[Content note: this was difficult for me to write not only because it exposes some of my deeper insecurities but is liable to come across as a 7,000-word humblebrag, and I just wasn’t adept enough to express it so that it would come out any other way. For the record, I think what I say here should be relatable to anyone in any walk of life provided they feel they’re failing to meet their own lofty expectations (warning: scrupulosity-adjacent issues).]
In my last post, I made some minor allusions to the arrogance I see when looking at my ten-years-younger self. Today I want to expand on the reasons for and the effects of that arrogance, and on some of the difficulties I have today in facing the fact that somehow I haven’t turned out the way I expected.
I’ve been in quite a slump lately where writing for this blog is concerned. Writing here, for whatever reason, relies on a certain sense of momentum psychologically — the longer I’ve gone without completing a major blog entry, the weaker I feel when it comes to opening the “Write” window and starting a new one. (In this way it’s really an awful lot like going to the gym!) It seems that I’ve developed a tradition of starting up again with a more raw and awkward personal ramble and, this being the longest gap in my Hawks-and-Handsaws-posting, it may accordingly turn out to be the most raw and awkward of all my personal rambles here!
At the same time, this post doesn’t feel all that spontaneous, because I’ve intended to write it for at least two years (I remember it was at the top of the list in my mind when I resolved for the year 2017 to move away from my cerebral persuasive writing tendencies), and what I have to say is thoughts that I’ve held consciously for much longer than that. I think the main thing that has held me back is the risk of feeling embarrassed afterwards. I’ve written a lot of essays for this blog during the past three years — a few I’m quite proud of, and most others I look back on as visibly flawed in some way but still fine because I’m still putting some good points into writing and I don’t have to be perfect. But there are a small handful that have made me wince intensely from almost the moment they were published. And I distinctly remember from when I was first setting out to write them how I had no idea they would turn out anywhere near so cringeworthy. This post I know with almost complete certainty will make me want to wince to some substantial degree. I guess it does take some courage to set out writing something knowing full well that it’ll instill a feeling of acute embarrassment shortly afterwards, so that’s something to be proud of, I guess?
(For this post I have to get into the gear of focusing my writing on certain insecurities that I have. Judging by that last paragraph, so far so good.)
I haven’t really told anyone about this for a long time, but as a child, I was very much a math prodigy.
I don’t remember learning how to count and do basic arithmetic, because I was already doing that before my autobiographical memory properly kicked in. I do remember in my early childhood thinking that basic arithmetic was about the fun and exciting thing out there, at least if the numbers involved were big enough. My parents tried their best to contain their amazement at my ability to multiply large numbers so quickly in my head, while other parents suggested I be put on television.
My first inkling that I was in any way unusual was when I was about to enter kindergarten, and my mom sat me down one day to warn me that the other kids in school weren’t really going to be into “number games” to the extent that I was; that in fact the real term for “number games” was math; and that the kind of math taught at kindergarten wouldn’t involve any long division, square roots, and analysis of repeating decimals but would be more to the tune of learning to count to high numbers and telling time. I don’t know what amazed me more: the revelation that none of the other kids my age could do long division, or the revelation that none of them particularly wanted to, that many of my peers might actually consider math to be unpleasant!
I learned trigonometry at home when I was in the third grade and was a little disappointed that my dad couldn’t give me a proof of the Law of Cosines off the top of his head. I remember distinctly that one day we sat back to back with pencil and paper and each came up with a proof of the Law of Cosines. When he saw mine, he immediately declared it more elegant than his, which as I recall involved naming three different angles. Maybe it was this day, more than any other, that convinced very-young-me that my passion and aptitude for math involved not only understanding but understanding why, and that proving mathematical truths was something I could get very serious about.
When I was nine, on what is for me a very memorable New Year’s Day, I picked up a copy of Calculus The Easy Way by Douglas Downing at the local library. (For those not familiar, those books in the Easy Way series written by Douglas Downing are given as a series of novels in which the characters discover algebra, trigonometry, and calculus. Despite the fact that the target audience probably doesn’t include nine-year-olds, I’d say the characters and plot content are quite ideally suited for that age group!) After a few months of greedily devouring all the calculus concepts and methods presented in the book, by my tenth birthday I had gained a firm understanding of all the main ideas of first- and second-semester calculus, from finding slopes of tangent lines to the basics of differential equations. By that time, my prowess for learning advanced math was common knowledge, including among all the kids in elementary school (many of whom, if they remember me today, probably mainly remember me for that). I remember when I was in fifth grade, I had a friend who was in third grade who had evidently misunderstood something his parents told him about me and believed that I held a some kind of world record for Best Ten-Year-Old At Math. I corrected him, saying that no, I couldn’t possibly be the best in the world, nobody had verified anything like that. But my protest probably came off as pretty weak, because while I had some clue that the world is too big a place for me to be the best for my age, none of us kids (nor our parents) had really heard of a ten-year-old who was better.
I had plenty of weaknesses too. I was highly prone to carelessness and inaccuracy when it came to doing elementary arithmetic — not when I was four and thought it was The Most Awesome Thing Ever, but later when it because boring to me — and I wasn’t a great test-taker in large part due to that. I tended towards laziness and lack of discipline in studying math, since I had been accustomed from day one to finding everything easy and learning things low-pressure in that arena. I was confident enough in my mathematical intuition that at times I was overconfident to the point of distrusting what reliable sources said (of course, at that age, I had a much dimmer perception of reliability).
One summer in my early teenage years, I was reading An Imaginary Tale: The Story of [square root of -1] by Paul Nahin (a book I highly recommend to any mathematical enthusiast, layman or otherwise, who is interested in the history of and mathematics surrounding complex numbers) and discovered the following quote.
There are two kinds of geniuses: the ‘ordinary’ and the ‘magicians’. An ordinary genius is a fellow whom you and I would be just as good as, if we were only many times better. There is no mystery as to how his mind works. Once we understand what they’ve done, we feel certain that we, too, could have done it. It is different with the magicians. They are, to use mathematical jargon, in the orthogonal complement of where we are and the working of their minds is for all intents and purposes incomprehensible. Even after we understand what they have done, the process by which they have done it is completely dark. They seldom, if ever, have students because they cannot be emulated and it must be terribly frustrating for a brilliant young mind to cope with the mysterious ways in which the magician’s mind works.
— Mark Kac, from Enigmas of Chance: An Autobiography
Apparently, Kac was saying this in the context of describing Richard Feynman as one of the “wizards”, but the author of the book was adopting Kac’s quote for the context of expressing awe at the Renaissance mathematician Scipione del Ferro’s discovery of how to solve cubic equations. I’m not sure I would call that key step of del Ferro’s method a form of wizardry exactly because I do see a sort of follow-your-nose logic in how he might have arrived at that algebraic trick (although I have to heap massive amounts of additional credit on anyone who discovered anything algebraic back around 1500 when notation was so poor that even negative numbers couldn’t explicitly be written down). I’m not even sure I regarded his trick as full-on wizardry at the time. But I was certainly awestruck by del Ferro at the level of “ordinary genius” and was determined to become as clever at algebra as he was. (Unfortunately, I channeled a lot of this determination into fool’s errands like trying to find a general solution for fifth-degree polynomials, because I didn’t care if mathematicians claimed to prove it impossible, I could feel in my bones that there just had to be a solution dammit — another example of the overconfidence I mentioned earlier.)
I recount all this to stress that, from my limited perspective as a kid, and even from the perspective of the adults around me, there appeared to be nothing whatsoever standing in the way of my going as far and as high-up in my pursuit of mathematics as I wished — and certainly I wished for the moon. As soon as I came to the full realization as a teenager that professional research mathematicians actually get paid to discover and prove new theorems and formulas, I knew beyond all doubt that I wanted to get into that profession as fast as I could, and I couldn’t imagine what might possibly hold me back from not only entering it but becoming one of its shining stars. Even the weaknesses I’ve mentioned above weren’t going to create any significant difficulty.
Fast-forward 15 years or so to the present day. I managed to get into a good graduate program. My progress in graduate school had its ups and downs, and there were times when I found myself on the brink of despair that I might never get any substantial research result of my own, but I got my PhD in the end with a passable but not great dissertation. I took six years to do so, two years longer than my initial goal of four (in retrospect, a unadvisable ambition for anyone, regardless of their level of talent, unless they’re in a hurry to get onto a non-academic track). I had to apply to a lot of jobs and cross my fingers for a long time before finally getting offered my current position at almost the last possible minute. At my current postdoc I’ve managed to do some okay things, but much too slowly, and I’m now drowning in a record number of academic job applications that I’m doing so that I can have maximize my chances of getting maybe one decent offer for next year. (This, along with increased traveling, is largely responsible for my recent blogging slump, in fact.)
In short, the outcome of my experiment in becoming a world-class mathematician is… meh. I am a mediocre, barely passable researcher whose few original results are little-known and who has trouble envisioning the day when it won’t feel like an endless struggle to keep his head above water. Getting tenure one day feels quite daunting at best, and becoming a full professor, let alone any kind of big name in the mathematical community, just doesn’t quite feel feasible.
I’m constantly reminded that lots of researchers, young and old, feel this way, as though they are borderline-incompetent at research and consistently among the dumbest in the room at conferences but are somehow barely faking their way through anyway. I fully acknowledge that Imposter’s Syndrome is very much a thing for many academics, and I regularly observe acute cases of it, but I would flatly deny that I am one such case. All I can say to back this up is that I consider myself fairly sharp at observing and evaluating my own psychological processes and where they lead me astray (this is pretty much the main point of my interest in rationalism, after all) and that I do believe I could present concrete objective evidence that everyone has Imposter’s Syndrome except for me. (Momentary aside: at least one positive consequence of all this is that I’ve gained some intellectual humility, and so I realize that I may still be assessing some aspects of my situation wrongly. For instance, I could be offered a dream job in the next few months by people who think my research is really strong, however unlikely this scenario seems to be now, and if so, I will feel more grateful than embarrassed for being wrong!)
The way my mathematical life is turning out is a source of bitterness and frustration for me. It rarely hits me all at once, but it’s constantly hovering somewhere in the background of my emotional state when turned towards what’s going on with me in the present. And part of me knows that it really shouldn’t bother me like this. All that should matter is that I’m doing something I enjoy and which feels worthwhile and will likely keep me employable in the long run. Yet it still eats away at me. And I think it’s obvious what’s to blame here.
All during my childhood and adolescence, I was treated by my peers with almost a celebrity status because of my gift. Don’t get me wrong: part of me enjoyed the attention… up to a certain point. Eventually I started to feel weighed down by the expectations and assumptions that came with the label of “math genius”. (This has contributed to my deep wariness of labels in general.) By the time I entered college, I was relieved to have halfway escaped from that identity — although a lot of people from my high school went to that same university, their presence was now diffuse enough that I had at least a bit of a fresh start.
When I went away to graduate school, I arrived with a completely clean slate, definitely no longer seen as “the math guy”. I never once mentioned to anybody how unusual I had been when I was younger (although it’s entirely possible that I wasn’t the only childhood math prodigy in the program anyway). Social norms against bragging, of course, made it easier to conceal this aspect of my past.
But by then the damage was done. Growing up with adults thinking you should be on TV and peers assuming you hold some kind of world record and friends of your parents reacting to your coming in second place in a statewide math competition with a shrug and a “Why didn’t he get first?”… these things can really mess with one’s self-perception. I had internalized the identity which had been thrust upon me by society at large through most of my life, to the point that I had a very hard time handling the weakness, struggle, and even anxiety (math anxiety up to that point had been completely unknown to me) that came with approaching the ceiling of my math abilities, which unfortunately appears to fall within the zone of standard research-level mathematics. (And now I look back and am able to appreciate how well my parents did at painstakingly guarding against my coming to view myself the way most everyone around me seemed to view me, and a few teachers made some effort in this direction too. I can easily imagine another kid very similar to me but without any steady influences close to them like what I had!)
Sometimes I venture even further and speculate that such an experience shares some blame for my weakness itself (rather than my difficulties in coping well with it). Some of it may be attributable to my not having grown up with a very strong growth mindset where math was concerned. I recall experiencing a profound “Aha!” moment when I was an older graduate student and I was first educated on Carol Dweck’s celebrated study showing that children whose positive feedback consists of “You must have worked very hard on that!” tend to develop more successful mindsets than those who hear “You must be very smart!”. Because although the adults in my life did make some visible attempts to limit the “you must be smart” reactions to my work, I can’t recall getting much in the way of “you must have worked hard” or any strong impression that much was to be gained by my working hard in this particular arena. Suddenly all the counterproductive banging-head-against-desk moments of “Why am I suddenly too dumb for this?” that popped into my life over the previous few years made so much more sense. (It’s only fair to add that I know of at least one attempt to challenge this study’s findings.)
But my resentment isn’t towards my childhood peers or even the grown-ups who influenced me at the time. It’s towards me. Me for having internalized all this and for, despite all my precocious cleverness, not having been smart enough to understand how small my local community was with respect to the world community and how much more extraordinary someone would have to be to achieve the kind of greatness I dreamed of and most people seemed to expect of me.
The longer this has gone on, the more I keep thinking back to that Kac quote that I first read as a youthful and optimistic teenager. The thing is, to use the terms defined in that quote, it’s not truly being extraordinary but rather a certain ordinariness that I want to achieve. I’ve never lusted after becoming a “wizard genius”, who as Kac rightly says would be (to a certain degree) condemned to a life of loneliness and intellectual isolation. I think I always had my sights set on being one of his ordinary geniuses. The great mathematical results I most enjoy reading are in fact the ones of ordinary geniuses, whose mental processes are immediately apparent once I understand what they did and who therefore inspire me the most. By Kac’s definition, those are the geniuses whose abilities I could match if only I were several times better — now why I can’t I be several times better? It sounds like such a silly complaint as expressed in my word choice here, and yet, perhaps one can see why for a teenager, multiplying one’s mental strength and agility by a high enough factor to wind up one of the geniuses seems like a perfectly reasonable outcome to strive for.
As I’ve pondered this personal issue over the years, I’ve often made a connection with another, much smaller episode in my development. Much as I feel embarrassed almost just by bringing it up, I wouldn’t be doing justice to the overarching point of this very personal essay without putting this other example out there. Although it doesn’t involve the bitterness invoked above nor does it have such a central role in my life, its parallels to some elements of the whole Underestimating How Good The Best Are thing are unmistakable in my mind.
If you have read enough of my other articles on this blog, you might notice that I refer to the writing of Scott Alexander (host of Slate Star Codex) a lot. More than I cite anyone else, which makes a lot of sense considering how much more Slate Star Codex I’ve read than any other blog. Now I read it and cite it a lot for the obvious reason that its content includes a lot of rationality stuff (in the modern internet movement sense) that I’m extremely interested in, but the reasons for it being my very favorite blog go deeper.
I first discovered Slate Star Codex and the entire internet rationalist movement back when I was nearing the end of graduate school, still reeling from the revelation from my previous years in the program that I didn’t have the mathematical superpowers I’d thought I did. Throughout those preceding years (and even back in college), I had done a lot of thinking about how I seemed to analyze conflicts and disagreements somehow differently from everyone around me and from pretty much every public intellectual I knew of at the time (which in fairness was rather limited), although I had never made a full attempt to carefully flesh out any of my thoughts (the closest I had come was that brief stint in 2008 with the original Hawks and Handsaws). I felt a persistent nagging feeling that I had something to say and that I should try to say it, even if it was only to a mostly empty room. I think that nagging feeling was quite valid. The element of it which bordered on now-obvious arrogance, however, was the conviction that I really had something original to say that virtually no one else out there was saying and that perhaps very few were even thinking. And after all, I may not have been turning out that extraordinary at math, but I was still a pretty smart guy who had gotten lots of compliments on being a good writer. Just maybe, even if I had no real hope of achieving greatness as a mathematician, I could take comfort in a much more far-fetched dream of somehow achieving a minor bit of greatness as a writer.
And then I ran into Slate Star Codex and its author Scott Alexander (and along with it a much wider community containing scores of intellectuals who also run circles around me, but I won’t even get into that). And my entire perspective changed. Here was a guy who was committed to viewing the world of argumentative discourse and personal conflict in the same particular way I was. Except that he was doing it bigger and better, even a bit more grandly than anything that I in my flights of fancy had ever imagined myself achieving.
That wasn’t even the deepest emotional impact of the major revelation brought on by this discovery. That came shortly later, when I stumbled upon Alexander’s LiveJournal, his earlier blog which eventually had given way to Slate Star Codex. I recommend this LiveJournal to anybody who wants to get a more raw glimpse into who Scott is as a person, because this was before he became the number-crunching debating intellectual Big Deal on the Internet and de-facto Head Rationalist we see today. The impact on me came by watching, in the form of what began as essentially diary entries displayed for a small public audience, the development of someone who stumbled into a leading role in a serious online intellectual movement.
At the start of his accessible LiveJournal entries, Scott was (for all means and purposes relevant to this discussion) a nobody. He was a nobody whose cultural background, interests, and general personality were strongly relatable to me, but who appeared to have no lofty aspirations of becoming a minor celebrity among online intellectuals. He was just writing in his public diary. And by reading through that diary, I was able to view a gradual evolution in his writing as Less Wrong came into being and Scott became involved in it and picked up followers from there, and his posts gradually became less about this week’s activities and musings and more about long-form arguments for some nuanced, carefully-considered stance until they became early SSC posts all but in name. This was particularly meaningful to me because even at the height of my ambitious fantasies I always felt a barrier in terms of… I don’t know what I would call it, but some kind of professional legitimacy? Sure, the internet in principal could allow anyone with any set of credentials to reach a ton of people, but in reality it seemed like to have such influence and engagement with a wider community required some semi-mysterious rite of passage granted by the Establishment in the form of an advanced degree program at the very least. Scott’s blogging history — which shows an everyman just writing down his thoughts for a few people to read, then finding that he was getting really good at it and a whole lot of other people really wanted to engage with his work because it was just that good, then winding up at the helm of a large-scale online and real-life ideological subculture — provided a counterexample to this.
Almost immediately my thoughts harked back to Kac’s notion of the two types of genius. It was clear that I had stumbled upon a genius, but it was just as clear that this was a genius of the “ordinary” kind. There was no mysterious secret or hidden passage that led to Scott Alexander’s particular form of greatness. This was clearly demonstrated by the process of evolution from just-out-of-college guy writing down his thoughts being laid bare for all to see.
Yet at the same time, it was immediately clear once I had actually seen that level of greatness that it was far more daunting than the way I’d imagined it in the abstract. My own foray into blogging has only magnified this realization, much more than I had anticipated when I first set out to do it. It turns out, writing is hard. (For me, at my current blogging objectives and standards, that is.) This entry will probably wind up at 5,000 words or so (Edit: Okay, that estimate was short by over 2,000!), and figuring out what they should be and how to put them together to convey the shades of meaning I want has been going way more slowly than I like to admit. Imagine writing an essay of around that length, whose style is more polished and whose content is somewhat higher-level, several times a week or so during a few hours of spare time, and now you’re Scott Alexander.
Thus, once again, I discovered that some realm of excellence was vaster than I’d imagined and that its mountains were much higher than I’d assumed.
I don’t yearn to be a wizard or even to understand the wizards. I’ve never been one of the people who needs to know the secret behind every amazing magic trick I see. I enjoy being amazed and alieving that others have mysterious superpowers beyond my comprehension. But those ordinary geniuses, whose power I can comprehend but constantly feel unable to match… well, every now and then observing them drives me a tad crazy. I’m happy to stay separate from the wizards and let their wizardry sweep me away, but I do strive to achieve the greatness of the ordinary genius — for ordinary greatness, if you will.
The prospect of not being able to succeed in a career path which I tied much too closely to my own identity sometimes gives me the feeling of walking into an impending existential crisis. I can’t explain why I’m so obsessed with achieving some form of outstanding greatness in the first place, but the closest I can come to describing it is as follows. Many people (including me) are on some level afraid of death — not in terms of the process itself or of something unpleasant that might lie beyond death, but just the idea of ceasing to be, which almost feels like a fundamental contradiction. I go a step beyond that in that I have a fear not so much of death per se but of dying without having lived a sufficiently outstanding life. There’s the existential quandary that really gets to me: I know I exist in an immediate way, somehow I’m me and not someone else, yet I’ll cease to exist just like all the rest, and moreover it’s statistically unlikely that I’ll be an extremely outlying human along any axis… no, that can’t be — I experience my own existence firsthand and that means I have to be extraordinary in some way. And from more of an ethical perspective, I have only this one life to live, so I feel desperately obligated to make it an outlying, outstanding life of greatness in one form or another. Seeing greatness only just beyond my reach therefore strikes me in the deepest “Why am I here?!” underbelly of my self-awareness.
I’m not saying these lines of thinking are sound. I’m just “writing out loud” the sequences of thoughts and emotions that I’m finally fully observing in myself, because it seems that only then do I have a chance of knowing what to do with them. Much as I’ve tried over the past few years, I can’t fully get rid of them, but I can describe a few minor insights that do seem to work as partial retorts.
First off, much as I usually hate responding to anyone’s genuine pain by pointing out how privileged they are, I’ve actually found it quite helpful in this case to remind myself that just in experiencing these emotions, I am incredibly privileged.
The complaining I’ve done throughout the whole of this (already overlong) post has been aimed at what is not only practically the epitome of a first-world problem, but a problem that is contingent upon my being extremely fortunate. In fact, I apologize in all sincerity to anyone who has gotten this far despite feeling hurt from my words of what essentially amounts to whining about how lucky I am.
For anyone who doesn’t see it that way, think about it: how many humans in the world in this day and age, let alone throughout history, have energy and emotions to spare on worrying that they might just manage a reasonably happy and more-successful-than-average life without achieving anything super outstanding? I’m guessing not many. My experience with other humans has been mostly restricted to humans in developed countries, and many if not most of even those humans seem to be struggling week by week, or even hour by hour, to keep their heads above water. In particular, my last few years substantially interacting with people online have shown me just how many people spend their childhoods not being able to imagine ever being adults one day and how many adults can’t imagine actually having a future even one or two years from now. Those of us who are constantly envisioning their futures being successful but fretting over those futures not being distinctive enough have got to be among the most privileged humans ever to walk the earth.
To be clear, this (and other appeals to privilege) is not meant to imply that I should hate myself for feeling how I feel or for daring to put those frustrated and angsty emotions into writing. Everything is relative (a theme I’ll get back to shortly!), and even the most privileged people can feel legitimate bitterness over genuine problems because certain aspects their lives could always be better, while for even the least privileged people there is always some way they could be worse off. I think I speak for most of us when I say that judgmental reminders of privilege tend to have only an unpleasant and counterproductive effect on the parties they’re aimed at.
No, what I’m doing here is reminding myself (and anyone else who relates to my situation) that actually I have it pretty darn good! It’s extremely tricky to divorce such revelations from conclusions like “And therefore I have no right to ever complain about my prospects not being even better!” and carry on down a path which leads to my seeing myself as a terrible person, but in principle and even in practice I’ve discovered that it can be done. I can remind myself that I have a PhD and am pretty certain to make a comfortable living doing something I find engaging, which when I stop and think about it is really awesome, and that really does put a smile on my face when my “not good enough” insecurities have got me down.
Secondly, I must bear in mind that everything is relative. For any given person, someone else on their radar will be higher on the ladder of success while another person in their vicinity will be lower on that ladder. And no matter how high you are, there will be someone else higher whom you will aspire to reach, while no matter how worthless you might feel for not being able to climb to that point, there will always be others gazing up at where you are and feeling awestruck at your abilities and achievements. I know that there are people who look at my personality and occupation and think I’m pretty awesome, maybe even one of their ordinary geniuses. They probably imagine from afar that my life is a fairy tale. It isn’t, of course, but trying to look at my life from their point of view does help me to gain some perspective. Or, as a good friend of mine put it in a phone conversation where I was venting frustration at struggling to make progress in my dissertation work, “You’ve gotta remember to step back and think of the rest of us dumbf***s who can’t imagine doing what you’re doing.”
The (perhaps overly-broad) statement that everything is relative doesn’t negate the fact that some levels of achievement are more worthy of satisfaction than others in some absolute sense — I assume some people really have reached almost maximal levels of fulfillment (in some objective sense) while others are so far from any kind of fulfillment that they have every reason to feel generally unhappy. What “everything is relative” does mean, though, is that different heights in the ladder look and feel much more alike, at least locally speaking: everyone’s view encompasses a certain radius and includes higher places tantalizingly close to them that they yearn to climb to. I don’t know what it’s like to be a highly acclaimed mathematician, but it’s entirely plausible that from their point of view their achievements don’t seem like so much and they’re just struggling to emulate the Fields Medalists. I don’t know firsthand what it’s like to be a semi-celebrity Intellectual On The Internet either, but my favorite one of those has confirmed my impression in an article where he makes this exact point:
Every so often an overly kind commenter here praises my intelligence and says they feel intellectually inadequate compared to me, that they wish they could be at my level. But at my level, I spend my time feeling intellectually inadequate compared to Scott Aaronson. Scott Aaronson describes feeling “in awe” of Terence Tao and frequently struggling to understand him. Terence Tao – well, I don’t know if he’s religious, but maybe he feels intellectually inadequate compared to God. And God feels intellectually inadequate compared to John von Neumann.
So, given that all parts of the ladder come with views of both ahead and behind, it seems that the real trick is in finding the proper balance between staring at what lies ahead and acknowledging what lies behind.
(As a side-note, another thing that’s really hit home for me only from online interactions in the last several years is that when those people I look up to for their greatness in terms of ethics are, on average considerably more scrupulous than I can imagine ever being and therefore considerably more insecure and self-critical than I am! So while from where I’m standing I’d feel less worthless if I were them, there’s a good chance that if I actually were them I’d feel more worthless instead. Perhaps I’m better off being who I am, even if the world isn’t.)
A variant on this is knowing when and how to reduce the demographic scope of the group that we’re viewing ourselves in. Part of my problem growing up, as you’ll see from reading above about my experiences as a locally famous math prodigy, is that I (and most other people around me, including the adults!) really didn’t have a great sense of scale. I was famous very locally — as in, at the schools I went to. Turns out, there’s quite a sizeable number of children all over the world who are at least as mathematically precocious as I was — recently I’ve learned of them just through family connections and tutor-student relationships with mathematicians that I know now (and in one case, a fellow mathematician who was a prodigy himself, who lately has had to leave academia and expresses very similar laments to mine!). And it turns out that to achieve greatness on the global scale, which of course is the kind of greatness we’re all most familiar with from a distance, it’s necessary to stand out not locally but, well, globally. It tautologically follows that roughly 0% of the locally outstanding people are going to wind up doing that. So maybe instead of setting our sights on greatness according to the largest scale possible, we each have to learn to adjust the scale and allow ourselves to feel plenty of satisfaction (maybe not 100% satisfaction, but more than enough) at achieving greatness within our communities, the institutions we work for, or even our immediate social circles.
Finally — and I think this is really the most important — I have to appreciate and gain to the fullest from being able to observe the kind of greatness I aspire to.
Once I was watching the Olympics with my family, and I remember my mom commenting how fortunate we were to be able to see the incredible extremes at which humans are able to perform, whether it’s flexibility, swimming, or sprinting — isn’t it breathtaking that that’s something that people can do. I’ve often thought of her words during math conferences when I watch one of the biggest names in my field expounding upon a brilliant and powerful idea. Presentations given by the greatest mathematicians aren’t shown on TV for everyone to see like the Olympics is, in large part because their content would sound like a useless jumble to a lot of the public (plenty of mathematical talks sound like total nonsense to me too!). But just about everyone understands what math is and what some level of prowess at understanding numbers looks like. Relatively few people get the opportunity to watch a sampling of the greatest mathematical minds describing their work or (even more exciting) mulling over new ideas in discussions.
Yes, this can be humbling in a negative way for much weaker mathematicians like myself, and I’ve left some conferences feeling overwhelmingly like the research I saw presented there was a damning verdict on my ability to be a competent mathematician. But I can also recognize the positive effects that should come out of it, and I’d like to think that getting the chance to be around those geniuses has helped inspire me to learn more of their background concepts and to reach my full potential. If I hadn’t been exposed to that kind of brilliance, I might very well still be piddling around with elementary problems without having outgrown the cockiness from my younger days when I assumed that I could get as far as I wanted to go in math just by feeling passionate enough.
It’s still a struggle for me to channel these experiences into a gain in confidence rather than insecurity, probably in part because success as a professional mathematician still involves a lot of competition, as all professions do. But here’s where my example of Scott Alexander becomes very relevant. Because witnessing his achievements (and those of the other leading members of his online community) has had a similar effect in how I discovered that greatness is somewhat further away and less attainable than I’d always imagined; yet, that effect has not culminated in bitterness or frustration. Rather, it’s been an unambiguous net positive.
I look at it this way. That weekend when I stumbled upon Slate Star Codex and the online rationalists and Alexander’s earlier LiveJournal and realized that the vague dreams I’d entertained had already been realized by others, I could have reacted by throwing up my hands and concluding that there was no point in my even trying. After all, there was an incredibly verbose person already out there, already with a sizable following, with interests similar enough to mine that he’d surely get onto every possible topic I had something to say about, right?
To some small extent of course this is true. But actually, there are way too many distinct adjacent topics out there for even a writer as efficiently prolific as Alexander to have a chance to discuss. And even some of the specific topics of our mutual interest have been treated in his essays in ways that I sharply disagree with (much as I may sound like his biggest fanboy here, I’ve of course spent much more time criticizing his opinions than those of anyone else)! And even for some of the concepts and experiences we view similarly, I still want to express them in my own way despite the fact that he already put them in an essay. (For example, take today’s theme of disappointment at not having achieved greatness as one gets older. He already wrote an essay on it called “Growing Old” over four years ago! Didn’t stop me from finding it worthwhile to write this one.)
No, discovering the existence of online rationalist writing didn’t discourage me — it inspired me. It materialized my very fuzzy ideals of written-down investigations of my vague questions into actual results that I could see before my eyes, and in doing so, showed me a path forward. It didn’t matter whether I could ever had a chance of reaching the end of this path. The point was that now I knew much more clearly what direction I might take; in fact, I could even proceed with the assurance that greater minds had already done a lot of the work for me to make my path easier.
And so I have. Thanks entirely to the example of a certain cluster of online writers, and Scott Alexander most of all, my one-time lofty imagining turned from a vaguely-conceived fantasy into, not a failed, ungrounded project like my 2008 shot at Hawks and Handsaws, but an actual tenable endeavor that involves not only this blog but some direct engagement with an amazing group of people. It may not be headed towards my highest ideal of what such a project should look like, and it may always remain a relatively insignificant presence in a large community. But it’s already an endeavor that has freed me, allowed me new insights, and generally added a whole new dimension to my life during these past few years. Ultimately, this presence of others’ greatness in my life is why I am here.
That is exactly how I’m learning to be thankful for the ordinary geniuses.