Editing Twenty questions (section)

==Computers, scientific method and situation puzzles==

The abstract mathematical version of the game where some answers may be wrong is sometimes called [[Ulam's game]] or the [[Rényi–Ulam game]]. The game suggests that the information (as measured by [[Claude E. Shannon|Shannon]]'s [[information entropy|entropy]] statistic) required to identify an arbitrary object is at most 20 [[bit]]s. 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 allow the questioner to distinguish between 2<sup>20</sup>&nbsp;= {{val|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 2<sup>20</sup> and, pointing to skilful caution, said:
{{Quote|Thus twenty skilful 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 half a century of work.<ref>Peirce, C. S. (1901 MS), "On The Logic of Drawing History from Ancient Documents, Especially from Testimonies", manuscript corresponding to an abstract delivered at the [[United States National Academy of Sciences|National Academy of Sciences]] meeting of November 1901. Published in 1958 in ''[[Charles Sanders Peirce bibliography#CP|Collected Papers]]'' v. 7, paragraphs 162–231; see 220. Reprinted (first half) in 1998 in ''[[Charles Sanders Peirce bibliography#EP|The Essential Peirce]]'' v. 2, pp. 75–114; see 107–110.</ref> Testing the smallest logical components of a hypothesis one at a time does not mean asking about, say, {{val|1,048,576}} subjects one at a time, but 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 [[Falsifiability|falsity]] (test for a "no") or vice versa.

In developing the [[participatory anthropic principle]] (PAP), which is an [[Interpretations of quantum mechanics|interpretation of quantum mechanics]], theoretical physicist [[John Archibald Wheeler]] used a variant on twenty questions, called ''surprise twenty questions'',<ref>{{cite book | last1=Wheeler | first1=John Archibald | last2=Zurek | first2=Wojciech Hubert | title=Quantum theory and measurement | publication-place=Princeton, New Jersey | date=1983 | isbn=978-1-4008-5455-4 | oclc=888216845 | page=202}}</ref> to show how the questions we choose to ask about the universe may dictate the answers we get. In this variant, the respondent does not choose or decide upon any particular or definite object beforehand, but only on a pattern of "yes" or "no" answers.  This variant requires the respondent to provide a consistent set of answers to successive questions, so that each answer can be viewed as logically compatible with all the previous answers. In this way, successive questions narrow the options until the questioner settles upon a definite object. Wheeler's theory was that, in an analogous manner, consciousness may play some role in bringing the universe into existence.<ref>{{Cite book |url=https://books.google.com/books?id=zBsDkgI1uQsC&q=participatory+universe |title=Q is for Quantum: An Encyclopedia of Particle Physics |last1=Gribbin |first1=John |last2=Gribbin |first2=Mary |last3=Gribbin |first3=Jonathan |date=2000-02-22 |publisher=Simon and Schuster |isbn=9780684863153 |language=en}}</ref>