They cannot compel you to divulge a password, but they can mandate a thumb unlock, just as while they cannot compel you to divulge a safe combination, they can mandate you give them a key.
You might also know these as flowcharts when applied to program flow control.
I don't think I answered the original question well. I just wanted to point out that math is more than just equations. Others have done a much better job in this thread.
That was the second part of my answer: a graph on paper. Draw nodes of execution and represent the branch as two arrows coming from the node and heading to new nodes. Label the arrows with the predicates of the branch.
This is both definitely useful and definitely math.
You don't need to know category theory. You just need to understand a few things that came from it, like `Maybe`, which is the most obviously useful and trivially easy monad. Just forget about the fact that it's a monad and any general rules about monads and just learn how to use `Maybe`.
From there, input handling is just a state machine. Easy to draw on paper as a graph.
> Part of the benefits with modelling a program on paper should be to make communication easier. And to require people you communicate with to have knowledge in category theory to understand your design fells silly.
This is an odd complaint, because you can also say:
requiring people you communicate with to have knowledge in (state machines | graphs | `if` statements | ...) to understand your design feel silly.
I agree that that is the pragmatic approach given market constraints, but the market is not providing greater value in driving this hack-and-patch approach.
The difference in those targets is that they're uncertain, and that that uncertainty compounds as you reach further into the future. I don't think the nanopass-in-reverse approach lends itself well to resolving uncertainty, because you'd start from the point of most uncertainty, which sort of begs the question a bit.
The alternative is to do nothing and that will result in death and destruction. If the ability to harm the environment and other people is a freedom people are up in arms about losing, it's a shitty freedom to have in the first place. One person's freedom should not impinge on others'.
Given the choice between the state taking away coal or mass extinction, I'm choosing the former.
Information versus material.