Metaphysics and Number
In the early 1700′s, the French Jesuit Joachim Bouvet introduced Gottfried Leibniz to the Chinese Classic, the I Ching.
Following a dispute between Pope Clement XI and the Chinese Emperor Kangxi, Bouvet’s attempts to reconcile ancient Chinese wisdom with that of the Catholic tradition came to an official conclusion.
Kangxi’s decree on the dispute stated:
“Westerners are petty indeed. It is impossible to reason with them because they do not understand larger issues as we understand them in China. There is not a single Westerner versed in Chinese works, and their remarks are often incredible and ridiculous.”
Leibniz, however, welcomed Bouvet’s efforts, and found the mathematical structure of the I Ching to be of great interest.
Leibniz was still seeking historical and theological justification for his metaphysics when the prominent Jansenist theologian Antoine Arnauld abruptly broke off their correspondence, remarking to their liason, the Count Ernst von Hessen-Rheinfels:
“I have received, Monseigneur, the metaphysical thoughts which Your Highness sent me from Mr. Leibniz as a witness of his affection and his esteem for which I am very grateful to him. But… at the present time I have such a bad cold that all that I can do now is to tell Your Highness in a couple of words that I find in his thoughts so many things which frightened me, and which, if I am not mistaken, almost all men would find so startling that I cannot see any utility in a treatise which would be evidently rejected by everybody.”
Although the initial reasons for Leibniz’s interest in Bouvet’s work with the I Ching were mathematical, the metaphysical and theological dimensions were not insignificant.
Leibniz’s willingness to investigate and blend disparate belief systems within the context of Catholic theology bears a resemblance to Christian Gnosticism, which synthesized wisdom from Gospel and Tanakh traditions with Mithraic and Persian concepts to a more visible degree than the Nicene Church. The mildly Gnostic flavor of Leibniz, however, is probably less a product of specific Gnostic beliefs, and more a product of his methodology’s resemblance to Gnosticism as an example of syncretic practices in Christendom. Which is to say: the Gnostic flavor of Leibniz is not so dissimilar from the Rabbinic flavor of Pascal.
As Leibniz traversed theology, psychology, and quantitative science, he stumbled upon what he could only have considered to be a marvelous fragment of ancient Chinese wisdom: a snapshot of what might be described as analogous to the Book of Genesis in Taoism. To Leibniz’s syncretic sensibilities, as he investigated what has since been divided into the secular and the sacred, this thread of Chinese thought must have seemed eerily familiar. What Christian syncretism contributed to the history of Western Thought, in certain respects, is not so different from what happened in the history of Taoism as the traditions built around the Daodejing became an institutional religion in China (incorporating ideas from Buddhism, searching for political reconciliation with Confuscianism, and re-incorporating alchemical principles from its shamanic roots).
My book of Leibniz’s writings contains his Metaphysics, Monadology, and Correspondence with Arnauld; the printing is from the 1960′s but the translation is from 1902. The translator’s 1902 introduction, by a philosophy professor then at Yale, addresses the 2000-year-old debate between Western natural philosophers who conceived of matter either as atomistic or as an infinitely-divisible continuum. It’s illustrative of Leibniz’s intelligence to read the translator’s introduction discuss the nature of atoms — just ten years before Niels Bohr modeled the hydrogen atom based on the results of 19th-Century spectroscopy (Newton, with whom Leibniz collaorated on the development of calculus, was also big on spectra. Leibniz’s faith in a reality that is strictly perceptual — yet for the most part imperceptibly so — mirrors Newton’s faith in an invisible and mechanically inexplicable force of gravity that can nevertheless be described with great mechanical precision).
Vestiges of Leibniz continue to haunt contemporary science: a 1995 paper by Max Tegmark called “Does the Universe In Fact Contain Almost No Information?” examines certain cosmological problems from the perspective of quantum mechanics (the fundamental equations of which don’t really care whether time goes forwards or backwards, and which has yet as a scientific program to formulate a coherent theory of gravity) interpreted through the vocabulary of algorithmic information theory.
Algorithmic information theory holds that the information content of a system can be understood in terms of the shortest possible description of that system. A series of 100 letter R’s can be foreshortened by the statement: “100 R’s”; whereas a series of 100 randomly-alternating R’s and Q’s will contain few regularities, and therefore will not admit a shorter description than the full series itself; in this way, the sequence of randomly alternating R’s and Q’s is understood as having a higher information content (which is in turn related to systems theory and thermodynamics through studies on entropy conducted by Claude Shannon, Warren Weaver, and Ludwig Boltzmann).
This has a number of interesting consequences; for example: information can be measured as a quantity like speed. However, either through the metaphysical constraint that what is infinite is by definition incapable of being measured, or in the sense wherein the Copenhagen Interpretation of Quantum Mechanics holds that the measurement apparatus becomes the object which is quantified by one’s measurement rather than some other “external” subject, the nature of measurement itself implies an absolute upper-limit to how complex information can be (just as there is a limit to the speed with which objects can traverse quantifiable space-time, which is found in Einstein’s most famous equation: that is, when a sequence of values admits no shorter description than the sequence itself, one has encountered the “speed of light” for complexity). This is related to why, in practical computing, some files can “compress” smaller than other files.
It is worth noting in this regard that the number pi — the ratio of a circle’s circumference to its diameter — although an irrational number (that is, a non-ending and non-repeating decimal sequence) contains relatively little information because it can be most precisely represented as a constant ratio.
So the thrust of Max Tegmark’s argument is really that the fundamental laws and conditions of the Universe might quite possibly be very simple; and that the complexity we see around us might be a sort of illusion, the product of processes metaphysically not unlike what happens when we try to reason about pi based on its decimal sequence rather than its ratio form. Tegmark discusses this possibility in teleological terms not unlike those used by Leibniz: demonstrating that one can reasonably suppose the Universe to be mechanistically evolving towards some definite state.
Tegmark ends with a consideration of pessimistic and optimistic interpretations of this possibility: that it amounts to a humiliation for humankind, that we see only complexity and confusion everywhere there is really only order and simplicity; that even the “grandeur” of reality is in a sense illusory. And he speaks with optimism that if we “force ourselves” to “restrict our value judgments to empirical considerations, the picture put forward here would have quite positive implications for our ability to do science in the future.”
Tegmark is studying the Cosmos; a literal meaning of Cosmos — from the Greek — is “ornament.” Tegmark’s identification of aesthetic grandeur with complexity bears a distinct bias that was not found in the ancient Chinese philosophy which Leibniz stumbled upon while working out his elegant system of binary arithmetic (which today is taken for granted every time anybody uses a cellphone or a computer). The highest Grace in that lineage of Chinese thought is simplicity: the image of the “uncarved block” found in the Daodejing.
One finds in Leibniz the following passage in his considerations of infinity in Pascal:
“The basic ‘almost-nothing,’ in coming up from nothing to things, since it is the simplest of things, is also as it were the highest ‘almost-everything’ in descending from the multitude of things towards nothing…”
Leibniz and Pascal each equate the infinitely subtle with the infinitely grand. The simple is grand because it speaks to the ornament in all its grandeur, identifying with its simplicity the essential nature of the ornament. Leibniz, like the ancient Chinese authors of the I Ching, understood quite well how much can be said about what is profoundly simple, about how a grain of meaning in a sea of nonsense can open up a Cosmos…