This a computer, and you likely own one. It's a hydraulic analog computer.
It’s essentially a machined analog computer that computes with fluid instead of electronics: pump pressure is routed through passages that act like wires, while spool valves, springs, orifices, and check balls perform the equivalents of comparators, logic gates, delays, and one-way elements.
What it “calculates” is the machine’s current operating state, whether conditions have crossed a threshold to justify changing state, how strongly to apply each output, and how quickly to make that transition without instability or shock.
It does this by continuously balancing forces—pressure on different valve areas against spring preload and feedback pressure—so each valve shifts only when one hydraulic condition outweighs another, while restrictions and chambers add timing and smoothing.
In plain English, it is a real-time fluidic state machine that solves “if this pressure is greater than that one, route flow here; otherwise hold, delay, soften, or override” entirely through geometry and oil.
They're used in every car with an automatic transmission, where it makes choices like what gear to be in and how hard to apply clutches, etc....
And some dude worked it all out on paper back in the 1960s.