Mathematics is a mental construct created to reliably manipulate abstract concepts. You can describe mathematical statements as elements of the mental models of intelligent beings. A mathematical statement can be considered “true” if, when an intelligent beings use the statement in their reasoning, their predictive power increases. Thus, ” ‘4+4=8’ is true” implies statements like “jslocum’s model of arithmetic predicts that ‘4+4=8’, which causes him to correctly predict that if he adds four carrots to his basket of four potatoes, he’ll have eight vegetables in his basket”
I’m no sure that “use the statement in their reasoning” and “their predictive power increases” are well formed concepts, though, so this might need some refining.
I really like the idea overall.
Serious ideas:
games that help explain ideas like ‘screening’ variables, rules for propagating information up and down different branches of the network, etc.
more advanced topics like estimating the normalization constant for a very large hypothesis space?
more advanced gameplay mode where you have a scenario and a list of hidden and observable variables, and have to figure out what shape the network should take—you then play out the scenario with the network you made—success requires having constructed the network well!
Bad jokes:
A character named Gibbs who runs an energy drink stand and gives out free samples.
The Count of Monte Carlo should make an appearance.
A face-off against agents of the evil Frequentist, hell bent on destroying all that is (probably) good and (likely to be) held dear.