Seeing the Flow of Ideas is the fourth element of effective thinking and the fourth chapter in “The 5 Elements of Effective Thinking,” The subtitle is “Look Back, Look Forward.” As was mentioned in an earlier post, this is something that is fairly easy to do with respect to technology in this age of technology. Centuries before developments were occurring at a snail’s paste and this task was much more difficult. I attended some very interesting lectures on the development of pre-human species, which was an extremely long process. This is painstaking research, limited by the scant available evidence, and it needs to be carefully place together.

Looking back and looking forward fits nicely into the concept of memory as a device for time travel. Perhaps the primary purpose of memory is to look back in terms of personal and collective knowledge (transactive memory), for the purposes of looking forward or trying to predict the future. Drs. Burger and Starboard chose this to be one of the elements of effective thinking.

All too often people conceive of an idea springing forth from the mind of a genius. Actually, it is a matter of an individual building upon previous ideas and producing the future. It is not surprising that the authors, being mathematicians, chose calculus as one of their examples. In the popular mind, the calculus was developed independently during the same period by Newton and Leibniz. As the authors note, Newton and Leibniz each built upon the work of previous mathematicians. Newton himself noted that if he had seen further than others, it is because he stood on the shoulders of giants. The authors noted that Leibniz’s initial essay on calculus was just six pages. They noted that today’s introductory calculus textbook is over 1,300 pages. And that is just for introductory calculus. Calculus itself has advanced far beyond that to say nothing of the multitude of applications of calculus in science and engineering. Moreover, many other areas of mathematics have been developed and refined. Understanding the past development of mathematics facilitates not only its understanding, but also provides insights into future developments and applications of mathematics.

One individual who did the most by seeing the flow of ideas was Thomas Edison. He was extremely successful at inventing product after product, exploiting the maxim that every new idea has utility beyond its original intent. Edison wrote, “I start where the last man left off.” He also noted that many of life’s failures are people who did not realize how close they were to successes when they gave up.”

One of the exercises to provoke effective thinking is to ask “What Were Thy Thinking.”

In an earlier post I asked the hypothetical question as to what the colonizing powers have done given the morality of today. So the early colonies in America killed many of the native populations and made their property their own. They also used slavery. What were they thinking? How did they justify what today would be regarded as crimes against humanity? And consider today, how might some version of colonialism succeeded without stealing and killing native americans, and without slaves. This should be an interesting, and, I hope, an enlightening exercise.

The authors asked the question, which is an especially relevant question for educators, why are there grades of “F,” After all, the second element of effective thinking is fail to succeed. So why are Fs derogatory? What is of interest is what the individual did to correct or remove the F. It appears that the formal grading procedure is based on a faulty premise.

Of course, there is much more to this chapter, and I urge the reader to read the original chapter itself.

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Tags: Calculus, Dr. Burger, Dr. Starbird, ideas, Leibniz, Newton, Thinking, Thomas Edison

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