20. Analog and Digital

     Whatever is "out there" in the wild of the world-in-itself must be tamed by mind in order to be perceived at all. What appears in experience is not wilderness but something domesticated by mind. The nature of the partnership between world and mind can be elucidated through an exploration of the concepts of analog and digital.

     An analog domain must be digitized in order to read it-- for it have significance which can be acted upon. A mercury thermometer, for instance, must be calibrated into units, which give a measurable meaning to the continuous level of the mercury. A thermometer without markings, like a clock without hands, is a perfect analogue of the temperature, but can only roughly and intuitively be interpreted. It tells us only "more or less" the temperature. A digital scale, on the other hand, tells us only "either/or": either the temperature is x or it is not. (If it is not x, the closest to x that it can be is either x+1 or x-1, where x is an integer). The digital is divided into discrete units. It is precise-by-definition, but is accurate only to the limit of definition. The analog is undivided and ambiguous until read by means of a digital scale imposed upon it. It is precise-in-fact, since it maps a function perfectly, but is uninterpretable since it cannot be read.

     An analog domain is concrete and infinitely dense if assumed to exist at all mathematical points (while strictly speaking it is defined at no point). A digital domain is defined only at specific points, which are the boundaries of undefined gaps within it. These gaps, upon closer examination, may be considered analog domains in their own right. The space between markings on a thermometer, for example, can only be estimated until a finer set of markings is applied to it in turn. An analog domain is a territory, while a digital domain is a map-like grid employed for the purpose of relative comparison. The analog is implicit content. The digital is formal, explicit, contentless. The analog is Nature, the thing-in-itself; the digital is artifact, measure and idea imposed upon the world.

     A digital process involves binary decisions. Through a series of cuts in some ensemble of possibilities, alternatives are systematically discarded until but one remains. A digital process is implied whenever there is a mandate to decide, to choose, to discriminate, to reach a state of certainty which rests upon the elimination of alternatives.

     Since action must have a basis in certainty, the relationship of animals to their environment involves binary processes. A plant can draw from the soil and air what it needs just as it needs it, on a continuous basis. It has no possibility and no need to act. While it is true that grazing animals can browse as they require, they enjoy the possibility as well of moving to another location when a food supply is depleted, or of fleeing when threatened by a predator. Hunter and hunted alike are obligated to discrete actions requiring decisions. Relations within the organism may be largely analog, but relations with the world have inevitable digital aspects, because the creature is itself a unit. Information concerning the world must be organized to facilitate choices required by the mandate to act in the interest of survival.

     The concept of information is technically defined as the number of binary decisions required to reach a state of certainty-- to completely specify a unique alternative out of many. But the amount of information presented by a situation depends on how the situation is digitized. A day, for instance, can be divided in two (into a.m. and p.m.), into hours, minutes, seconds, etc. Only one bit of information (i.e. binary decision) is needed to specify the time of day if all that matters is whether it is morning or afternoon. More information is required to pinpoint the time more exactly. If time can be indefinitely divided, the amount of information required for infinite precision would be infinite. In practice, there is a tradeoff between speed and accuracy.

     Digital processes involve a reduction, or "chunking", of information. At any moment, a creature (or other system that depends on making choices) must reduce the plurality of options to a manageable set-- ultimately to one. There are an infinite number of options that Hamlet could have pondered besides whether or not to be: whether to eat or shave, take up mathematics, change his name, speak in tongues, invent a character named Shakespeare, etc. All these choices were set aside in order to formulate what he considered the pressing matter.

     Information must be discarded in a cognitive system; things which are different in detail must be treated as the same. In order that choices can be made between broad categories, irrelevant details ignored, cognitive processes bracket together masses of information, thus reducing the information load on the organism. In this way, we recognize the half-dozen colors of the rainbow out of the continuum of visible wavelengths, sort out domestic plants from a background of weeds, find people likeable or dislikeable.

     What is gained through this chunking is a presentation of simplified alternatives with which the decision maker can cope. What is lost is knowledge of the finer points-- as well as knowledge of the decision-making process itself. An election, for instance, passes through several stages of chunking in which the candidates or issues are pre-selected. The electorate as a whole does not participate in this process, but decides only among the final edited choices.

     Cognitive processes in general involve decision making among a pre-defined set of choices or categories which are accepted as given. This given then appears as an analog domain, concrete and real, an inherent part of the world rather than a prior pre-processing stage of discrimination. The decision maker recognizes the intentionality of participation in the conscious decision , but not that of the prior decisions that went into defining the perceived alternatives. The political issues on the ballot simply appear as the issues. We may be aware of choosing according to our tastes, but are rarely aware of how and why we organize experience into the categories these tastes represent. A man may desire a beautiful woman without understanding the meaning to him of beauty.

     As we have seen, the cognition of any system (including possible intelligent machines) is intentional. A cognitive domain is a schema projected upon the world-in-itself by an intentional agent. A true analog domain has no schema projected upon it, is not calibrated, chunked, categorized, digitized. But if no scale is imposed upon it, it cannot be read or interpreted. It would fall outside any possible cognitive process, and so could not be experienced at all. It would be nothing other than the inscrutable world-in-itself. There is therefore a problem of cognitive domains inherent in the concept of the analog, when conceived as an accessible domain. The analog is actually a product of intentional definition-- a digitation carried out to an indefinite fineness-- but recycled as the aboriginal domain upon which cognitive operations are performed.

     Applied to perceptual domains, the term 'analog' denotes nothing substantial or fixed, but a relationship. There can be no true analog domain in the perceptual process, but only domains which are already chunked and read on differing scales, so that one may appear continuous and dense in comparison to another. In an absolute sense, information is necessarily digital, just as perception is necessarily cognitive. If information is binary choice, then the alternatives chosen from must already have been defined as discrete possibilities.

     Since analog and digital are relative to scale, there is an interplay of these aspects in any system. In particular, it is possible to represent an analog domain digitally to any desired approximation. A TV screen, for instance, gives a digitized representation of an (analog) optical image. The screen could be made up of more or less pictels, yielding a finer or cruder approximation. By the same token, a digital computer can simulate analog processes as closely as desired.

     A nervous system involves a complex interplay of stages of information processing. It is presented initially with an analog display-- for example, an image on the retina. (It could be argued, because of the quantum nature of light, that the optical image is ultimately digital). This image is digitized by the mosaic of the receptors. These, however, do not discharge in a simple digital mode like micro-switches, but with analog aspects, like sending water waves down a canal. Overall patterns are conserved to some extent as analogues of each other in successive stages of processing, while chunking at each stage must be performed on domains that are relatively continuous. At the level of the organism as a whole, the creature makes grossly binary choices, but these rely on a global representation of the environment it inhabits. Its perceptual system begins and ends as an analogue of the world. In between, the system overall is intentional, hence digital.

     A clock with hands is an analog device with a digitized scale. If the face of the clock indicates hours only, there cannot be agreement about the time to the minute, since the position of the minute hand must be estimated by a judgment call. With a digital clock no estimation is called for, or even possible, since a digital clock displays no visible analogue of the passage of time on which a judgment call can be made. From a digital clock that indicates only hours, we can but guess what time it "is" between hours-- and this through a subjective sense of time provided by us, not by the clock. With such a clock, the entire duration of time between 3 o'clock and 4 o'clock is defined to be 3 o'clock. It is either precisely 3 o'clock or it is not 3 o'clock at all-- there is nothing in between. In one sense, a digital readout eliminates uncertainty. But since we suspect that time continues to pass during that hour, in another sense digitation increases uncertainty. If we had no analogic notion of time independent of our digital definition, we would always know exactly what time it is by our digital clock. There would simply exist no time between the defined graduations. But if we believe that digital time is merely a convention, and that all the while a real time is continually passing, then we must view digital time as inexact in principle. Uncertainty is relative to the possibility of a finer-grained cognitive domain.

     The analog/digital distinction parallels that between cause and intention. The causal world of physics appears to us as an analog domain. Nature may be unfathomably rich, or its infinite complexity may be merely an appearance based on limited experience. While we make a distinction between natural and artificial systems, is it conceivable that there are no natural systems-- that what we call Nature is intentional, digital, artificial and limited (even if infinite), a product of our definitions? If a bottom could be found to the complexity of Nature (e.g. truly elementary particles), would this be evidence that the universe is an intentional construct-- a play whose script is the laws of Nature, whose characters are sparsely-defined and therefore fictional? What are we to make, ultimately, of the quantum behavior of matter and energy (and perhaps of space and time)? Is it a property of the world or of our ways of looking?

     The advantage of digital communication is that a message can be repeated indefinitely without accumulating error. Its draw-back is the initial built-in error due to chunking. To put this another way, the advantage of digitation is that only what is intended is transmitted. But this is also its disadvantage, because in one situation some information is gladly discarded as noise, while in another the same lost information may represent a regrettable insensitivity. Digital processes chunk information in order to minimize the complexity and uncertainty of the situation. The stress load of response is reduced by streamlining the representation of the world. But in the long run the stress load may be increased if the oversimplified map corresponds too poorly to the territory.

     An analogic mode of response may be adequate in equilibrium situations, when there is unlimited time to adjust perfectly to changes in a basically stable environment. In pre-literate societies, for example, cultural knowledge is global and ubiquitous; everyone is a competent and relatively interchangeable member of the collective. But in crises-- or in rapidly changing societies, such as our own, which are virtually in perpetual crisis-- the analogic mode of thought cannot deal with the flux of information. Cultural knowledge must be specialized, chunked, processed in hierarchies. Specialized experts are needed to deal competently with increasingly delineated areas. The rest of us must be content with cliches, with highly simplified popularizations of the experts' models. This poses a problem for democracies in the modern world, which are supposedly directed by the will of the people rather than technocratic elites.