Perhaps the main thing we do with our computers is to store data on them, so what's a relatively low-tech way to store non-trivial amounts of data?
Fragile wires is an attractive way to create write-once (PROM) microchips. Though in some way or other we'd probably use magnetism again to store data. A grid of wires, with the columns using thicker wires & being wrapped around the rows is an attractive approach that was quickly overshadowed in our history.
2/3?