I'd have to give him the point there. At SOME level, everything is digital. With tape, each grain is a discrete entity although, as I recall, the alignment is not an either/or proposition. Each atom (or is it molecules?) has a discrete "field strength", but can still be aligned in a pretty much infinite choice of directions. How (statistically) all the atoms are aligned will determine how the grain they make up is magnetized (if they're random, then it will be "null" because they all cancel out; if they're all lined up one way, then it will be strongly magnetized in that. Now, at a larger scale, the magnetic field on that area of tape will depend on how strongly all the GRAINS are magnetized, and how consistently THEY are lined up. So you have two levels of granularity, all resting on a very small discrete (digital) basis. I suspect that, the stronger the applied field, the stronger each GRAIN is magnetized AND the more exactly they are aligned - both.The magnetic "signal" is strongest when all the particles in a given area are "fully magnetized" AND are aligned in precisely the same direction.
In any case, however, there is a "digital bit grain", and that is the individual magnetic domain (the atoms). Above that is a SECOND digital grain, the size of the grains. Likewise, vinyl records are obviously digital as well, since they are composed of molecules.... therefore, under a powerful enough microscope, vinyl isn't smooth at all
Even worse, most of it has plain old lumps (both because plastic molecules are HUGE in the scheme of things molecular, and because most records include all sorts of recycled crud anyway, not to mention how well - or not - the original petroleum which they are made from is filtered and homogenized. All together, we call that SURFACE NOISE..... which has a rather close resemblance to a specific "random" dither pattern.) You could figure it out and model it, if it mattered, by analyzing which way the lumps are usually arranged.
The term "quantization" is really just a general term that refers to fitting analog distributions into number "bins". Long before digital AUDIO, quantization was a major subject for storing pictures. The GIF format only allows 256 colors, so photos, with an infinite number of possible colors, don't fit very well. (GIFs can have only 256 colors, but you can pick WHICH 256 you want for a particular GIF from a much larger palette.) The quantization algorithm was what you used to decide WHICH 256 colors would work best for a given GIF, and the quantization error was the difference between what you started with and what you ended up with - due to the granularity (and inaccuracy) of the bins you were required to "force" the original colors into. The best quantization ALGORITHM was the one that could pick 256 color bins for YOUR GIF that were able to store all the colors in your original photo while producing the LEAST error between the resulting GIF and the original. Likewise, "quantization error" would be a fair way to describe the difference between the values stored in a digital file and the original analog numbers they represent (this is BEFORE any errors generated during reconstruction). With color, the problem end sup being very complex and "multi-dimensional" by most representations. With digital audio, you just increase the bit depth (and so make "the bins" smaller, and so make each error smaller) - which you can arbitrarily continue to do forever - or until you are as close as you need to get to perfect.
The thing that most analog proponents don't seem to realize is that, for a 24 bit digital file, the errors introduced due to quantization error are already SMALLER than the errors (noise) you get on a record from the individual grains of vinyl (which is why the S/N of even a very good record never gets even close to the 124 dB or so you get with a "perfectly recorded" 24 bit digital file).
Tom-There is nothing digital about analog. I also don’t agree with your use of the word “quantization” with regards to analog waveforms. Quantization is used to describe a digital process for recording digital audio. Sometimes in the interest of making a simple analogy, we can try and jam a square peg into a round hole and say the square peg is now round, but that doesn’t make it true.
Analog represents the continuous recording, storage, and playback of waveforms, not waveforms that are recorded digitally in discrete bits that are later reconstructed into analog waveforms.
