The Fundamental Growth Curve (Part 3)

by radimentary

Last time we introduced the basic model of growth, which looks like this:

The thesis is that noticeable growth is typically punctuated by a long intermediate period of low return on investment, which we call “the Wall.” In the remaining posts on this topic, I plan to cover (a) the common failure modes that arise due to the existence of the Wall, and (b) prescriptions for how to minimize or completely skip over the dreaded wall.

Failure Modes

Skill and complexity creep

In the year that League of Legends launched, you could become a top player in three months of unstructured training by focusing on one hero and drilling mechanics. The level of play is always this low at the beginning of things. Nowadays, it takes years of dedicated practice and encyclopedic game knowledge to reach the same relative status in the game.

Creep is an ever-present threat to the health of every community of skill: consider the research field where the low-hanging fruit has been picked barren, the video game where the barrier-to-entry is a hundred hero by hundred hero table of matchup knowledge, or the industry where the pool of interview questions grows ever more esoteric and adversarial. Left unchecked, the wall grows higher and higher, until new blood stops bridging the gap altogether and the entire community dies out.

Picking the wrong-sized pond

As a child, my parents told me the typical Asian advice that I should befriend older, smarter kids from whom I had much to learn. Thankfully, I mostly ignored this advice. I’ve seen friends try to follow this strategy, usually to their detriment.

The farther down you start in the status hierarchy, the further away those sweet positional gains become. And imagine, god forbid, that you really imbibe this backwards advice and continuously try to jump up hierarchies to where you don’t belong. You’ll spend your whole life being the odd one out, the real impostor, the weakest link, the lowest-status grunt who is passed up for every opportunity and promotion.

Conversely, it is also possible to be too big of a fish in too small a pond. They say that if you’re always the smartest person in the room, you’re in the wrong room. There’s a different kind of stagnation that happens when you reach the peak of your local hierarchy and don’t search for greener pastures.

Bringing down the Wall

Artificial divisions

It is common knowledge that only children can become chess grandmasters. Neuroplasticity and ability to learn probably plays a role, but another important factor is that there exist long and delicate pipelines of positional gains for bootstrapping children through the Wall. For example, in tournaments and classes, young children are carefully subdivided into two-year age brackets and locality; this artificial partitioning of the population allows for that many more first place trophies to win and local mini-ladders for kids to climb. A seven-year old prodigy can start winning games in the county at the under-8 level with only a bit of talent and study, then the state level, then the next age bracket, and so on. The positional gains are thus paid to her in installments that keep her coming back. Adults who want to learn chess have no such luck.

Systems for training difficult skills can be optimized by placing people in granular divisions with comparable peers. Conversely, as an individual, one should judiciously hop between ponds to find places where fruitful positional gains are within reach. As a rule of thumb, the sweet spot seems to be rooms where you’re around the 75th percentile.


One way difficult disciplines can prosper is by subdividing in a different way, specializing into mutualistic subdisciplines. A software engineering team might be a hostile, zero-sum competitive environment if everyone is trying to be the best at everything. But suppose the team members each leverage their unique strengths, and you end up with a one expert in frontend, one in backend, one who knows how to speak the voodoo language of customers and product managers, and that one machine learning guy. Suddenly everyone has the benefits of high status in their respective domain and access to mentors who can help patch up their weaknesses.

One problem math academia faces today, and part of why the wall called graduate school is so difficult to get over, is the insufficient specialization of labor. Sure, we specialize in subject matter, but whether you’re an algebraic topologist or a knot theorist, you still have to excel at research proper, paper-writing, mentorship, public speaking, etc. etc. Effectively, all these sub-dimensions of competence are projected onto a single massive meta-ladder that is impossibly tall (man am I mixing metaphors today) for the novice to climb.