More from this great site presenting the work of David Bohm.

**Will Keepin, Ph.D.**

An inquiry into the nature of order was a central theme that persisted throughout David Bohm’s work. To understand why Bohm undertook a study of order, it is important to step back a moment and survey the evolution of his thinking.

**Evolution of Bohm’s Thinking**

Bohm began with the troubling concern that the two pillars of modern physics–quantum mechanics and relativity theory–actually contradict each other. Moreover, this contradiction is not just in minor details but is very fundamental, because quantum mechanics requires reality to be discontinuous, noncausal, and nonlocal, whereas relativity theory requires reality to be continuous, causal, and local. This discrepancy can be patched up in a few cases using mathematical “renormalization” techniques, but this approach introduces an infinite number of arbitrary features into the theory that, Bohm points out, are reminiscent of the epicycles used to patch up the crumbling theory of Ptolmaic astronomy. Hence, contrary to widespread understanding even among scientists, the “new physics” is self-contradictory at its foundation and is far from being a finished new model of reality. Bohm was further troubled by the fact that many leading physicists did not pay sufficient attention to this discrepancy.

Seeking a resolution of this dilemma, Bohm inquired into what the two contradictory theories of modern physics have in common. What he found was undivided wholeness. Bohm was therefore led to take wholeness very seriously, and, indeed, wholeness became the foundation of his major contributions to physics, as well as his distinctive epistemological style of scientific inquiry. In this respect, Bohm’s developmental process was similar to Einstein’s in creating relativity theory: Einstein took* seriously* the experimental observation that the speed of light is the same in all reference frames. This–when coupled with the premise that the laws of physics should be the same in all reference frames–required that space and time could no longer be absolute; hence came the theory of relativity. No one before Einstein had been willing to contemplate something so radical.

Bohm’s postulate of undivided wholeness is equally radical, but for a different reason: it questions the prevailing assumptions about order and fragmentation. Just as Einstein was the first physicist to seriously question our understanding of space and time, Bohm is the first physicist to seriously question our understanding of order. The implications are far reaching, because the very essence of science is a quest for natural laws of general applicability, and the* sine qua non* for such laws is the existence of natural order. Hence, to inquire into the nature of order is to inquire into the foundations of science itself.

In his characteristic way, Bohm went well beyond the bounds of physics in this quest. During the 1960s, he made a systematic inquiry into the nature and function of order in art, and he maintained a seven-year correspondence with American artist Charles Biederman. His correspondence with Biederman focused in particular on order in the paintings of Monet and Cezanne, and this was the seed for the insights described in the next paragraph. Bohm concluded at the time that the order in a painting is equivalent to the order in quantum theory, to which he gave the name the implicate order.

**Topology of Order**

Bohm’s contributions on order are complex and sophisticated, and they are worthy of thorough study that goes quite beyond what can be included here. Nevertheless, even a cursory glimpse of his thinking is very worthwhile. Bohm proposed that through our perceptions of similarities and differences, we create categories that are the precursors to order. For example, because some creatures transport themselves through air while others do so through water, the categories of birds and fish are created. Each of these categories is refined further, based on perception of finer differences. So we create the categories of sparrows, crows, hawks, eagles, and so on, as well as the categories of minnows, trout, salmon, and sharks. Now observe that the difference between a minnow and a trout is similar to the difference between a sparrow and an eagle (being in this case the difference of relative size). This introduces a notion that Bohm calls* similar differences*, which can be used to define an order that cuts across various categories of experience. A striking example would be Helen Keller’s legendary flash of insight, when she suddenly recognized the essential* similarity* of different experiences of water.

A different kind of order could be defined by considering, for example, the similarity between a young bird and a young fish, which is* different* from the similarity between an aging bird and an aging fish. This observation defines an order in terms of* different similarities*. These are simple examples of concepts that Bohm used to develop a sophisticated topology of order in physics. For example, Bohm showed that Newtonian mechanics is encompassed within the definition of order through similar differences, and .Newton’s legendary tale about the apple and the moon was essentially a perception that the order of similar differences in the motion of the falling apple is the same as the order of similar differences in the orbit of the moon. Hence, Newton’s central insight was one of perceiving a* unity of order* underlying the outward manifestation of two seemingly unrelated dynamical systems.

In addition the above concepts, Bohm developed a way to measure the complexity of order. To illustrate this with the simplest of examples, consider the infinite sequence of digits 2525252525. . . This sequence is said to have order of second degree, because* two* items of information (the digits 2 and 5) are required to fully specify the sequence. By the same token, the sequence 264926492649. . . has order of fourth degree, because four digits are required to specify it (namely, 2, 6, 4, 9). Now consider the sequence 601324897. . . What is its order? This is difficult to say. At first glance, it appears to be an arbitrary sequence of digits because there is no discernible order. However, as the sequence continues, we might discover that it is really the following sequence: 601324897601324897601324897. . . in which case it has ninth degree, because the first nine digits are repeated forever. Or, we might find out that it is a sequence of hundredth degree, or millionth degree. Or, the sequence might never exhibit any discernible order whatever, in which case we say it is a sequence of infinite degree. Such a degree we usually think of as a* random* sequence. In any case, notice that we must know the* context* to determine the order of the sequence.

**Randomness Dependent on Context**

The foregoing example hints at a much deeper insight that Bohm developed in a very general context: randomness is not an intrinsic property of the order of a system, but rather* randomness depends on context.*(3) This is a subtle but very important point, which is likely to have powerful consequences in science for decades to come. An example will illustrate the idea. Consider a “random number generator,” which is a type of computer program that generates a sequence of digits that appears to be random. If such a program is left running day and night, it will generate a sequence that has an order of extremely high degree (or practically “infinite”). Such computer programs work in different ways, but they all share an important characteristic: the process used to generate the sequence is a simple deterministic process.(4) If the program is run again with the same starting number, it will produce exactly the same sequence. Hence, the program that generates this sequence has an order of very low degree. Now comes the essential point. In the context of the computer program, the succession of numbers is determined by a simple order of low degree and, therefore, the order in the resulting numbers is also of the same low degree–which is far from random. However, in a narrower context that includes only the numbers themselves but not the computer program–that is, not the “meta” level–the numbers cannot be distinguished from a purely random sequence, and so the order of the numbers is essentially random.

From this, it follows that randomness depends on context, a result that Bohm demonstrated consistently in many examples throughout science. Randomness has played an essentially ontological role in science, being deemed intrinsic to certain natural processes. However, Bohm’s findings imply that randomness may vanish whenever the context is deepened or broadened, meaning that randomness can no longer be viewed as fundamental. Bohm’s insights into randomness and order in science are summarized in the following statements (Bohm and Peat 1987).

“Randomness is… assumed to be a fundamental but inexplicable and unanalyzable feature of nature, and indeed ultimately of all existence. . . (p. 134) [However,] what is randomness in one context may reveal itself as simple orders of necessity in another broader context (p.133) It should therefore be clear how important it is to be open to fundamentally new notions of general order, if science is not to be blind to the very important but complex and subtle orders that escape the coarse mesh of the “net” on current ways of thinking. (p. 136)

**Order in Science**

The implications of this are potentially very far reaching for all of science. The new field of chaos theory has rigorously demonstrated that in virtually all nonlinear deterministic systems (which characterize most scientific models of physical processes), there is a domain in which the system behaves as if it were random, even though it is actually deterministic. The epistemological implications of this are sweeping: in any discipline of science, when scientists describe the behavior of a natural system as* random*, this label may not describe the natural system at all, but rather their degree of understanding of that system–which could be complete ignorance. Random empirical data provide no guarantee that the underlying natural process being investigated is* itself* random. Thus, while “randomness” may usefully characterize the empirical* observations* of the natural process, this reveals little about the actual nature of the process. Hidden orders or subtle variables may be operating at a level that is beyond the ability of current instruments or concepts to detect. The far-reaching implications of this are evident when one considers, for example, the possibility that the “random mutation” that underpins Darwin’s theory of natural selection may soon be regarded as just one arbitrary hypothesis among many. The observed randomness of biological mutations gives no assurance that unknown subtle processes are not operative–hidden beyond the veil of today’s empirical science. Such unknown forces could include such “taboo” possibilities as teleological factors, divine design, Sheldrake’s morphogenetic fields, and so on.

Bohm’s conclusion about order in science is unequivocal and sweeping: the prevailing mechanistic order in science must be dropped. Mainstream physics–from Newton’s laws to the most advanced contemporary quantum relativistic field theory–all utilize the same mechanistic order, symbolized by the Cartesian coordinate system. This reflects a particular mechanistic order that has characterized physics for literally centuries, and it is this order that Bohm challenges directly. Science must open itself to far more sophisticated and subtle forms of order, including what Bohm calls generative orders, which are orders that generate structure. The implicate order is perhaps the most important example of a generative order.