Mathematical objects

There is no mathematics in a clock. I have devised new, mathematical clock. Every second, a new clock will be created with the hands in a different position.

There is no mathematics in a gun. When you pull the trigger on my ``mathematical gun'' an object with a bullet hole will appear, together with another copy of the gun where the bullet has been fired. The original object and gun will be unchanged.

Driving a car has nothing to do with mathematics. Turning the steering wheel should create a new car moving in a different direction. The fuel tank of this new car would have slightly less fuel than the previous car. This car will be on a new road which is in a slightly different relative position to the car.

>>27
If a function modifies its input, then the input is part of the output.
Conversely, if it does not modify its input, then there is nothing to modify that is the same type as its input. Thus, all output must be created, rather than being a modification of the input (tautologically so). In addition, type theory is homomorphic to pretty much everything to be discussed in CS theory.

>>30
Each example is arguably a left-fold over the input and the current state; the state may be part of the input but it is not all of the input. I still think you are misunderstanding and/or I don't see what point you are trying to make.