4.17 Signal Information Distinction

The distinction between signal and information is fundamental to understanding communication in the framework of cybernetic communication theory. A signal is a physical phenomenon: a variation in voltage, pressure, electromagnetic field, or any other measurable quantity that propagates through a medium and can be detected by a receiver. Information, in the technical sense established by Shannon, is the measure of the reduction in uncertainty that a signal produces in the receiver. These are distinct concepts operating at different levels of abstraction, and conflating them leads to confusion about the nature and limits of communication.

A signal exists in the physical world with definite measurable properties: amplitude, frequency, duration, phase, and waveform shape. Information is not directly observable in the physical sense; it is a relational quantity that depends on the statistical context in which a signal occurs. The same physical signal, carrying the same waveform with the same amplitude, can convey vastly different amounts of information depending on what other signals it might have been instead, and how probable each alternative was. If a radio station always broadcasts the same tone, the reception of that tone carries no information despite being a well-defined physical signal. If the same tone appears as one of many possible equally probable signals, its reception carries maximal information for that signal set.

This separation becomes clearest when considering the relationship between signal energy and information content. Physical signals have energy, and transmitting them requires power. Shannon's channel capacity theorem establishes that the amount of information transmissible is bounded by the signal-to-noise ratio, connecting the physical properties of signals to their information-bearing capacity. However, the capacity is a function of the ratio between signal power and noise power, not of signal power alone. A very powerful signal in a very noisy environment may carry less information per transmission than a much weaker signal in a quiet environment.

Multiple different signals can carry identical information, and a single signal can be encoded or modulated in many different ways without altering the amount of information it represents. A spoken word, a written representation of that word, a Morse code equivalent, and a binary digital encoding of the word all carry the same semantic content and, if mapped with one-to-one correspondence to the same source distribution, carry the same amount of Shannon information. The choice of signal is a matter of the physical channel and the encoding scheme; the information content is a property of the source and the statistical mapping.

This distinction also clarifies what it means for a signal to be corrupted. Noise does not directly corrupt information; it corrupts signals. When noise modifies the physical properties of a signal during transmission, the received signal may differ from the transmitted signal, causing the receiver to decode a different message from the one sent. At the information level, this is measured as an increase in the conditional entropy of the source given the received signal, or equivalently, as a reduction in the mutual information between source and received signal. The noise has introduced uncertainty that was not present in the original message, degrading the information content of the received signal.

The signal-information distinction also illuminates the distinction between carriers and content in communication. A carrier wave in radio transmission is a high-frequency signal whose sole function is to propagate through the channel. The information is imposed on the carrier through modulation, altering some property of the carrier, such as its amplitude, frequency, or phase, in correspondence with the message. The carrier has high energy and physical presence, but conveys no information by itself. The information lies in the modulation pattern, in the structured variation of the carrier's properties according to the coding scheme that maps messages to signal variations.

In cognitive and social contexts, the signal-information distinction maps onto the distinction between medium and message. A text message and a spoken statement can convey identical information while being radically different physical signals. McLuhan's observation that "the medium is the message" can be read as a challenge to this distinction: he argued that the properties of the signal medium itself shape the information that can be conveyed through it, implying that signal and information are not cleanly separable in social communication. Cybernetic communication theory acknowledges this complexity while maintaining that the formal distinction between physical signal properties and information-theoretic quantities provides an essential analytical tool for understanding what communication systems can and cannot accomplish.