When I was trying to choose a PhD supervisor one of the things I did was read through recent grads' acknowledgments. While no one ever mentioned their advisor with anything but gracious words, you could get a pretty good idea of what working with that faculty member was like.
It's true that professors rely on grad students/postdocs to do work. And, at least in my experience, advisors are actually pretty good about giving students credit for their work -- having successful students reflects well on the advisor. But a student is even more dependent on their advisor than vice versa. It's not like undergrad where the main thing that matters to your future employment is to collect the diploma, because for most fields the main reason to get a PhD is to continue in academia, and academia right now is an extreme employer's market. The things you need to leave grad school with are 1) impressive recommendation letters, like "best student in N years, reminiscent of <mid-career hotshot> at that age", and 2) (lots of) refereed publications. If you manage that, the diploma should be automatic.
Yes, you can push back against advisors who require 12 hrs a day in lab. But if that means you take longer to produce work, your letters might be just good instead of positively glowing, which might mean you fail to launch in academia. Several hundred other people will apply for each tenure track job you apply to; those with "just good" letters tend to get crowded out. The tenured advisor might have a bruised ego because their publication rate has slowed, or be more frazzled because they have to save money and write more proposals, but at least they still have a job.
Also, PIs themselves generally work a lot as well (often the ones insisting on lots of hours from their students think, rightly or wrongly but based on their own experience, that that's the only way to succeed....). I agree academia is broken, but think it's at a deep structural level, and more complicated than schools exploiting students and hanging them out to dry.
I think your comment is pretty spot on. Just three things I'd add to, are that 1) the advisor is not intentionally downgrading your letter to "just good", but it's that they're obligated to write a better than "just good" letter for someone who has been more productive both in terms of research and in being a leader in the community (these two things go hand in hand). Writing the same letter for two students regardless of what they accomplish would be unfair.
And 2) sometimes getting more funding is simply not possible, as in the advisor has basically reached the limit of what they can do. There's a limit to the number of proposals that one can submit and the number of calls that fit their research agenda. So what I think you're missing is that if an advisor has less funding, there's going to be more pressure to finish sooner and less freedom to explore ideas beyond what's written in a previous grant proposal.
3) I've never heard of a tenured professor that concerned about their publication rate. In fact, most of them don't even update their CVs or websites with the last few years of papers. It's always the student who is trying to get more papers.
Just having the good new ideas isn't really enough, though. You have to be really persistent about figuring out all the details and making them work. This is related to, but definitely not the same as, being fascinated/obsessed by the topic.
Of course Einstein had great ideas. But he also spent many years working out the consequences of, eg, his first ideas about the fixed speed of light in vacuum and its consequences in physics, initially during downtime at his patent office job. Nearly all of the impact of the theory is in that working-out.
Work ethic is super important. The ability to grind on your ideas. And I think having some extrovert nature really helps in getting your ideas out there.
I was Paul's definition of smart, w/o good ideas. I loved to learn things. But I didn't really have the work ethic to build new things. I feel like I've done fine in life, but had you asked my middle school and high school teachers -- and even university... I've probably underperformed.
In contrast my son is bright, but not the academic star I was. But he has crazy work ethic in ideas he cares about. I've really nurtured his work ethic and played down the "smart" academic angle. If wants to finish a personal project and not study for that French quiz -- I'm fine with that. He gets an A-/B+ for the year, rather than an A. So what. The passion he pours into his ideas though is great and I think will serve him better over the course of his life.
I do compliment it. But probably more than that I emphasize that things worth doing are often hard and hard things often take time. So I taught him that setting short term goals along the way to long-term goals will help him stay on track. So he's becoming really good at showing me various intermediate states to his work, and I'm really excited when I see it. Whether its a game that he's writing or a business that he's creating.
As a younger kid he loved Legos. I think that contributed. He'd just do progressively larger and larger sets. As a kid I never could do a large Lego set. I had them, but they all remained unfinished.
So I'm totally on board with everyone knowing something about the liberal arts and trying to expand your world outside your traditional scope.
But I think "understanding" can mean just making connections within a single tech field, even without involving liberal arts. For example, a grade school math problem: "Assume the earth is a perfect sphere with radius 6378 km, and you have a piece of string just long enough to reach all the way around the earth's equator at the earth's surface. How much longer would your string have to be to make a perfect circle exactly one meter above the earth's equator at every point?"
The answer is 2(pi) meters. That's true for any spherical planet of any size -- that's what it means for the derivative of 2(pi)(r) with respect to r to be 2(pi). That is sometimes not the first thing people think of though, because of the grade-school context they associate with this problem....
Nice article! I guess it's obvious in retrospect, but I hadn't known of all the systematized study devoted to this topic. I'm happy to learn about it because I've found myself thinking about effective teaching and learning pretty often (I'm an academic), and what to do about "the stuff where, when you try to explain it concretely to someone else, your explanation doesn't really make sense unless the other person already knows what you're talking about".
In subjects I've tried to learn and teach, my experience is that talking to someone with a lot of such knowledge really only gives you an idea of the sub-topics and considerations you should try to understand better on your own. It is helpful in narrowing down what you should prioritize and maybe giving you a useful point of view to organize your thoughts from, but that doesn't save you from doing the thinking and understanding for yourself.
I agree that emulation helps somewhat by forcing you to make choices that are reasonable even if, as a beginner, you lack the knowledge to choose wisely yourself. But if the ultimate goal is to come up with new ideas using the knowledge, I think there's such a thing as too much emulation. You don't want to become a carbon copy of your mentor either.
I agree that deliberate practice and acquiring tacit knowledge are not the same thing. To me, deliberate practice is about repeating a certain activity -- one that you typically can describe in words to someone who doesn't already know it -- enough times that it's available to you as a tool, eg playing scales as a musician, times tables in elementary school math. Tacit knowledge has more to do with how you decide to apply those skills to best effect.
But my experience has been that they have kind of a symbiotic relationship. If you didn't have some tacit knowledge to begin with, you wouldn't know what to practice, or when you had practiced enough to be good. At the same time, it may not be possible to acquire enough tacit knowledge to become an expert if you don't have an immediate command of certain skills developed through deliberate practice. I.e. there's feedback -- more tacit knowledge should make your deliberate practice more effective, and better skills make it easier for you to acquire tacit knowledge.
Actually, even the first two tables comparing the frequency of 1,2,3,4,5,6 when obtained using primes vs. a fair die suggest that consecutive primes do not give a truly random (uncorrelated) way of choosing congruence classes mod 7.
If I throw a fair die 10^6 times, the probability of getting any given single outcome should behave according to Poisson statistics. On average, if I repeat a trial of 10^6 die-throwings many times, the number of outcomes of "4" (let's say) should be on average 10^6/6 = 166,667 , as mentioned in the article.
However, the exact number of times "4" comes up in a given trial itself follows a distribution around that average whose spread is about sqrt(166,667), or about 400. So the typical "error" in the frequencies given in the table should be ~few hundred.
By this reasoning, the deviations in the top table, the one given by the primes, are surprisingly small -- of order tens rather than hundreds. In other words, primes are more equitably distributed among congruence classes than we would expect independent die roll outcomes to be.
Yes, at the bottom of the article is an Addendum that covers this:
Addendum 2016-06-14. I noted above that the distribution of primes mod 7 seems flatter, or more nearly uniform, than the result of rolling a fair die. John D. Cook has taken a chi-squared test to the data and shows that the fit to uniform distribution is way too good to be the plausible outcome of a random process. His first post deals with the specific case of primes modulo 7; his second post considers other moduli.
He would sometimes eat lunch with us postdocs (just randomly, on a whim) when I was a postdoc at IAS. He would always have something interesting to say or ask, generally about science but often offbeat or unexpected -- you couldn't help but notice both his wide-ranging intellectual interests (our field was not quite within his main expertise) and his very gracious manner in starting conversations that both he and we would learn from.
Thanks for sharing — yea completely agree, it’s always so much fun to be around people like Dyson. There’s more like him at Princeton (and everywhere else, I was at university if Illinois for undergrad and the story is the same there), they just get a kick out of being curious, and always are genuinely interested to learn and hear new things, no matter how old they get. Such a pleasure to be around — they aren’t bitter or insecure, they don’t have anything to prove, they just think that some things are just so gosh darn cool, and that fun energy is contagious.
I had a professor in graduate school like that. He was probably 70 and did natural product chemistry.
Unlike the other professors who were hard asses because: 1) they were still making a name for themselves or 2) they dealt with it in grad school, so you should too, he was the friendliest, most curious person. You could be a 2nd year undergrad and if you asked an interesting question, he’d get genuinely excited about it.
There is a parallel with one of pg's other essays, 'Why nerds are unpopular'[1]. He says (I paraphrase): 'nerds care more about being smart than being popular'. But that's another way of saying nerds think the tests you have to pass to be popular are (on balance) a waste of time, ie bad tests.
As of earlier today you could still follow links from WSJ social media, for example their official twitter feeds, and get access to the whole article. Any way to set that up as a link in HN?
Rota was quite the celebrity, at least among students. In addition to advanced classes in his specialty, he taught differential equations, which was required for at least two thirds of undergraduates, so everyone knew him. Each semester he would pay a diffeq student to have a can of Coke ready for him at each class, so he could drink it while he lectured. Also, anyone who asked a question during lecture (a room of ~350 people) would get a free Hershey's bar after class. That he had worked in (and sometimes taught) philosophy as well as math was kind of the icing on the cake.
There was also a persistent rumor that he'd once given a diffeq multiple choice exam (scored like the SAT, so that a fraction of a point was deducted for every wrong answer) on which the average score was 1 or 2 percent, ie simply handing in a blank exam would probably have given a passing score. But I never confirmed that.
