Set Theory in a Suitcase
Demonstrating basic set theory in Mathbreakers
This week, we spoke with our friend and mathematician Jon Hull, who helped us devise a way to express set theory in our game.
Despite having a rather famous-sounding name, set theory is not all that complicated — at least not at early levels. Basically, you need to understand a few basic rules:
• Sets are groups of objects that can contain ANYTHING, including other sets
• The empty set is not “nothing”
• You cannot have duplicates of a single item in a set; one item is enough
• Representing operations between sets can be shown with Venn diagrams
To make this work inside our game, we introduced a new item called a Suitcase. You can put anything inside it, but at first we only give you one suitcase and a few numbers that you must match to a glyph on a machine. It gets progressively harder from there as you work with making sets and putting them in various machines.
The machines we made are Union, Intersect, Difference, Equality, and Unpack. The first three are the familiar operations on sets — you drop a suitcase on either side of the operator machine, flip a switch, and the operation is performed. Equality compares a suitcase to another; we use this to tell if the player has beaten the puzzle. The unpack machine will take the contents out of a briefcase so you can modify the set.
With these devices we build challenges by providing a limited number of sets of a certain type, then requiring you to use the machines in the right order and configuration to get to a target set.
This is just one of the many applications of our 3-D math game. If you have your own idea for our next whiteboard session, please write to us at team@imaginarynumber.co with your suggestions!
Support our Kickstarter if you want to see more cool math (or if you or someone you know would like to learn more about math in 3D) ;-]
