Henry, Sorry, but in my opinion, you and John Ellison are wrong. "Wrong" in the sense that your and his analysis is very incomplete. "Signal loss" due to R is not the only thing to consider when comparing transmission along a single piece of wire from A to B to transmission of the same signal across several different pieces of wire, interrupted by several physical connectors along the way from A to B.
First, your analysis, and John’s, assumes that resistance across a connector is zero. Of course, it is not zero; it is some number of Ohms that would and should be added to your and his calculation of total resistance. This will be different for every connector along the way and also dependent upon its cleanliness, the use of contact enhancers, etc. (And by the way, do you also mean to say that all connectors sound the same and that all connectors are tonally neutral?)
Second, at each physical connection in the interconnected second circuit there is introduced a capacitance and an inductance that would be expected to affect the signal in (admittedly) tiny ways. And finally, I would predict that the pure effect of wire R must not be so audible as perhaps are connectors per se. To support my contention, I would point out that many audio circuits deliberately introduce much larger values of R in series with the signal, in the form of physical resistors to prevent oscillation. In tube circuits, this is called a "grid-stop"resistor. Tubes with very high transconductance typically require a grid-stop resistance of at least 100 ohms. In many phono stages, there is a 100-ohm or higher value grid-stop resistor right after the input connection to the first gain device (tube or transistor). Transistors have much higher transconductance than tubes, typically, and also require "gate-stoppers". The value of these Rs, which are also in series with the signal, is many thousands of times the resistance of the wire. You might argue that if we could get away with removing these latter physical resistors, we might hear the difference, but we cannot do that, and their value in Ohms completely swamps R of the wires and any connectors as well.
As to audibility, I have come to the conclusion for my own purposes that high quality headshells with cleaned and contact-enhanced connectors have no detectable negative effect as compared to a straight shot from cartridge to phono input, for MM or MI cartridges. But I have heard faint differences between the two alternatives, in favor of the straight through connection, for very LOMC cartridges. So, for my LOMCs, I try to use either one of my two tonearms that provide the direct wire connection, my Triplanar and my Reed. Surely, you cannot demand scientific proof that someone other than yourself is hearing a small difference in a situation such as this. It is equally OK then to ask you for "scientific proof" that the use of headshells and a plethora of connections is superior. I am sure that the small difference I hear is measurable, but I have no idea how to measure it. It does not seem to be so simple as an effect on frequency response.
First, your analysis, and John’s, assumes that resistance across a connector is zero. Of course, it is not zero; it is some number of Ohms that would and should be added to your and his calculation of total resistance. This will be different for every connector along the way and also dependent upon its cleanliness, the use of contact enhancers, etc. (And by the way, do you also mean to say that all connectors sound the same and that all connectors are tonally neutral?)
Second, at each physical connection in the interconnected second circuit there is introduced a capacitance and an inductance that would be expected to affect the signal in (admittedly) tiny ways. And finally, I would predict that the pure effect of wire R must not be so audible as perhaps are connectors per se. To support my contention, I would point out that many audio circuits deliberately introduce much larger values of R in series with the signal, in the form of physical resistors to prevent oscillation. In tube circuits, this is called a "grid-stop"resistor. Tubes with very high transconductance typically require a grid-stop resistance of at least 100 ohms. In many phono stages, there is a 100-ohm or higher value grid-stop resistor right after the input connection to the first gain device (tube or transistor). Transistors have much higher transconductance than tubes, typically, and also require "gate-stoppers". The value of these Rs, which are also in series with the signal, is many thousands of times the resistance of the wire. You might argue that if we could get away with removing these latter physical resistors, we might hear the difference, but we cannot do that, and their value in Ohms completely swamps R of the wires and any connectors as well.
As to audibility, I have come to the conclusion for my own purposes that high quality headshells with cleaned and contact-enhanced connectors have no detectable negative effect as compared to a straight shot from cartridge to phono input, for MM or MI cartridges. But I have heard faint differences between the two alternatives, in favor of the straight through connection, for very LOMC cartridges. So, for my LOMCs, I try to use either one of my two tonearms that provide the direct wire connection, my Triplanar and my Reed. Surely, you cannot demand scientific proof that someone other than yourself is hearing a small difference in a situation such as this. It is equally OK then to ask you for "scientific proof" that the use of headshells and a plethora of connections is superior. I am sure that the small difference I hear is measurable, but I have no idea how to measure it. It does not seem to be so simple as an effect on frequency response.