Logical reasoning can help one to come up with highly imaginative ideas. It involves observing evidence (signs,symptoms and symbols), hypothesizing a theory (by recognize the possibility, evaluate the situation), and then verifying the hypothesis (by carrying out experiments). An example of logical reasoning involves the Wright brothers. During the period in which they were developing the airplane, people believed that the reason birds were able to fly was because they flapped their wings. Consequently, a number of airplanes were built which incorporated the feature of flappable wings. None of these devices succeeded in staying aloft. The Wright brothers, however, making countless and detailed observations of the flight behavior of birds, noticed that whenever a bird soared in the wind with its wings fully outstretched and in a horizontal position, it gained altitude. On the basis of this phenomenon, they developed the hypothesis that a bird's wing produces lift not only because it flaps, but because of its characteristic shape, i.e., arched on its upper surface and flat on its lower surface. The brothers subsequently built a wind tunnel to test their hypothesis. When they saw it being verified, they proceeded to design and construct the airplane. Interestingly, although they were certain that it was the shape of the bird's wing that was responsible for its lift, they did not know precisely why this was the case. Only later people were able to use Bernoulli's principle to provide an explanation of this phenomenon. Because the Wright brothers got their idea from watching the birds, their wing design had a hollow at the bottom. Later on people used mathematics to design the wing. Their wing design was flat at the bottom.

Of the four methodologies, I would assign the highest priority to logical reasoning. First, in recent years, logical reasoning has been sorely neglected--both in our educational system and by our research establishments. This situation has now reached critical proportions, and can only be reversed by ensuring that students and graduate researchers are given the opportunity, support, and time needed to carry out independent, creative, and curiosity-driven problem-solving.

Second, logical reasoning, as a methodology, has been responsible for the vast majority of major technological breakthroughs throughout the course of our history. Among such breakthroughs I would include Nicolaus Otto's conjecture that the steam energy inside a steam engine could be replaced by burning a mixture of compressed air and vaporized gasoline. This conjecture resulted in an internal combustion engine that was lighter, quicker to start, and easier to operate. I would also include Chester Carlson's revolutionary idea that an electric photoconductor could effectively replace chemical film, an idea whose development totally changed the printing industry.

Typically, such breakthroughs are preceded by the discovery of important new knowledge. For example, in inventing the phonograph or 'talking machine', Edison uncovered the fact that each vocal sound had its own unique vibration waveform. Similarly, in inventing the airplane, the Wright brothers uncovered the fact that air lift could be created only if the wing's upper surface was in the shape of an arch and its lower surface flat. In each case, they applied their innovation (i.e., their new knowledge) toward creating an invention.

One way to master logical reasoning is to practice practical problem solving. I recall that as a child I attempted to solve the problem of how a rainbow is formed. However, our present education system does not provide us with opportunities to grapple with such ‘impractical’ problems. It teaches us only how to apply known knowledge, not to learn how to uncover new knowledge. Some educators, for example, believe that robotics competitions can improve one's inventiveness. Unfortunately such exercises entail only the application of known technology or knowledge and not true creation of new knowledge. Because logical reasoning training is not provided within our education system, those who have trained with logical reasoning skill by themselves, are not recognized by the society at large.

Although we tend to neglect logical reasoning in our research environments, we use it extensively in crime solving. In the 1996 Atlantic City Olympic village bombing, a security guard had been warning people to stay away from an unattended bag, not long before a bomb in the bag exploded. FBI detectives suspected that he was the bomber and began investigating him. After learning that this man had been warning people to stay away from the bag, the detectives hypothesized that he probably was the bomber. They tested their hypothesis by searching his house and investigating his activities. From this example, we can see some of the characteristics of logical reasoning, as listed below:

1. Logical reasoning is not necessarily learned in school. It can also be learned in one’s environment.

2. Logical reasoning cannot provide a guarantee that a hypothesis will always be verified. However, it creates a context in which this becomes a possibility. As it turned out, the aforementioned security guard was innocent. However, in another case involving the Oklahoma City Federal Government Building bombing, the suspect was caught and convicted. In short, logical reasoning is successful only a percentage of the time.

3. With a strong hypothesis, we have no choice but to seek verification. It would have been wrong for the detective not to investigate the Atlantic City security guard, ( even if the hypothesis turned out to be wrong) because the benefit of apprehending the bomber was exceedingly great.