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Eventually that problem was solved for digital flight control systems, and now everybody goes digital. Analog computers still crop up in all sorts of places these days but have become very niche and are typically a small part of an otherwise larger system. It's rare to see a general purpose analog computer outside of a very small number of research labs and FPAAs exist but are expensive novelties.

As digital processors continue to get better and we develop better ways to work with them, there just isn't the need for the cost and effort required to make analog computers. Some common places where you might see one is in audio driver amplifiers where it is common to implement a bit of trans-linear logic at the output stage to reduce distortion. Same in some high quality power supplies. Sometimes very high performance sensor systems will have an analog pre-processor to perform some calculation on the incoming signal before handing it off to the digitizers and DSP.

Think multi-microphone arrays. Perhaps I missed it, but the point of the article seems to be that eventually a complex "neuro" computer will be to complicated to understand and produce unaccountable results. The Author makes a few poor assumptions about analog vs digital computing and seems to ramble a lot, but ultimately, his main point doesn't have much to do with either. Perhaps I'm missing the more grandiose point, but I think his message is simple: digital computing is a handy abstraction for humans who like to count, but computing is essentially analog. This layman likes to refer to something about genetic algorithms and magnetic flux for reference on this.

There is no such thing as "analog". Everything in this Universe is digitized, down to elemental particles inside atoms. What you experience as "analog" is just digitization with a very fine grain, or if you like it, with better sampling. So no, the future of computing is not analog at all, it will still be digital, just with better sampling, aka quantum computing. Quantum, Analog, and Fuzzy Logic - are different terms that I believe some bright person in the future will prove as describing exactly the same underlying phenomenon. Also, if this could be accomplished, the next step in human evolution might be proving that the entire universe is a giant Analog computer, but that's Sci-Fi at this point in time I have no problem with building something without understanding how or why it works, but I do have problem of using something without at least some sort of guarantee on its behavior.

You may, but the vast majority of the population is already way past that with an iPhone and search bubbles, apps. And honestly, even if you're in tech, this feild is so broad and so many people are doing so many cool things that there's almost no way to keep up with it unless you're a ludite. If the case we are talking about involves building a single giant computer that no one knows how to use, you won't have much say in that.


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I suspect that the 'excess' precision of digital computers could be able to be retargeted towards some other use, negating any benefit that a analog computer had. In art, sometimes you want "happy accidents", even if they are not always reproducible. Can anyone recommend any good books or resources to learn more about analog computing? Does anyone know how to contact the author?


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Everytime I see large digital systems, the deterministic nature fades and it starts looking probabilistic, noisy.. I've been saying this for a while. The main problem with old school analog computers is that they were based on electricity which ended up causing rift imprecision that gets worse over time. The claim about relative performance of continuous variable models versus circuit models is completely unsubstantiated.

Is there any Complexity Theory work published about continuous variable models? And photonic systems do not magically fix the noise issue. Noise grows in a fast non-linear fashion with the size of the system, so the "constant factor" noise suppression you gain from switching to photonic systems is quickly washed away. Is there anything published on the fact that this cannot be overcome?


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Just looking at the wiki pages for Real Computation is enough to see it is not a physically realizable model. For more detailed discussion of the problem you can see the essay "NP-complete Problems and Physical Reality". To quote from it "The problem, of course, is that unlimited-precision real numbers would violate the holographic entropy bound".

At every level of physics there is a bound on precision, from boring things like classical macroscopic thermodynamics and noise, to quantum noise, to bounds that emerge in speculative theoretical physics. Basically, anything capable of encoding an infinitely precise real number in a finite amount of space will collapse and form a black hole.

In case this is not convincing enough, to your question about how this noise can not be overcome: if there was a method that can overcome the noise asymptotically in photonic systems, then that method would work in electric systems too. And there is actually such a method: turning the computer into a digital computer thanks to error correction codes. The claim that Real Computation can be realized in our universe is comparable to the claim one can construct a perpetual motion machine or some other generator of free energy.

They are both preposterous given our understanding of physics. And yes, I would celebrate if either of one turns out to actually be possible, but incredible claims require incredible evidence. This computer is literally at the physical limit reality can take.

analog-to-digital conversion

This number is actually quite high, although not unlimited. Furthermore, and this is important, this computer allows for a fundamentally different type of computation. Correct, this can be accounted for. Don't press on details, you won't be satisfied with the answers.

PLC Basics - Programmable Logic Controller

Can we talk about would be possible if this computer were possible and work backwards? As a mental exercise. Also what if I'm fundamentally more interested in probabilistic computation and this error can actually be a foundation of my computation. Electricity is fundamentally more "unstable". This error compounds. This of the difference in attenuation rate in electric vs optical media.

Where does this attenuation come from? Think of it as averaging unstable signals. The result is very much continuous.

Digital electronics - Wikipedia

You are getting too hung-up on the infinity aspect. Let's talk more about what sort of programming model this would allow for. A Turing machine technically has a tape of infinite length, while current computers don't. Does that mean that no Turing machine has ever been constructed? Does the answer to this question matter? Also, and this is important, compared with a normal computer, this computer would not heat up. Current CPU's can't get much larger because they can't dissipate heat fast enough.

Analog Digital Hybrid computers

What if you could have a CPU of the size of a cube of the volume of one cubic meter? This type of thought experiments is how much of physics progresses. But their results should be contemplated seriously. Assuming it is possible to prepare a system that works like your computer, it will immediately collapse into a black hole, because it breaks the holographic principle and plenty of other bounds.

Similarly we can imagine what happens if FTL was possible: time paradoxes. Or if we could measure both position and momentum: UV catastrophe. The infinity aspect is what makes Real Computation more powerful than other types of computation. It is also what makes it impossible in our universe. It has absolutely nothing to do with the type of countable infinity that is the length of a Turing machine tape. You can make asymptotic statements that are useful about Turing machines or logic circuits. The only useful thing you get out of Real Computation is strictly after you take the limit to infinity.

Otherwise you have old boring less-powerful analog computers which are nonetheless marvels of engineering and their creators deserve praise.

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This is just nonsense. By the way, the majority of continuous variable hardware is actually in the microwave regime, which is closer to the fields of electrical and radio engineering, than to the fields of lasers or THz systems. Lastly, yes, I completely agree that such hardware might be interesting in many cases. But claiming that Real Computation is possible as oppossed to just admitting that small analog computers are occasionally useful is far fetched. Claiming that such hardware can be built when it flies in the face of everything we know about physics is like claiming you can build a perpetual motion generator.

As I said, extraordinary claims require extraordinary evidence. Originally they were the size of a large room, consuming as much power as several hundred modern personal computers PCs. The Z3 was an electromechanical computer designed by Konrad Zuse. Finished in , it was the world's first working programmable , fully automatic digital computer. At the same time that digital calculation replaced analog, purely electronic circuit elements soon replaced their mechanical and electromechanical equivalents.