As an example, consider water rolling down hill. (Let’s keep the volume small, a gentle trickle and not a Biblical deluge that’s about to wash away an entire town.) In a sense, nothing could be simpler. It just is what it is, and it moves naturally and without calculation. Things only get complicated when we start to analyze the phenomenon; depending on the granularity of that analysis, things will rapidly become intractably complex as our equations of analysis become non-linear in their form. Non-linear equations enjoy (and we then suffer) the feature of being extremely sensitive to their initial conditions. Trivial changes at the beginning lead to massive differences later on. Konrad Lorenz used the example of a butterfly flapping its wings in Beijing the effects will amplify to a thunderstorm in New York a few months later. This is the famous “butterfly effect.” This sensitivity to initial conditions means it is impossible to calculate very far in advance how a process is going to run. But notice that the complexity is in our equations; the process itself simply runs.
Whitehead touched on this in a way in his book The Concept of Nature (CN), and the basic hierarchy running from the most concrete to the increasingly abstract. The primary divisions of this hierarchy are Fact – Factor – Object. To begin with, note that “Fact” is not this or that particular object that we colloquially call a “fact.” What Whitehead means by “Fact”i is all of reality, all at once; it is a whole that envelops us, even smashes into us like a tsunami (a term I’ve used in publication on numerous occasions.) And Fact is the most concretely real thing of all, the one truly, simply, and genuinely concrete thing there is, because it is all that there is in its most immediate ‘isness.’ Every step away from the concretely real, away from Fact, is an act of abstraction that introduces divisions that do not exist in Fact, but only operate as cognitively valuable tools in our attempts to contain Fact within our concepts.
After Fact comes Factor, which is constituted by those large scale relational structures that can be abstracted from the whole of Fact and more or less handled cognitively as global realities in their own right. The next higher level of abstraction is Object, which is basically comprised of objects in the ordinary sense. But objects (and Object) are abstractions, and not primary realities. The objects of Object are where the staggering and frequently intractable complexities of our theories really begin to manifest themselves. The thing to understand here is that these abstractions are not “falsifications” of the real, but they are abstractions from the real: as such they are not “the real,” they are not Fact, in themselves. They have distanced themselves from the ultimate, self-contained “simplicity” of Fact. Thus Fact is “atomic” in the ancient Greek sense of the word, which meant “uncut,” “undivided.” And that which is undivided is, in a very real sense, ultimately simple. But, of course, undivided in Fact does not preclude division in concept and analysis.
Whitehead’s discussion wasn’t specifically directed at the difference(s) between simple and complex, but rather to the analysis of how and why scientific inquiry and abstractive reasoning worked. The nuanced version of realism that he developed was a position I began calling “radical realism.” This is a deliberate homage to William James’ concept of “radical empiricism,” which Whitehead’s position extends with his vastly deeper concept of relational realities and their manifestations in experience. But Whitehead’s position – as continued and further developed in Process and Reality (PR) – still bears some interesting connections to some very ancient notions about the simple and the complex.
Thus, as Randy and I argued in our book The Quantum of Explanation, Whitehead’s discussion of “atomic occasions” has been widely misunderstood by much of the secondary literature. Because of how the term “atomic” has been incorporated into science, many people assumed that Whitehead was referring to micro-physical events when he spoke of atomic occasions. It probably didn’t help that one of Whitehead’s favorite examples here was that of an electron, though since his characterization of an electron was as a field of effects that occupied and “felt” the entire universe, a certain measure of caution was still called for. In any event, as his discussion of Fact in CN helps clarify, Whitehead was using “atomic” in the above mentioned sense of the original ancient Greeks: he means an undivided whole. (This is also made unambiguously clear by the fact that Whitehead is adamant that his speculative philosophy in PR is logically prior to any considerations of measure. So speaking of something being “micro” physical, which is by definition measure dependent, is literally meaningless at this stage of thought.)
For the Greeks, anything that was atomic (in their sense) was also an “ultimate simple.” Because for them, that which was undivided was indivisible – it had no parts, and thus was absolutely unitary.ii Whitehead’s discussion of what can be divided in analysis versus what is undivided in Factiii helps us see how a whole that is “simple” as that which it simply is, and is yet wildly complex as a subject of analytical differentiation and abstraction. One can also see here why it is that Whitehead never pursued set theory in his analyses, even though that would seem like the “logical” next step, him being one of the coauthors of the Principia Mathematica and all. But having nursed the monster for ten years along with Bertrand Russell, and then paid for its publication at Cambridge out of his own pocket, Whitehead was well and thoroughly done with the thing. His work required an analysis of part-and-whole that was not reducible to “atomic” elements, as in set theory. Consequently, he became one of the two modern re-inventors of mereologyiv (which, after some criticism, he turned into his own unique mereotopology.) Here he was able to develop a theory of mutually interdependent parts and wholes, in which the parts had no minimal “unit,” nor did the whole have any ultimate “container.”
I’m convinced that Whitehead is correct about Fact-Factor-Object, and the real direction from the concrete to the abstract. But for all of that, I have no dog in the fight over whether complexity is ontologically real – a matter of Fact in itself – or strictly (or even only mostly) conceptual – a matter of our analysis. I think it is worth being aware of the puzzle, but I’m not sure the puzzle is interesting beyond that. Because whatever side one takes, the only way we can measure complexity is in our analyses. I’ll pick this up in part 2.
– – – – – – – – – –
i For purposes of clarity whenever I use the term “Fact” – or, for that matter, “Factor” or “Object” – in the Whiteheadian sense, I will capitalize the word. Hopefully, none of them will ever begin a sentence, and thus commence grammatical gymnastics.
ii I’m mashing up a lot of nuances here that will cause my former professors and no few of my peer academics something akin to apoplexy. But if you think you can express a Ph.D. of subtlety in a 1500 word blog post, then I can only wish you the joy of trying.
iii Aristotle also discussed such notions at length. Hopefully the enthusiasm with which I was being damned to hell previously is abated slightly with this note.
iv The other inventor was the Polish logician Lesniewski, whose work predated Whitehead’s by several years. But Lesniewski’s publications were all in Polish, and were not available to English speaking audiences until decades later when Alfred Tarski migrated into that world.