Look deep enough, and every modern digital circuit is emulated by an analog circuit, just because the components are analog in their nature, and the 0s and 1s are an interpretation of analog data. That includes digital computers.
Does this make digital computers inherently unstable? Clearly, simple enough computations both of digital and analog kind are good enough to be useful. So there must be a breaking point further away, but on what axis?
A transmission line accumulates noise at it increases in length. Eventually the signal to noise ratio is too high. In old school analogue comms, the solution is to decode the signal to the digital domain before it reaches that point, which allows us to drop the noise. Then the data is reencoded back to a clean analogue signal again.
In digital logic, this process happens at every gate. Hence the reliability of digital logic.
Analogue logic doesn't do this. So analogue logic is only useful if the noise introduced at each step is lower than the error from your source data was already (at whatever point in the computation you have reached). If there is a way round this, I don't know it.
There is a way around this: discretize your values. That's how analog calculations can be a basis for digital calculations.
That's why I think the original comment was about a specific, limited meaning of "analog computation" that does not allow for emulating anything digital. But I struggle to come up with one that doesn't throw the baby of being universal out with the bath water of emulating digital computations.
Exactly! And under that lens all fundamentals applying to analog also apply to digital: that they are inherently unstable and that noise will always win in the long run.
Which sounds at the very least imprecise to me, considering that I'm writing it on a digital (and therefore analog) computer.
In fact, Von Neumann proved mathematically that it's possible to build a reliable system out of unreliable components. But, modern digital logic uses a simpler mechanism: the thing you are missing is that noise does not propagate or accumulate in discretize (digital) systems, as long as it remains below a threshold, and circuits are designed so that it is far below the threshold.
Look deep enough, and every modern digital circuit is emulated by an analog circuit, just because the components are analog in their nature, and the 0s and 1s are an interpretation of analog data. That includes digital computers.
Does this make digital computers inherently unstable? Clearly, simple enough computations both of digital and analog kind are good enough to be useful. So there must be a breaking point further away, but on what axis?