[chris (OP)]

Today, switching on the dishwasher, the red light came on to tell me that it has run low on the salt it uses to soften the wash water.

You top it up by just tipping salt into a reservoir, so how does the dishwasher know that it's run out of salt?

[alancalverd]

Float switch.

An early description of a hydrometer appears in a letter from Synesius of Cyrene to the Greek scholar Hypatia of Alexandria. In Synesius' fifteenth letter, he requests Hypatia to make a hydrometer for him. Hypatia is given credit for inventing the hydrometer (or hydroscope) in the late 4th century or early 5th century.

Getting the float to actuate a microswitch took another 1500 years, but we got from Kitty Hawk to the Moon in my parents' lifetime. Unpredictable stuff, progress.

[Colin2B]

Because the regeneration of the softener is an ion exchange process I would guess at a conductivity measurement.

[wolfekeeper]

FYI the latest dishwashing tablets don't need additional softening unless your hardness is literally off the charts. In fact mine was off the charts, but it was still narrowly within the range they claimed it handled.