Imagine writing a program if every time you wanted to change something you had to cut a new gear, or design a new mechanism, or build a new circuit. Imagine the sheer complexity of debugging a system if instead of inspecting memory, you have to disassemble the machine and inspect the exact rotation of hundreds of gears.
Analog computing truthfully doesn't have enough advantages to outweigh the advantage of digital: you have one truly universal machine that can perform any conceivable computation with nothing but pure information as input. Your application is a bunch of binary information instead of a delicate machine weighing tens to hundreds of pounds.
Analog computing is just too impractical for too little benefit. The extra precision and speed is almost never enough to be worth the exorbitant cost and complexity.
Neural networks are a very good application for analog computing (imo). You have a ton of floating point operations that all need to happen more or less simultaneously. And what are floating point numbers if not digital approximations of analog values? :)
This can be implemented as a network of transistors on a chip, but driven in the linear region instead of trying to switch them on as hard as possible as fast as possible. Which is, I believe, what researchers are trying to do.
There are also some interesting ideas about photonic computing, but I'm not sure if that's going anywhere.
A few months back, someone on YouTube attempted to design a mechanical neural network as a single 3D printed mechanism. It ended up not working, but the concept was pretty solid.
Perhaps that's only because we haven't begun to understand analog yet. And our crude original perceptions have long suffered for being ignored. For example, I have yet to actually hear any digital music yet ... that didn't have to pass through a DtoA converter. Hell, we may even learn that braining is not really the product of individual neurons at all, but a coordinated ballet oscillating like seaweed. I'll go bigger: is consciousness analog?
Both domains are extremely well understood. Analog electronics is an incredibly deep field, and forms the foundations of basically all of our electronic infrastructure. For instance, the transceivers that power cell stations are all analog and are incredibly complex. This stuff would seem like alien magic to anyone from even 30 years ago. The sheer magnitude of complexity in modern analog circuits cannot be overstated.
As for analog computing, well, it's just math. We can design analog computers as complex as our understanding of the physics of the system we want to model. There's not really any magic here. If we can express a physical system in equations, we can "simply" build a machine that computes that equation.
> I have yet to actually hear any digital music yet ... that didn't have to pass through a DtoA converter.
This is simply not true. There are plenty of ways to turn a digital signal into sound without an intermediate analog stage. See PC speakers, piezo buzzers, the floppotron. You can also just pump a square wave directly into a speaker and get different tones by modulating the pulse width.
The reason we use an intermediate analog stage for audio is because direct digital drive sounds like total trash. I won't go too much into it, but physics means that you can't reproduce a large range of frequencies, and you will always get high frequency noise that sounds like static.
Edit: I didn't notice your username before. All 8 bit systems make heavy use of the square wave voice, which is a digital signal. But it's typically passed through an analog filter to make it sound less bad. Music on e.g., the first IBM PCs was purely digital, played through a piezo beeper on the motherboard.
The strength of digital is that your logic is implemented as information instead of physical pieces. Your CPU contains all the hardware to perform any operation, and your code is what directs the flow of information. When you get down to bare basics, the CPU is a pretty simple machine without much more complexity than a clockwork mechanism. It's an extremely fascinating subject and I very highly recommend Ben Eater's breadboard CPU videos on YouTube. But I digress.
The real trick is that digital computers are general purpose. They can compute any problem that is computable, with no physical changes. It's purely information that drives the system. An analog computer is a single-purpose device[0] designed to compute a very specific set of equations which directly model a physical system. Any changes to that set of equations requires physical changes to the machine.
[0] general purpose analog computers do exist, but generally they're actually performing digital logic. There have only been a few general purpose true-analog computers ever designed AFAIK. See Babbage's difference engine.
Most DNA errors turn out to be inconsequential to the individual. If a cell suffers catastrophic errors during reproduction, it typically just dies. Same for embryos, they fail to develop and get reabsorbed. Errors during normal RNA transcription tend to encode an impossible or useless protein that usually does nothing. Malformed RNA can also get permanently stuck in the cellular machinery meant to decode it, but this also has no real effect. That transcriptase floats around uselessly until it's broken down and replaced. You've got a nearly infinite number of them.
DNA and all the machinery around it is surprisingly messy and imprecise. But it all keeps working anyway because organisms have billions or trillions of redundant copies of their DNA.
*take with a grain of salt, I last studied this stuff many years ago.
'Imperfect components' is a value judgement. Apparently an analog world was a necessary part of self-replicating 'mechanisms' arising while floating in the analog seas.