追逐梦想，并不是人生的全部--哈维穆德学院2024年毕业致辞
追逐梦想，并不是人生的全部 | 哈维穆德学院2024年毕业致辞
Grant Sanderson (3Blue1Brown)
Thank you, President Nembhard, for that very warm introduction and for inviting me.
感谢 Nembhard 校长如此热情的介绍和邀请。
And thank you to the class of 2024 for including me in such a special day.
感谢 2024 届的同学们邀请我参加如此特殊的日子。
I had the joy of getting to know many of you last year on this visit, and I distinctly remember coming away with the feeling that a future in your hands is a bright future indeed.
去年来访时我有幸结实了你们中的许多人，我清楚地记得当时的感觉是，未来握在你们手中着实是光明的。
For those in the audience who don’t know who I am, I focus on making videos about mathematics with an emphasis on visualizations.
如果有同学不认识我的话，我专注于制作侧重可视化的数学视频。
It’s a weird job.
这工作还挺怪的。
I do love it though, and it’s no exaggeration to describe it as a dream job.
但我确实很喜欢这份工作，而且毫不夸张地说这是一份梦想中的工作。
A common cliche is for someone who was lucky enough to land in a dream job to stand confidently in front of a group of fledgling graduates and to compel them to follow their dreams.
那些有幸找到了一份梦寐以求的工作的人，自信地站在一群初出茅庐的毕业生面前，劝说他们追随自己的梦想，已经是老生常谈了。
Frankly, on its own, I don’t think this is very good advice.
坦率的讲，就其本身而言，我认为这个建议并不是很好。
To be clear, there is truth behind the cliche.
当然，老生常谈的背后自有其道理。
It is true that those who make the biggest ripples are the ones who are fueled by passion.
诚然，被激情驱使的人会激起最大的浪花。
It is true that the life you live is much more enjoyable if you can find something doing what you love.
诚然，如果你能找到自己喜爱的事情，生活会更加愉快。
And it’s also true that you shouldn’t feel shackled by societal constraints.
诚然，你也不会觉得被社会的条条框框所束缚。
But for one thing, not everyone has a pre-baked dream sitting there waiting to be followed.
但是首先，并不是每个人都有一个现成的要追寻的梦想。
That’s completely okay.
这完全没有问题。
And even if you are one of the lucky ones who has a passion that you want to roll into a career, I think there are a few pragmatic concerns that don’t always fit very neatly into an inspirational speech that are required to make this actually work.
即使你很幸运，想要将热爱作为事业，我认为为了真正实现这一目标，也需要一些务实的考虑，这可能和励志的演讲氛围不太搭。
Now, I know I’m talking to a very nerdy audience, so I’m tempted to describe my aims here a little bit more mathematically precisely, where in the vector space of all possible advice. If you consider the follow your dreams vector, I want to explore its orthogonal subspace.
我知道在座的各位都是知识精英，所以我打算将要表达的思想用数学语言描述得更精确一些，在由所有可能建议组成的向量空间中，我想讨论的是追梦向量的正交子空间。
Maybe though it’s better if i just start with a story.
也许还是从故事讲起好了。
Before i entered college, i was one of those who knew what I wanted to major in.
进入大学之前，我就知道自己想学什么专业。
There’s no surprise here: it was math.
毫无疑问那就是数学。
This is a topic that I had loved for as long as I can remember.
这是我从小到大都喜欢的科目。
When I was in college, I was plenty seduced by the adjacent field of computer science and programming, and I would spend my summers interning at software startups, but I distinctly remember coming back at the end of each of those summers and thinking, man, you know what, I really want is to spend more time doing math.
大学时，我也曾被计算机科学和编程这些相近的领域所吸引，我暑假时会到软件初创公司实习，但我清楚地记得，每到暑假结束回来的时候，我都在想，哎，其实我更想做的就是多花些时间搞数学。
So I had a passion; I had something I would want to follow, but in hindsight, that passion was a lot more arbitrary and maybe a little more self-centered than I would have liked to admit at the time.
我意识到我有一份热爱，我有我想要追随的东西，然而回想起来，那种热情其实并没有太多的逻辑支持，或许我比我当时原意承认的要更自我中心。
Why did I love math?
为什么我喜欢数学？
If I’m honest, I think it had its roots in the fact that when I was young, the adults emphasized this as an important topic to learn, and they told me I was good at it. This makes me spend more time on it, spending time with something is how you get better at something, and that kicks off a positive feedback loop, in both senses of the word positive feedback.
老实说，我觉得这源自于我小时候，大人总强调学好这门学科很重要，他们还跟我说我擅长数学，于是我花了更多时间在数学上，时间花在哪儿，成果就出在哪儿，这就触发了正反馈循环，正面的反馈促成了良性的循环。
Now, as time went on, I do believe it became less about perceptions.
到了后来，我相信这和别人的评价越来越无关了。
When I was in college, I remember genuinely enjoying the aesthetic delights that beautiful math problem-solving has to have.
我记得在大学时自己开始真正享受解决数学问题所带来的美学乐趣。
But thinking of it as a career ambition, not just a bobby, this had the fatal flaw that I was viewing the world through a lens of what I personally enjoyed, not giving enough weight to a plan for how exactly it would add value to others.
但是要视其为职业抱负而非仅仅是爱好，却存在一个致命的缺陷：我只是从个人喜好的角度来看待世界，而未足够重视该如何确实地为他人提供价值。
I don’t know if you’ve felt it yet, but today marks a day in your life when a fundamental goal changes.
我不确定你们是否已经意识到了，今天标志着你们人生中基本目标的改变。
When you are a student, the fundamental goal is to grow, to learn, to become better.
当你还是学生时，基本目标就是成长、学习、进步。
So many institutions and structures around you are there to support you in growing, learning, and getting better, and to reward you for doing so.
你身处的学校、院系、组织都在支持你成长、学习、进步，并对此加以奖励。
In life after college, the goal changes a little, and success hinges on how effectively you’re able to add value to others.
而大学毕业后，目标就有些变化了，成功与否取决于你能否有效为他人创造价值。
These aren’t at odds with each other; in fact, they go hand in hand.
这两者并不矛盾，实际上是相辅相成的。
You’re much better positioned to make a difference if you’re armed with expertise and if you spend your life honing that expertise.
如果你有一技之长，并在一生中不断精进它，那你就能更好地发挥影响力。
But there is a big difference between personal growth being the end in and of itself versus being a means to an end.
不过，将个人的发展本身作为终极目标，还是达到目标的手段， 两者是有很大的区别的。
By way of comparison, I also loved the violin when I was growing up.
打个比方，我也从小就拉小提琴。
And let’s take a moment to imagine two distinct music students.
我们花点时间想像两位截然不同的音乐生。
I’m going to name them Paganini and Taylor.
要不管他们叫帕格尼尼和泰勒吧。
Both of them are talented, very talented, but Paganini pushes for technical excellence.
两个人都很有天赋，都是天才，帕格尼尼追求技术的卓越。
He tries to perfect virtuosically challenging pieces.
他在演奏技巧上精益求精，喜欢挑战性极高的乐曲。
Taylor strives to write music that speaks to people, that resonates with them emotionally.
而泰勒努力创作能打动人们，在情感上产生共鸣的音乐。
Now in a music school, Paganini is going to get the better grades every time.
在音乐学校里，帕格尼尼每次都会拿到更好的分数。
He’s always going to get the better position.
总是会得到更好的排名。
But pursuing music careers, Taylor’s at the clear advantage.
但在追求音乐事业方面，泰勒则明显处于优势地位。
My first piece of advice, something I would have told myself if I could go back in time and be in the seat where you are now, is that if you have a passion that you want to incorporate into a career, take a step back and recognize the fact that this is a passion that grew in a time of your life when the goal was to learn and to grow.
如果可以回到过去，坐在你们现在的位置上的话，我给自己的第一个建议是，如果你想要将热爱作为志业的话，请稍等一下，要认识到，你形成这份热爱时的人生阶段主要目标是学习和成长。
But you are transitioning to a period when the primary aim shifts to adding value to others.
而你正要过渡到一个新的阶段，主要目标是为他人创造价值。
The cliche to follow your dreams overlooks how critical it is that the dreams you have are about something more than yourself.
追梦的老生常谈所忽略的关键点在于，你的梦想不仅仅关乎你自己。
Those who excel in their first jobs are the ones who make life easier for everyone around them, even when it involves doing things they don’t love.
在第一份工作中表现出色的人，会让周围的人生活得更轻松，尽管他们做的实际工作不一定是他们的热爱。
Those who excel in PhD programs are the ones who recognize how their work fits into a broader research community, not just the ones who view it as the next chapter in school.
那些在博士项目中表现突出的人，往往能意识到自己的工作，能在更广泛的研究领域中扮演什么角色，而不仅仅是把读博视为上学的一种延续。
The successful entrepreneurs are the ones who have a relentless focus on making sure that what they have to sell is what people want to buy, not just those who are looking to make something impressive.
成功的企业家，往往不懈地专注于确保自己所售的产品正好是人们想要购买的，而不仅仅希望创造厉害的产品。
Now, for some people, when you hear the words “follow your dreams,” it falls flat because you don’t have a defining passion.
“追逐梦想”这句话，对有些人来讲，显得平淡无奇，因为他们没有明确的梦想。
Like I said earlier, that’s completely OK.
就想我之前说的，这完全没问题。
If anything, it might put you in an advantage.
说不定，这反而会给你带来优势。
I think you’ll do just as well if you start by seeking out opportunities where the skills that you’ve developed here intersect with adding value to others, and from there, I promise the passion will follow.
我认为，如果你开始利用自己积累的技能，为他人创造价值，那你同样会收获成功，从那时起，我向你保证，激情会随之而来。
One of the best piece of advice I remember receiving from a friend many years ago is that action precedes motivation.
多年前一位朋友给我的最好建议是行动本身先于动机。
Now, in my own story, what happened after college involves a fair bit of luck, but luck can come in a lot of different forms, and I think with a little bit of foresight, you can actually avoid having to rely on chance in quite the same way.
在我自己的故事里，大学毕业后的事情，可以说十分地幸运，当然，幸运也有许多不同的表现形式，或许，稍微把眼光放长远一点，你其实就可以避免像我那样，完全依赖随机的运气。
There’s a post I like on the webcomic XKCD that shows a man standing on a stage, and he has bags of cash surrounding him.
我喜欢网络漫画《XKCD》上这样的一篇，有一个人站在舞台上，他周围堆着大包小包的现金。
“Never stop buying lottery tickets,” he says.
他说“永远不要放弃买彩票。”
“No matter what people tell you, I failed again and again, but I never gave up, and here I am as proof that if you put in the time, it pays off.”
“无论别人怎么说，我一次又一次失败，但我从未放弃，此刻的我就是证明，只要付出时间，就会有回报。”
The caption notes that every inspirational speech should come with a disclaimer about survivorship bias.
旁注是，每个励志演讲都应附带关于幸存者偏差的免责声明。
The obvious way that “Follow Your Dreams” is susceptible to survivorship bias is that for all of the high-risk, high-reward paths, things like professional athletics, starting a social media company, making a career in the arts, it’s only the few who rise to the top who are in a position to give that advice at all.
“追随梦想”容易受到幸存者偏差影响的显见之处在于，对于所有高风险，高回报的职业道路来说，例如职业运动员、创建社交媒体公司、在艺术领域发展事业，只有少数成功登顶的人才有资格给予建议。
But there’s also a more subtle way that survivorship bias applies here.
但这里，幸存者偏差还有一种更微妙的体现。
It’s not just about the odds of winning a particular game.
这并不仅仅关乎某种游戏的胜率。
It has to do with whether the game you choose to play, meshes well with the way that the future unfolds.
而更重要的是，你所选择的游戏，是否与世界未来的发展相契合。
If you were a software enthusiast in the late 1980s, you would be well-poised to ride the dot-com boom in the decade that followed.
如果你是一个1980年代末的软件爱好者，那么在接下来的十年，你将很可能乘上互联网的热潮。
If you were someone with a niche interest in and knack for film production, you would find yourself with an unexpected opportunity when YouTube and other film sharing platforms started to rise in prominence.
如果你对视频制作有特别的兴趣和技巧，那么当YouTube等视频分享平台开始崛起时，你会发现自己赶上了意想不到的机遇。
When I was finishing my undergrad, one of these ways that I scratched that itch to do more math was to hack together a very rudimentary Python library for making math visualizations, and I used it to make a couple videos about neat proofs and problems that I enjoyed and posting them online.
当我快要完成本科学业时，我满足自己的数学瘾的一种方式是动手码出了一个非常粗糙的Python库，用于数学的可视化，然后用它制作了几个视频，讲述我喜欢的有趣证明和问题还发到了网上。
I was not planning for this to be a career.
我当时并没有计划把这当作职业。
I had an appreciation for how valuable personal projects are, but it didn’t go much beyond that.
虽然我深知个人项目的价值所在，但这仅是一个小项目。
This led to conversations with Khan Academy, a group I had great respect for, and it turned into a job there, making more lessons online.
这促成了我与可汗学院的对话，我非常尊敬这个组织，我因此得到了一份工作，为他们制作更多在线课程。
In the meantime, I continued my own channel as a side hobby, and it didn’t blow up, but there was very modest growth of others who enjoyed the same kind of visualizations that I did, and I saw it in just a steady tick up in the audience size.
与此同时，我继续将自己的频道当作一个业余爱好， 虽然没有大火，但是和我同样喜欢可视化的人慢慢变多，我看到观众的规模在稳步增长。
Now my original plan, I think, was to spend a year or two doing this online education stuff, working at Khan Academy, and maybe returning to do a PhD.
我原本的计划，是在可汗学院工作一两年，做这件在线教育的事儿，然后没准回去读个博士。
But as time went on, something between the gratitude that I saw from many students around the planet for the lessons I put out and the slow and steady growth on my own channel let me to doubling down and forming a somewhat unorthodox career in online lessons and math visualization.
但随着时间的推移，来自世界各地的学生对我发布的课程所表达的感激之情，以及我自己的频道缓慢而稳定的增长，促使我一不做二不休，形成了我现在做的，在线课程加数学可视化，这个非传统的职业。
Now looking back, it would feel very incomplete if I were to somehow ascribe the success that I found, to the extent there was any, to the fact that I was following a dream, pursuing a passion.
回顾过去，非常不完整的一个说法是，我自己所获得的成功（如果这算得上成功）仅仅是因为我追求了梦想，投身于热爱。
Passion plays into it. You can’t have good lessons without a teacher who cares, but we can’t ignore the other factors at play.
热爱确实是一个因素。没有用心的老师就不可能有好的课程，但是我们也不能忽视其他的影响因素。
I already brought up the biggest one: success is a function of the value you bring to others, so a pursuit equally fueled by love, but which did noting to help or to entertain people, just wouldn’t had a chance to work.
我已经提到了最重要的一点：成功是你为他人带来价值的函数，一份同样源于热爱的事业，如果无法帮助或娱乐他人，那也注定没有可能成功。
But another factor I want to focus on is how I was very lucky with the timing.
另一个我想强调的因素是，我在时机上非常幸运。
If I had been born ten years earlier, I don’t think I could have reached the same number of people posting lessons on a much more infant version of the internet, where there was less infrastructure that could have existed to help form a career doing so.
如果我早生十年，我自认为在早起的互联网上发布课程并不可能触及到同样数量的观众，那时的基础配套条件更少，难以维系这样一份职业。
If I had started ten years later, the space would have been a lot more saturated.
而如果我再晚十年开始，这个领域将会更加饱和。
So another piece of advice that I’d like to offer, another little ingredient that makes following your dreams a little more likely to work out, is to ask yourself waht’s possible now that wasn’t possible ten years ago and which might get harder ten years from now?
因此，我想提供的另一个建议，另一个让追随梦想更可能成真的小配方，就是想一想，有什么现在可以实现的事情，十年前并不可能而十年后又将会变得更难呢？
There are more opportunities in a less crowded landscape; there are more chances to grow if you’re part of a rising tide, but this requires pushing past the inevitable discomfort that comes from following a path that has little to no precedent.
在人少的领域里总有更多机会，处在不断增长的潮流中，也就有更多成长的机会，但这需要你克服随之而来的不可避免的不适感，因为你所走的道路几乎没有前例可循。
Now, next, I want to take a moment to talk about whose dreams you should be thinking about because it’s not just your own.
现在，接下来，我想花一点时间谈谈你应该考虑的是谁的梦想，不仅仅是你自己的。
When I was visiting Harvey Mudd last year, I had the pleasure of talking to one of the gems in your math department, Talithia Williams, and I asked her, “Hey, what made you pursue math in the first place?”
去年我去 Harvey Mudd 时，我有幸和你们数学系的明星人物 Talithia Williams 聊了聊，我问到“话说你当初为什么选择了数学？”
She had a very clear story.
她的故事非常清晰。
She told me she hadn’t thought about it very much until one distinct day in her high school calculus class, her teacher Mr. Dorman pulled her aside and said, “Talithia, you’re really good at this. You should consider majoring in math.”
她说，她开始并没有这种想法，直到有一天，在她高中的微积分课上，她的老师 Dorman 先生，把她拉到一边说“Talithia，你真的很擅长数学，你应该考虑主修数学。”
Evidently, she had never thought about it before, but that one comment was enough to knock over the first in a series of dominoes that led to a very flourishing career in the topic.
她以前从未考虑过这种可能性，但这一句话足以触发一连串多米诺骨牌，让她开启在数学领域蒸蒸日上的事业。
Over the years, I’ve asked a lot of mathematicians the same question, and you would be shocked how often I hear a very similar answer: there was this one particular teacher, and one seemingly simple thing that they did that was the beginning in a long series of encouragements.
多年来，我问过很多数学家相同的问题，令人惊讶的是，我经常听到非常类似的回答：有这么一位老师，做了一件看似简单的事情，却是一连串激励的开始。
Never underestimate just how much influence you can have on others, especially the one who are younger that you are.
请不要低估自己对他人的影响力，尤其是比你年轻的人。
Growing older is a process of slowly seeing the proportion of people around you who are younger that you are rise inexorably closer to 100%.
随着年龄的增长，你会慢慢看到，周围比你年轻的人的比例，不可避免地逐渐接近 100%。
As this happens, you stand to have as much influence by shaping the dreams of those behind you as you do by following those of your own.
在这个过程中，你通过塑造身后那些人的梦想所发挥的影响力，将与追随自己的梦想时一样大。
And as a very last point, the biggest risk in the “following your dreams” cliche is the implication that there’s one static target point at all.
最后我想说的一点是，“追逐梦想”这一陈词滥调中最大的风险，是它暗示存在一个固定的目标点。
In the next 10, 20, 30 years, the world around you is going to change a lot, and those changes are going to be unpredictable.
在接下来的10,20,30年中，你周围的世界将发生很多变化，那些变化将会是无法预测的。
I hardly need to emphasize this point: you are the class who spent your formative tansition from high school to college - under a pandemic.
我几乎不需要强调这一点：这届同学从高中到大学的重要阶段是在疫情期间度过的。
But it’s not just the world around you.
不仅仅是你周围的世界。
Tonight when you’re celebrating your graduation and hopefully remembering to celebrate Mother’s Day as well, take a few moments to ask the people who are older than you how they’ve changed, how their personalities, how their value systems have changed since they were a student.
今晚当你们庆祝毕业时，希望你们也别忘了庆祝母亲节，花点时间问问比你年长的人，他们发生过什么变化，从学生时代到现在，他们的个性、价值观有怎样的变化。
You’ll notice that essentially all of them have an answer, which suggests you have every reason to expect there’s going to be something fundamental about you that changes as well in the coming decades, probably unpredictably.
你会发现，他们每个人都有自己的答案，这说明你有充分的理由相信在未来的几十年里，你也会发生一些根本上的改变，谁也不知道会变成什么样。
Almost everyone I know has undergone some kind of shift since college.
我认识的几乎每个人在大学毕业后都经历过某种转变。
Some came to place more value on having a family than they used to.
有些人开始更重视家庭。
Some shifted from a trajectory that was oriented towards an academic career to going into industry.
有些人的职业轨迹，从学术界转向业界。
Some went the other way around and after spending some time in industry returned to grad school.
有些人则反过来，先在业界工作了一段时间，再回到研究生院深造。
And so, so many of them have jobs that simply didn’t exist at the time of their graduation.
而且，他们中很多人的工作，在他们毕业时还根本就不存在。
So rather than having any one paticular goal that defines who you are, you’ll take better advantage of whatever the future has to offer you if you remain nimble and if you’re responsive to the changes in the world and if you anticipate change within yourself.
所以与其让某个特定的目标决定你是谁，要想利用好未来所能提供的各种机会，你应该保持灵活，积极响应世界的变化，并预计自己会发生的变化。
My final piece of advice is to not treat passion as something to follow.
我的最后一条建议是，不要将热爱视为追随的目标。
Think of it as an initial velocity vector.
而要把它看作一个初始速度向量。
It gives a clear direction to point yourself, and loving what you do can have you move quickly.
它为你指明了一个方向，对工作的热爱又可以让你迅速行动。
But you should expect, and you should even hope, that the specific direction that you’re moving in changes based on the force vectors around you.
但你应该准备好，甚至应该期待，自己前进的具体方向，会因周围的力量而改变。
Now, in these unpredictable decades that come, your generation is the one that holds more sway than any other over how it unfolds, and you, the graduating class of Harvey Mudd, represent some of the most talented and thoughtful minds in that generation.
在未来不可预知的几十年里，你们这一代人比任何人都更能左右未来的发展，你们 Harvey Mudd 的毕业生，代表了这一代人中最有才华、最有思想的人。
Influence is not distributed uniformly in the population, and I, for one, would feel a lot more comfortable if it was you who were at the helm, guiding this crazy ship that we’re all riding.
影响力在人群中并非是均匀分布的，就我个人而言，如果我们所在的这艘疯狂的巨轮是你们在掌舵的话，我会感到更加放心。
If you step into the next chapter of life with an implacable focus on adding value to others, you’re more likely to be the ones at the helm.
如果你在踏入人生的下一个篇章时，能够坚定不移地为他人创造价值，那么你就更有可能成为掌舵者。
If you recognize that action precedes motivation, you’re more likely to be at the helm.
如果你意识到动起来比找动力重要，那么你就更有可能成为掌舵者。
And if you ask what’s possible now that wasn’t ten years age, you’re more likely to be at the helm.
如果你关注现在有哪些十年前还做不到的事，那么你就更有可能成为掌舵者。
If you appreciate just how much power you have to shape the lives of the generation that follows you, you’re more likely to be at the helm.
如果你意识到你有多大的能力，可以塑造你之后一代人的人生，那么你就更有可能成为掌舵者。
And if you remain adaptable to a changing world, treating passion not as a destination but as a fuel, following not dreams but opportunities, you’re more likely to be at the helm.
如果你能适应不断变化的世界，不把热爱视为终点，而是一种动力，追随机会而非梦想，那么你就更有可能成为掌舵者。
One final time, would everyone please join me in congradulating the class of 2024 on what they’ve done to get here, and make some noise to let them know how excited we are to see where they go from here.
最后，请大家和我一起祝贺2024届的同学们为走到现在所做出的努力，让我们热烈鼓掌，让他们知道我们多么期待看到他们未来的发展。
