How is a number like a hero? How is an equation like a tragedy?
First: The world as we perceive is not the world as it is. As we perceive the world we live in, through our sense of sight and sound and touch, we break everything down into symbols that our brain can comprehend and work with. Because those symbols are internally consistent, we can still interact with the world as though we are part of it – which, of course, we are. Our minds are always at one level removed: The brain sees the world, converts it into a symbolic understanding, and then operates on those symbols to decide what to do next, sending instructions to the body which thereby affects the world, and so forth.
This symbolic system is unique from person to person, comprised by the specific tissues and issues of each brain. Therefore, we create an other symbol system, language, to translate between these. It’s kind of like the same OS running on different kinds of hardware: The programs are the same, but the metal that interprets them is different, and sometimes this causes problems. Realistically, the languages we use are prone to a lot more error than actual programming languages, relying a lot more on abstractions and inferences. Much gets lost in communication. It remains to be seen whether this aspect of language is feature or bug.
We have another language we created, one that’s not prone to losing information: Mathematics. The only thing that makes mathematics useful and relevant is that it’s possible to convert real world systems to mathematical systems, operate on them as mathematical systems, and then convert back to real-world systems and have the effects translate perfectly.
Couldn’t we do that with any internally consistent system? Actually, we have: Geometry is a discipline separate from mathematics, though they are often used together, and itself represents an internally consistent system. Perhaps the different instruction sets of computer hardware could be regarded as such, though they are so mathematically grounded and implemented that it is difficult to separate them from the field of mathematics. It’s scary to think, though, that maybe we missed one. Maybe there’s an internally consistent system of symbols that, if we were to use it, could completely open up a whole new fields of thought. Maybe there are an infinite number of such systems, each one boundless in its applications and implications.
It’s interesting how, viewed through this lens of internally consistent simulations built of symbols, the mathematics we use start to resemble the stories we tell. We craft a reality that operates on its own internally consistent rules (build the world), operate on it (tell the story), and then translate that back to our own world (find the message/moral). Mathematical problem solving is a form of very specific parable for solving very quantifiable problems.
And now we have the video game, which exists with one foot in each world; built on mathematics, scripted by storytellers, a literal world of possibilities waiting to be expanded. What could we discover, as we did with storytelling, as we did by math and geometry, with the parables these worlds could tell us?