I wanted to make a CCD processor back in the eighties that could do digital and analogue calculations. You could have a digital number or a charge packet. The CCD technology could duplicate charge packets, invert, and add or subtract charge packets.It would have an A/D and a D/A convertor so you could convert from charge to digital, and back. You could multiply a charge by a digit. You could divide a charge by a charge and get a digit. And so on.
It turned out the whole idea had been patented by Motorola in 1978.
Analogue, asynchronous circuits are a nice idea. They ought to be very powerful. However, without some sort of binary logic and clock, we can’t really design the things, program them, or do a repeatable experiment. It’s sometimes hard to tell whether they are working at all. But we are making strides with AI, so we may beat the analogue barrier in time too.