Trial and error process

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Trial and error is a fundamental method of problem-solving^[1] characterized by repeated, varied attempts which are continued until success,^[2] or until the practicer stops trying.

According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (1852–1936) after trying out similar phrases «trial and failure» and «trial and practice».^[3] Under Morgan’s Canon, animal behaviour should be explained in the simplest possible way. Where behavior seems to imply higher mental processes, it might be explained by trial-and-error learning. An example is a skillful way in which his terrier Tony opened the garden gate, easily misunderstood as an insightful act by someone seeing the final behavior. Lloyd Morgan, however, had watched and recorded the series of approximations by which the dog had gradually learned the response, and could demonstrate that no insight was required to explain it.

Edward Lee Thorndike was the initiator of the theory of trial and error learning based on the findings he showed how to manage a trial-and-error experiment in the laboratory. In his famous experiment, a cat was placed in a series of puzzle boxes in order to study the law of effect in learning.^[4] He plotted to learn curves which recorded the timing for each trial. Thorndike’s key observation was that learning was promoted by positive results, which was later refined and extended by B. F. Skinner’s operant conditioning.

Trial and error is also a method of problem solving, repair, tuning, or obtaining knowledge. In the field of computer science, the method is called generate and test (Brute force). In elementary algebra, when solving equations, it is guess and check.

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

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[edit]

Trial and error has traditionally been the main method of finding new drugs, such as antibiotics. Chemists simply try chemicals at random until they find one with the desired effect. In a more sophisticated version, chemists select a narrow range of chemicals it is thought may have some effect using a technique called structure–activity relationship. (The latter case can be alternatively considered as a changing of the problem rather than of the solution strategy: instead of «What chemical will work well as an antibiotic?» the problem in the sophisticated approach is «Which, if any, of the chemicals in this narrow range will work well as an antibiotic?») The method is used widely in many disciplines, such as polymer technology to find new polymer types or families.

Trial and error is also commonly seen in player responses to video games — when faced with an obstacle or boss, players often form a number of strategies to surpass the obstacle or defeat the boss, with each strategy being carried out before the player either succeeds or quits the game.

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[edit]

References[edit]

Further reading[edit]

• 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

Trial and error, or trial by error, is a general method of problem solving for obtaining knowledge, both propositional knowledge and know-how. In the field of computer science, the method is called generate and test. In elementary algebra, when solving equations, it is «guess and check».

This approach can be seen as one of the two basic approaches to problem solving and is contrasted with an approach using insight and theory.

Process

Bricolage -In trial and error, one selects a possible answer, applies it to the problem and, if it is not successful, selects (or generates) another possibility that is subsequently tried. The process ends when a possibility yields a solution.

In some versions of trial and error, the option that is a priori viewed as the most likely one should be tried first, followed by the next most likely, and so on until a solution is found, or all the options are exhausted. In other versions, options are simply tried at random.

Methodology

This approach is more successful with simple problems and in games, and is often resorted to when no apparent rule applies. This does not mean that the approach need be careless, for an individual can be methodical in manipulating the variables in an attempt to sort through possibilities that may result in success. Nevertheless, this method is often used by people who have little knowledge in the problem area.

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 generalise a solution to other problems.
* non-optimal: trial and error is 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.

Examples

Trial and error has traditionally been the main method of finding new drugs, such as antibiotics. Chemists simply try chemicals at random until they find one with the desired effect.

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 is also a form of trial and error. Random mutations and sexual genetic variations can be viewed as trials and poor reproductive 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 can be viewed as a trial and error approach to sorting a list.

In mathematics, the method of trial and error can be used to solve formulae — it is a slower, less precise method than algebra, but is easier to understand.

ee also

* Brute force attack
* Brute-force search
* Empiricism

Notes

Trial and error is a fundamental method of problem-solving.^[1] It is characterized by repeated, varied attempts which are continued until success,^[2] or until the practicer stops trying.

According to W.H. Thorpe, the term was devised by C. Lloyd Morgan (1852–1936) after trying out similar phrases «trial and failure» and «trial and practice».^[3] Under Morgan’s Canon, animal behaviour should be explained in the simplest possible way. Where behavior seems to imply higher mental processes, it might be explained by trial-and-error learning. An example is a skillful way in which his terrier Tony opened the garden gate, easily misunderstood as an insightful act by someone seeing the final behavior. Lloyd Morgan, however, had watched and recorded the series of approximations by which the dog had gradually learned the response, and could demonstrate that no insight was required to explain it.

Edward Lee Thorndike was the initiator of the theory of trial and error learning based on the findings he showed how to manage a trial-and-error experiment in the laboratory. In his famous experiment, a cat was placed in a series of puzzle boxes in order to study the law of effect in learning.^[4] He plotted to learn curves which recorded the timing for each trial. Thorndike’s key observation was that learning was promoted by positive results, which was later refined and extended by B. F. Skinner’s operant conditioning.

Trial and error is also a method of problem solving, repair, tuning, or obtaining knowledge. In the field of computer science, the method is called generate and test (Brute force). In elementary algebra, when solving equations, it is guess and check.

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

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 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 antibiotics. Chemists simply try chemicals at random until they find one with the desired effect. In a more sophisticated version, chemists select a narrow range of chemicals it is thought may have some effect using a technique called structure–activity relationship. (The latter case can be alternatively considered as a changing of the problem rather than of the solution strategy: instead of «What chemical will work well as an antibiotic?» the problem in the sophisticated approach is «Which, if any, of the chemicals in this narrow range will work well as an antibiotic?») The method is used widely in many disciplines, such as polymer technology to find new polymer types or families.

Trial and error is also commonly seen in player responses to video games — when faced with an obstacle or boss, players often form a number of strategies to surpass the obstacle or defeat the boss, with each strategy being carried out before the player either succeeds or quits the game.

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

• Ariadne’s thread (logic)
• Brute-force attack
• Brute-force search
• Dictionary attack
• Empiricism
• Genetic algorithm
• Learning curve
• Margin of error
• Regula falsi
• Voodoo programming

References

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

На основании Вашего запроса эти примеры могут содержать грубую лексику.

На основании Вашего запроса эти примеры могут содержать разговорную лексику.

Experts agree it is a trial-and-error process.

Developing such a strategy is a trial-and-error process that takes a lot of time and patience.

Разработка такой стратегии — процесс проб и ошибок, который требует много времени и терпения.

At its simplest, the third memory works by a trial-and-error process that can be seen as yet another analogy to natural selection.

Упрощенно третья память работает благодаря процессу проб и ошибок, который можно понимать как еще одну аналогию естественного отбора.

As, inevitably, a trial-and-error process, democratization is a complex and unpredictable path beset with challenges.

Будучи экспериментальным процессом, демократизация неизбежно является сложной и непредсказуемой стезей, полной трудностей.

the nonavailability of a trial-and-error process converging to an optimum position.

The whole history of mankind is a trial-and-error process and, without it, we would never get to where we are today.

Вся история человечества основана на пробах и ошибках, и без них мы никогда не попали бы туда, где находимся сегодня.

It’s a trial-and-error process, during which we may not get the right notes all the time.

Это процесс проб и ошибок, во время которого мы не можем всё время придумывать правильные ноты.

But given that much of these efforts were done solo, and with a trial-and-error process, it’s difficult to pinpoint the exact beginning of SEO.

Но учитывая, что большая часть этих усилий была выполнена соло, и с процессом проб и ошибок, трудно точно определить точное начало SEO.

As a consequence, the measure of goodness of actions in anything except a tolerable-intolerable sense is lost, and the possibility of an individual’s converging to the optimum activity via a trial-and-error process disappears.

Как последствие, измерение доброты действий в что-нибыдь за исключением терпимый-невыносимого чувства потерянный, и возможность индивидуала сходясь к оптимальной работе через trial-and-error процесс исчезает.

The experiential approach can offer nothing but a trial-and-error process for achieving this, a process which is slow and which offers no real guarantee of achieving this goal.

Подход, основанный на опыте проживания, не может предложить ничего, кроме процесса проб и ошибок, медленного и не дающего гарантии достижения этой цели.

Development is a trial-and-error process and the future is uncertain-that is, movement toward any particular goal may never reach a point where it triggers a transition to a new socioeconomic model.

Развитие будет идти методом проб и ошибок, будущее неопределенно, то есть момент достижения сингулярности как точки невозврата в достижении разных целей и переходе на новую социально-экономическую модель развития может и не наступить.

To learn its signature melody, the male songbird uses a trial-and-error process to mimic the song of its father, singing the tune over and over again, hundreds of times a day, making subtle changes in the pitch of the notes…

Чтобы имитировать мелодию своего отца, певчая птица мужского пола использует метод проб и ошибок, напевая мелодию снова и снова, сотни раз в день, делая небольшие изменения в высоте нот.

Videogames are often a trial-and-error process where players become accustomed to failure, and learn from it.

Компьютерные игры часто проходятся методом проб и ошибок, когда игроки привыкают к поражениям и учатся на неудачах.

It plays a major role in adapting and fine-tuning motor programs to make accurate movements through a trial-and-error process (e.g., learning to hit a baseball).

Он играет важную роль в адаптации и настройке моторных программ, чтобы сделать движения точными через процесс проб и ошибок (например, обучение бейсболу и другим играм, для которых требуется движение тела).

By nudging prices up or down in a trial-and-error process, the city will seek a structure of prices that vary by time and location throughout the city, yielding one or two open spaces on every block.

Действуя методом проб и ошибок — повышая или снижая цены — власти попытаются создать систему цен, варьирующихся в зависимости от места и времени, чтобы одно-два места у каждого дома оставались свободными.

Ничего не найдено для этого значения.

Результатов: 15. Точных совпадений: 15. Затраченное время: 39 мс

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The Use of Trial and Error To Solve Problems

Some complex problems can be solved by a technique that is called trial and error. Trial and error is typically good for problems where you have multiple chances to get the correct solution. However, this is not a good technique for problems that don’t give you multiple chances to find a solution.

Trial and error is also an excellent tool for inventors. The inventor will first imagine a device they would like to invent, and then they may go through the trial and error process to find the best ways of inventing the device. While trial and error is an extremely powerful tool that can be used to solve problems, it also has some weaknesses. I mentioned this briefly in the first paragraph. Trial and error is inefficient in situations where making an error can lead to serious injury or death. A good example of this would be the attempts that were made by aircraft engineers to break the sound barrier. Though they succeeded, many pilots died because they would use the trial and error process. In the situation, and error would often lead to the plane crashing.

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Trial and error, or trial by error or try an error, is a general method of problem solving, fixing things, or for obtaining knowledge.
«Learning doesn’t happen from failure itself but rather from analyzing the failure, making a change, and then trying again.»^[1]

In the field of computer science, the method is called generate and test. In elementary algebra, when solving equations, it is «guess and check».

This approach can be seen as one of the two basic approaches to problem solving and is contrasted with an approach using insight and theory.

Process

Bricolage —
In trial and error, one selects a possible answer, applies it to the problem and, if it is not successful, selects (or generates) another possibility that is subsequently tried. The process ends when a possibility yields a solution.

In some versions of trial and error, the option that is a priori viewed as the most likely one should be tried first, followed by the next most likely, and so on until a solution is found, or all the options are exhausted. In other versions, options are simply tried at random.

Methodology

This approach is more successful with simple problems and in games, and is often resorted to when no apparent rule applies. This does not mean that the approach need be careless, for an individual can be methodical in manipulating the variables in an attempt to sort through possibilities that may result in success. Nevertheless, this method is often used by people who have little knowledge in the problem area.

Simplest applications

Ashby (1960, section 11/5) offers three simple strategies for dealing with the same basic exercise-problem; and they have very different efficiencies:
Suppose there are 1000 on/off switches which have to be set to a particular combination by random-based testing, each test 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) would take 500 seconds; while
• a parallel-but-individual testing of all switches simultaneously 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. This leads us to:

Trial-and-error 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 by first 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».

The basic strategy in many fields?

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:

• Darwinian evolution 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 immune system.

An ambiguity: Can we have «intention» during a «trial»

In the Ashby-and-Cybernetics tradition, the word «trial» usually implies random-or-arbitrary, without any deliberate choice.
However amongst non-cyberneticians, «trial» will often imply a deliberate subjective act by some adult human agent; (e.g. in a court-room, or laboratory). So that has sometimes led to confusion.

Of course the situation becomes even more confusing if one accepts Ashby’s hierarchical explanation of intelligence, and its implied ability to be deliberate and to creatively design — all based ultimately on non-deliberate actions! The lesson here seems to be that one must simply be careful to clarify the meaning of one’s own words, and indeed the words of others. [Incidentally it seems that consciousness is not an essential ingredient for intelligence as discussed above.]

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 generalise 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 antibiotics. Chemists simply try chemicals at random until they find one with the desired effect. In a more sophisticated version, chemists select a narrow range of chemicals it is thought may have some effect. (The latter case can be alternatively considered as a changing of the problem rather than of the solution strategy: instead of «What chemical will work well as an antibiotic?» the problem in the sophisticated approach is «Which, if any, of the chemicals in this narrow range will work well as an antibiotic?») The method is used widely in many disciplines, such as polymer technology to find new polymer types or families.

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 is also a form of trial and error. 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.

Issues with trial and error

Trial and error is usually a last resort for a particular problem, as there are a number of problems with it. For one, trial and error is tedious and monotonous. Also, it is very time-consuming; chemical engineers must sift through millions of various potential chemicals before they find one that works. Fortunately, computers are best suited for trial and error; they do not succumb to the boredom that humans do, and can potentially do thousands of trial-and-error segments in the blink of an eye.

References

• 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.

See also

• Brute force attack
• Brute-force search
• Empiricism

References

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Словосочетания

Автоматический перевод

методом проб и ошибок

Перевод по словам

trial  — суд, испытание, пробный, испытательный
error  — ошибка, погрешность, заблуждение, отклонение, рассогласование, грех, блуждание

Примеры

approach, device, manner, mean, method, mode, practice, procedure, system, technique, technology, theory, way

* * *

ме́тод

м.

method; procedure; technique

агрегатнопото́чный ме́тод — conveyor-type production [production-line] method

аксиомати́ческий ме́тод — axiomatic [postulational] method

ме́тод амплиту́дного ана́лиза — kick-sorting method

вариацио́нный ме́тод — variational method

весово́й ме́тод — gravimetric method

ме́тод взба́лтывания — shake method

визуа́льный ме́тод — visual method

ме́тод возду́шной прое́кции — aero-projection method

ме́тод враще́ния — method of revolution

ме́тод вреза́ния — plunge-cut method

ме́тод вре́мени пролё́та — time-of-flight method

ме́тод встре́чного фрезерова́ния — conventional [cut-up] milling method

ме́тод гармони́ческой линеариза́ции — describing function method

голографи́ческий ме́тод — holographic method

гравиметри́ческий ме́тод — gravimetric(al) method

графи́ческий ме́тод — graphical method

графоаналити́ческий ме́тод — semigraphical method

систе́ма рабо́тает групповы́м ме́тодом — the system operates on the grouped-frequency basis

ме́тод измере́ния, абсолю́тный — absolute [fundamental] method of measurement

ме́тод измере́ния, конта́ктный — contact method of measurement

ме́тод измере́ния, ко́свенный — indirect method of measurement

ме́тод измере́ния, относи́тельный — relative method of measurement

ме́тод измере́ния по то́чкам — point-by-point method

ме́тод измере́ния, прямо́й — direct method of measurement

ме́тод измере́ния угло́в по аэросни́мкам — photogoniometric method

ме́тод изото́пных индика́торов — tracer method

иммерсио́нный ме́тод — immersion method

ме́тод и́мпульсов — momentum-transfer method

ме́тод инве́рсии — inversion method

интерференцио́нный ме́тод — interferometric method

ме́тод испыта́ний — testing procedure, testing method

ме́тод испыта́ний, кисло́тный — acid test

ме́тод испыта́ний, пане́льный — panel-spalling test

ме́тод иссле́дований напряже́ний, опти́ческий — optical stress analysis

ме́тод истече́ния — efflux method

ме́тод итера́ции — iteration method, iteration technique

ме́тод итера́ции приво́дит к сходи́мости проце́сса — the iteration (process) converges to a solution

ме́тод итера́ции приво́дит к (бы́строй или ме́дленной) сходи́мости проце́сса — the iteration (process) converges quickly or slowly

ме́тод картосоставле́ния — map-compilation [plotting] method

ка́чественный ме́тод — qualitative method

кессо́нный ме́тод — caisson method

коли́чественный ме́тод — quantitative method

колориметри́ческий ме́тод — colorimetric method

ме́тод кольца́ и ша́ра — ball-and-ring method

кондуктометри́ческий ме́тод — conductance-measuring method

ме́тод коне́чных ра́зностей — finite difference method

ме́тод консерви́рования — curing method

ме́тод контро́ля, дифференци́рованный — differential control method

ме́тод контро́ля ка́чества — quality control method

ме́тод ко́нтурных то́ков — mesh-current [loop] method

ме́тод ко́нуса — cone method

корреляцио́нный ме́тод — correlation method

ко́свенный ме́тод — indirect method

лаборато́рный ме́тод — laboratory method

ме́тод лине́йной интерполя́ции — method of proportional parts

ме́тод магни́тного порошка́ () — magnetic particle [magnetic powder] method

магни́тно-люминесце́нтный ме́тод () — fluorescent magnetic particle method

ме́тод механи́ческой обрабо́тки — machining method

ме́тод ме́ченых а́томов — tracer method

ме́тод микрометри́рования — micrometer method

ме́тод мно́жителей Лагра́нжа — Lagrangian multiplier method, Lagrange’s method of undetermined multipliers

ме́тод наиме́ньших квадра́тов — method of least squares, least-squares technique

ме́тод нака́чки () — pumping [excitation] method

ме́тод наложе́ния — method of superposition

ме́тод напыле́ния — evaporation technique

ненулево́й ме́тод — deflection method

ме́тод неопределё́нных мно́жителей Лагра́нжа — Lagrangian multiplier method, Lagrange’s method of undetermined multipliers

ме́тод неподви́жных то́чек — method of fixed points

неразруша́ющий ме́тод — non-destructive method, non-destructive testing

нерекурси́вный ме́тод — non-recursive method

нето́чный ме́тод — inexact method

нефелометри́ческий ме́тод — nephelometric method

ме́тод нивели́рования по частя́м — method of fraction levelling

нулево́й ме́тод — null [zero(-deflection) ] method

ме́тод нулевы́х бие́ний — zero-beat method

ме́тод нулевы́х то́чек — neutral-points method

ме́тод обеспе́чения надё́жности — reliability method

ме́тод обрабо́тки — processing [working, tooling] method

ме́тод объединё́нного а́тома — associate atom method

объекти́вный ме́тод — objective method

объё́мный ме́тод — volumetric method

окисли́тельно-восстанови́тельный ме́тод — redox method

опера́торный ме́тод — operational method

ме́тод определе́ния отбе́ливаемости и цве́тности ма́сел — bleach-and-colour method

ме́тод опти́ческой корреля́ции — optical correlation technique

ме́тод осажде́ния — sedimentation method

ме́тод осредне́ния — averaging [smoothing] method

ме́тод отбо́ра проб — sampling method, sampling technique

ме́тод отклоне́ния — deflection method

ме́тод отраже́ния — reflection method

ме́тод отражё́нных и́мпульсов — pulse-echo method

ме́тод отыска́ния произво́дной, непосре́дственный — delta method

ме́тод па́дающего те́ла — falling body method

ме́тод парамагни́тного резона́нса — paramagnetic-resonance method

ме́тод пе́рвого приближе́ния — first approximation method

ме́тод перераспределе́ния моме́нтов () — moment distribution method

ме́тод пересека́ющихся луче́й — crossed beam method

ме́тод перпендикуля́ров — offset method

пикнометри́ческий ме́тод — bottle method

ме́тод подбо́ра — trial-and-error [cut-and-try] method

ме́тод подо́бия — similitude method

ме́тод по́лной деформа́ции — total-strain method

ме́тод полови́нных отклоне́ний — half-deflection method

полуколи́чественный ме́тод — semiquantitative method

ме́тод поля́рных координа́т — polar method

ме́тод попу́тного фрезерова́ния — climb [cut-down] milling method

ме́тод посе́ва — seeding technique

ме́тод после́довательных исключе́ний — successive exclusion method

ме́тод после́довательных подстано́вок — method of successive substitution, substitution process

ме́тод после́довательных попра́вок — successive correction method

ме́тод после́довательных приближе́ний — successive approximation method

ме́тод после́довательных элимина́ций — method of exhaustion

потенциометри́ческий компенсацио́нный ме́тод — potentiometric method

пото́чно-конве́йерный ме́тод — flow-line conveyor method

пото́чный ме́тод — straight-line flow method

приближё́нный ме́тод — approximate method

ме́тод проб и оши́бок — trial-and-error [cut-and-try] method

ме́тод программи́рующих програ́мм — programming program method

ме́тод проекти́рования, моде́льно-маке́тный — model-and-mock-up method of design

ме́тод простра́нственной самофикса́ции — self-fixation space method

прямо́й ме́тод — direct method

ме́тод псевдослуча́йных чи́сел — pseudorandom number method

ме́тод ра́вных отклоне́ний — equal-deflection method

радиацио́нный ме́тод — radiation method

ме́тод радиоавтогра́фии — radioautograph technique

ме́тод радиоакти́вных индика́торов — tracer method

радиометри́ческий ме́тод — radiometric method

ме́тод разбавле́ния — dilution method

ме́тод разделе́ния переме́нных — method of separation of variables

ме́тод разме́рностей — dimensional method

ра́зностный ме́тод — difference method

ме́тод разруша́ющей нагру́зки — load-factor method

разруша́ющий ме́тод — destructive check

ме́тод рассе́яния Рэле́я — Rayleigh scattering method

ме́тод ра́стрового скани́рования — raster-scan method

ме́тод расчё́та по допусти́мым нагру́зкам — working stress design [WSD] method

резона́нсный ме́тод — resonance method

рентгенострукту́рный ме́тод — X-ray diffraction method

ме́тод самоторможе́ния — retardation method

ме́тод сви́лей — schlieren technique, schlieren method

ме́тод сдви́нутого сигна́ла — offset-signal method

ме́тод секу́щих — secant method

символи́ческий ме́тод — method of complex numbers

ме́тод симметри́чных составля́ющих — method of symmetrical components, symmetrical component method

ме́тод синхро́нного накопле́ния — synchronous storage method

ме́тод скани́рования полосо́й — single-line-scan television method

ме́тод скани́рования пятно́м — spot-scan photomultiplier method

ме́тод совпаде́ний — coincidence method

ме́тод сосредото́ченных пара́метров — lumped-parameter method

ме́тод спада́ния заря́да — fall-of-charge method

спектроскопи́ческий ме́тод — spectroscopic method

ме́тод спира́льного скани́рования — spiral-scan method

ме́тод сплавле́ния — fusion method

ме́тод сплошны́х сред () — continuous field analog technique

ме́тод сре́дних квадра́тов — midsquare method

статисти́ческий ме́тод — statistical technique

статисти́ческий ме́тод оце́нки — statistical estimation

ме́тод статисти́ческих испыта́ний — Monte Carlo method

стробоголографи́ческий ме́тод — strobo-holographic method

стробоскопи́ческий ме́тод — stroboscopic method

субъекти́вный ме́тод — subjective method

ме́тод сухо́го озоле́ния — dry combustion method

счё́тно-и́мпульсный ме́тод — pulse-counting method

табли́чный ме́тод — diagram method

телевизио́нный ме́тод электро́нной аэросъё́мки — television method

телевизио́нный ме́тод электро́нной фотограмме́трии — television method

тенево́й ме́тод — (direct-)shadow method

термоанемометри́ческий ме́тод — hot-wire method

топологи́ческий ме́тод — topological method

то́чный ме́тод — exact [precision] method

ме́тод травле́ния, гидри́дный — sodium hydride descaling

ме́тод трапецеида́льных характери́стик — Floyd’s trapezoidal approximation method, approximation procedure

ме́тод триангуля́ции — triangulation method

ме́тод углово́й деформа́ции — slope-deflection method

ме́тод углово́й модуля́ции — angular modulation method

ме́тод узловы́х потенциа́лов — node-voltage method

ме́тод уравнове́шивания — balancing method

ме́тод усредне́ния — averaging [smoothing] method

ме́тод фа́зового контра́ста () — phase contrast

наблюда́ть ме́тодом фа́зового контра́ста — examine [study] by phase contrast

ме́тод фа́зовой пло́скости — phase plane method

ме́тод факториза́ции — factorization method

флотацио́нный ме́тод — floatation method

ме́тод центрифуги́рования — centrifuge method

чи́сленный ме́тод — numerical method

ме́тод Шо́ра — Shore hardness

щупово́й ме́тод — stylus method

ме́тод электрофоре́за — electrophoretic method

эмпири́ческий ме́тод — trial-and-error [cut-and-try] method

энергети́ческий ме́тод

ме́тод энергети́ческого бала́нса — power balance method

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