In the post Why good writing is one of the hardest things ever I discuss why writing is possibly harder than STEM, even ‘hard math’, but I wish to expound on this. As someone who has done both I think I am qualified to make this determination. I’ve written math papers, read countless papers, done some coding, read plenty of medical research reports (such as in regard to posts on obesity, diets, and metabolism), done research into quantitative finance (e.g. options pricing models and developing strategies), etc. [1] So I guess I can say I’m ‘fully immersed’ in STEM. (The only thing I have not done enough is research into AI, but Zvi has that covered.) On the opposite verbal side of the spectrum is writing this blog and reading others’ blogs.
So why is writing harder?
I believe a lot of confusion from math, or why math has the notoriety of being a hard subject, comes from poor exposition. I have seen this myself, such as papers or textbooks where key steps are omitted or explained poorly. Often the author explains a lesser concept in great detail and then insufficiently explains the key concept, or fails to tie the intermediate steps with the crucial step that leads to the final result. So there will be two concepts, A and B , each explained in depth, but minimal effort to tie them together. I think math ability is to some extent innate and correlated with IQ, but it’s not as hopeless or innate as verbal ability. (This is different with competitive-level math, in which innate ability plays a greater role, as practice tends to be controlled for.)
Being tutored can help immensely. When I tutored math, concepts suddenly ‘clicked’, when the textbook and the teacher’s instructions were insufficient. If a certain notation didn’t make sense, I could explain what the author meant and show the omitted steps as to how a result was obtained. [2] This is also observed by Bloom’s so-called “2 sigma” phenomenon. Likewise, I too was tutored in math. Many of history’s ‘greats’ in the sciences or the humanities were tutored. Even John von Neumann, the prolific polymath and pioneer of fields as diverse as computer science, atomic physics and game theory was not above being tutored. Same for Norbert Weiner, whose 1948 groundbreaking book Cybernetics laid the groundwork for understanding dynamical feedback systems, was tutored as a youth by his father. Or most famously, John Stuart Mill, whose dad, James Mill, basically speed-ran his son’s education. All of these people were brilliant to begin with, and then tutoring helped them to unlock this potential to its fullest extent.
But when it comes to writing, unlike math, almost everyone already knows how to do it, and has plenty of practice. Everyone writes, whether it’s social media, text messaging, email, or the occasional blog post. It’s not like people cannot write; they can, but just aren’t that good at it. And because the rules are already known and almost everyone is familiar with the basics, such as how to write sentences, it’s not like poor exposition is the problem, unlike math.
There is no critical impasse that must be cleared for writing skill to be unlocked. Writing allows for great precision in terms of articulating something, but ironically, there are no precise rules or steps on how to do it well, which in turn makes it hard as there’s no blueprint. Yet in spite of this arbitrariness, there is undeniably skill involved. Successful writers consistently put out quality prose that is well-received by the intended audience, but it’s not possible to reverse engineer this. This makes writing more innate than math owing to the near-impossibility of teaching good writing, only that good writing exists and we know it when we see it.
Again, it bears repeating that writing is damn hard. Pundits constantly deplore how high school or college grads cannot write well or how schools do not teach students how to write well:
This does not come as a surprise at all to me that students cannot write well. It’s like saying that most people cannot fly a plane well. Those who can are called pilots, which is a profession, yet for some reason pundits have this notion that being a writer or good at writing is something that you just ‘pick up’ through cultural osmosis or is involuntary, like speech or breathing, but this is no more true than picking up the piano and expecting to play at a concert level. A few years of school does not suddenly make someone a competent writer, any more than a few years of music lessons make someone a professional musician.
The Washington Posts asks “Why can’t college graduates write coherent prose?” I have been writing for years, and got good marks in school for my writing, and still my prose isn’t always that good or could be improved. Many famous, successful authors have been criticized for their prose, such as Ayn Rand or Stephen King, the latter whose writing is described as “blandly functional, a ‘plain’ style occasionally gussied up with pseudo-colorful idioms.” What chance does a college student stand when even professionals not uncommonly fall short?
This difficulty of writing, and verbal ability overall, is also corroborated by IQ tests or GRE scores. On the full-scale IQ test, the verbal section, vocabulary, is even more g-loaded than numeracy. On the GRE, top scores on the notoriously hard verbal section are rarer than top math scores. Same for the SATs, until recent revisions were made to make the verbal part easier, such as in 2005 removing the loathed analogy section. Some of this is possibly due to math having a lower ceiling, but verbal means having to infer and process large passages of text and unfamiliar words under a strict time limit, which unlike math, there are no generalizable methods or rules for this. With math, if you learn how to solve a type of problem, you can solve similar ones.
The final reason: unlike STEM, a much lower tolerance for mistakes as far as readers are concerned. As my aforementioned article discusses, for short-form writing to succeed, the entire piece has to be good. There cannot be logical fallacies, weak spots, unfounded assumptions, etc. as those will be noticed and condemn the writing to failure. The typical consumer of short-form non-fiction is much less forgiving than other mediums of content, such as film, podcasts, or YouTube. Superhero movies, for example, are constantly criticized for being derivative, yet are consistently successful.
People will listen (or watch on YouTube) in rapt attention as a podcaster interviews a guest who rambles and repeats himself for 2 hours, but when it comes to reading will hit the back button without hesitation, sometimes proclaiming if comments permit “I stopped reading here” just to make it abundantly clear that his time was wasted as he goes back to his 2-hour podcast. A math paper that presents novel results will not be doomed by poor exposition, unlike writing, where it has to be one-hundred percent dialed in from start to finish. Not only does the writing have to logically make sense, but unlike in math, aesthetics like ‘turn of phrase’ matter too.
[1] This includes multiple answers in MathExchange/Overflow of difficult questions, including a question that eluded an answer for almost a decade, among others. A second result was an analytic proof of a number-theoretic result, that also had eluded others for a long time. I used a Mobius transform to derive the minimum polynomial proves a set of identities. So when I say ‘math is earlier’, I am speaking from a level of math that is on par with research level, not just intro calculus or something.
[2] This is out of out of practicality: if a math textbook explained everything in detail, it would be 10x as long, yet such brevity also leads to confusion. When I write a paper only 5% of my notes goes into it.