We are trained to think reproductively, logically and exclusively. By thinking reproductively I mean that whenever we are confronted with a problem we fixate on our past experiences, then analytically select the most logical approach and apply that to the problem, excluding all other lines of thought.

Correct this formula with a single stroke 5 + 5 + 5 = 550.

Many of us have difficulty with this problem because of our past experiences of arithmetic and arithmetical formulas. We were taught how to handle problems and new phenomena with fixed mental mindsets (based on what past thinkers thought) that predetermine our response to problems or situations. We are also taught to be exclusive thinkers and to disregard everything that is not immediately related to the way we were taught to handle arithmetical problems. This kind of thinking will keep you focused on the wrong items in the formula and make it impossible to solve the problem.


This problem can only be solved by approaching the problem on its own terms and by thinking inclusively with an open mind. By thinking inclusively, I mean you consider all approaches to the problem and consider all the elements in the problem. It is only when we start thinking inclusively that we start tinkering with everything in the formula including the symbols. You take the first addition symbol + and with one single diagonal stroke change it into a 4. Now 5 + 5 + 5 = 550 becomes 5 4 5 + 5 = 550.

I first became interested in Charles Darwin in college when I read about his thinking process that created his theory of biological evolution. When Charles Darwin returned to England after he visited the Galapagos, he distributed his finch specimens to professional zoologists to be properly identified. One of the most distinguished experts was John Gould. What was the most revealing was not what happened to Darwin, but what had not happened to Gould.

Darwin’s notes show Gould taking him through all the birds he has named. Gould kept flip-flopping back and forth about the number of different species of finches: the information was there, but he didn’t quite know what to make of it. He assumed that since God made one set of birds when he created the world, the specimens from different locations would be identical. It didn’t occur to him to look for differences by location. Gould thought that the birds were so different that they might be distinct species.

What was remarkable to me about the encounter is the completely different impact it had on the two men. Gould thought the way he had been taught to think, like an expert taxonomist, and didn’t see, in the finches, the textbook example of evolution unfolding right before him. Darwin didn’t even know they were finches. So the guy who had the intelligence, knowledge and the expertise didn’t see it, and the guy with far less knowledge and expertise comes up with an idea that shaped the way we think about the world.

Darwin came up with the idea because he was an inclusive thinker. He generated a multiplicity of perspectives and theories. Gould would compare new ideas and theories with his existing patterns of experience. He thought reproductively and exclusively. If the ideas didn’t fit with what he had been taught, he rejected them as worthless. On the other hand, Darwin was willing to disregard what past thinkers thought and was willing to entertain different perspectives and different theories to see where they would lead.

Most of us are educated to think like John Gould. We were all born as spontaneous, creative thinkers. Yet a great deal of our education may be regarded as the inculcation of mindsets. We were taught how to handle problems and new phenomena with fixed mental attitudes (based on what past thinkers thought) that predetermine our response to problems or situations. In short, we were taught more “what” to think instead of “how” to think. We entered school as a question mark and graduated as a period.

Consequently, we tend to process information the same way over and over again instead of searching for alternative ways. Once we think we know what works or can be done, it becomes hard for us to consider alternative ideas. We tend to develop narrow ideas and stick with them until proven wrong. Let’s say to advertise our product, we use television commercials during a popular prime time sitcom. We are fairly happy with the results and the television campaign seems to work. Are we going to check out other ideas that we don’t think will be as good or better? Are we likely to explore alternative ways to advertise our product? Probably not.

Even when we actively seek information to test our ideas to see if we are right, we usually ignore paths that might lead us to discover alternatives. Following is an interesting experiment, which was originally conducted by the British psychologist Peter Watson, that demonstrates this attitude. Watson would present subjects with the following three numbers in sequence.

                                                                                      2         4         6

He would then ask subjects to explain the number rule for the sequence and to give other examples of the rule. The subjects could ask as many questions as they wished without penalty.

He found that almost invariably most people will initially say, “4, 6, 8” or some similar sequence. And Watson would say, yes, that is an example of a number rule. Then they will say, “20, 22, 24″ or “50, 52, 54″ and so on– all numbers increasing by two. After a few tries, and getting affirmative answers each time, they are confident that the rule is numbers increasing by two without exploring alternative possibilities.

Actually, the rule Watson was looking for is much simpler– it’s simply numbers increasing. They could be 1, 2, 3 or 10, 20, 40 or 400, 678, 10,944. And testing such an alternative would be easy. All the subjects had to say was 1, 2, 3 to Watson to test it and it would be affirmed. Or, for example, a subject could throw out any series of numbers, for example, 5, 4, and 3 to see if they got a positive or negative answer. And that information would tell them a lot about whether their guess about the rule is true.

The profound discovery Watson made was that most people process the same information over and over until proven wrong, without searching for alternatives, even when there is no penalty for asking questions that give them a negative answer. In his hundreds of experiments, he, incredibly, never had an instance in which someone spontaneously offered an alternative hypotheses to find out if it were true. In short, his subjects didn’t even try to find out if there is a simpler or even, another, rule.

Creative geniuses don’t think this way. The creative genius will always look for alternative ways to think about a subject. Even when the old ways are well established, the genius will invent new ways of thinking. If something doesn’t work, they look at it several different ways until they find a new line of thought. It is this willingness to entertain different perspectives and alternative ideas that broadens their thinking and opens them up to new information and the new possibilities that the rest of us don’t see.

As I wrote these final words, I was reminded of an ancient Chinese story about a rainmaker who was hired to bring rain to a parched part of China. The rainmaker came in a covered cart, a small, wizened, old man who sniffed the air with obvious disgust as he got out of his cart, and asked to be left alone in a cottage outside the village; even his meals were to be left outside the door.

Nothing was heard from him for three days, then it not only rained, but there was also a big downfall of snow, unknown at that time of the year. Very much impressed, the villagers sought him out and asked him how he could make it rain, and even snow. The rainmaker replied, “I have not made the rain or the snow; I am not responsible for it.” The villagers insisted that they had been in the midst of a terrible drought until he came, and then after three days they even had quantities of snow.

“Oh, I can explain that. You see, the rain and snow were always here. But as soon as I got here, I saw that your minds were out of order and that you had forgotten how to see. So I remained here until once more you could see what was always right before your eyes.”