Comment by Swizec
2 days ago
My favorite lens on this comes from Hamming:
> It is well known the drunken sailor whos taggers to the left or right n independent random steps will, on the average, end up about sqrt(n) steps from the origin. But if there is a pretty girl in one direction, then his steps will tend to go in that direction and he will go a distance proportional to n. In a lifetime of many, many independent choices, small and large, a career with a vision will get you a distance proportional to n, while no vision will get you only the distance sqrt(n). In a sense, the main difference between those who go far and those who do not is some people have a vision and others do not and therefore can only react to the current events as they happen.
Just a tiny bit of bias towards a direction will get you very far very fast.
I once modeled+visualised this with a bit of javascript[1] and it's quite surprising to see the huge difference from even a tiny multiplication factor on each random/probabilistic decision.
Hamming was also writing from a highly privileged position. He was able to work at Bell Labs for the majority of his career. That just doesn’t exist today.
The Art of Doing Science and Engineering is a great book but it needs context. The last edition was released in 1994. Programmers had a lot of labour power back then.
Today though? The median house costs more than a third of the median income. Inflation has raised costs of living to unsustainable levels. And for programmers there have been hundreds of thousands of layoffs since 2023 and a low number of job openings.
I don’t think it’s unreasonable to take what job you can get or stay in a job you don’t care for until the trade winds return.
This is a framing issue. You can't control the times, but good advice is applicable in good and bad times. If Hamming was operating from a "good time", it should be true that his policies are also applicable in the "bad times".
His advice to "work on the worlds hardest problems" was spoken to people who had worked their way past the initial difficulties. General advice to "Move towards important problems", which is precisely the same thing, applies in good and bad times, and is very likely to produce in you a valuable expertise.
Personally, I find the advice useful. Most who provide a framing for causes of success either do not place it in relation to anything, or relate it primarily their own situation, and their argument becomes susceptible to interpretation as survivorship bias. Some try to extend their argument to cover more cases, but can be seen as overconfident based on limited experience. It's hard for one writer to "prove" what general success rules are.
What are the important problems today? Do you mean AI? I'm not sure I'd agree or that it's obvious what the "important" problems are.
It's not about good or bad times. All compasses are broken so any particular direction you believe you are walking deliberately might as well be uniformly random.
"Direction" and "design" are probably the wrong metaphors for careers.
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> Hamming was also writing from a highly privileged position.
Hamming had a lot of career capital. He was the only person in the world with his track record. If you needed his kind of research/output/teaching/etc, he was the person you needed.
Cal Newport talks a lot about this. Great books.
Have something [unique/valuable] to offer and you'll be surprised how many doors it opens. Yes it takes time to stairstep your way there. A fresh grad has less career capital than a seasoned engineer with a track record of building billion dollar companies.
>I don’t think it’s unreasonable to take what job you can get or stay in a job you don’t care for until the trade winds return.
Having a goal does not seem at all at odds with weathering a storm. Your choices can then be what you learn in your free time, or what horizontal moves you make at that job, or which people you get closer to, for example.
When I got into the industry over 20 years ago, it was unheard of for an IC software engineer to retire early. Unless you got extremely lucky like working at Microsoft or Apple pre-IPO, you just weren't making the kind of money big law or doctors made.
That is not the case now. Yes the competition is incredibly fierce but the pay has skyrocketed.
There were a lot of factors that went into making salaries sky-rocket. One of those was leverage: there was more demand for skilled programmers than there were available. You also had the ZIRP era from 2008-2021ish. If you could write fizz buzz and breathe you could get a good paying job.
In the 90s inflation-adjusted salaries were still rather high. A 75k USD salary in 1995 is roughly 150k USD today. And the median house was less than a third of your income. And in the 90s there was even more demand for programmers.
The early 2000s were a bit rough unless you were insulated inside Google and big tech.
But 2025 is a very different landscape. I’ve talked to lots of highly talented developers who’ve been consistently employed since the early 2000s who have been on the job search for 9 months, a year.
It’s one thing to have a goal for one’s career but it’s not like you can wait around to find that perfect opportunity forever, right?
Some times you have to find something and work. It might not fit into your plans for your career but it might provide you with the income you need to keep your family afloat and maybe let you indulge in a hobby.
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> Programmers had a lot of labour power back then.
Huh? Back then, there was very little glamor to software engineering. Computing just wasn't serious enough. There was relatively little competition, salaries were unremarkable, and sure, you could land a job for life, but that still exists today. If you are an IT guy for a lumber mill, a regional ISP, or a grocery store, it's not going to be as cutthroat as Big Tech. It's just that you're not gonna be making millions.
We're pretending that this type of cozy tech jobs don't exist anymore, but they do. They just don't come with IPOs and RSUs.
> The median house costs more than a third of the median income
That sounds like a steal, in my city the median home price across all types is 10-20x the median annual household income
Did they mean perhaps taking a 25 year mortgage on the median house would consume a third of the median income?
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It ultimately doesn't change the advice. Strongly deciding I wanted a career change led me to putting in some extra time and tripling my income. It's easier if you can reduce obligations and noise and focus on what matters to optimize for whatever you want. It may not be easy, but you have some degree of power to alter your trajectory to some extent
Is this still a valuable read today (specially taking it into account)? It's been in my reading list for a while now but I'm always postponing :|
I read/skimmed it this year. I don't feel it was worth it. The first few and last few chapters have some nuggets but for the most part it's pretty highly technical stuff that feels not super relevant or interesting for a software engineer today (in my opinion).
That's really nice, but the point where the vision is should move too. You learn as you progress. What you enjoy changes. The entire industry moves. Being focused on the goal you defined 30 years ago is almost certainly wrong for most people.
After ~15 years, I've realized that no good things come to you without sustained focus / attentiveness, and gentle pressure in the direction of attention. What everyone here is saying is "be closed loop", vs the drunkards "open loop". Combined with a bit of progress every day, it's (so far, at least) magical what happens.
Another bit to consider: It took a long time to realize that basically everyone wants basically everyone to succeed, as long as incentives align. It was very easy to imagine I was swimming upstream early in my career - especially my early mentors urging me to specialize to find success. My initial temptation was to "specialize" in hot/attractive topics in an effort to be the "indispensable X authority". But my PhD advisor urged me to "not swim in red water", where the incentives are inherently conflicting - everyone wants to be "the X person".
Much better to find a team working on a good problem somewhat like the ones you want to solve and just push along with them. You can save yourself a lot of energy by slotting yourself into a system that aligns with your preferred direction of travel, even if only a little bit. The current carries you.
I literally fell into anti-fraud and email security back in 2012 and spent a totally unexpected chunk of my career around those topics.
The amount of people I've heard of say they want to go into email security is very small.
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I always wondered about that.
Seemed like everyone was doing topics in the “red water” and felt useless to not.
I found my areas of interest were the “red water” of 20 years prior and there was little left and it didn’t solve problems relevant to industry.
Quit PhD and got a job where I was grossly underpaid until the next one.
I can’t emphasize this enough. Every 5 years or so I reassess what my goals are and refocus my vision on where I want to apply my skills.
Things change fast in our industry so being able to pivot to something nearby is paramount for maintaining a career in this field.
Not everyone has the fortune to spend 15 years at a FAANG or other large corporation. Sometimes you have to build it.
Every five years or so, my wife asks me, "What do you need to learn now for the next five years of your career?"
It's the same as what you do, except I need the reminder...
>>Being focused on the goal you defined 30 years ago is almost certainly wrong for most people.
I think there are certain things that are not likely to change, and must be aimed for. For starters, being healthy, proactively working towards a retirement nest egg, so that you don't end up homeless and starving in case things go south too fast.
There are many such things I hold as things I would want several years from now. Good health, free time and enough money to not need a job to just put food on the table, and a roof above my head.
>> Good health, free time and enough money to not need a job to just put food on the table, and a roof above my head.
Sound like the utility function for a lot of people I would say.
Do people actually perform a random walk though? All terrain - both metaphorically and physically - is not equal, so wouldn't a more accurate description be 1. float on the water and go where the current/tides take you, or 2. decide when you're going to paddle against it towards the lighthouse? or more simply, "most people walk downhill"?
It is not something I share very often, because people assume a lot when I do, but von Braun[1] shared a similar idea. Ignoring for a moment his past, one cannot say that he had no achievements further supporting position noted by OP.
[1]https://en.wikipedia.org/wiki/I_Aim_at_the_Stars
https://en.wikipedia.org/wiki/I_Aim_at_the_Stars
> Despite his moral quandaries, von Braun participates in the Nazi's V-2 rocket program during World War II to further his ambitions in rocket engineering. The film carefully depicts his efforts to reconcile his love for scientific exploration with the knowledge that his work is being used for destructive purposes.
I have a similar short story idea where a person of the calibre of Elon Musk who works so hard is made to feel and see his successful moonshot projects being used for destroying and subjugating nations. This would be similar to Oppenheimer. Another twist I can take with the story is Hero "Elon" knows about this outcome but still in the hope of change in institutional ideology over decades hopes for better use for his technology. In the movie Watchmen, Ozymandias feels the pain of millions he is going to kill to save future billions.
Watchmen: Killing millions to save billions
https://www.youtube.com/watch?v=Tu2DdkOxLNs
Comment is interesting because its only confirmation bias material and doesn't hold up under minimal scrutiny. If you want to stay in pretentious CS analogy territory, then consider that if you can react to current events you can be a heuristical pathfinding algorithm that adjusts its goal based on locally optimal heuristics, making each individual step more efficient. This all a straight ass pull that will not translate to real world performance either, but it will serve to sound impressive to a fool.
This is a lovely mental model and also makes me feel a host of existential dread. I had a semblance of vision before gen AI and I think that vision needs serious revision
Which is fine. Goals shift and can even completely disappear, forcing you to pick another one. But having and pursuing long term goals at most times is still the ticket for success. My 2c.
It's a lovely metaphor, but I find myself at odds with the logic. What you sacrifice with vision I think is flexibility to respond to serendipity.
Vision is not a dictator, it's just having half an idea of where you'd love to be in X years.
It can and probably will move as you age and gain experience.
But if you're thinking you'd love to be your own boss and, as you have that vision, you find something much more interesting, you can still re-assess.
This resonates with me.
Three years ago, I left academia after finishing my PhD in Economics, frustrated by how little real-world impact my hard work seemed to have. I moved into IT, wanting to build things that would be more immediately useful and practical. Still, the dream of using science to create positive change never left me.
I was invited to work with AI at a company that develops software for the public sector. It wasn't the dream (I wouldn't be using my academic expertise) but it felt like a step closer. At least I'd be providing tools to support people who directly affect others' lives. From the start, I told my boss that I hoped someday to offer not just AI tools, but real socioeconomic statistical analysis as a service for the public sector. And while I've been happy working with AI, I've always sought out opportunities on projects that were more data-driven.
Three years later, some clients expressed interest in having our AI chatbot provide real-world socioeconomic data analysis. My boss just gave me a promotion to lead both the AI team and this new socioeconomic data initiative.
I was reflecting the other day on how fortunate I am, my dream "chased me." But it wasn't simply luck. I had always stayed attuned to the opportunities that arose.
That's a good point. I find it very hard to find the optimum balance between flexbility / vision.
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I also really treasure that quote. Your visualization really made it hit home again though.
It does make me reflect on this piece I wrote 9(!!) years ago though, which hasn't completely materialized. I think I'm due for a re-alignment of priorities.
https://www.jrishaug.com/Who-do-you-want-to-be/
> n independent random steps will, on the average, end up about sqrt(n) steps from the origin
AKCSHUALLY
The root of the mean of the squared distances is sqrt(n).
The phrase as you quoted is the mean of the absolute distance. In general those are different. I don't know the latter from memory, and a quick look at the wikipedia page for Brownian motion doesn't have it.
You're right, sqrt(E[d^2]) > E[|d|] because of Jensen's inequality. The latter is about 0.8 sqrt(N).
Wait, are you saying that for a symmetrical random walk, the expected distance is of the order of sqrt(n), but even for a slightly biased random walk (like 0.5000001 chance to take right) it's of the order of n?
Edit: well of course it is. I was thinking expected position (which should be 0) not distance
yep
"expected distance" is average abs(coordinate), so for biased walk (and big enough time) it's simply abs(bias)*time, and for unbiased it's deviation==sqrt(variance)
Oh right, makes sense.
The “expected distance” is not what you think here.
For a binomial distribution of probability p and (1-p), after N steps the expectation value of right steps is Np.
The Variance is Np(1-p), so the standard deviation (or Root-Mean-Square) scales as Sqrt(N).
I think the beauty of this quote is working more than its content.
Most people, even when they do not sit down and think about it, follow one of the two career paths:
- Some people will actively pursue the next logical progression (senior, lead/manager, head/vp, exec).
- Some will happily stay in their position unless the next one is offered to them.
Being deliberate will always work better compared to being random, but it is not like all people who succeed in their careers deliberately planned to get where they are.
I would even guess that for the vast majority of successful careers, competency and luck played a much bigger role than being deliberate about it.
I just can’t understand people whose life goal is like to be a CTO by some date; I have never tried for a promotion since I first shifted into a job where I was paid to make software. Due to the random walk of promotion rules (and most likely the good work of bosses that believed in me), I have been promoted enough that I had to put thought leader into my linked in, but I do believe just making sure whatever you are working on is useful and successful to other people is enough worry; if you are skilled in software and thinking, the other things will work them selves out.
> would even guess that for the vast majority of successful careers, competency and luck played a much bigger role than being deliberate about it.
I think this is true. I had a while where my career was doing really well constant steps up, I was learning, getting promoted, was working on great projects and problems that were engaging and led to easy promotions. Then I got a new manager and it was downhill. Then I got a new job and the problems are insignificant and there's no room for growth of any kind. If my latest job was earlier in my career my career would be very different.
I never really had a plan for a career but I never settled. I borderline almost did at my last job as it paid enough and I loved the people like family but the move from that job landed me in the most interesting and well paying job I've had yet. Luck totally played a part in most of my jumps and the ones I thought were good were often bad and the ones I wasn't interested in ended up being the most interesting.
I have generally had strong vision in my career but this year due to external forces at play at work I have been much more reactive to the chaos and generally felt off the whole year, this was a nice mental model to step through, liked the visualization.
I don't think jus the raw distance (from here) is the metric to necessarily optimize for. It may be more useful to throughly search the nearby area, for example - especially if you feel you're in a good neighborhood already.
https://www.sciencenews.org/article/sharks-use-math-hunt
A new study suggests that some sharks and other marine predators can follow strict mathematical strategies when foraging for dinner. The work, reported online June 9 in Nature, is the latest aiming to show whether animals sometimes move in a pattern called a Lévy walk.
Unlike random motion — in which animals take similar-sized steps in any direction, like a drunk stumbling around — Lévy walks are punctuated by rare, long forays in any direction. Draw a Lévy walk on a graph, and its squiggly pattern echoes a fractal, the mathematical phenomenon whose shape remains similar no matter the viewing scale.
Great point, and great blog post (as usual).
PS Tangent - FYI there's a typo "Minset" should be "Mindset" in the reference to your book. HTH
What a terribly flawed model. Being opportunistic can be classified as "vision" too.
That's basically diffusion versus drift.
But I think it is the wrong view, as generally people do move into the direction they want to go. Take a person doing plumbing but wanting to be in art. The problem is not the direction, the problem is taking the first step.
In general, many people dislike changing jobs, so they don't take steps. The steps are the problem, not the direction.
You don’t know anyone in your life that “talks big game?
Or someone else that “can’t get their stuff together?”
A lot of people never even “move”.
Drift made me think of electron drift under applied voltage or electric field.
The vision doesn't have to be accurate, it just has to be directional
This reminds me of a take on art, that goes something like "you don't need talent, but you do need to have taste". Taste is the same kind of driver as direction in this case.
Probably butchered the quote, can't remember who said it, but the message stuck.
Taken out of context, this line seems like a valid description of our ethos these days lol.
Premature optimization would like a word.
Tonight on Top Bit: I formally verify a theorem, James designs a dbms, and Richard writes a blog.
Ok but how do you know that the pretty girl isn't a succubus?
That's just a bonus.