Sometimes I wonder whether computing would have been possible if electricity and its related effects could not be harnessed for logic and computation. In that alternate universe I could imagine us creating quite sophisticated devices running off of compressed air; perhaps not to the atomic level of precision we can achieve with solid state devices, but extremely capable nonetheless.

Manipulating free electrons in electronic logical devices has important advantages in enabling miniaturization, low energy consumption, high speed and long life, but it is possible to make logical devices, including computers, using a great variety of other techniques.

You can easily make logical gates, automata or complete computers using pneumatic or hydraulic or electro-mechanical or purely mechanical devices.

These 4 kinds are still in use in certain applications, where their advantages remain important, but even more implementation techniques are possible, for instance with optical devices or with devices based on controlling ionic flows instead of electron flows or with devices based on controlling the kinetics of chemical reactions (i.e. an enzyme whose activity can be modulated, e.g. it can be inhibited, can be seen as the equivalent of a transistor or a relay, because it can allow or prevent the conversion between 2 chemical substances, i.e. the flow of matter between the 2 substances, like a relay can allow or prevent the flow of electrical current). The latter 2 kinds of devices are exemplified by the living beings.

Charles Babbage designed his difference engine that was mechanical and used punch cards for loading programs. The machine was mechanical and used a steam engine to power it.