Second, I do it because I don't like the idea of being mistaken. If, like other eras, we believe things that will later seem ridiculous, I want to know what they are so that I, at least, can avoid believing them.
Third, I do it because it's good for the brain. To do good work you need a brain that can go anywhere. And you especially need a brain that's in the habit of going where it's not supposed to.
Great work tends to grow out of ideas that others have overlooked, and no idea is so overlooked as one that's unthinkable. Natural selection, for example. It's so simple. Why didn't anyone think of it before? Well, that is all too obvious. Darwin himself was careful to tiptoe around the implications of his theory. He wanted to spend his time thinking about biology, not arguing with people who accused him of being an atheist.
In the sciences, especially, it's a great advantage to be able to question assumptions. The m.o. of scientists, or at least of the good ones, is precisely that: look for places where conventional wisdom is broken, and then try to pry apart the cracks and see what's underneath. That's where new theories come from.
A good scientist, in other words, does not merely ignore conventional wisdom, but makes a special effort to break it. Scientists go looking for trouble. This should be the m.o. of any scholar, but scientists seem much more willing to look under rocks.
Why? It could be that the scientists are simply smarter; most physicists could, if necessary, make it through a PhD program in French literature, but few professors of French literature could make it through a PhD program in physics. Or it could be because it's clearer in the sciences whether theories are true or false, and this makes scientists bolder. (Or it could be that, because it's clearer in the sciences whether theories are true or false, you have to be smart to get jobs as a scientist, rather than just a good politician.)
Whatever the reason, there seems a clear correlation between intelligence and willingness to consider shocking ideas. This isn't just because smart people actively work to find holes in conventional thinking. Conventions also have less hold over them to start with. You can see that in the way they dress.
It's not only in the sciences that heresy pays off. In any competitive field, you can win big by seeing things that others daren't. And in every field there are probably heresies few dare utter. Within the US car industry there is a lot of hand-wringing about declining market share. Yet the cause is so obvious that any observant outsider could explain it in a second: they make bad cars. And they have for so long that by now the US car brands are antibrandssomething you'd buy a car despite, not because of. Cadillac stopped being the Cadillac of cars in about 1970. And yet I suspect no one dares say this. Otherwise these companies would have tried to fix the problem.
Training yourself to think unthinkable thoughts has advantages beyond the thoughts themselves. It's like stretching. When you stretch before running, you put your body into positions much more extreme than any it will assume during the run. If you can think things so outside the box that they'd make people's hair stand on end, you'll have no trouble with the small trips outside the box that people call innovative.
When you find something you can't say, what do you do with it? My advice is, don't say it. Or at least, pick your battles.
Suppose in the future there is a movement to ban the color yellow. Proposals to paint anything yellow are denounced as "yellowist," as is anyone suspected of liking the color. People who like orange are tolerated but viewed with suspicion. Suppose you realize there is nothing wrong with yellow. If you go around saying so, you'll be denounced as a yellowist too, and you'll find yourself having a lot of arguments with anti-yellowists. If your aim in life is to rehabilitate the color yellow, that may be what you want. But if you're mostly interested in other questions, being labelled as a yellowist will just be a distraction. Argue with idiots, and you become an idiot.
The most important thing is to be able to think what you want, not to say what you want. And if you feel you have to say everything you think, it may inhibit you from thinking improper thoughts. I think it's better to follow the opposite policy. Draw a sharp line between your thoughts and your speech. Inside your head, anything is allowed. Within my head I make a point of encouraging the most outrageous thoughts I can imagine. But, as in a secret society, nothing that happens within the building should be told to outsiders. The first rule of Fight Club is, you do not talk about Fight Club.
When Milton was going to visit Italy in the 1630s, Sir Henry Wootton, who had been ambassador to Venice, told him that his motto should be "i pensieri stretti & il viso sciolto." Closed thoughts and an open face. Smile at everyone, and don't tell them what you're thinking. This was wise advice. Milton was an argumentative fellow, and the Inquisition was a bit restive at that time. But the difference between Milton's situation and ours is only a matter of degree. Every era has its heresies, and if you don't get imprisoned for them, you will at least get in enough trouble that it becomes a complete distraction.
I admit it seems cowardly to keep quiet. When I read about the harassment to which the Scientologists subject their critics, or people branded as anti-Semitic for speaking out against Israeli human-rights abuses, or researchers threatened with lawsuits under the DMCA, part of me wants to say, "All right, you bastards, bring it on." The problem is, there are so many things you can't say. If you said them all you'd have no time left for your real work. You'd have to turn into Noam Chomsky.
The trouble with keeping your thoughts secret, though, is that you lose the advantages of discussion. Talking about an idea leads to more ideas. So the optimal plan, if you can manage it, is to have a few trusted friends you can speak openly to. This is not just a way to develop ideas; it's also a good rule of thumb for choosing friends. The people you can say heretical things to without getting jumped on are also the most interesting to know.
Perhaps the best policy is to make it plain that you don't agree with whatever zealotry is current in your time, but not to be too specific about what you disagree with. Zealots will try to draw you out, but you don't have to answer them. If they try to force you to treat a question on their terms by asking "are you with us or against us?" you can always just answer "neither."
Better still, answer "I haven't decided." That's what Larry Summers did when a group tried to put him in this position. Explaining himself later, he said "I don't do litmus tests." A lot of the questions people get hot about are actually quite complicated. There is no prize for getting the answer quickly.
If the anti-yellowists seem to be getting out of hand and you want to fight back, there are ways to do it without getting yourself accused of yellowism. Like skirmishers in an ancient army, you want to avoid directly engaging the main body of the enemy's troops. Better to harass them with arrows from a distance.
One way to do this is to ratchet the debate up one level of abstraction. If you argue against censorship in general, you can avoid being accused of whatever heresy is contained in the book or film that someone is trying to censor. You can attack labels with meta-labels: labels that refer to the use of labels to prevent discussion. The spread of the term "political correctness" meant the beginning of the end of political correctness, because it enabled one to attack the phenomenon as a whole without being accused of any of the specific heresies it sought to suppress.