An early diagram of Leibniz’s based on the combinatory principles of Raymond Lull.

By: Jay Dyer

I have written before about the importance of Leibniz, especially when it comes to complex metaphysical questions.  Some have wondered in the past why I have seen him as important, and I want to explain what I began to notice several years ago.  This is not to say that I think all of his ideas are correct. Indeed, several of his ideas seem a bit strange, but there are definitely crucial insights and ideas handed down in the western tradition that Leibniz brought to light that would ultimately lead to the computational machine we call the computer. Certainly others were involved in this long process, such as Pascal and other mathematicians, but Leibniz occupies a central role.
As readers of my site may have noticed, my interview with James Kelley highlighted several questions surrounding figures of that era speculating on optics and the ability to influence men and nations for propaganda and psy ops purposes. Specifically, Dr. John Dee theorized different notions about magical mirrors that might be erected to influence others.  James Kelley offered the tantalizing idea that the “007” symbolism Dee used in his communiques with Elizabeth may be two mirrors with the seven occupying the point of light reflecting outwards, with the two 0s being mirrors placed like two mirrors would have been in the optical experiments of his day.  Kelley mentioned the theory of Dee being that the universe was a vast body of luminous light corresponding to the androgynous Adam Kadmon of Jewish Kabbalistic lore, and the light in the eye of the human being the means by which the rays that refracted off objects could thus transmit the emblems of information-knowledge into our heads.
Much needs to be said here. For one, this theory is very close to Aristotle’s view that the mind abstracts universals from the phantasm that enters the mind through sense experience.  In similar fashion, Enlightenment theorists, including the esoterists, were fascinated by these notions, as well as the Platonic illuminist theory of epistemology that Augustine argued for. Ron Nash has an interesting book contrasting the Augustinian and Thomistic conceptions of knowledge, with Thomas following Aristotle in the great synthesis more than Plato, though Aquinas did think he had synthesized the two by placing the archetypes of forms of things in the divine essence.  In this regard, Augustine’s illuminism is very similar to Aquinas’, as both seek to base human knowledge on the reflected analogies that are in man’s mind that lead him to a contemplative journey back to the One.
For both Aquinas and Augustine the archetypes or forms of things that are in the divine essence become a kind of mental path the convert must make, as he is led through life on the perilous quest to see the true nature of things in God, yet the fatal flaw that the East elucidates here is that the goal of this quest is to find the essence of God.  For Aquinas and Augustine, the foundation of natural and supernatural knowledge is the illuminating grace God gives to see the true forms of things in the absolutely simple divine essence.  Thus, for both theologians, the divine essence is literally spoken of as a kind of mirror of reality that the mind of man refracts, leading him from the creaturely analogies back to the true forms in the essence of the One, the divine essence of God, synonymous with the divine Mind.
This is divine exemplarism, but with a unique twist that distinguishes the western view from the eastern: Maximos the Confessor placed these archetypes or logoi as energies of God in the one Logos, not as the divine essence.  This has crucial implications for theology, but in terms of my focus here, there are massive implications for epistemology.   James has laid out many of these implications in his book Anatomyzing Divinity, but as he mentioned in our interview, there appear to be interesting parallels with the track of western civilization as its top scientists and philosophers like Bacon, Leibniz, Descartes, Dee and Newton take this alchemical-Platonic view of “trinities” everywhere and reverse engineer them into a technological idea of a great god computer, if you will.
For many Renaissance and Enlightenment thinkers, the mind is a mirror of the world, capable of “imaging” anything in the world, and following the Platonic and Aristotelian theories of illumination, in a sense potentially infinite.  The form of any thing can enter the mind through the eye,  be stored in the mind and reproduced via memory, etc.  Thus for many of these thinkers, not only does it appear they had a mechanistic view of man as their presupposition for the scientific revolution, but a more esoteric notion of creating a computing machine.  With the assumption of man as a kind of biological machine, it was thus posited that a mechanical being might be created.

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Readers will immediately think of the ancient kabbalistic legend of the Golem, the mechanical man that can be created with the proper symbols and magic.  Rabbi Isaac of Luria supposedly created one, being a master of the kabbalistic arts. However, rather than pass away into the bin of history as an unknown myth, I suspect that in the esoteric societies of Dee and Leibniz and company, the myth persisted, and when combined with these other theories of Augustino-platonic illuminism, Augustinian epistemic mirror emblemism, etc., the stage was set for the proposal of concepts that would evolve into the complex computing systems we now have.
In this article, I want to analyze some of the ideas of Leibniz.  We know that Leibniz was the founder of calculus, and particularly theories that would be instrumental for the creation of the computer, but are there esoteric ideas beyond mere mathematics at work?  Do the concepts of mirror-imaging and reflecting, the monadology, space and extension in Leibniz, demonstrate any possible connection to the what we see before us in these complex instruments known as personal computers? What about the ideas that Dr. John Dee had, as James Kelley as noted, that served to influence later scientists to create great eyes in the sky that could peer anywhere, as well as projecting images everywhere, propagandizing masses?

Leibniz was interested in finding a characteristica universalis, a universal langauge of symbols that would function as a universal lexicon of symbols that would represent all the functions of reason.  The idea here would eventually evolve into the creation of the computer—a “logic machine” that could perform complex algorithms.  While a machine might be created to count (a primitive calculator), what about more complex machines that could encode data?  Could that data be stored?  Though I am not schooled in the history of technology, the question as a student of philosophy does pique my interest.  We would be told by most modern-day technicians and scientists that pure materialist trial and error was the birthplace of these techno marvels we now see, but I suspect this is false.  I am much more inclined to believe that behind these “logic machines” are vast metaphysical speculations, as well as profound metaphysical truths.
Readers will also notice that I have often referred generally to the “platonic tradition” as more correct than the empirical tradition, and it is worth noting that Leibniz is certainly within that strand of thought.  I am not advocating rationalism here, or “platonism,” but that core ideas in that tradition stand in stark contrast to the materialist and empirical traditions that dominate our world to this day.  Indeed, as I mentioned, most computer scientists will likely posit that computers emerged from a long process of materialistic, scientistic endeavor.  Yet when we look at Leibniz, we do not see someone enveloped in materialism and mechanistic views of the world, but rather someone with an elaborate scholastic worldview that hearkens to Platonism.
Leibniz’s monadology is his metaphysical theory of reality being composed of infinite, rational, simple monads, that function like a little spherical mirror.  The monads mirror all of the rest of reality, but do not directly interact with one another.  God has pre-established a perfect harmony between them, and it is correct to say that, properly speaking, the monads are “spirit,” as opposed to matter.  Leibniz rejected the idea that fundamental reality was made up of material atoms, and posited instead that mind, particularly the divine mind, was the ground of reality, manifest in all the infinite monads.  In this theory, Leibniz actually presages many twentieth century developments in quantum physics, including the theories of Wolfgang Pauli and Carl Jung regarding the continuity of the inner concepts of the psyche and the outer archetypes encountered in the world of physics.  For Jung, psyche or mind bridged that gap, and Leibniz would agree, arguing that reality is, at base, conscious.  I also see similarity between Maximos the Confessor and his logoi.  For all these thinkers, reality is grounded in the Mind of God, though they differ quite a bit in what that entails and how that is.
Philip Weiner explains in my copy of Leibniz’s works (Leibniz Selections):
“Monads come into existence as “fulgurations” or sparks of the divine, falling within the limits of pre-established harmony.  They are spiritual, rather than physical points….Each monad is graded according to its powers of mental activity, the higher monad perceiving changes within itself more clearly, distinctly, or adequately than the lower ones, and in so doing, “mirrors” more of the objective relations of the entire universe of monads from its point of view.  The ensemble of these points of view forms an order of co-existence, and space is nothing but the simultaneous perception of co-existing qualities, and time is nothing but the order of successively perceived qualities.  The spaces and times of each monad will be relative to the point of view of each….
The inherent effort of each essence to realize the maximum existence is the metaphysical basis for Leibniz’s defense of a spontaneous freedom of the will…in the case of each individual men’s essences….The ultimate individuals (monads) of the universe are then active centers of energy containing all that they have been or will be within themselves.” (pg. xli-xlii)
Unfortunately, Leibniz was still working within the context of the Augustino-platonic tradition which defined God as an absolutely simple monad, where all attributes and actions are conceived of as wholly synonymous with that divine essence.  For God, what He is the exact same as what He does.  This is the classic western doctrine of divine simplicity from Augustine on, but to be fair to Leibniz, he does consider God as the Great Monad to be of a different order than the rest of reality, though still part of that continuum in the Great Chain of Being, since the monads all mirror the Great Simple Monad.
Leibniz writes in his First Principles: Foundations of the Sciences:  “The most Perfect Being is the one that contains the most of essence.  Quality is being, capable of having ideas and reflections, for this multiplies the variety of things as a mirror does.” (pg. 93)
Leibniz’s only book to be published in his lifetime was his book Theodicy, attempting to make sense of the problem of evil.  However, that is not my interest here: I want to focus on his metaphysics.  In the section “Identity in Individuals and True Propositions,” he writes:
“In my opinion each individual substance always contains the marks of whatever has happened to it and the features of that which will ever happen to it….Now every individual substance of this universe expresses in its concept the universe into which it has entered….Now what is it to say that the predicate is in the subject if not that the concept of the predicate is in some manner involved in the concept of the subject?  Since from the very face that I began to exist it could be truly be said of me or that this would happen to me, we must grant that the predicates were principles involved in the subject or in the complete concept of me which constitutes the so-called ego and is the basis of the interconnection of all my different states.  These have been known to God from all eternity.” (pgs. 96-7)
Leibniz does not use the word exemplar or logoi, but the principle he is discussing is remarkably similar.  Since the ground of a thing’s being is the divine Mind, it follows that contained in the idea or form of that thing is all events that will occur in relation to that thing.  God, being omniscient, is able to know all these infinite relations, but this brings to mind the logoi of Maximos Confessor, who argues that the logoi are the archetypes or forms of things that are also uncreated divine energies.  Leibniz continues: “This is a very important proposition that deserves to be well established, for it follows that every soul is as a world apart, independent of everything else but God; that is not only immortal and impenetrable but retains in its substance traces of everything that happens to it….That is to say, every substance expresses the whole sequence of the universe in accordance with its own viewpoint or relationship to the rest, so that all are in perfect correspondence with one another.” (pg. 98)
These are fascinating speculations. For Leibniz, the definition of a thing includes all the predicates included in the subject.  This is, so to speak, the divine vantage point, which has determined the time and course of a thing’s existence and thus knows all the infinite relations of that thing to all other things.  But Leibniz also seems to hint at the idea of what would be discovered in DNA, with the genetic history of a living thing’s entire lineage.
Though we needn’t accept Leibniz’s idea of no physical interaction between the monads, there is an element of the macrocosm/microcosm doctrine here, in that every monad contains within it all the traces of the events of the rest of the universe. In other words, we may have a correlation here with the modern discovery that light encodes information.  In fact, light can even be used to transfer data, hearkening to the thesis of Dee mentioned above.  “…The smallest particle should be considered as a world full of an infinity of creatures.” (pg. 99) Leibniz again hints at future discoveries of biology and quantum physics, yet because we are not the divine Mind, we cannot infer all the infinite relations.
“I judged, however, that we must not be indifferent to the different grades of minds or reasonable souls, the higher orders being incomparably more perfect than those forms buried in matter, being like little gods by contrast with the latter, and made in the image of God, having in them some ray of the light of Divinity.  That is why God governs minds as a Prince governs his subjects…” (pgs. 108-9) Leibniz thinks that God, being the Great Monad, has governance of the minds of his subject monads, while the material and animal order are governed like machines.  The light of divinity, however, does penetrate into the minds of the sentient beings under God’s providence, so here we again see the doctrine of illumination.
He continues: “Every mind being a world apart, sufficient unto itself, independent of any other creature, containing the infinity, expressing the universe, is as enduring, as subsistent, and as absolute as the very universe of creatures.” (pg. 116).  Leibniz seems to picture these simple monads like the Great Monad.  They are miniature versions of God, the Great Simple Mind.  But what is of particular note is the idea that, as the ground of reality, each monad expresses the universe in itself. The ray of divinity itself penetrates all these “divine sparks,” giving them an Entelechy, as Leibniz says, using Aristotle’s term, or a primeval force.
He continues: “Monads are the grounds not only of actions but also of resistances or passivities, and their passions reside in their confused perceptions.  This also comprehends matter or the infinite numbers.  I have always been very pleased, ever since my youth, with the morals of Plato and to some extent his metaphysics: also these two sciences go together as mathematics and physics.” (pg. 189)  This is an unclear section, but he appears to say that the energies or forces of nature are ascribed by Leibniz, not to blind forces, but to divine monadic guidance.
Explaining further, Leibniz writes:
“Furthermore every substance is like an entire world and like a mirror of God or indeed of the whole world which it portrays, each one in its own fashion; almost as the same city is variously represented according to the various viewpoints from which it is regarded.  Thus the universe is multiplied in some sort as many times as there are substances, and the glory of God is multiplied in the same way by as many wholly different representations of his works.  It can indeed be said that every substance bears in some sort the character of His wisdom and omnipotence, and imitates him as much as it is able to; for it expresses, although confusedly, all that happens in the universe, past present and future, deriving thus a certain resemblance to an infinite perception or power of knowing.  And since all other substances express their particular substance and accommodate themselves to it, we can say that it exerts its power upon all others according to the omnipotence of God.” (pgs. 301-2)
Leibniz sees the monads as mirrors that each reflect God, showing in a small part the infinite perfections of the Deity, each being stamped with the characteristic perfections of God through the ray of Divine light that penetrates all things.  But the next quote is the most interesting in terms of my thesis on these speculations and Dr. John Dee.  Leibniz postulates in his “Monadology”:
“17. It must be confessed, moreover, that perception and that which depends on it, are inexplicable by mechanical causes, that is by figures and motions.  And, supposing that there were a machine so constructed as to think, feel and have perception, we could conceive of as enlarged and yet preserving the same proportions, so that we might enter into it as into a mill.  And this granted, we should only find on visiting it, pieces which push one against another, but never anything by which to explain a perception.  This must be sought for, therefore, in the simple substance and not in the composite or in the machine.  Furthermore, nothing but this (namely perception and their changes) can be found in the simple substance.  It is also in this alone that all the internal activities of simple substances can consist.  18. The name of entelechies might be given to all simple substances or created monads, for they have within themselves a certain perfection; there is a certain sufficiency which makes them sources of internal activities, and so to speak, incorporeal automata.” (pg. 536)

The monads seem to operate like an anima mundi for Leibniz, but are created.  However, they also seem to be able to contain information and function in an automated fashion.  In the same section, a large, artificial machine is posited as a possibility, yet Leibniz denies that it would be more than a machine.  In other words, the functioning of a monad, as a self-contained data-storing automaton mirror of the rest of reality is directly linked to the idea of a large humanoid robot.  Since reality contains a regular, uniform functionality and consistency, it would be possible to construct a replicant monad, yet it would not be a sentient being in the sense that humans or God are.  In other words, could monads be reverse engineered—could an artificial monadic machine be constructed that functioned automatically?  In fact, it would appear so, since Leibniz is a key figure in the development of the logic-machine we call the personal computer.
Consider Leibniz’s process of inference, though.  Because Leibniz accepted some basic Platonic presuppositions, he was able to deduce a host of inferences about metaphysics which, even if they aren’t all correct, were correct enough to be the basic starting points for how to construct a unified machine that uses algorithms to replicate and store amazing amounts of data, as well as doing a host of other activities.  Indeed, the amazing advance of artificial intelligence has a direct connection to the ideas of Leibniz and the Kabbalistic idea of the Golem, since what Leibniz here describes is very close to the Golem theory.  That theory would only be possible if certain metaphysical assumptions about the nature of reality, its uniformity, etc., were true.  While the Augustinian identification of the mirrored archetypes in reality should not be identified with the divine essence, it is true that the Renaissance and enlightenment notion of man’s mind as a mini mirror of God was the basis for Leibniz’s idea, yet he expanded it to encompass all reality—all reality is made up of infinite little rational mirrors.  Light is ultimately derived from God in Genesis 1, and when combined with the theory of Dee, we can see the development of the idea that light encodes information.  And, amazingly, this can be reproduced in the world artificially.  Dee writes in his Monas Hieroglyphica of the monad at length, adopting this Pythagorean and Platonic tradition with Leibniz:

“THEOREM XVIII

From our Theorems XII and XIII it may be inferred that celestial astronomy is the source and guide of the inferior astronomy. Before we raise our eyes to heaven, kabbalistically illuminated by the contemplation of these mysteries, we should perceive very exactly the construction of our Monad as it is shown to us not only in the LIGHT, but also in life and nature, for it discloses explicitly, by its inner movement, the most secret mysteries of this physical analysis. We have contemplated the heavenly and divine functions of this celestial Messenger, and we now apply this co-ordination to the figure of the egg. It is well-known that all astrologers teach that the form of the orbit traversed by a planet is circular, and because the wise should understand by a hint, it is thus that we interpret it in the hieroglyph shown, which conforms in every detail with all that has gone before.”
For Dee, the monad is also an all-encompassing explanation of the mysteries of metaphysics.  You’ll notice as well he includes the imagery of the egg which comes from the ancient Greek mysteries as the form of the universe itself.  Is it possible Leibniz saw a similar idea in his version of the monad as Dee did that led him to posit the idea of a machine that could operate in this fashion? Could a “magic mirror” machine be created that would, in an imitative sense, perceive and record data, as well as transfer it through energy?  Do we have with the ideas of the aether and monads the beginning of the idea of a logic machine that could “mirror” concepts like the human mind “mirrors” concepts through the light given to it by the divine rays that emanate from the Deity?  Dee sees his monad as elucidated in life and nature, as did Leibniz. I think so, inasmuch as the computer itself functions in many ways like the monads of Leibniz and Dee. Indeed, Leibniz wrote about this in his De Progressione Dyadica.  This page on the history of computers explains his formulation of binary computation:
Though hard to believe, in his 3-pages treatise De progressione Dyadica, Leibniz even outlines a calculating machine which works via the binary system: a machine without wheels or cylinders—just using balls, holes, sticks and channels for the transport of the balls: “This [binary] calculus could be implemented by a machine. The following method would certainly be very easy to be implemented. [A machine with] holes, which can be opened and closed. They are to be open at those places that correspond to a 1 and remain closed at those that correspond to a 0. Through the opened gates small cubes or marbles are to fall into channels, through the others nothing to fall. It [the gate array] is to be shifted from column to column as required for the multiplication. The channels should represent the columns, and no ball should be able to get from one channel to another except when the machine is put into motion. Then all the marbles run into the next channel, and whenever one falls into an open hole it is removed. Because it can be arranged that two always come out together, and otherwise they should not come out.”

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