Stanislaw Ulam

What is the Player’s Grid?

When I had the vision for what at the time was simply known as “The Year Long Game,” there was one component of it, that stuck out – The Grid. It was a way for every player to be organised in a highly visual manner, one that appealed to me instinctively. It’s a concept that’s resonated with everyone I’ve told about it, which is a good sign. Here’s the basic idea:

  • Every player in the game is assigned a unique number.
  • There are 100m players in the book, so they’re numbered from 1 to 100 million.
  • Number 1 is at the very centre of the grid
  • Number’s 2 – 9 surround it, numbers 10 – 25 surround them, and so on, all the way to 100m
  • The groups that players are in are determined by their number: odds, evens, quadrants, primes, fibonaccis and so on

It was only later on that I discovered that this layout actually had a name – it’s known as an Ulam Spiral. From wikipedia:

The Ulam spiral, or prime spiral (in other languages also called the Ulam Cloth) is a simple method of visualizing the prime numbers that reveals the apparent tendency of certain quadratic polynomials to generate unusually large numbers of primes. It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling during the presentation of a “long and very boring paper”


I thought that my next challenge was to get hold of such a grid – for all 100 million numbers – so that I would know which quadrant Nova was in, as it’s a relatively important thing in the book. I couldn’t find one anywhere – every Ulam Spiral out there has been created with the sole purpose of identifying prime numbers, and the associated patterns that they make … not for the purpose of locating unique numbers within it, like I was trying to do. So what do you do when you’re stuck? You ask Reddit of course!

People told me what I had expected – that it would be a ridiculously large file (I wanted it in Excel, so that I could easily navigate to any number within it). And I think the person who tried, gave up when his computer nearly died on him. But, like Nova the protagonist from the book, I ended up getting what I needed, rather than what I thought I wanted, when u/zifyoip gave me a link to a site with a Java applet that I could navigate around.

If, after reading all of this, you’re still wondering what on Earth the Player’s Grid looks like, wonder no more. The colours have no meaning, there’s only there to make it more visual. Oh yeah, and the old dude? That’s Stanislaw Ulam…

Player's Grid

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