A run through Geometry Wars unfolds in a few distinct phases. The first 100,000 points are your adolescence: skittish, erratic, awkward. There are too few enemies on screen at any given time to truly compel a route, and your cannons don't have the surgical precision necessary to pick off individual shapes with any ease. As a result, the easiest strategy is to tentatively approach slower targets to pick them off and retreat from faster shapes that can close in on you before you're able to land a hit. For a seasoned player, dying this early in the game is a failure that will inevitably cast a pallor of doubt over the rest of his run. Yet even though a skilled Geometry Warrior will rarely encounter any difficulty in this passage, it's hard not to feel a bit fragile.
Between 100,000 and 500,000 points, a transformation occurs. The spawn patterns stay the same, but the number of enemies thrown at you increases exponentially. It's no longer possible to move away from one group of enemies without running directly into another. And this is where a novice player will typically hit a brick wall.
My friends and I went through a multitude of half-baked, one-off strategies in our attempts to push past the half-million mark. One memorable tactic instructed the player to keep as many black holes in the center of the screen as possible by scuttling from one engorged circle to another and pruning the extra mass away with cannon fire until it became less prone to explode. This created an all-consuming vacuum in the center of the screen from which no enemy could escape, but it wasn't sustainable. While the rotating coronas of red light provided some amazing eye-candy, it always resulted in a cascading explosion of blue ringlets.
We spent the better part of our winter break searching for ways to move beyond the 500,000-point threshold, with little success. We even experimented with different screens and viewing distances; still, the half-million mark taunted us, tantalizingly out of reach. And then, weeks after we had gone our separate ways, we found a prophet that would guide us deeper into the grid than we thought possible.

***
His name (or Gamertag, rather) was K4rn4ge, and over the course of what had to be a 90-minute session of continuous gameplay, he achieved a world-record high score of over 16 million points, more than doubling his previous record of 7 million. Best of all, he had the foresight to record the last 20 minutes of his run, which shows him scoring the final 4 million before no doubt collapsing into a heap on the floor and sleeping for three days.
We treated this document with a mixture of curiosity and reverence. Here was someone who, in the course of 20 minutes, had shattered every assumption we made about a game that we had spent weeks practicing. We discovered the difficulty actually ceases to increase after around 4 million points; perhaps the developers never imagined anyone surpassing that mark. K4rn4ge had reached a level of mastery where the only thing preventing him from continuing on to infinity was his own crude biological needs for food and sleep.