[travisjungroth]

One way of viewing it is that math is games. Not in the winner sense, but in the activities with rules sense. Addition is a game.

Some games make you better at other activities. Like, playing chess could make you better at logistics because you’re practicing planning and managing losses.

Some games match some real world situations so tightly that we can go through them step by step and solve the real world situation in the game. You can play addition to figure out two apples and two more makes four apples.

Whether the game is “real” or not is immaterial. It just needs to be internally consistent and matched to the right thing.

There’s also the idea that math is another world that we can visit, similar to the dream world. But that’s a whole other thing.

[fasa99]

The idea that it's an abstraction is 100% accurate. That physics is a discrete set of fields with field rules and interaction rules, and what we observe is a scaffold on top of that. It's like okay, let's say the math is right and we have a set of fields, what are they and where are they from, how do we manipulate them. Then the physicists, often driven by ego, is want for an explanation and points to vibrating strings and such, and finally they knock on the door of the empiric physicist and say "can you do an experiment to show that I'm right" "sure, build a machine the size of the universe and I could test that" and that's the state of physics the last gorillion years

https://www.youtube.com/watch?v=FYJ1dbyDcrI

[travisjungroth]

So in the viewpoint I’m describing you can definitely call it an abstraction. And abstraction has a vibe of intentionality to it, at least for me. That brings up something I didn’t mention, which is you can make a math game on purpose, to match with something in the real world. You can also make them up for fun (people don’t usually call it “for fun”, but that’s actually a fair label for theoretical mathematics IMO) and then discover the application later.

This is neat! I think it happens less in the physical world, just making up a tool and then finding its application later. It does happen in chemistry.