"The mark of a true genius is the ability to hold two seemingly contradictory ideas in mind at once." -- attributed to Albert Einstein

I remember, my first week of college, I had lunch with my advisor for the normal "how are things going?" chat. I said that I really liked my physics course, but I thought the psychology/neuroscience seminar was frustratingly vague. I liked that there was always a right answer in physics, but in psychology there're all these competing theories, and some experiments will point one way while others point the opposite. It was all a contradictory mess of evidence, and you seemingly couldn't draw any conclusions from it.

He replied that once you get to the higher levels of physics, it was like that too. (He'd done his Ph.D at Harvard as part of the team that won the 2001 Nobel Prize for discovering Bose-Einstein condensates.) There are not clear right and wrong facts, there's only data, and sometimes the data will point one way and sometimes it will point the other. And in order to make sense of that data, you need to be able to hold all the possible ideas, both right and wrong, in your head at once, so that you can sort them out.

I basically ignored him and then floundered through college. But once I got out and into the working world, I found that pretty much all the leaders I admired had this ability to hold multiple contradictory ideas in mind at once and yet still make a decision. And the authority figures I didn't respect lacked this ability, as did most of the people who never managed to rise into leadership positions. It was a pretty discomforting realization, since I wanted to move into a leadership position and yet my whole life up till then, I'd been seeking certainty in my intellectual life.

When you reach a contradiction, there're a couple of possible responses. You can go narrower, discarding the evidence that doesn't fit your hypothesis. This is the Ayn Rand approach - "Whenever you think you are facing a contradiction, check your premises. One of them is sure to be false." Or you can go deeper, unpacking each idea into its constituent parts and keeping those parts that you can reconcile between the two. This is the Hegelian synthesis.

It's not that one approach is necessarily better than the other, but if you want to have a big impact on the world, your thinking has to encompass the world, including all the parts that don't fit with your preconceptions. If you limit yourself to faith, then the only people who can relate to your ideas are those that themselves believe on faith, while if you limit yourself to evidence, then the only people who can relate to your ideas are those who themselves believe in evidence. You've excluded half the world from being able to hold a dialogue with you.

That's why I mentioned Kuhn and the Structure of Scientific Revolutions above. Kuhn's contribution was to document how prevailing scientific thought shifts over time. And he found that during periods of "normal science", scientists operate under the Randian paradigm - they sweep evidence under the rug that doesn't agree with the prevailing hypotheses. But once in a while, someone will come along that actually looks at the experimental results that have been recorded as anomalies, and instead of discarding them, turns them over in his head until they can be made to make sense with the existing body of evidence. Like Einstein and relativity. And then you have a paradigm shift, and the body of knowledge advances to include both the old laws and the new evidence that has been discovered.