When I first learned about computer science at the age of 11 or so (and in 1982 or so) the first page of the text book put digital and analogue computers on what seemed to be an equal footing. And then proceeded to ignore the latter for the rest of the book. Apart from a few notable exceptions ( https://en.wikipedia.org/wiki/Phillips_Machine ) I've often wondered about analogue computing.
If you want to understand the issue with analog computers, design a SHA-256 circuit for one of them and consider the consequences of trying to push a megabyte of data through it. While that is an extreme example I chose precisely to make the issues clear, much real computing has many of the same characteristics, just distributed a bit more widely in time and space.
Or, to put it another way, you can make anything sound good if you consider only the positives and anything sound bad if you only consider the negatives. Analog computing sounds amazing when you read the brochure and consider only the positives. But when you bring the negatives back in, it makes sense why it is not frequently used. It is not a case of the mainstream keeping some great idea down because, uh, Big Digital or something, it's a case where digital computing turns out to be a stonking good idea and it's hard for the analog world to compete and it's virtually impossible for them to ever be anything but a niche.
Neural networks are an interesting possibility for a future successful niche, although even so, it would be neural networks specifically that may grow in importance and not analog computing in general. And I still wouldn't guarantee it'll be a good idea... we may have a lot of trouble keeping what would be very deeply nested analog circuitry stable in the real world and digital may still win out, e.g., an analog neural net that has a noticeable personality shift when it gets warmer may not be the best engineering solution. That's a question for 20 or 30 years from now.
Is SHA-256 something that makes sense in analog realm, or is it something that only needs to exist due to digital constraints?
The use case of "I have a big pile of data and I need to ensure that it survived transmission intact" isn't going anywhere. Just being in an analog computing world would not make the way some data needs to be precise go away. Not everything is a TV signal being consumed by human eyeballs.
But if you want an even better exercise, sure, work out how to send, say, precise stock market transactions where a "$5.04" becoming a "$5.05" is a very big deal to some people who have lots of money, and work out a mechanism for verifying the integrity of a lot of such data efficiently.
Bear in mind "efficiently" in this case includes the idea that "$5.04" and "$5.05" are actually close together, not separated by quite a lot of signal bandwidth. It should be of a similar size to the current digital world where that is a single bit; if you're throwing more bandwidth at your representation you've already lost to digital. Or to put it in analog terms, that needs to be pretty close to the noise barrier already; it's not a solution to make it so that you end up with "$5.04 +/- 0.000001" and "$5.05 +/- 0.000001" as the two signals you send. That is, after all, what digital is in the first place: All signals are analog in the end, and we send 0s and 1s with enough separation that the receiver can then re-amplify them into a 0 or a 1 without loss. It's not really analog if you're not hard up against the noise floor, it's just digital wearing an analog wig.
If analog is supposedly "better" than digital... at least, for the sake of argument, I recognize you did not make that claim... that would include being able to do some of these things that we do in the digital world quite comfortably. If it's just a niche... well, that's exactly where we are now in the world anyhow.
Quite a lot of real-world data is quite digital in nature. This message I'm posting is intrinsically digital. Even if I were to write something by hand, we all know, and knew even before computers, that the essence of that message is captured by a stream of letters. When we read the Gettysburg Address it doesn't even occur to us to worry about the theoretically vast amount of information we lose by not having the handwritten original. While those can be of historical interest we all know the payload is in the digital stream of letters and words. You have probably never worried before about whether the nuances of Hacker News posts are lost because they're typed in a fixed-width font but displayed in a proportional one, because the digital text carries the vast majority of the content. Even in an "analog world" there is no escape from quite a lot of digital-characteristic data. And there is no escape from the many, many issues with truly analog solutions, such as the inability to copy data without loss. This text has undergone literally dozens of copies by the time it gets from my keyboard to you eyes, and that would drive the analog world insane. Either accept much more degradation than any of us are used to, or dedicated much much larger amounts of bandwidth to everything in a way we would find horribly inefficient in our real world.
Noise and component imprecision has always limited analog computing.
And a general lack of reconfigurability to solve general problems. There’s been interest in analog neural networks for a long time.
Those problems you mention are important in music synthesis where people could live with limited reconfigurability but reliability is at a premium: synth players in early touring bands (e.g. Yes) had to be electronics technicians and instruments have to survive being packed in boxes and transported everywhere. The Yamaha DX-7 made FM synthesis mainstream because digital FM synthesis was absolutely reliable.
Analog synths are a lot more reliable these days though.
In neutral networks, we seem to be pushing towards ever lower precision floats, and we use noise for all sorts of useful things.
Also true: all computing is analog computing.
My father designed processors. He says all electronics are analog. Some just pretends to act digital.
At the end of my undergrad, I remember a UW professor being poached by intel to work on analogue computing research project, the chair of the department at the time said that it was an opportunity that might not ever happen again and he had to take. I don’t think it went anywhere (since I never heard of intel coming out with a product), but I at least knew there was an attempt.
Quantum annealers (D-Wave machines) are basically analogue computers, with Josephson junctions as the primary component as opposed to oscillators. I wonder if they could render these images, too?
Take a look at extropic. AFAICT it's a form of analog computer.