"How long will you need to find your truest, most productive niche? This I cannot predict, for, sadly, access to a podium confers no gift of prophecy. But I can say that however long it takes, it will be time well spent. I am reminded of a friend from the early 1970s, Edward Witten. I liked Ed, but felt sorry for him, too, because, for all his potential, he lacked focus. He had been a history major in college, and a linguistics minor. On graduating, though, he concluded that, as rewarding as these fields had been, he was not really cut out to make a living at them. He decided that what he was really meant to do was study economics. And so, he applied to graduate school, and was accepted at the University of Wisconsin. And, after only a semester, he dropped out of the program. Not for him. So, history was out; linguistics, out; economics, out. What to do? This was a time of widespread political activism, and Ed became an aide to Senator George McGovern, then running for the presidency on an anti-war platform. He also wrote articles for political journals like the Nation and the New Republic. After some months, Ed realized that politics was not for him, because, in his words, it demanded qualities he did not have, foremost among them common sense. All right, then: history, linguistics, economics, politics, were all out as career choices. What to do? Ed suddenly realized that he was really suited to study mathematics. So he applied to graduate school, and was accepted at Princeton. I met him midway through his first year there--just after he had dropped out of the mathematics department. He realized, he said, that what he was really meant to do was study physics; he applied to the physics department, and was accepted.
I was happy for him. But I lamented all the false starts he had made, and how his career opportunities appeared to be passing him by. Many years later, in 1987, I was reading the New York Times magazine and saw a full-page picture akin to a mug shot, of a thin man with a large head staring out of thick glasses. It was Ed Witten! I was stunned. What was he doing in the Times magazine? Well, he was being profiled as the Einstein of his age, a pioneer of a revolution in physics called "String Theory." Colleagues at Harvard and Princeton, who marvelled at his use of bizarre mathematics to solve physics problems, claimed that his ideas, popularly called a "theory of everything," might at last explain the origins and nature of the cosmos. Ed said modestly of his theories that it was really much easier to solve problems when you analyzed them in at least ten dimensions. Perhaps. Much clearer to me was an observation Ed made that appeared near the end of this article: every one of us has talent; the great challenge in life is finding an outlet to express it. I thought, he has truly earned the right to say that. And I realized that, for all my earlier concerns that he had squandered his time, in fact his entire career path--the ventures in history, linguistics, economics, politics, math, as well as physics--had been rewarding: a time of hard work, self-discovery, and new insight into his potential based on growing experience."
As the narrator says, this is not an usual pattern for people to migrate from one thing to next. And if that's the case, then chances are there are many many more people which may end up never finding "that calling". In a way, the above story illustrates the anti "pure hill-climbing" approach: the initial assumption/premise is that you should find a hill and then go really, really far in hopes of making a big contribution. Whereas Ed Witten's story shows that picking one single hill is not necessarily a good idea (local minima!) ... In fact, every once in a while (or systematically), you could jump to a different hill and still come out as a winner. Now the real puzzle is:
a) You could make the argument that your chances of finding the optimal hill for you, on the first try, are very slim. Hence, you should jump at least a few hills.. i.e, your real aptitude lies somewhere else.
b) Jumping too much will/may cause not enough time with anyone subject to make significant contribution - hence it's an optimization problem.
c) The "cross-discipline" question: its often acknowledged that bridging different knowledge areas is very helpful in terms of making interesting discoveries. Does that, in turn, mean that you should jump at least a few hills? If so, how many, and how much time?
Fun questions to ponder... Clearly there is no black and white answer either! Depends on your field, context, etc.
I had been depressed for years, but then one day, it dawned on me that I should drop out and pursue what I knew I wanted in life. I picked up programming again, am now an aspiring web developer, and I'm quite happy now.
Sometimes I think of how much better things would've been if I had started on the right foot, but Ed's story goes to show it's never too late to discover your calling. And when you find it, you may be destined to do great things.
That was quite a motivating story. Thanks for the share.
More generally, if you can get into one Ph.D. program you can probably get into most of them. Profs, like any employer, want the two key things: be smart, and get enough done to justify their investment in you. Except that students are really cheap, especially in the first year or two, and especially in math or theoretical physics where their cost is mostly in office space, ever-cheaper computer time, adviser hours and coffee.