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How Does the Genius Think?

The short answer is, “Who knows. Ask one.” However, there are markers I’ve noticed over many years having worked with and read about a few of them.
a. Finding the “genius” solution is more than just picking up the right pebble on the beach. It is rejecting what doesn’t work. Researching a topic means sifting and winnowing idea after idea. The genius can reject the bad ideas quickly and move on. There is an anecdote about John von Neumann, who worked on the “Super,” H-bomb, and with the military. The report is that some engineers were working on a project for months, and one day handed it to von Neumann. He rifled through the pages for a few minutes, looked up and said it wouldn’t work. After months more of work, the engineers concluded, it doesn’t work. This is legend to the point that, “If Johnny says it will work or not, that is it.” BTW, Von Neumann was considered the best mathematician of the 20th century. Johnny had a great memory and one night at a party he got into an argument with a Byzantine scholar over some arcane facts of that time. When checked, Johnny was correct.
b. The genius, because of mental speed, can determine what needs to be done, while us mortals do what we can do. They don’t waste their time filling in gaps; they move forward to where the subject should be. Their finely honed intuition, based on vast knowledge, tells this to their inner eye. Never under estimate the power of intuition. This was the mark of Einstein, who using thought experiments, considered events scarcely imagined by conventional physicists.
c. The genius is relentless, focusing hours, days, and even years on the single purpose of their goal. Said Newton, “I focus on a topic completely until I see clear through it.” Geniuses have a capacity for work absent in most of us. Later in life Newton indicated he no longer could manage the rigor of thought he had during his greatest discoveries. Total concentration to the point of losing consciousness altogether is an asset they all possess. Archimedes of Syracuse, greatest of the ancients, was so focused on solving a problem, he was killed by a soldier when ordered to move.
Very rare is the genius that can spaz out the solution to a big problem. Geniuses have very deep knowledge, and read all materials.
Most geniuses pay attention to origins, and derive independently almost everything including that known. Example. Richard Feynman was famous for his notebooks and thoroughness of understanding everything he could. 
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