‘Minecraft’ seems, at first glance, to be the last place we would go to look for a mathematical constant associated with perfect circles. Its world is made of cubes, its landscapes rise block by block and almost everything we see in the game has edges. That is precisely why what Molly Lynch of Hollins University and Michael Weselcouch of Roanoke College have done is so striking: finding a way to approximate π within Minecraft without turning the game into a conventional calculator.
What are we trying to calculate?. π It is the constant that appears when comparing the length of a circle with its diameter. It is an irrational number with infinitely many non-repeating decimals. On paper, it seems like an idea inseparable from continuous geometry, of clean circles without edges. ‘Minecraft’ plays in another terrain: everything there is represented by discrete units. That is why the challenge is not only to obtain a number, but to translate a mathematical idea into a gridded world.
Too heavy a possibility. ‘Minecraft’ has already proven to be Turing complete, a technical way of saying that, in theory, any program can be implemented within the game if the right mechanisms are built. This opens the door to calculating π as a machine would do, with logical instructions transferred to the universe of blocks. But Lynch and Weselcouch didn’t want to solve the problem by brute force. Translating records, logical operations and steps of an algorithm into ‘Minecraft’ actions would have turned a teaching idea into a huge and inaccessible construction.
The choice. Choosing was not a whim, explains Spektrum. Lynch and Weselcouch wanted to bring mathematics closer to young people, and they saw the game as a particularly useful tool to do so. The point was not to demonstrate that Minecraft could replace a computer or to search for a particularly brilliant approximation of π, but rather to take advantage of its internal rules to construct a comprehensible explanation. That’s why his work explored relatively accessible methods for calculating known constants within the game, without turning the experiment into a difficult-to-follow technical demonstration.
The darts method. The mathematical key chosen by Lynch and Weselcouch was a technique known as the Monte Carlo method, which the aforementioned publication explains with a very simple image: throwing darts at random against a circular target inscribed in a square. If all the impacts fall within the square, but only some within the circle, the proportion between them allows us to approach π/4. Then it is enough to multiply this result by four to obtain an estimate of π, although we are always talking about a statistical approximation.
The translation to the game. Lynch and Weselcouch brought that idea to ‘Minecraft’ by first building a kind of red circle with a radius of 11 blocks, then enclosed within a blue square. From there they needed random events that could be counted, which they found in two creatures in the game: the slimes, which continue moving even if there are no players nearby and change direction at random, and the zoglins, which kill them. To record these eliminations, they used hoppers, funnel-shaped blocks capable of automatically picking up objects that fall on them.
The final figure. The researchers recorded 619 dead slimes, of which 508 were eliminated within the circle, and with that data they arrived at π ≈ 3.283. To do this, they compared the deaths recorded within the circular area with the total deaths in the square. It is not a particularly precise approximation, and Lynch and Weselcouch do not hide it: the method would gain precision with a larger structure and with many more recorded deaths. But that limitation does not ruin the proposal. On the contrary, it helps to understand that the goal was to turn an abstract mathematical idea into something visible within Minecraft.
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