Principles of problem-solving

To figure out how things, work, how to do things, and how to make things work that aren’t working, there are some basic principles that actually seem to help, pretty reliably. It is better to use these than to rely on intuition and dumb luck.

Logic

Logic is the process of linking truths to each other, seeing what the causal relationships between various objects and phenomena are. The application of logic is critical. See the five rules below. The first three of those are a fundamental exercise in logical construction.

Analysis

Analysis means “thinking about it.” Analysis is study of the problem you’ve got, or an examination and visualization of “what it is that you are trying to do or accomplish.” Most problems yield quickly to simple but careful analysis.

Observation

“Watching” a process or object work is an essential part of problem solving. Just sitting, staring, observing and “coming to know” the object is really useful, in many cases, if logic and analysis haven’t gotten the job done.

Measurement

“To measure is to know,” Lord Kelvin said. When you’re stuck, start making measurements. If you want to really get to know a system, measure it. Learn what measurement means, and the rules of measurement. It is an invaluable tool.

Documentation

“If you don’t write it down, you can’t prove it happened,” is what they say in physics labs. When you are measuring, observing, analyzing or problem-solving, documenting what you are doing can be invaluable if you can’t get things done in one sitting.

Criteria for Fact-based Critical Thinking and Problem Solving: The Fundamental Rules of Scholarship

Over the years, I’ve run across five rules that I believe are central for science and scholarly research. The first three are at the center of scientific method and, through their application, ARE the scientific method. The last two are recommended qualifying standards, to help us maintain reasonable rigor and integrity.

The “theory” referred to is what we believe or what we are testing. “Facts” are established data that we’ve gathered and can cite.

For a Theory to be considered proven or true, in the scientific sense, it must comply with:

1. The Basic Rule: The theory must fit the facts.

2. The Range Rule: The range of the theory must fit the range of the facts.

3. The Wild-Claim, or Coincidence, Rule: The counterstatement of the theory must be incompatible with the facts. This is also sometimes called the “null hypothesis.”

4. Kelvin’s Rule: We must be able to express the theory clearly in numbers, words and pictures.

5. Feynman’s Rule: We must show that the theory fits the facts in even the worst case.

• The Basic Rule is obvious.
  
  
• The Range Rule demands a linkage connecting the “real world” application of our theory to the facts we call upon to support it.
  
  
• The Wild Claim Rule is the standard that rules out coincidences, insisting that our theory can’t be both “true” and “untrue” at the same time.
  
  
• Lord Kelvin observed that until we can speak of something in numbers, our understanding of it is “meager and unsatisfactory.” Given that mathematics is a central language of science, it is essential we be able to describe our theory in math (which is where equations come from). Similarly, to demonstrate that we clearly understand the theory, we should also be able to express it verbally and graphically, at the very least.
  
  
• Richard Feynman insisted that it is the responsibility of the researcher to discover and answer all objections, weaknesses and deficiencies in his or her theory, as a demonstration of procedural thoroughness.

When we can comply with the above rules and cite the facts upon which we base our assertions, our analysis may be considered “scientifically” valid and in agreement with the general rules of fact-based scholarship. Until we satisfy all of these rules, our analyses must be considered incomplete and possibly flawed (although not necessarily wrong or invalid). The burden of proof remains with us until we have satisfied all of these rules.

The application of these rules in our work is an excellent on-going exercise. Even when we can’t satisfy all five rules (which is most of the time), our increased awareness of where our work stands in terms of science and scholarship is illuminating and vital to our understanding of things, not to mention to our own intellectual integrity.