Started reading this but didn't get very far before I found myself objecting:
The analog's main characteristic is not in terms of continuity vs discontinuity but it's basis in analogy, which both analog systems and digital systems are capable of coding. For example, both analog and digital cameras create images analogous to the optical images otherwise falling on their respective sensors. It is only with the growth of digital systems (characterised by discrete encoding) that the older analogy systems will be distinguished from the newer analogy systems by this continuity/discontinuity distinction.
In other words it is a digital-centric position to characterise the difference between the analog and the digital in terms of continuity vs discontinuity. In short, the digital (the discrete) is no less capable of analogy. But even more more important is that in analog systems, such as a photochemical image, there are discontinuities. Indeed light itself is characterised in terms of discontinuities called "quanta".
Another important point is that the so called "non-substantial" or "conceptual" relationship between discontinuous components (such as between photon detections, pixels, or frames in a film) are in fact physical relationships. They are not (as otherwise suggested) any less substantial, or more conceptual, than any other relationship that might be suggested. This is because information is physical, be it in the form of discrete information (such as photon detections) or otherwise represented in terms of a continuous signal (such as a wave function).
What then would be the non-analogous? The answer might be given in the two sides of any coding system: the encoding, and the decoding. It doesn't matter if this is done by analog or digital means. Between that which is encoded and it's subsequent *decoding* will be what we might call the analogous relationship. But between that which is encoded and it's subsequent *encoding* will be a non-analogous relationship. For example, an exposed and processed film is not analogous to the image used to expose the film. To recover the analogous component of the film (the image) requires decoding the film, which involves (amongst other things) shining light through the film.
When otherwise sitting in a film can, the image is sitting in an encoded state. The relationship between the film in a can, and the image (be it the source image or destination image) is a non-analogous relationship. The same can be characterised in the digital domain. In a digitally encoded state the encoding (bits in memory) is in a non-analogous relationship with the image. When the bits are decoded (involving display technology) it is the reconstructed image which is analogous to the original image.
The difference between traditional analog systems and newer "analog" systems, such as digital, is not in terms of continuity vs discontinuity but in terms of random sampling vs regular sampling. Between a statistically regulated system and a mathematically (or numerically) regulated one. It is this distinction which plays the far more important role in hybrid analog/digital systems (such as analog capture/digital distribution). It is not continuity/discontinuity distinctions.