Kirkus, I do have a problem with this:
And then there's the source degeneration resistor R4 . . . this is feedback exactly like R2, no? Why is it somehow more okay?
Degeneration occurs in real time against the signal and so is not part of this argument. It is different from loop feedback in that regard and that is why it is 'somehow more okay'.
Further, Nelson has succeeded in building wide-bandwidth amplifiers wherein the passband is unaffected by the addition of feedback, much like our amplifiers are. So the -6 db slope issue does not play into this. Now I have mentioned this before but I see in your responses that you always go back to the rolloff issue. I concede your point that that regard, but don't see it as relevant- it applies to opamps and similar circuits of the type you have described. However I should point out that it is those circuits that do enhance odd orders, so if not my explanation than what is it?
I have avoided the proof in the pudding aspect of all this, but at some point it will come to bear on this in a big way if Nelson's and my explanations are not to be accepted by you, I am hoping you will explain what the phenomena really is, since your explanations so far have not addressed that.
As to Chaos, an initial comment: we are really, seriously, **NOT** talking about *anything* with the word 'quantum' in it! As far as audio goes, use of the word 'quantum' is the nutbag identifier, IMO/IME :) Seriously. Chaos theory OTOH is a science of complex systems, wherein a simple set of rules governs what seems a complex behavior, often with unexpected results.
FWIW, in any field of endeavor, when Choas theory is applied, there is usually a howl of protest from the establishment. That is, until said establishment realizes the actual implications. The result has been improved weather forecasting, improved aircraft efficiency, improved hydraulic pumps, improved genetics, improved disease control, improved exhaust and combustion and now I am suggesting that it can improve audio reproduction as well.
So, to Chaos:
In common usage, "chaos" means "a state of disorder",[19] but the adjective "chaotic" is defined more precisely in chaos theory. Although there is no universally accepted mathematical definition of chaos, a commonly used definition says that, for a dynamical system to be classified as chaotic, it must have the following properties:[20]
1.it must be sensitive to initial conditions,
2.it must be topologically mixing, and
3.its periodic orbits must be dense.
condition 1 is satisfied, as the signal and gain conditions are always different. Even a digital source can't be assumed to be 100% *exactly* repeatable, humidity in the room can affect the way the loudspeakers behave, which will affect the way the amp responds. Keep in mind that we are talking about a wide range of amplifiers here.
There is a great example of how water dripping from a tap is an example of a Chaotic system. People walking in other parts of the building, variations in water pressure, temperature and actually a huge variety of other issues all come into play. The same is true of an audio signal, there are all sorts of variations that affect it as audiophiles are only too keenly aware: line voltage, noise on the line, noise in the environment, warmup of the amp, break-in considerations, interaction of cables, corrosion of components (such as inside semiconductors and inside switches) and connections; this is a list that knows no end!
condition 2 is satisfied by the fact that the bifurcation that arise are not consistent. The problem is the only means we have of analyzing distortion is through steady-state waveforms, which tell us nothing about the dynamic state of the amp.
condition 3 is satisfied by the strange attractor, which is quite dense. I refer you to Norman Crowhurst on that one. His writings may be old, but it would be foolhardy indeed to cast them aside by using the logical fallacy known as 'guilt by association'.
Frankly, given the research I have done, I suspect that Crowhurst is spot on. Occam's Razor suggests that when his writings and Chaos agree on so many points (only a few of which have been touched on here), the simple explanation is that he is probably right. The very complex explanation is that he is wrong, but it just turns out that in spite of that, things behave the way he and Chaos say they do but for entirely different reasons. I think the point of this is that there is a frontier here; I find the idea that we know everything already is arrogance and nothing more.
