[Answer] How Do Highly Capable People Think Differently from Ordinary People When Facing Problems?

[Answer] How Do Highly Capable People Think Differently from Ordinary People When Facing Problems?

This reminds me of an anecdote.

There is a classic math problem: A and B are s meters apart and walk toward each other at speeds a and b. A little dog runs back and forth between them at speed c, instantly turning around each time it reaches one of them. The question is: by the time A and B meet, how far has the dog run?

An ordinary person’s way of solving it is to notice that the dog and the two people are moving for the same amount of time. A and B meet after s / (a + b), so in that time the dog travels a total distance of s * c / (a + b).

It is said that one day someone posed this problem to Gauss (or perhaps some other near-godlike mathematician), and Gauss gave the correct answer instantly. The questioner said, “Gauss, you must have heard the standard solution to this problem before, right?” Gauss replied in surprise, “There’s a standard solution? I computed it by integration.”

This is probably one of the most intuitive examples of the difference between how exceptional people think and how ordinary people think. And ultimately, that difference is caused by a difference in ability. For someone like Gauss, who could produce an answer like that, it is hardly surprising that he also came up with the formula for the sum of an arithmetic series.