one thing to give you a feeling for why we can do such amazing and fast operations with electronics, is that electrons (and similarly charged particles, like "holes") have a very, very high "charge to mass ratio". now since you cannot compare charge to mass directly (it's like "comparing apples to oranges"), there are these sort of universal units called Planck units (that are defined so that the constants that are properties of free space just go away) and in Planck units, the charge on an electron is roughly about 1/11 of a unit charge but the mass of an electron is about 20 sextillion times less than the unit mass.
so there isn't hardly any mass to resist pushing them around, but there is sufficient charge to push these electrons around real good. so, mechanically, electrons can be shoved around at very high speeds and accelerations very easily.
now, if you leave radio out if it, virtually all of the models we have that are used in electronics can be replaced with a hydrodynamic model with water instead of electrons, pipes instead of wires, valves instead of transistors or vacuum tubes, and some other analogs. but this hydrological computer would be horribly large and damn slow. the reason for this is because water is much, much harder to shove around than electrons.