Humans are pattern seekers. We are sense-makers. This is observably true through our creation of complex representative languages which take observed and experienced phenomenon and substitute grunts and scribbles to stand-in-place of moving or touching or interacting with such things directly.
Language is faster than physical movement.
In our sense-making, we notice similar lines of motion among otherwise distinctive systems.
We notice they perform similar functions within their own systems.
So, we can represent a wide variety of physical systems by the same idea.
We’ve formalized much of it in mathematics, which is an even more succinct way to manipulate symbols instead of objects.
So, what now? What do we do with these similarities (say, between, hydraulic, electric, thermal and mechanical)?