On Uchii Soshichi’s “Monadology, Information, and Physics Part 1: Metaphysics and Dynamics”

Dr. Uchii Soshichi's paper "Monadology, Information, and Physics" (released recently in preprint: http://philsci-archive.pitt.edu/10599/) explicates his informational interpretation of Leibniz's Monadology. This interpretation attempts to reconstruct Leibniz's dynamics, and the metaphysics upon which it is founded, using the terminology of contemporary information theory. The gist of Dr. Uchii's paper is that such reconstruction is a fruitful approach towards attaining a general understanding of Leibniz's system. Part 1 deals with Leibniz's dynamics and metaphysics, and Part 2 with space and time, though it is uncertain how many parts there will be in all. Here I will only take up Part 1. The paper's abstract and preliminary overview may at first seem erratic, in that Dr. Uchii does not so much argue for his interpretation as simply assert it in the form of analogy, but the reader who follows the ensuing discussions will gradually find Dr. Uchii's reading to be convincing. While it need hardly be said that Leibniz did not know concepts such as "transition function" and "recursion," Dr. Uchii's paper gives compelling evidence that Leibniz indeed had in mind, albeit in perhaps a vague and incomplete form, something that corresponds neatly to these concepts. In what follows, I would like to address some points of concern, and then conclude with a few remarks on the fruitfulness of reading contemporary concepts into the thought of great minds of the past.

Deriving Vis Viva from Solicitatio

My first concern deals with a technicality I was unable to understand. In Section 5, where Dr. Uchii discusses Leibniz's distinction between vis viva (living force) and vis mortua (dead force), he takes up the concept of solicitatio, or "infinitely small urge (to motion)." Apparently, solicitatio is an infinitesimal increment of velocity, the accruement of which gives rise to macroscopic acceleration. Now, Dr. Uchii expresses the solicitatio of a falling body by dx, speed by x, and from these, attempts to derive the vis viva (macroscopic acceleration) of the body. For the sake of brevity I shall quote the entire paragraph in question, replacing x and dx with v and dv respectively (pp.16-17):

Accumulation of solicitatio increases the amount of speed, as we have already seen in Figure 2. And the body continues to fall with increasing speed. Thus, the solicitatio needs time to increase the speed, and the body needs time also, for falling with the increased speed (thus, square of time!). So let solicitatio be expressed by infinitesimal dv, speed by v (which increases with time); then, in order to obtain the living force of the body, we have to consider some quantity that depends on the square of time, and that quantity is nothing but the distance the body has fallen; in short, the square of speed, the crucial quantity, is obtained, technically by an integration of product of solicitatio and (infinitesimal) distance. Since Leibniz often ignores constant factor, he uses "v²" for expressing living force, in the letter to de Volder. Of course this corresponds to the kinetic energy of classical mechanics (in the standard notation, mv²/2).

In classical mechanics, kinetic energy is derived by integrating the product of applied force F and infinitesimal distance dx (or dot product in the case of two or more dimensions), i.e. by the operation ∫ F • dx. Using p to denote momentum, this can be rewritten thus: ∫ dp/dt • vdt = ∫ v • dp = m ∫ v • dv. We can therefore see that vis viva is none other than the accruement of the product of velocity v and solicitatio dv (though Leibniz writes v² instead of v²/2). Multiply this by mass m (derivative passive force) and we get kinetic energy mv²/2. Now what I don't understand is why Dr. Uchii writes that "the square of speed, the crucial quantity, is obtained, technically by an integration of product of solicitatio and (infinitesimal) distance." This sounds as though solicitatio were force F rather than infinitesimal increment of velocity dv. And why does he say that the quantity to be derived is "the distance the body has fallen?" Clearly, distance is not energy. What is going on here?

Does Infinite Recursion Give Rise to a Universal Monad? 

An important concept in Dr. Uchii's informational interpretation of Leibniz's system is recursion, by which is understood the iteration of a certain program. Of particular significance is the notion of nested recursion, i.e. the application of a program to itself, in such a way as to give rise to a nested hierarchy of programs, "going down from the single dominant program (corresponding to entelechy) to subprograms, which again controls respective subprograms, and ad infinitum" (p.1). According to Dr. Uchii, although Leibniz never used words such as "recursion" or "recursive function," he was well aware of the recursive structure of both the organization of monads and the phenomenal world (p.33). And the function that is iterated in this recursive structure is that which dictates the elastic collision of bodies (pp.43-48).

Now my concern is this: if recursion—the nested hierarchy of programs—is infinite, then how can there be a single dominant program, above which there is no further program controlling it? Just as the microorganisms in the human body may be considered subprograms under the human entelechy, the human entelechy should be a subprogram within the macrocosm of society, which in turn is embraced by the ecosystem, the solar system, and so on ad infinitum. Do each of these comprehensive programs each correspond to an entelechy? If so, then wouldn’t there be an all-embracing entelechy, a kind of world-soul under which all other monads in the universe are subprograms? This seems to be the logical consequence of the view articulated by Dr. Uchii, but is this the view of Leibniz?

On the Fruitfulness of Reading Contemporary Concepts Into the Thought of Past Thinkers

Reading Dr. Uchi's paper, one may be compelled to ask: what is the point of reading contemporary concepts into the thought of a past thinker? Of course, it helps us to gain a multi-faceted understanding of the thinker in question, but should this be considered an end in itself, or are there further reasons why we should interpret past thinkers in light of new ideas? While Dr. Uchii focuses on understanding Leibniz's system as an end in itself, I can think of one reason why contemporary readers should be interested, apart from a sort of antiquarianism: we can gain insights relevant to today's science. It is simply amazing how far geniuses like Leibniz are able to probe into the depths of reality, and there is no reason to think that we have fully plundered the repertory of fruitful ideas that these giants have spun out of their immeasurable minds. Relationist and information-based interpretations of quantum theory, relationist dynamics, digital physics, background-independent approaches to quantum gravity: these are all areas where the pioneering work of Leibniz will serve as a guide light. Seeing how his system can be translated into the language of today's science should aid us in reconsidering our deep-seated intuitions of fundamental concepts, such as space and time.

Perhaps I am getting ahead of myself, as this is only Part 1 of Dr. Uchii's paper. His follow-up is eagerly awaited.

P.S. [04/14] My first concern was found to be based on a misreading on my part. Dr. Uchii's claim is not that energy=distance (of course), but that kinetic energy is to be derived by integrating force by path length (which, in the case of a falling body, depends on the square of time). Also, contrary to what I wrote, for Leibniz solicitatio actually is a kind of force.