Signal to Noise Ratio and TC

I wanted to open up a discussion on signal transmission and information theory, because I think the new tools and theory in this area are very pertinent to Textual Transmission problems.

The first thing an engineer notices in looking at the spread of attestation, is that it is remarkably like something he sees everyday in engineering problems, a signal/noise spread:

From the diagram you can see a typical transmitted signal, and the accompanying noise.

How do we tell signal from noise? One of the very obvious ways, is the distinction shown graphically above, namely, a massive disproportion in the size of the signal (hence signal/noise ratio), and also a complete lack of consistency and uniqueness in the noise. The noise is spread all over the spectrum, cropping up randomly in all different locations and sizes.

These are not "special" features of a 'lucky' transmission signal. These are the constant norm, confronted daily in thousands of different engineering and scientific situations. Even the worst-case scenarios (picture the lousy audio quality on a CB-radio or a cheap walkie-talkie set), show this very blatant dichotomy in quality and nature. Virtually ALL transmission situations exhibit this dichotomy between signal and noise, enabling us to identify with near-certainty at least the bulk of noise components and the likely signal.

Of course signals break up, and suffer losses of information. But even then, the information can often be recovered by clever techniques such as error-correcting codes. Humans have a built-in method of dealing with signal loss, which is very robust without being clever at all:

Trucker 1: "Travelling down highway )(*&*^&^$, over."

Trucker 2: "Repeat please: signal broke up, over."

Trucker 1: "Highway 401, over. "

Trucker 2: "401?, over."

Trucker 1: "Roger that, 401, out."

By simple repetition and redundancy, the message was preserved, checked and transmitted without error, even through an intermittent error-prone transmission line.

Similarly, the NT has four gospels. It first appears that a large amount of error has been transmitted alongside the signal. But the redundancy of four gospels effectively protects the completeness and integrity of the message, in spite of small lapses in transmission at points in the text.

Likewise, Paul's letters overlap and appear redundant in their material. But this redundancy and re-iteration in different words and formats protects Paul's meaning and message. This is an even more sophisticated form of error-protection called "permutational variation of transmission".

From an engineering point of view however, all these situations are ordinary transmission-line cases. There is no reason to think or expect that most errors will not be identifiable and have certain behavioral features, even if we can't with certainty identify every error as an error.

The key point here, is subtle but not difficult with careful consideration. The idea is that we could have a transmission failure occasionally in a system with redundancy and even permutational variation.

But just as probabilities (being fractions) shrink rapidly when compounded (multiplied together), so the likelyhood of being wrong most of the time regarding errors is extremely unlikely, even when the likelyhood of being sure in any specific case of a potential transmission error is very low.

Applied to the Textual problem, we can expect that the majority of mss will preserve the original reading most of the time. This is because although in any one particular case, the majority of MSS could be wrong, the likelyhood of the majority of the majority readings being wrong as a group is extremely low even allowing for the possibility of individual cases of failure.