Magical+Number+Seven

§1 There are three areas of "human information processing" where G. Miller (1956) observes the workings of the "magical number seven plus or minus two". These are (1) the span of absolute judgment ("channel capacity") for "one dimensional continua", (2) subitizing, a handy word for "direct perception of numerosity", or counting with out enumerating, and (3) the span of immediate memory, which is usually thought of as memory for event sequences such as melodies or the digits of a phone number.

§2 Of these three areas, the one I find the most interesting is the span of absolute judgment ("channel capacity") for one-dimensional continua, such as pitch (frequency), loudness (sound intensity), brightness (light intensity), and duration. My preferred way of thinking about the span of absolute judgment is //the number of categories or "places" along a continuum that we can cognitively "keep track of"//, one index of which is the ability to assign names to said places in a reasonably reliable and consistent manner. The paradigmatic example here is the existence of 6-8 "names" for musical dynamic levels, from pianiss(iss)imo to fortiss(iss)imo. When we increase the dimensionality of the universe of objects we are interested in, we get an increase in channel capacity, but it is substantially less than the 7x7x...x7 value we would presumably observe under "ideal" conditions; there are "diminishing returns" with each added dimension, so the story goes.

§3 A complication arises when we take a closer look at the notion of "dimension", and our putative criteria for establishing dimensionality. For example, is pitch one dimensional? On the one hand, clearly we can generate all possible pitches simply by varying the frequency of a tone; but on the other hand, it seems equally clear that musical pitch can be – must be? – seen as having two independent dimensions, height and chroma, the former being rectilinear and the latter cyclical ("pitch class"). The sometimes mysterious and controversial ability of absolute pitch, I suggested, is basically the direct perception of tone chroma. A similar issue can be seen to arise in the visual realm for the case of color: How many dimensions? Even if we take the simplest possible (some would say impoverished) view of color as being a function of the wavelength (1/frequency) of light, which would imply "one dimension", even the simple colors generated thereby seem to fall into a natural circular arrangement, not a linear one.

§4 Backing up, and looking at all three sets of phenomena – absolute judgment, subitizing, and immediate memory – we can ask, as Miller did, whether there is some underlying connection between/among them, that leads all three to be subject to the "7±2" constraint. Miller's answer to this question is negative: a "pernicious, Pythagorean coincidence", he says. On the face of it, this seems right, since there appear to be three distinct mechanisms involved. But I have come to find this answer increasingly unsatisfactory. Although the connection, if there is one, defies easy formulation, that doesn't mean that it is nonexistent. DIfference in mechanism is not by any means a slam-dunk criterion for asserting "no connection", one could counter.