Between 1919 and 1922, Whitehead published three works (the “triptych”)ii that are typically classified as “philosophy of science” but would more appropriately be described as “philosophy of nature” or, even better, “natural philosophy.” While the triptych dealt extensively with matters of physical science, the central issue was nature itself and what it means for an activity such as science to produce claims of knowledge about nature. So we do not see issues like the “demarcation problem”iii raised in these books. Rather, his questions were more about nature itself, as a relational whole, and what it means to develop abstractions that select, capture, and properly represent these relational structures of nature. But these works failed in their goal of attracting the attention of the scientific community, and this failure arguably contributed to Whitehead’s “metaphysical turn,” which first announced itself with the 1925 publication of his Science and The Modern World (SMW).iv

By the time of PR (1929), Whitehead’s speculative philosophy was penetrating to depths rarely seen in all of western thought. Nature had never been the “be-all-and-end-all” of reality for Whitehead, and indeed is little more than a peculiar feature of how our “cosmic epoch”v happens to express itself. Other such expressions are possible, even if we are largely incapable of even imagining what these might be. In PR he centers nature upon a more primary logical foundation in which time and space themselves are not fundamental characters of reality, but merely emergent properties of a more primary fundament. That fundament is itself characterized by two main relational structures, prehension and extension. Extension is the one that so many scholars jump over (skip to pg. 337). Two of the sub-characters of extension are strains and flat loci.

Whitehead’s natural philosophy in the triptych backed away from the sweeping assumptions that dominated (and continue to dominate) thought as to the “nature of Nature,” and instead developed a logically more primary theory of mereology (which later developed into his mereotopology in PR)vi which treated both space and time as emergent characters of reality rather than irreducible “givens.” But he later realized that simply situating the material world in his schema of “extensive connection” (developed in the much skipped-over part IV of PR into his mature theory of extension) was not enough to provide a fleshed out theory of nature. Things do not merely occupy extended positions in space and time, they also exercise influences on other things. Contemporary physics breaks these modes of influence out as electromagnetism, gravity, and the weak and strong nuclear forces. There might be more, but these are the ones we’re sure of. In a different cosmic epoch, they would likely be different. But each of these modes of influence characterizes a “tug” – a push or a pull – between two or more regions of extensive connectedness (what I call “exetensa”) that manifests as a strain between them. Thus the theory of strains is a general theory of what in the specific context of current physics we call “forces.” But it is, as noted, a general theory, so it is not limited to the narrow context of just and only physics, or even this cosmic epoch.

Flat loci are where things get fun. Let us start with a simple plane figure, a circle. A circle is known as a “convex” figure, because the shortest line between any two points within the figure (the circle, in this specific example) is itself entirely contained within the figure. But how do you know it is the shortest path? Protesting that you can just see that it is, even with simple plane figures, does not carry any logical of mathematical weight. Consider a shape like the outline of a bell, sealed off at the mouth. Choose a point just inside the widest part, and a second at the top of the throat. Does a line between the two stay inside the “bell”? Even if you draw a line between the two, your straight-edge is too imprecise and your pencil line to thick to draw any legitimate conclusions in any but the most blatant of cases.

Back in our simple case, you can take your ruler (a metrical instrument) and measure the length of the line, and show that all other lines are longer than this one. And this will work well enough with plane geometric figures, but how do you know you’re dealing with plane geometry? This issue comes up in relativity theory: light does not “bend” around a star or other large mass; it is, according to theory, following the shortest straight line, called a “geodesic.” So when it comes to the geometry of space and time, as conceived within orthodox cosmology, your plane geometry ruler is simply wrong!vii

Which brings us to Whitehead’s theory. The theory of flat loci is a non-metrical theory of convexity. “Non-metrical” means it does not take any kind of ruler for granted, for such metrical instruments presuppose what is “flat”; a glance at your typical ruler, and you can “just see” that it has the assumption of plane geometry built into its manifestation of flatness.

Allow that little BB to rattle around inside the ping-pong ball, and see if the cats don’t want to chase it.

Using nothing but the logic of mereology enhanced with topology, Whitehead presents a technique for establishing flatness – hence what will qualify as a “straight” line – at least within the scope of some particular locale. (Or collection of such; the old-school plural of “locale” is “loci.”) I’ll not attempt to explain how this is managed. Even if I felt comfortably facile with Whitehead’s argument, a blog post is not the place for it.

But in any event, this is not merely “interesting,” it is staggering and revolutionary.

And it is ignored.

Because the people who ought to be paying attention to it either skip to page 337, or skip PR altogether.

iThe Quantum of Explanation: Whitehead’s Radical Empiricism, Routledge, 2019. While the book came out after I started this blog, we’d already given that title to the MS. So the blog is named after the book.

iiEnquiry into the Principles of Natural Knowledge (PNK), The Concept of Nature (CN), The Principle of Relativity with Applications (R). All were originally published through Cambridge University Press. The abbreviations in parentheses are standard throughout Whitehead scholarship.

iiiWhich is to say, what separates, or “demarcates”, science from non-science &/or pseudo-science?

ivWe are now able to witness some of the stages of this turn in the recently discovered notes taken by students – many of whom went on to become notable philosophers in their own right – of Whitehead’s Harvard lectures from his time there beginning in 1924.

vA technical term of Whitehead’s that broadly means some “local” manifold of events. Our local manifold, our cosmic epoch, is what we refer to as all of space and time as these manifest themselves in nature.

viMereology is the theory of part and whole. It is much more basic than set theory, in that it does not presume the existence of “elements” – basic units beneath which there is nothing else. Mereotopology incorporates ideas from topology of contact, separation and non-metrical notions of “neighborhood.”

viiI develop these issues with considerably greater detail and care in my book (based upon my dissertation) Whitehead and The Measurement Problem of Cosmology.