Trial and error
This article needs additional citations for verification. (April 2008) |
Trial and error is a fundamental method of
or until the practicer stops trying.According to
Trial and error is also a method of problem solving,
This approach can be seen as one of the two basic approaches to problem-solving, contrasted with an approach using insight and theory. However, there are intermediate methods which for example, use theory to guide the method, an approach known as guided empiricism.
This way of thinking has become a mainstay of Karl Popper's critical rationalism.
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 [5]
Simplest applications
- 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 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 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 Jerne and 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.
Features
Trial and error has a number of features:
- solution-oriented: trial and error makes no attempt to discover why a solution works, merely that it is a solution.
- problem-specific: trial and error makes no attempt to generalize a solution to other problems.
- non-optimal: trial and error is generally an attempt to find a solution, not all solutions, and not the best solution.
- needs little knowledge: trials and error can proceed where there is little or no knowledge of the subject.
It is possible to use trial and error to find all solutions or the best solution, when a testably finite number of possible solutions exist. To find all solutions, one simply makes a note and continues, rather than ending the process, when a solution is found, until all solutions have been tried. To find the best solution, one finds all solutions by the method just described and then comparatively evaluates them based upon some predefined set of criteria, the existence of which is a condition for the possibility of finding a best solution. (Also, when only one solution can exist, as in assembling a jigsaw puzzle, then any solution found is the only solution and so is necessarily the best.)
Examples
Trial and error has traditionally been the main method of finding new drugs, such as
Trial and error is also commonly seen in player responses to
Sports teams also make use of trial and error to qualify for and/or progress through the playoffs and win the championship, attempting different strategies, plays, lineups and formations in hopes of defeating each and every opponent along the way to victory. This is especially crucial in playoff series in which multiple wins are required to advance, where a team that loses a game will have the opportunity to try new tactics to find a way to win, if they are not eliminated yet.
The scientific method can be regarded as containing an element of trial and error in its formulation and testing of hypotheses. Also compare genetic algorithms, simulated annealing and reinforcement learning – all varieties for search which apply the basic idea of trial and error.
Biological evolution can be considered as a form of trial and error.[6] Random mutations and sexual genetic variations can be viewed as trials and poor reproductive fitness, or lack of improved fitness, as the error. Thus after a long time 'knowledge' of well-adapted genomes accumulates simply by virtue of them being able to reproduce.
Bogosort, a conceptual sorting algorithm (that is extremely inefficient and impractical), can be viewed as a trial and error approach to sorting a list. However, typical simple examples of bogosort do not track which orders of the list have been tried and may try the same order any number of times, which violates one of the basic principles of trial and error. Trial and error is actually more efficient and practical than bogosort; unlike bogosort, it is guaranteed to halt in finite time on a finite list, and might even be a reasonable way to sort extremely short lists under some conditions.
Jumping spiders of the genus Portia use trial and error to find new tactics against unfamiliar prey or in unusual situations, and remember the new tactics.[7] Tests show that Portia fimbriata and Portia labiata can use trial and error in an artificial environment, where the spider's objective is to cross a miniature lagoon that is too wide for a simple jump, and must either jump then swim or only swim.[8][9]
See also
References
- PMID 13690223.
- ^ Concise Oxford Dictionary p1489
- ISBN 978-0-03-053251-1
- ^ Thorndike E.L. 1898. Animal intelligence: an experimental study of the association processes in animals. Psychological Monographs #8.
- ^ X. Bei, N. Chen, S. Zhang, On the Complexity of Trial and Error, STOC 2013
- ^ Wright, Serwall (1932). "The roles of mutation, inbreeding, crossbreeding and selection in evolution" (PDF). Proceedings of the Sixth International Congress on Genetics. Volume 1 (6): 365. Retrieved 17 March 2014.
- ^ Harland, D.P. & Jackson, R.R. (2000). ""Eight-legged cats" and how they see - a review of recent research on jumping spiders (Araneae: Salticidae)" (PDF). Cimbebasia. 16: 231–240. Archived from the original (PDF) on 28 September 2006. Retrieved 5 May 2011.
- . Retrieved 8 June 2011.
- JSTOR 4535886.
Further reading
- Ashby, W. R. (1960: Second Edition). Design for a Brain. Chapman & Hall: London.
- Traill, R.R. (1978–2006). Molecular explanation for intelligence…, Brunel University Thesis, HDL.handle.net
- Traill, R.R. (2008). Thinking by Molecule, Synapse, or both? — From Piaget’s Schema, to the Selecting/Editing of ncRNA. Ondwelle: Melbourne. Ondwelle.com — or French version Ondwelle.com.
- Zippelius, R. (1991). Die experimentierende Methode im Recht (Trial and error in Jurisprudence), Academy of Science, Mainz, ISBN 3-515-05901-6