Editing Trial and error (section)

==Methodology==
The trial and error approach is used most successfully with simple problems and in games, and it is often the last resort when no apparent rule applies. This does not mean that the approach is inherently careless, for an individual can be methodical in manipulating the variables in an attempt to sort through possibilities that could result in success. Nevertheless, this method is often used by people who have little knowledge in the problem area. The trial-and-error approach has been studied from its natural computational point of view <ref>[https://arxiv.org/abs/1205.1183 X. Bei, N. Chen, S. Zhang, On the Complexity of Trial and Error, STOC 2013]</ref>

===Simplest applications===
[[William Ross Ashby|Ashby]] (1960, section 11/5) offers three simple strategies for dealing with the same basic exercise-problem, which have very different efficiencies.  Suppose a collection of 1000 on/off switches have to be set to a particular combination by random-based testing, where each test is expected to take one second. [This is also discussed in Traill (1978–2006, section C1.2]. The strategies are:
*the perfectionist all-or-nothing method, with no attempt at holding partial successes. This would be expected to take more than 10^301 seconds, [i.e., 2^1000 seconds, or 3·5×(10^291) centuries]
*a serial-test of switches, holding on to the partial successes (assuming that these are manifest), which would take 500 seconds on average
* parallel-but-individual testing of all switches simultaneously, which would take only one second

Note the tacit assumption here that no intelligence or insight is brought to bear on the problem. However, the existence of different available strategies allows us to consider a separate ("superior") domain of processing — a ''"meta-level"'' above the mechanics of switch handling — where the various available strategies can be randomly chosen. Once again this is "trial and error", but of a different type.

===Hierarchies===
Ashby's book develops this "meta-level" idea, and extends it into a whole [[recursion|recursive]] sequence of levels, successively above each other in a systematic hierarchy. On this basis, he argues that human intelligence emerges from such organization: relying heavily on trial-and-error (at least initially at each new stage), but emerging with what we would call "intelligence" at the end of it all. Thus presumably the topmost level of the hierarchy (at any stage) will still depend on simple trial-and-error.

Traill (1978–2006) suggests that this Ashby-hierarchy probably coincides with [[Jean Piaget|Piaget]]'s well-known theory of developmental stages. [This work also discusses Ashby's 1000-switch example; see §C1.2]. After all, it is part of Piagetian doctrine that children learn first by ''actively doing'' in a more-or-less random way, and then hopefully learn from the consequences — which all has a certain resemblance to Ashby's random "trial-and-error".

===Application===
Traill (2008, ''espec. Table "S" on p.31'') follows [[Niels Kaj Jerne|Jerne]] and [[Karl Popper|Popper]] in seeing this strategy as probably underlying ''all'' knowledge-gathering systems — ''at least in their initial phase''.

Four such systems are identified:
*[[Natural selection]] which "educates" the [[DNA]] of the species,
*The brain of the individual (just discussed);
*The "brain" of society-as-such (including the publicly held body of science); and
*The [[adaptive immune system]].