1) An n^2 algorithm runs in polynomial time, but it is no longer good enough when n ~= 100000000. Assuming 1000000 operations a second, that is still a few hundred years. I have never thought of it because I've just never encountered that sort of scale. I may never do, but it was still a revelation for me.
2) It confirmed that I am really rusty at algorithms due to one too many jobs writing CRUD web apps. I need to do something about this. For a start, practice in my free time and secondly, look for a job that allows me to develop in that area.
I'm not saying that it wasn't disappointing even though I knew my chances weren't good, but I gave it my best shot and I am choosing to use the experience positively. Is that serendipity?
"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.
When you take the mindset that planning exists to help you observe and react to future discoveries rather than to detail exactly what you're going to do regardless of future discoveries, all sorts of serendipity is showered on a development effort.
Thanks, Paul, and sorry about the alliteration.
The most important thing to take from the article is this:
> I was skeptical of their business (Google) and didn't expect it to last long, but it seemed like it could be fun and educational, so I accepted.
Live a little, and take chances!
You should think enough (and just enough, no more) about what you want in life so that when unusual opportunities arrive, you notice them, and jump at them.
This is more or less my take on it. There are opportunities all around us (IE: the luck part of the equation). But, if you don't have the knowledge, expertise, or ambition to act on them, you won't be able to take advantage of it (the skill part of the equation).
Key points from the article
"unlucky people miss chance opportunities because they are too focused on looking for something else"
"lucky people generate good fortune via four basic principles. They are skilled at creating and noticing chance opportunities, make lucky decisions by listening to their intuition, create self-fulfilling prophesies via positive expectations, and adopt a resilient attitude that transforms bad luck into good."
It sounds less like luck and more like skill when it's put this way.
I measure my success in many ways.
1. Do I havea loving family. Check.
2. Do I have fulfilling hobbies. Check.
3. Do I have enough money to fulfill my responsibilities and hobby, doing things I love. Check.
4. Do I have as much money as I would want to call myself successful. Not yet.
Tying my success to many parameters I can feel a little successful everyday, and continue to feel lucky, and continue to work toward what I would call a successful startup.
If you feel he's a good role model, then what do we make of him being cast out of Eden by his own board, and then having NeXT going basically nowhere until Apple begged him to come back and bought the company for its OS and as a talent acquisition?
I suspect he's been happier in a certain sense when his actions have been validated by the market, but at the same time, I strongly suspect he has certain other motivations that drive him and he's happy when he acts in harmony with those motivations. The marketplace validating his work is probably just icing on the cake.
That's all just speculation I pulled out of my Ass, of course!
This is even stronger than Pasteur's famous, "Chance favors the prepared mind" - if you are not actually working on a problem, there is no possible way to benefit from serendipity.
I've found most chances come only once, and never again. That job interview, the cute girl right beside you in the produce section (etc) are opportunities we need to instinctively take (instead of instinctively shy away from).
Jason Shen is an excellent example of hunting down ego-fear: http://news.ycombinator.com/item?id=1811868
How does he explain all the happy-go-lucky young fliberdygibbits who ended up serendipitously taking their first job offer in 1998 from Pets.com? Or those of us who labored under the impression that "as soon as DataPower takes off" there'll be bonuses raining from the sky?
Right time, right place. Right age group. Right skill set. 25% of the above are things you can plan for.
Nor does he have a hard time explaining what he did. He has spoken several times at Startup School about his approach to solving problems. I've learned a lot from him.
Sometimes reasons to hope are not best expressed by those who have nothing to regret. This is one of those times.
While it's interesting to speculate if PB had chosen a pets.com instead of google what would have happened to his career, it's not particularly constructive.
The idea that our success is largely beyond our control is sufficiently pernicious that we're all better off just pretending it is not the case and keeping our heads down and trying our damnedest.
There are no guarantees. Ever. Our lives are ruled chance. You can't duplicate my life, but you can create an interesting life of your own.
edit: yeah, rate me down for telling you what you didn't want to hear. I'm not the one who throws $18k at a time down a well just to get a high school kid to suck up to me and think I'm a god.
So what would you tell kids? Do not aspire for anything because chances are, you will likely fail.
You can choose how you look at things.
"For every good story, there is a bad story."
"For every bad story, there is a good story."
I choose the latter.
There could very well be a cafe owner down the road who might exactly say the same thing about serendipity as PB did in this blog post. He could be happy with the choices he made in his lifetime and the chances he took that got him all that is good in his life (by his definition).
It all comes down to whether a person has a positive outlook or not. One can keep regretting the things that didn't work out, or choose to see the good things in his/her life.
I just posted an interview with the writer and professional asshole Tucker Max, who said almost the same thing: http://jseliger.com/2010/10/22/tucker-max-interview-assholes... :
Tucker Max: People create all these narratives explaining away why they haven’t had the courage to take their personal path, or explaining away my success, or anyone else. Anyone who succeeds in anything, there’s always going to be people who don’t have the courage to do that. They get upset about it, either explain it away, or dismiss it away.
JS: It sounds like you almost found out by accident. In Assholes Finish First you say that when you and your friends graduated from law school, “We were slowly realizing that the ‘real life’ we’d chosen really fucking sucked. A lot.” Sounds like you’re trying to tell people how not to do that.
TM: As much as I’d like to sit here and be like, “Yeah, I had the courage to do all this stuff, and I had the vision to see where I was gonna go and I knew I would get there.” That’s fuckin’ bullshit. That’s not true. That’s the narrative I might tell when I’m 70, and I can’t remember all this stuff.
JS: Trying to inspire your grandkids?
TM: Right. The true, true story is it’s a combination of some determination and some talent on my part. Some talent, a lot of determination, a lot of luck, and a lot of serendipity. And a lot of failure. I was fired—
JS: There’s a section about failure in the book.
TM: I was fired from the legal profession, basically. I wasn’t just fired from Fenwick and West—you read the first book, the story’s in there. I got fired in such a public way that there was almost no way I was going to get back into law. I would have to go back and be a public defender or something if I wanted to be a lawyer. Seriously.
This, of course, isn't true at all.