questioning. A limit on their likeness to the scientific process of trying hypotheses is that a hypothesis, because of its scope, can be harder to test for truth (test for a "yes") than to test for falsity (test for a "no") or vice versa (see Falsifiability).