In property law, there is a distinction drawn between two processes which can redraw a shoreline or riverbank and, consequently, redraw the geographic lines separating two pieces of property, or one political jurisdiction from another. The two processes are accretion and avulsion, and the distinction between them is a question of time. In accretion, the line between land and water shifts slowly, imperceptibly, as sediment is deposited or washed away year after year. When accretion occurs, the property line or the jurisdictional border changes with the land itself. If a sand bank grows by ten centimeters over a hundred years, the person who used to own the property reaching up to the former water’s edge will now own ten centimeters more land. Avulsion is the opposite: the rapid, sudden, catastrophic redrawing of a land-water border, as in a hurricane or a flood. Here, the border remains fixed in an abstract planar geometry at the location where the former shoreline ran. Therefore, if a piece of beachfront property gains a hundred feet of new sandbar after a violent storm, the property owner does not gain title to this new extension.
There is no material distinction between accretion and avulsion; both involve the same mundane process of dirt or sand or clay being picked up and moved from one place to another. The only difference is how this change occurs in relation to our human-scaled perception of time and mutability. The accretion principle is a basic extension of the ontological principle of object permanence: namely, things that do not seem to change very much or very rapidly remain ontologically the same thing. Of course, everything is infinitely changing, not just shorelines. My own property has no water borders, but it is defined in one corner by an iron pin. That iron pin is moving at some tiny, imperceptible rate nearer or further away from the street centerline, and meanwhile all the other points of definition on my property are constantly moving too, gradually slouching down the hill or stretching through the infinitesimally minute process of crustal deformation. Because these changes are so imperceptible, we do not account them changes at all, and so the border one day is the same as the border the next and the border ten years after that—even though, if we could measure with a close enough precision, we would find those borders changing every second.
This is true of the “borders” that define all objects. My own body is losing and gaining atoms at all times, in constant flux with the world around it, so that if we were to look closely enough and at a fine enough temporal resolution, we would struggle to define any concrete boundary between the spatial area “is” my body and what “is not.” As Whitehead put it regarding Cleopatra’s Needle: “Where does [it] begin and where does it end? Is the soot part of it? Is it a different object when it sheds a molecule or when its surface enters into a chemical combination with the acid of a London fog?”
In contrast to the principle of object permanence, which states that slow, gradual changes are not really changes at all, in avulsion the object itself changes, because the transformation occurs before our very eyes. When a storm forces a river into a new course, we can still vividly remember where the old course was. Such a process results not in a continuous transformation of the same object, but the ontological destruction of the former object and its replacement by another. This is similar to the Ship of Theseus paradox: if we replace all the parts of a ship little by little over a long period of time, it remains the “same” ship. If we destroy a ship all at once and then build a replica to the exact same specifications, it is not the same object but a new object entirely. Why?
The best conclusion is that nothing is ever really the same object at all, and that it is only an approximation within the spatial and chronological scale of human experience that we call one object in space-time the “same” as another object in space-time. My house today is not the same object as my house yesterday, but a new object whose list of changes, if I could perfectly document them, would be innumerable. Similarly, my laptop changes at every keystroke, and my self—the illusion of “self-sameness”—is in fact no stable thing at all, but merely the appearance of spatial-chronological stability.
Accretion is essentially the rounding-down of small changes to no change at all. If the border between my property expanded a millimeter every decade, it would still be the “same” border—and in about 200 billion years, my property would be the whole globe.
Our distinction between what happens rapidly and what happens gradually is at the root of numerous other distinctions. If people move from one place to another rapidly, in large numbers, then we call them “migrants” or “displaced persons” and subject them to a special and demeaning class of citizenship laws, because their move from one place to another has transformed them before our very eyes, startled us, created “something new.” If populations spread gradually, little by little, however, as for example in the peopling of Europe during the Paleolithic period, then we account that change as a natural, continuous change in the same object. What is the difference between a Dutch person on the shore of the North Sea and a Syrian person in the same place? Nothing more than the specious legal distinction between accretion and avulsion.