Insight

There is a story that is often told to demonstrate insight. It is not absolutely known to be true and it has evolved with the many tellings. Some scholars believe the incident never occurred at all.

Still it is an outstanding and wonderful story and it does indeed demonstrate the nature of insight as well as anything my mind imagines.

Johann Carl Friedrich Gauss, April 30, 1977 to February 23, 1855, was a great, German mathematician and scientist. His reputation has only grown since his death and deservedly so.

He was a real prodigy and there are numerous anecdotes about his early genius. The "insight" example is one of those.

In the version of the story I heard Gauss was in elementary school and his teacher assigned the entire class the task of summing all the integers from 1 to 100. The assignment as much as anything was to keep the students occupied for a while so the teacher could do something else.

The teacher was astonished as young Gauss within mere seconds raised his hand and reported the correct answer.

Gauss somehow had recognized that if one wrote the numbers 1 through 100 horizontally on the paper and then beneath them wrote the numbers 100 through 1 that the sum of each pair of numbers was always 101.

  1   2   3   4 ...  97  98  99 100
100  99  98  97 ...   4   3   2   1
--- --- --- ---     --- --- --- ---
101 101 101 101     101 101 101 101

So it wasn't very hard for Gauss to multiply 101 by 100 which is 10,100. Then he divided by 2 to get 5,050 which is the correct answer of the sum of the integers 1 through 100.

Even if this did not happen almost everyone has had enough experience with insight, either one's own or another's, to know it might be true.

Giving an example of insight or even experiencing insight itself is so far from explaining insight.

I recall once a long time ago when I was trying to help my son learn to tell time with an analog clock. After many frustrating days my own solution was to simply do away with analog clocks in favor of digital ones. But the rest of the world seems unwilling to adopt that solution. Finally one day my son just "got it" which is another way of admitting that insight occurred.

So many things are like that. Those images for instance that if you look at them casually at first you see one thing but if you keep staring then you see another. And finally you get to where you can easily see one or the other or even both sometimes.

Insight is far removed from anything I know how to do with computer programming.

I have a friend who likes to say "in my logical thinking" a lot. And often his thinking is extremely good and useful. But it rarely is logical. Rather it is often insight.