E11 Perception as acquisition of information

Topic

Perception is fundamentally a process of acquiring, transmitting, and processing information about the environment surrounding the perceiver; Shannon’s information theory provides a precise quantitative framework for this process, wherein each environmental stimulus carries an information content that increases as the stimulus becomes less probable relative to the set of all possible stimuli in that environment. Consequently, the less probable—or more unexpected—a stimulus is within the range of all possible stimuli in that environment, the greater the information content it carries.

According to the Shannon-Hartley theorem, the capacity of a sensory channel—that is, the amount of information it can transmit per unit of time—is limited by both the channel's bandwidth and the ratio of the useful signal to the accompanying noise; this fundamental limit applies equally to the human optic nerve and to any other biological or artificial receptor. Thus, a wider sensory channel bandwidth or a more favorable signal-to-noise ratio results in a higher channel capacity.

Mutual information between an environmental stimulus and a sensor's response measures precisely how much uncertainty regarding the stimulus is reduced upon learning the sensor's response: a perfect sensor completely eliminates uncertainty about the stimulus, whereas a completely noisy sensor does not reduce that uncertainty at all. Consequently, mutual information unifies the evaluation of any sensory system—whether biological or artificial—under a single common metric. The fact that a sensor is noisier means that the mutual information between the stimulus and the sensor's response is lower, and consequently, uncertainty regarding the stimulus remains higher after the response is known.

Both the Weber-Fechner law and Stevens' power law describe—empirically—the relationship between the subjective magnitude perceived by the subject experiencing a stimulus and the stimulus's actual physical intensity; Fechner's logarithmic relationship implies that perception compresses vast ranges of physical intensity into ranges that are far more manageable for the perceiver. The human ear, for instance, covers a huge range of physical intensity in terms of sound pressure, yet perceives it as an approximately linear scale of loudness, precisely thanks to this logarithmic compression described by Fechner. As the physical intensity of a stimulus increases further, Fechner's logarithmic relationship dictates that the perceived subjective magnitude of that stimulus grows much more slowly than the physical intensity itself.

Thus, this model—incorporating the concepts of mutual information and logarithmic compression introduced earlier—quantifies a sensor's discriminative capacity within its environment using signal detection theory: a sensor with sufficiently high sensitivity effectively distinguishes a useful signal from accompanying noise, whereas a low-sensitivity sensor achieves only marginal detection of that same signal. Furthermore, this sensitivity metric is independent of the specific decision criterion adopted by the observer, making it fundamental for comparing the sensory capabilities of different species. Consequently, higher sensor sensitivity results in a greater capacity to discriminate the signal from the noise.

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