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| Some Advanced Strategies |
Some Advanced Strategies
If the basic strategies are ineffective, there are a variety of other approaches that can be applied to problem solving. These strategies involve models and analogies, logical analysis, and statistical analysis.
Models and analogies
The use of models and analogies allows you to create and examine a similar, but simpler problem. Analyzing the simpler problem often provides insights into the behaviour of the original and more complex system.
If the basic strategies are ineffective, there are a variety of other approaches that can be applied to problem solving. These strategies involve models and analogies, logical analysis, and statistical analysis.
Models and analogies
The use of models and analogies allows you to create and examine a similar, but simpler problem. Analyzing the simpler problem often provides insights into the behaviour of the original and more complex system.
For example, predicting the motion of a tornado in a turbulent atmosphere may be a daunting task beyond the power of a supercomputer. However, analyzing the motion of a rotating cone moving through a smoothly flowing fluid is a much simpler task and might provide useful insights and clues for predicting the motions real-world tornados.
Logical analysis
In a situation with clear definitions and rules governing relationships, it is possible to make use of logical analysis in problem solving. Algebra, geometry, calculus – in fact all branches of mathematics – are subject to logical analysis.
Situations that combine human interactions with logical analysis are ‘fuzzy’ in nature and require approaches that are more flexible. ‘Game theory’ has evolved as a branch of applied mathematics that deals with strategic interactions between humans, when the optimal choice of one person depends on the choices made by other participants.
The underlying assumption is that all participants will make rational decisions based on their own preferences.
Statistical analysis
In some situations there are no precise rules to govern interactions, but many observations have been made and lots of data is available. In those situations, a statistical analysis can reveal patterns in the data, and the patterns can be used for making predictions.
Weather forecasts are based on statistical analyzes. No one knows exactly how wind, sun and rain are going to interact over hours and days, but powerful computer analyzes of data collected from thousands of weather stations and weather satellites can be used to make reasonable forecasts of national and local weather patterns for the near future.
In modern cryptography, the breaking of secret codes involves statistical analyzes and powerful computers to examine millions of possible coding schemes. Alan Turing pioneered this approach at Bletchley Park, in Britain, during World War II. With the help of first-generation electric computers designed by Turing, the code breaking team at Bletchley Park was able to decipher many of the intercepted German communications. That information played a significant role in shortening the duration of the war.
Most studies of the safety and effectiveness of new medicines are based on statistical analysis. Biological systems are so complex that no one knows exactly what is happening at the molecular level in your body when you take a medicine. So, large groups of volunteers are required to test a new drug. Statistical analyzes are used to establish that most of the time when you take a particular drug, you can expect these benefits and occasionally those side effects.
Logical analysis
In a situation with clear definitions and rules governing relationships, it is possible to make use of logical analysis in problem solving. Algebra, geometry, calculus – in fact all branches of mathematics – are subject to logical analysis.
Situations that combine human interactions with logical analysis are ‘fuzzy’ in nature and require approaches that are more flexible. ‘Game theory’ has evolved as a branch of applied mathematics that deals with strategic interactions between humans, when the optimal choice of one person depends on the choices made by other participants.
The underlying assumption is that all participants will make rational decisions based on their own preferences.
Statistical analysis
In some situations there are no precise rules to govern interactions, but many observations have been made and lots of data is available. In those situations, a statistical analysis can reveal patterns in the data, and the patterns can be used for making predictions.
Weather forecasts are based on statistical analyzes. No one knows exactly how wind, sun and rain are going to interact over hours and days, but powerful computer analyzes of data collected from thousands of weather stations and weather satellites can be used to make reasonable forecasts of national and local weather patterns for the near future.
In modern cryptography, the breaking of secret codes involves statistical analyzes and powerful computers to examine millions of possible coding schemes. Alan Turing pioneered this approach at Bletchley Park, in Britain, during World War II. With the help of first-generation electric computers designed by Turing, the code breaking team at Bletchley Park was able to decipher many of the intercepted German communications. That information played a significant role in shortening the duration of the war.
Most studies of the safety and effectiveness of new medicines are based on statistical analysis. Biological systems are so complex that no one knows exactly what is happening at the molecular level in your body when you take a medicine. So, large groups of volunteers are required to test a new drug. Statistical analyzes are used to establish that most of the time when you take a particular drug, you can expect these benefits and occasionally those side effects.
