For example, you can't name the exact time that day becomes night, but it doesn't follow that there is no distinction.
A bunch of transistors being switched on and off, no matter how many there are, is no more an example of thinking than a single thermostat being switched on and off. OTOH, if we can't think, then this conversation and everything you're saying and "thinking" is meaningless.
So even without a complete definition of thought, we can see that there is a distinction.
There is actually a very detailed set of definitions of the multiple stages of twilight, including the last one which defines the onset of what everyone would agree is "night".
The fact that a phenomena shows a continuum by some metric does not mean that it is not possible to identify and label points along that continuum and attach meaning to them.
The math is putting the crate up on the rack. The crate doesn't act any different based on how it got up there.