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| Still More Strategies |
Still More Strategies
Despite your best efforts you will always encounter problems that seem unsolvable.
What do you do then?
Re-evaluation
Sometimes it is wise to stop and re-evaluate your problem solving efforts. Is this problem that important? Is it worth more of your time, energy, and resources? Are there more productive ventures you could work on?
You may want to upgrade the significance of a problem and bring in more resources; you may want to downgrade the significance of a problem and withdraw some of your resources. You may want to abandon a problem altogether. While re-evaluating the need to solve a difficult problem you should clarify your own motives and prepare a plan of action that will maximize your chances of success.
Luck
We are all ready to accept a quick solution to a problem that occurs by happenstance. Why work hard when you can get lucky? That is why gambling and the sale of lottery tickets are so popular. Some problems, such as solving a jigsaw puzzle, do involve an element of chance. The first piece you pick up may complete a challenging part of the puzzle, or you may have to search through pieces for several hours to accomplish the same task. More often, experience and a systematic method lead to a simple solution that makes it appear that luck played a role.
Luck can play a role in situations that require just one positive event to greatly simplify your problem. Most real world problems involve many steps and require a systematic approach in which luck has no potential role. Luck may play a role in your taking a different road home and avoiding a traffic jam, but luck will not help you paint the garage.
Hard work
Most challenging problems are ultimately solved with hard work over an extended period of time. If you face a difficult problem and are motivated to solve it, then be prepared to spend a lot of time and effort.
Suppose that one of your children is misbehaving on a regular basis. This is a major problem that can require years of effort, much patience, consultation with experts, trial-and-error, and lots of luck.
If you want to start your own business, you face a host of problems that have to be solved. It is not enough to have a good idea and a grand opening ceremony. Hard work over an extended period of time will be required to make your business a success.
Novel point of view
There is a tendency to stick with your initial approach and assumptions when working on a given problem. This tendency can lock you into a limited range of thought patterns that can, in turn, limit your ability to solve that problem.
We are creatures of habit and tend to reuse recently activated neural pathways when we repeat similar actions. If you sit in the same position, with the same information spread in front of you, as you repeatedly go over aspects of a difficult problem, there is a tendency to repeat exactly the same line of reasoning. When you get stuck on a problem and seem to be repeating the same steps over and over, a new approach can lead to a wider range of thought and action that may lead to better results.
Finding a novel approach may be as simple as sitting in a different chair, asking a different question, or changing an assumption.
In a procedure called ‘brainstorming’ you are encouraged to speculate, without restriction, and to write down all the ideas that come to mind. While a list of unrestricted speculations typically contains mostly irrelevant material, it can also include an idea that stimulates further thought in a new and useful direction.
Brainstorming can work with an individual, but it is more effective with a small group. Brainstorming with a group adds the possibility that one person’s wild speculation will stimulate novel thoughts in another person, and those novel thoughts may lead to a more practical problem solving approach.
Closest similar problem
A particular problem may prove very difficult to solve, but has features similar to other problems that have already been solved. It is possible to gain insights into your current problem by studying the solutions to these related problems. If your problem follows the pattern of the most closely related cases, then perhaps your problem will have a similar solution.
A Viking, lost at sea, could utilize sailing lore and conclude that a stationary smudge of clouds on the horizon might be surrounding the mountains of a distant island. His knowledge of similar situations could thus provide him with the ability to find land when none was in sight.
Medical diagnosis often employs similar-case analysis. When you visit a doctor with your own personal set of flu symptoms, your doctor may have already seen several patients with similar symptoms. Those other similar cases could then form the basis for an initial diagnosis of your particular situation.
Change a problem to make it simpler
Sometimes a problem, as you find it, is simply too difficult to solve. However, if you make one or two simplifying assumptions, then solving the problem may become a realistic task. This technique is often used in mathematics, science, and engineering.
The key to this technique is the judicious choice of simplifying assumptions. There is little point in solving your financial problems by assuming you are a millionaire, or solving a problem in rocket science by assuming you have invented an anti-gravity device. A good assumption eliminates awkward details while having minimal effect on the overall situation.
When estimating the amount of material required for a job, carpenters typically calculate the amount of wood in the finished product, and then increase that amount by ten percent to allow for waste (splits, knots, and short pieces that cannot be used). Experience has shown that expecting ten percent waste is a reasonable assumption in carpentry. It is not necessary to examine every piece of wood and preplan every cut before ordering material.
Einstein’s equations of general relativity are very difficult to solve for the real universe, so cosmologists usually begin by making a fundamental assumption.
Although the universe obviously contains planets, stars, and galaxies, on a very large scale it is useful to assume that the mass of the universe is evenly distributed in all directions. This basic assumption allows the equations of general relativity to be solved for a number of interesting cases and allows cosmologists to make predictions about the behaviour of the universe for billions of years into the future, and backward into the past.
Ask for assistance
When you are having serious difficulty with an important problem, ask for assistance. Almost always, there are others with expertise and experience who can help you with particular aspects of a problem. Often there are co-workers or friends who are pleased to be asked for help. In helping you they are able to make good use of their own skills, are able to feel a sense of satisfaction in providing assistance, and are helping to create a problem-solving network that they may someday need to access themselves.
Time for reflection
Compared to the speed of a computer, the human brain works at a snail’s pace. If possible give yourself time to mull over the different aspects of a problem. Your conscious mind has to work with the limitations of immediate-term memory, but your subconscious mind can sift through thousands of your memories. Give your subconscious mind time to do its work.
We have all had the experience of reflecting on a past conversation and thinking of more effective things that we could have said, if only we had thought of them at the time. Given time, your subconscious mind can often come up with better ideas.
Time for reflection is most beneficial when you have already organized, analyzed, and attempted to solve a problem. After that, your subconscious has all the pertinent information laid out before it and can peacefully chug away through your stored memories looking for items that might provide useful clues the next time you consciously consider the problem. Given more time, there is a better chance that you will find a better solution.
Despite your best efforts you will always encounter problems that seem unsolvable.
What do you do then?
Re-evaluation
Sometimes it is wise to stop and re-evaluate your problem solving efforts. Is this problem that important? Is it worth more of your time, energy, and resources? Are there more productive ventures you could work on?
You may want to upgrade the significance of a problem and bring in more resources; you may want to downgrade the significance of a problem and withdraw some of your resources. You may want to abandon a problem altogether. While re-evaluating the need to solve a difficult problem you should clarify your own motives and prepare a plan of action that will maximize your chances of success.
Luck
We are all ready to accept a quick solution to a problem that occurs by happenstance. Why work hard when you can get lucky? That is why gambling and the sale of lottery tickets are so popular. Some problems, such as solving a jigsaw puzzle, do involve an element of chance. The first piece you pick up may complete a challenging part of the puzzle, or you may have to search through pieces for several hours to accomplish the same task. More often, experience and a systematic method lead to a simple solution that makes it appear that luck played a role.
Luck can play a role in situations that require just one positive event to greatly simplify your problem. Most real world problems involve many steps and require a systematic approach in which luck has no potential role. Luck may play a role in your taking a different road home and avoiding a traffic jam, but luck will not help you paint the garage.
Hard work
Most challenging problems are ultimately solved with hard work over an extended period of time. If you face a difficult problem and are motivated to solve it, then be prepared to spend a lot of time and effort.
Suppose that one of your children is misbehaving on a regular basis. This is a major problem that can require years of effort, much patience, consultation with experts, trial-and-error, and lots of luck.
If you want to start your own business, you face a host of problems that have to be solved. It is not enough to have a good idea and a grand opening ceremony. Hard work over an extended period of time will be required to make your business a success.
Novel point of view
There is a tendency to stick with your initial approach and assumptions when working on a given problem. This tendency can lock you into a limited range of thought patterns that can, in turn, limit your ability to solve that problem.
We are creatures of habit and tend to reuse recently activated neural pathways when we repeat similar actions. If you sit in the same position, with the same information spread in front of you, as you repeatedly go over aspects of a difficult problem, there is a tendency to repeat exactly the same line of reasoning. When you get stuck on a problem and seem to be repeating the same steps over and over, a new approach can lead to a wider range of thought and action that may lead to better results.
Finding a novel approach may be as simple as sitting in a different chair, asking a different question, or changing an assumption.
In a procedure called ‘brainstorming’ you are encouraged to speculate, without restriction, and to write down all the ideas that come to mind. While a list of unrestricted speculations typically contains mostly irrelevant material, it can also include an idea that stimulates further thought in a new and useful direction.
Brainstorming can work with an individual, but it is more effective with a small group. Brainstorming with a group adds the possibility that one person’s wild speculation will stimulate novel thoughts in another person, and those novel thoughts may lead to a more practical problem solving approach.
Closest similar problem
A particular problem may prove very difficult to solve, but has features similar to other problems that have already been solved. It is possible to gain insights into your current problem by studying the solutions to these related problems. If your problem follows the pattern of the most closely related cases, then perhaps your problem will have a similar solution.
A Viking, lost at sea, could utilize sailing lore and conclude that a stationary smudge of clouds on the horizon might be surrounding the mountains of a distant island. His knowledge of similar situations could thus provide him with the ability to find land when none was in sight.
Medical diagnosis often employs similar-case analysis. When you visit a doctor with your own personal set of flu symptoms, your doctor may have already seen several patients with similar symptoms. Those other similar cases could then form the basis for an initial diagnosis of your particular situation.
Change a problem to make it simpler
Sometimes a problem, as you find it, is simply too difficult to solve. However, if you make one or two simplifying assumptions, then solving the problem may become a realistic task. This technique is often used in mathematics, science, and engineering.
The key to this technique is the judicious choice of simplifying assumptions. There is little point in solving your financial problems by assuming you are a millionaire, or solving a problem in rocket science by assuming you have invented an anti-gravity device. A good assumption eliminates awkward details while having minimal effect on the overall situation.
When estimating the amount of material required for a job, carpenters typically calculate the amount of wood in the finished product, and then increase that amount by ten percent to allow for waste (splits, knots, and short pieces that cannot be used). Experience has shown that expecting ten percent waste is a reasonable assumption in carpentry. It is not necessary to examine every piece of wood and preplan every cut before ordering material.
Einstein’s equations of general relativity are very difficult to solve for the real universe, so cosmologists usually begin by making a fundamental assumption.
Although the universe obviously contains planets, stars, and galaxies, on a very large scale it is useful to assume that the mass of the universe is evenly distributed in all directions. This basic assumption allows the equations of general relativity to be solved for a number of interesting cases and allows cosmologists to make predictions about the behaviour of the universe for billions of years into the future, and backward into the past.
Ask for assistance
When you are having serious difficulty with an important problem, ask for assistance. Almost always, there are others with expertise and experience who can help you with particular aspects of a problem. Often there are co-workers or friends who are pleased to be asked for help. In helping you they are able to make good use of their own skills, are able to feel a sense of satisfaction in providing assistance, and are helping to create a problem-solving network that they may someday need to access themselves.
Time for reflection
Compared to the speed of a computer, the human brain works at a snail’s pace. If possible give yourself time to mull over the different aspects of a problem. Your conscious mind has to work with the limitations of immediate-term memory, but your subconscious mind can sift through thousands of your memories. Give your subconscious mind time to do its work.
We have all had the experience of reflecting on a past conversation and thinking of more effective things that we could have said, if only we had thought of them at the time. Given time, your subconscious mind can often come up with better ideas.
Time for reflection is most beneficial when you have already organized, analyzed, and attempted to solve a problem. After that, your subconscious has all the pertinent information laid out before it and can peacefully chug away through your stored memories looking for items that might provide useful clues the next time you consciously consider the problem. Given more time, there is a better chance that you will find a better solution.
