What to Learn
danluu.com
danluu.com
The famous Scott Galloway (whom I had as a b-school professor) made this point like this: if you are a great guy, great father, great boss, etc, but once in a while you get violently drunk and hurt people in your life - THAT thing offsets everything else. You won't become better by "doubling down" on what you're already good at, but by fixing this flaw.
Another case - I used to manage a C++ developer. If you gave him a tight spec, he'd implement it perfectly. But the world we lived in required him to go talk to people to figure out what the real needs are, and he was bad at that. So his code always solved the wrong problem unless someone was helping him with this stuff.
Every year, his own developmental goal was to go learn the next C++ standard. And that would have been useless because he was already a great C++ programmer. Going from 97th percentile to the 98th wouldn't matter. The much bigger bang for the buck would be figuring out how to go sit down with a sales rep and say "OK, what's our client actually trying to do here?"
It sounds simple but I believe this held him back not just in work but in life. I happen to know that he didn't have great communication with his wife and kids either - solving this thing would make him so much better at all parts of his life.
The thing is - we all have glaring things like this - obstacles in our own trajectory that if we fix, our existing strength would really shine.
I think if we're starting with an individual with no obvious weaknesses, perhaps they are just average at many things for example, the ROI is better for things one has a natural aptitude in.
Correcting an obvious weakness would generate a better ROI as per your examples.
I didn't mean that the weaknesses have to be obvious. I agree the first example I used was a blatant one, but in the other case the person had lived 5 decades without recognizing the impact that lack of communication skills had on his life. He always just thought "that's how I am."
So in your case, of someone who is "just average at many things" - perhaps there's a fear of chasing a direction, a reluctance to commit, an inability to focus, etc. that probably got them to "just be ok" and living below their potential, and probably overcoming that thing is a meta-skill that they need to gain.
The point I am making and that I don't want to get lost is: there's a huge difference between "I am consciously choosing to be a C++ hacker" vs "I am falling into this bucket because I fear doing other stuff". First one is fine, second one means a person is under-living their potential.
First, are you living your own best life? If you ask him "do you want to be limited by comms skills for the rest of your life, in all the ways it affects you and home and at work" he's say "no, I'd rather not have this problem" but then we couldn't really get it to change. So he fell short of his own recognition of what his life could be.
Second, it just limits you. There's nothing wrong with writing parsers and someone has to do that, but there's a difference between "choosing" that and "being limited to it." Versatility and capability is important. Say he wanted to go work somewhere else, the more skills and versatility you have, the more options you have.
Third, even within such a job you're still limited. EG: are you having a technical debate on your team? The better you can communicate, the more likely you are to advocate well for your solution, the more likely your good ideas will materialize, etc.
For example, a very good coder who is OK but not great at presenting or writing may want to spend some effort on those areas.
You see someone who needs help, either go figure out how to help and help or shut the fuck up and keep walking.
No, he's saying that you don't tell someone who is hungry "if you would learn to fish, you wouldn't be hungry" and leave it at that. Especially don't do this if you don't know how to fish yourself. But do, if you know that "learning to fish" is good, team up with the other person and learn to fish together. At the very least, you can help them find an angler to teach them.
EG: if I have bad communication skills, yes ideally someone coaches me. But at least, random feedback of "wow that meeting went badly" - hearing that from many people over and over - may make me aware of the area and look into it myself.
Like, if I am starting to get fat, I want people to tell me when they see it, even if they don't have a diet and training regiment set up for me.
But would you want random people to tell you, unsolicited, "you're fat, you need to lose weight".
Also, I'm obligated to note that the energy balance model of weight gain and loss has come under close scrutiny in recent research, and it is never as simple as eat less, exercise more. https://www.nature.com/articles/ejcn2011132
It is probably not an all encompassing model, however it's still one of the best approximations for what the average layperson should do to lose weight.
With dieting and exercise, i went from a weight of 86 kg to 74 kg over a period of about 3 months (weighed myself daily, kept track of what i ate). Since then, with just dieting, i've gone from 74 to 70 kg in about 2 months.
Is it hard to get nutrition right in such circumstances? Sure. Are there more factors that should probably be taken into account? Of course. Can improperly done exercise cause damage to the body? Yes, that's why people repeat that you need good form so often.
However exercise most definitely works to some degree, even though i had to make myself to do a bit of it every day. I went from being able to do about 30 incline pushups to 150. From 30 situps to 150 as well. From being able to do 10 pullups, all the way to around 40, of course, all of the exercises divided into sets of repetitions with some rest inbetween. The numbers and targets could probably be fine tuned, but it was enough for me.
But at least you provide guidance on how and where to learn the solution as well, yes? I don't imagine anyone going around telling people what they should do but not being able or willing to guide them to where they can find out how to do something. Also, I don't see providing advice that is both unsolicited and uninformed as being a gift. That's the sort of thing that cause most people to react poorly and perhaps say, "mind your own business".
How do you do that?
Great question. I assume you're asking from the point of view of the person having the challenge rather than someone observing/helping them.
There's no easy or painless answer. The reason these deep flaws exist in us is precisely because we have been avoiding dealing with them for some deeply personal and painful reason. But I do think there's a general pattern that I can share from my own experience.
The first step is to recognize that the problem exists and be "fed up" with it. To recognize that you're selling yourself short in some way, that you're failing yourself or your relationships. "I don't want to have my work and family life suffer anymore because I am afraid to talk to people." Or even "I don't want to be out of shape and struggle to walk a mile" kind of thing. You can't solve problems like this unless you're seeing them clearly and desperate to get out.
They often say that you have to hit "rock bottom" as a requirement for curing yourself. I think this is what they mean.
Once you hate the problem, it's good to get some external data. Ask your boss, colleagues, family about how you are (eg: tell me where my communication skills are weak, what am I doing that is so obviously wrong?) and then listen to what they say. They may surprise you? Eg is there a pattern, you are bad at it in some contexts and good in others? What is that about?
From the above and other resources, come up with the list of behaviors that would be an improvement. For example: "I would be better at my job if before I dive into a project, I speak to 3 people who understand the problem space" is probably a non-controversial one.
Then you ask yourself: why does that feel hard? Why am I just reluctant to get up and ask the sales person what the context of the client need is? What is it about "going up to someone I don't know super well and asking them a question" that terrifies me? What do I think would happen if I did this? Would they mock me? Would I feel like an idiot? Would they tell my boss I don't know something I ought to know?
Reflect if the fears are real. Is anyone in the work environment actually going to react the way your fear would suggest?
If intellectually you know that the thing is right and safe, then you force yourself to do it. Hyperventilate at your desk and then suck it up and walk over to the sales guy. Ask them, get the information, have a conversation. Reflect in retrospect: was this a helpful activity, and did I get hurt the way I feared I would?
Keep doing it. Build up the experience/muscle of doing the thing, and prove to your anxiety that it's not a dangerous thing to do. Talk to others who got good at this thing despite being not good at it originally. Find people who are awesome at the thing and study what they do. Become a nerd on the thing that's scaring you and you will likely see it stop being scary.
And I would be remiss not to say that in most cases, our deepest problems (even if they simply manifest in work performance) stem from psychology and childhood experiences. The guy in my story must have had some rough experiences growing up, maybe he was called an idiot or ignored or mocked or whatever, which made it hard for him to be communicative/open later in life, including with his family. Making a little crack in the armor of anxiety through the work process would help, but when something is this deep, seeing someone like a therapist is often helpful as well.
But to rewind, the key thing is to recognize a gap between how you are and how you want to be. You fundamentally have to say to yourself "I don't want to be forever limited by this thing, I don't want to hurt myself and others because of this thing" -- everything else is problem-solving.
That person can help directly with several of these steps: noticing and characterizing the problem; exploring the unspoken assumptions; and formulating alternatives and plans.
This is like the quote of "Don't tell me what you value, show me your budget and I'll tell you what you value." Before you go and try and improve yourself, it's good to be honest about what you value and what your goals are. If what you value is moving up the corporate ladder, then learning even more about C++ is not going to help. On the other hand, if it's to be even better technically, then go for it. If you value improving your business all around, then the communication angle is a better place to spend your time.
But if I tell a developer who can't speak well or communicate lucidly that they need to work on their communication skills, that comes across as offensive.
There was a horrible architect at my previous organization who was universally loathed for his bad communication skills and general lack of empathy. He was a Korean, and his English was abysmal. To him, it felt like something to shrug about. We had to go to HR, multiple times, about his behavior. Nothing much changed because again, they didn't know how to address the core issue, which is he couldn't speak clear English. His lack of empathy became masked with indifference and some of the higher ups (also non native English speakers) supported him saying it was general culture differences. However his lack of communication severely hindered progress and made life difficult.
I once had a colleague who had horrendous body odour and wouldn't wear deodorant. It made working with him really difficult. And he was one of the best developers I've known. I've never told him this because I didn't want to offend him, but stuff like this should also be addressed. Communication, body language, writing skills and general personal skills need to be addressed.
How do you offer feedback in that sense without embarassing them or offending them?
To some extent, "you can lead the horse to water but you can't make him drink." In the case if the terrible architect, your big problem was that he didn't want to change / had his head up his ass / didn't see the problem.
If you are a peer, there's not much you can do in this case. If you're a friend, you can try to persuade him of the negative impact this is having on him: eg "you know how you always struggle to get your ideas implemented? This is because people have a hard time following you, so your good ideas die on the vine. Do you see that and does that bother you?"
If you are his manager, then you can make this more of a performance issue "as an architect, you are expected to clearly communicate solutions and you're not doing that."
At the end of the day there's a meta question. Does your company value people who are introspective and will want to evolve? If the answer is yes, they will screen for that in interviews and have it be part of the company culture (so the terrible architect would either not pass the interview because he didn't come across as self aware or he's be pressured to evolve by the culture where everyone else is trying to do better.) If your company doesn't value these traits then you'll end up with people who don't think their shit thinks and that's hard!
It is one thing to say fix your greatest weakness, if it is easy you should. However for many there is more gain from improving on a strength and avoiding situations where the weakness matters; than improving the weakness, even though a small improvement in the weakness is worth more than an improvement in the strength..
For your spelling, it's probably not as easy to find someone targeting you as a demographic, but I'd look for someone who does tutoring for kids with dysgraphia/dyslexia etc. There's a lot of quite specific techniques that are used based on increasing understanding of the underlying causes of spelling difficulties - if you've never learned any targeted at your weaknesses, I bet you could make a noticeable improvement quite quickly. I'd aim for someone who is using research-based methods, since there's still a lot of more folklore-based teaching around on core skills like writing.
Neurodiversity is a thing, but not every flaw and limitation can be attributable to an immutable biological fact about a person, and thus we have many opportunities to improve a grow.
If I told myself when I graduated college that I either had no problems or they were all permanent, I'd be a fucking mess of a 40 year today. In reality, so many good things professionally and personally came to me because at some point I looked at what I was/did and said "I don't want to do this anymore"
Did he improve? Or do you just think he could improve? Maybe he had already tried to work hard on his communication skills and this was as good as it gets, so to avoid the stress of failing over and over he just stopped trying? There is nothing wrong with that, having a programmer who can write good code is valuable even if you need a technical product manager to talk to him. It might not be as valuable, but at some point life is more important than stressing out about things you can't fix.
Similarly we don't blame all the product managers etc who never improve their technical skills enough to talk with such engineers. People have limits, some have more limits than others, we just have to learn to accept that people are different instead of demanding that they have the same skills as us.
So the Manager Tools podcast had a discussion about this I can't be bothered to find. Their advice, as best I recall it, was that you should focus on two things: fixing absolute deal breakers, and honing your strengths. Imagine you come up with N dimensions you want to rate yourself across on a 1 to 5 scale from worst to best. If you have any 1 out of 5's that are clearly blocking career progress, you should focus on that. If you're sitting at 2s and 3's, you should work on getting a 4 or 5, rather than leveling up across the board.
You have described scenarios that seem to be absolute deal breakers (likely because those are the memorable stories) but in most cases, I think the latter applies.
> Every year, his own developmental goal was to go learn the next C++ standard. And that would have been useless because he was already a great C++ programmer.
Well, those don't come around that often. But more to the point -- situation matters. If you're working on a major C++ product that is expected to last decades, the company is in trouble if _nobody_ is allowed to study improvements. Best case scenario the company has some talent management app that you can query to find out two other people intend to master C++20; worst case, every engineering manager focuses employees on short term wins and the mountain of tech debt becomes unclimbable. I fear though, that the worst case is also the average case!
Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, 'How did he do it? He must be a genius!'
Many data scientists like to jump into feature extraction and modeling the data with ML/DS tools because for us that’s the fun part. (we might look at some plots and summary statistics but we don’t dwell there for too long.) Few have the patience to just sit with the data for a week just to look at it, checking it against our intuition about the real world and the domain and basically just trying to put 2 and 2 together without models (except a mental model of the world) and just turning the data over in Tableau (or Excel). It’s actually not an easy skill to learn because it requires other meta skills. For one it requires an ability to match numbers to the real world — and for that you need experience and a good intuition of how the world works.
My first manager was exceptionally good at doing this. I’ve noticed too that folks in senior management — at least competent ones — tended to be good at looking at data and picking out things too. I suspect this is actually a make or break ability to get to senior management at most companies.
Data scientists, not so much. (Unless they worked in the field or came from the business side of things.)
i realize this makes me picky, but it seems to be reasonable, as that incorrect usage often is a signal of sloppy thought.
Try it:
>>> n=1000; sorted(abs(sum(random.randrange(2) for i in range(n)) - n/2) for j in range(128))
As it happens, in two dimensions the distribution is radially symmetric, and its radius is still proportional to the square root of the number of steps. This accounts for the astounding isotropy of lattice-gas automata, whose particles are doing such random walks simultaneously, and for the depressing popularity of Gaussian filtering in image processing, because the Gaussian convolution kernel is the only anisotropic separable kernel, and can be closely approximated in each dimension very cheaply with a different application of the central limit theorem.
Please do! A lot of discussions regarding workplace morale, both here on HN and elsewhere, seem to boil down to "your manager is very good/bad and that explains everything else you mentioned". I tend to agree; having a good manager can make a huge positive difference and having a bad manager a huge negative one. However, I'd be very interested in better ways to detect managerial quality upfront rather than when it is already too late.
I've been very fortunate to have mostly great managers throughout my 12+ year career, managers that actually care about their staff (as humans, not just fungible resources). In fact, that's why I joined AWS 5.5+ years back, a great manager (plug for @thomas_cantrell). On the flip side, I left because of irreconcilable misalignment with my previous manager.
Well, a manager being (only) messenger (in this situation) is one of the traits of bad manager, isn't it?
So, what you need is getting some kind of long-term view on that manager. There are a couple of ways:
* If you can get it, data. Retention/Turnover, how well people grow, internal surveys. That's almost exclusively available if you transfer within a company, so limited usefulness.
* References. Find people who worked for that manager and ask them. Even better if it's ex-reports, since they tend to be more frank.
* Are they listening? When you have a conversation with them, are they paying close attention to what you have to say, or are they busy delivering a message? You want listening :)
* Can they communicate clearly? Are they able to express what their team does, and what their main challenges are, in a coherent way? In less than a minute? Communication is a managers main job. If they fail at that, you'll have a horrible time.
* And finally, gut check. How do you feel around that manager? If you're in any way uncomfortable, see it as a warning sign. That doesn't even necessarily reflect on their skill as manager - there are just some people we're feeling good around, and some who make us miserable. Skip the miserable part. (If you have a skilled manager, they can minimize the misery somewhat, but you'll still both be miserable.)
- This is common advice anytime one talks about relationships and communication. Listening is a skill, listen 10, talk 1, almost to the point that is difficult to understand who's doing the talking if everybody is getting the same advice of listening. Then you have those, and some HR people came to my mind--just to keep things professional--, who listen and listen and then you realize they just did not (or did not want to) understand.
Now, my question is: if it is common knowledge that listening to your reports is important, along with being pretty cheap and not particularly challenging to do, why so few managers do it? Incompetence or there is an advantage in not listening much?
So, yes, incompetence is one of the reasons. And worse, it's often incompetence we're actively unaware of - "it's listening, how hard can it be".
There are also advantages in not listening, but I really believe this "looks easy, but actually hard to do" split is what creates a lot of the problems. We live in an entire culture that's rooted in aggressively talking (cf. school debate club), with little value attached to patient listening.
Managers, like everybody else, are a product of the surrounding culture. Breaking out from that conditioning is hard. That's why it's rare.
I think there is also a delayed gratification that is coming from listening, while the gratification that comes with talking or expressing oneself is immediate. There is also in the "manager should listen" from the parent comment a bit of asymmetry if not hypocrisy, where the manager is the agent prone to maliciousness and the report is the one who should be listened to. And also, and I have been guilty of it like anybody else, I believe that sometimes we don't feel our manager is listening to us because they are not agreeing with us. They listen, they just happen to have a different opinion, but we prefer to say they don't listen.
I would say that I am not terribly interested in being listened to beyond the obvious, I particularly appreciate managers who are appreciative, decisive, and smart.
Being good at managing largely overlaps with being good at being friends minus the chances of being fired. The manager-report is not the same relationship as friend-friend of course, but I have yet to find a good direct manager who I would not consider good at being friends (reliable, honest, entertaining, decisive etc.), granted, not with me, and viceversa.
Walking is extremely challenging for a lot of people so that argument would contradict your point.
But it is a good analogy, a lot of people who have problems talking to people and listening also have problems walking properly. So just as you say walking is trivial to some but others just can't get it right.
Active listening is much more involved. It involves, among other things, developing empathy for the person talking, trying to understand their emotions and deeper reasons. Not just taking in what they say, but trying to understand what it means, and why they say it.
It is very much a skill you are not exercising in this thread.
I am listening and disagreeing. I don't want you to agree with me, you do. I listen and form my opinion.
It is exactly what I was talking about. To you, listening means the listener agreeing with you. To me, it is the listener understanding your point, which I do. And I believe you are very wrong. If you come into a conversation expecting other people to "listen" the way that you intend (i.e., agreeing with you), you'll often be unsatisfied.
Now (I am empathetic here, wearing my manager's hat), it may very well be that I am wrong here (I am not), and surely I believe you have great potential (who knows) and the company needs people like you (whatever that means). We'll continue this conversation at the our next 1:1.
I struggle with this. All the time.
I always find it difficult to strike a balance between leveraging my strengths and filling gaps in my weaknesses. For the large part of my career, my attention was directed on the latter: constantly trying to improve myself based off of feedback from friends, family, colleagues, managers, etc.
But now ... I'm a solo entrepreneur and lately, I've been actually flexing a lot more of my strengths, identifying characteristics about myself that give me an edge. Of course, I'm not blind to my weaknesses (I think about it all the time) but I do agree that we should lean more into our strengths.
As a engineer and computer scientist, I appreciate all the work we do to build software that's robust, etc but to be honest, the more challenging parts (and equally rewarding, for me as a solo entrepreneur) is the Sales side of the house, business development, marketing.
Agree wholeheartedly. Floyd Mayweather doesn't know how to read, or so I hear, yet he's one of the very best at what he does, and no one can take that away from him.
Just one simple example. The 'struct' language feature is 1500 LOC in Lisp but only 10 LOC in FORTH (see below.) Are they equivalent? No, the Lisp one has lots of bells and whistles, while the FORTH one is minimalist in the extreme.
If you tried to write the feature-complete Lisp version in FORTH you would probably find it very difficult and unproductive. So you wouldn't do that. And this to me is what FORTH's peculiar brand of efficiency is all about.
If FORTH were a bar the only drink on the menu would be tap water. That bar would be extremely efficient to run.
Lisp: https://github.com/sbcl/sbcl/blob/master/src/code/defstruct.... FORTH: https://github.com/openbios/openfirmware/blob/master/forth/l...
Making good use of Forth seems to be contingent on identifying situations where you want to implement a very small and simple system (embedded systems, firmware, OS bootloaders, tiny IoT devices?), and using Forth there - and avoiding it like the plague in all other cases.
I very much doubt that implementing a VLSI CAD program, where you want as many features to help your design as possible (features which necessarily incur a complexity cost), is a good use of Forth, for example.
>Judo is a game of specialization. You have to use the skills that work best for you. You have to stick to what works and practice your skills until they become automatic responses.
>If you watch an anime or a TV series "about" fighting, people often improve by increasing the number of techniques they know because that's an easy thing to depict but, in real life, getting better at techniques you already know is often more effective than having a portfolio of hundreds of "moves".
Which is essentially,
I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times.
Bruce Lee
Let's take judo. While nobody has, say, 15 competition ready techniques, a critical decision needs to be made between 3 or 5, say. So it is not as easy as saying: specialize! In addition to find the right (for you, considering your opponents) techniques to specialize in.
What's the difference between a jazz musician and a rock musician?
A jazz musician plays 100,000 chords for 3 people. A rock musician plays 3 chords for 100,000 people.
So a newly minted black belt might have one or two techniques. 10 years later, they might have 5. 20 years later, maybe even a dozen. But it isn't a question of the right number of techniques - it is a matter of constant improvement. The goal is to keep practicing moreso than having a specific end point.
For lower level/amateurs/"lifers" the math change, but at that level it is a bit more (or a lot more) about having fun, not destroy one's body and other concerns not related to high-level competitions, so more techniques can bee added to the arsenal.
I bounce between specialization and breadth because on the one hand, I want to "win" also in practice, on the other hand "win" what exactly?
There is incredible breadth to discover once you go 1 level deep into something. Every technique worth specializing in will have a multitude of entries/setups, then you need to know how people defend/counter and how to counter that, there could be slight variants that work better against different body types etc ... really staggering amounts of breadth/depth involved in putting someone on their back.
There will also be some breadth provided by general meta concerns of each combat sport like grip/hand fighting, defense, strategy, conditioning etc ...
So even the people who are hyper-specialized still have to know loads of stuff.
https://en.wikipedia.org/wiki/Bill_Wallace_(martial_artist)
He injured his right knee very early in his career so he spent the rest of it specializing in kicking with his left leg. There are some pretty amazing videos on YouTube showing the incredible control and range he had with that leg.
The were two positive thing about my wife's cancer 1- She survived 2- The intense learning experiance.
P.s. You could add medical imaging to your list of interesting cancer related things to learn. It won't really help you but it is extremely interesting .
If you can get the DICOM files of your scans try to interpret them with the full radiologist report. I got started with the trial of radiant viewer¹ (it easy to use but you will probably hit a ceiling before the end of the trial) and then try 3D slicer² (it's a lot harder to use but I feel that I used maybe 10% of that software capability and I was able to cleanly isolate the tumor and make the rest of her body translucent).
1- www.radiantviewer.com 2- slicer.org
On one hand, it’s a bit addictive and without certain external factors or compensating techniques it’s possible to get used to it so much that one becomes averse to investing time into learning one thing in depth.
On the other hand, at least with the type of mindset I have, the idea of knowing what to learn seems foreign, enviable at times but more often smelling of a local maximum.
Learning is investment so I would say learn mostly in your area of competence to get better. Of course you want to broaden your area with time so you might spend 80-90% of your learning time on things that are directly in your area of competence. Then 10% or 20% to broaden that, when you start using those new things they will become your circle of competence and then you can go deeper with learning about those. If you won't use those - ditch those and go find another 20%.
Downside to this approach is that you need a starting point like "should I be a Python dev or Ruby dev" which mostly is asked by new fresh starters - and my answer is pick one, if it sticks and is your 80% (even if it is not really) continue if not go for another one.
I had link to article by Kent Beck who advises something similar so I also copied a lot of that approach from his article. Unfortunately I don't have a link now.
I remembering hearing in a podcast something like "If there's a fork in the road, pick it and stick with it. You'll end up in a better place two years later than if you just spend two years weighing the options. And if you stick with something for a period of time, it's usually easier to switch to something else than if you didn't do anything."
As for what concepts to learn first, I think Feynman's method helps: "You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say: 'How did he do it? He must be a genius!'"
Also good to have mentors which not only graciously answer your questions but which also challenge you and ask questions of you. The Socratic method. Old as dirt, but better than Stackoverflow for actual knowledge development.
"5 Every mathematician has only a few tricks
A long time ago an older and well known number theorist made some disparaging remarks about Paul Erdos' work. You admire contributions to mathematics as much as I do, and I felt annoyed when the older mathematician flatly and definitively stated that all of Erdos' work could be reduced to a few tricks which Erdos repeatedly relied on in his proofs. What the number theorist did not realize is that other mathematicians, even the very best, also rely on a few tricks which they use over and over. Take Hilbert. The second volume of Hilbert's collected papers contains Hilbert's papers in invariant theory. I have made a point of reading some of these papers with care. It is sad to note that some of Hilbert's beautiful results have been completely forgotten. But on reading the proofs of Hilbert's striking and deep theorems in invariant theory, it was surprising to verify that Hilbert's proofs relied on the same few tricks. Even Hilbert had only a few tricks!"
"Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say: "How did he do it? He must be a genius!" "
I've come across this before, but it got reversed in my mind to: every time you come across an unsolved problem, try using all your standard tricks on it. Probably none will help. But perhaps eventually one will and you'll seem like a genius for thinking of applying that trick to that problem.
@luu-- I'm sure a lot of people on here besides me would be very curious to read your thoughts on what distinguished these managers from the others, and how you would identify one (nevermind find one).
If you can and want to work in a large corporation, you should be able to get a fairly specific job title. This is advantageous because two specialists with advanced but complementary skills outperform two generalists with intermediate but overlapping skills.
Division of labor allows sophistication in processes, which can increase efficiency.
The downside is, the job pool is more limited (both for employers and for employees). You need specific employees/positions.
A startup might not afford such specialization. For instance, if the finances only afford 3 people on payroll, you're not going to find a job working on a 10th of the pipeline, even with 20x efficiency compared to a generalist doing half of the pipeline with 2x efficiency.
arguably "well roundedness" is key to major breakthroughs in science & engineering
while most of us work on incremental improvements, the real innovation often happens on intersection of two or more disparate fields that until then were considered weakly related, and it does require knowing a bit of everything
the best scientists and engineers I know are "knowledge omnivores" and will digest anything. It does require well developed "filtering" capacity though, picking up signal from a lot of noise, and a sort of information hoarding mentality