Prof. Eric Steinhart (C) 1999
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I cite sections of Leibniz's Monadology in quotes, then follow them with comments. The translation is by Robert Latta (1898) with my emendations; Latta's translation is, to the best of my knowledge, in the public domain. This is a work in progress.
14. "The passing condition, which involves and represents a multiplicity in the unit or in the simple substance, is nothing but what is called Perception, which is to be distinguished from Apperception or Consciousness, as will afterwards appear."
14. Monads perceive certain appearances. Since monads have "no windows" through which any information or effects can enter, they cannot receive their appearances from outside. All appearances in any monad are internally caused: monads perceive appearances they generate themselves, just as in dreams we perceive appearances that our subconscious (that is, unconscious) minds generate in us.
The interrelated qualities of a monad are like variables in equations that are self-moving; these qualities are a program. One subsystem of these monadic qualities is like the subconscious mind that displays appearances to us in our dreams; the subsystem that displays these appearances is a virtual reality (VR) subprogram. While the VR subsystem of the monad generates appearances, another subsystem perceives them. Each monad has some perceptive subprogram that comprehends what its VR subprogram displays.
The perceptive faculty in the monad is intelligent. Since God is the designer of this program, it is not unreasonable to speak of it as an artificial intelligence (AI). It is the AI subprogram in the monad, and it is coordinated with the VR subprogram. Monads are physically simple computers that are functionally complex because they are each running a complex program, composed of two subprograms, a VR subprogram that appears to the AI subprogram and an AI subprogram that perceives the VR subprogram.
The detail of each monad includes physical detail (the content of its VR subsystem) and psychic detail (the content of its AI subsystem). The detail of each monad is a VR-AI pair. This may seem redundant, as if the monad is talking to itself or showing itself its own reflection, but there's a purpose to it: the VR is a physical perspective on the universe, and the AI is a psychological perspective on the universe. These two perspectives are coordinated in the monad like two sides of the same coin. They are harmonized. Each monad takes the same perspective in two ways: mentally and physically, psychologically and physically. It may seems that the monads are all just dreaming; but these dreams are coordinated in such a manner as to be as real as real can be, to make up an objective physical world.
15. "The activity of the internal principle which produces change or passage from one perception to another may be called Appetition."
15. Monads have a kind of compulsion to the next state. Each monad is always generating its next internal state: it's VR displays the next subconscious (physical) state of the whole universe from the monad's perspective. Each AI perceives the next conscious (psychical) state of the world from the monad's perspective. The internal logical force of the monad drives both its VR and AI at once; they are synchronized, and the interrelated qualities in each are coordinated.
Supposing the internal program of each monad to contain internal detail transformed according to the rule of the game of life, we have a cellular automaton inside each monadic program. The patterns of values of points in the cellular automaton change, and the changes of those patterns are spatio-temporal motions. The internal cellular automaton is like a virtual reality (VR) program that perpetually generates distinct appearances. Each monad contains such a VR program, and all of those programs are synchronized to make a single (virtual) physical space-time.
So far the VR program generates only visual appearances, like an unfolding movie, but there is nothing to prevent it from generating other phenomenal qualities as well: the VR detail generates the entire sensory field of every monad, in all modalities (visual, auditory, tactile, etc.) of each monad. The internal monadic sensations include the internal muscular and organic (proprioceptive and kinaesthetic) sensations, as well as emotional qualities (adverbial qualifications of intentional relations, which we have yet to construct). All of this is only a mathematical way of saying that monadic detail is beautiful.
16. "We have in ourselves experience of a multiplicity in simple substance, when we find that the least thought of which we are conscious involves variety in its object. Thus all those who admit that the soul is a simple substance should admit this multiplicity in the Monad; and M. Bayle ought not to have found any difficulty in this, as he has done in his Dictionary, article 'Rorarius.'"
16. Our souls are functionally complex yet substantially simple. So there is no impossibility in the existence of a materially simple but functionally complex thing.
17. "Moreover, it must be confessed that perception and that which depends upon it are inexplicable on mechanical grounds, that is to say, by means of figures and motions. And supposing there were a machine, so constructed as to think, feel, and have perception, it might be conceived as increased in size, while keeping the same proportions, so that one might go into it as into a mill. That being so, we should, on examining its interior, find only parts which work one upon another, and never anything by which to explain a perception. Thus it is in a simple substance, and not in a compound or in a machine, that perception must be sought for. Further, nothing but this (namely, perceptions and their changes) can be found in a simple substance. It is also in this alone that all the internal activities of simple substances can consist. (Theod. Pref. [E. 474; G. vi. 37].)"
17. A machine contains parts that move in space; the computational monads are not machines in that sense, since they contain no parts that move. Computers are not like windmills. Monads put mathematics into motion; they do not put matter into motion. Monads transform information, but information is not material (it has a formal or ideal nature). Each monad algorithmically generates the appearances it perceives, and it perceives them algorithmically. To perceive algorithmically is not to perceive mechanically.
18. "All simple substances or created Monads might be called Entelechies, for they have in them a certain perfection (echousi to enteles); they have a certain self-sufficiency (autarkeia) which makes them the sources of their internal activities and, so to speak, incorporeal automata. (Theod. 87.)"
18. Artificial computers reveal their imperfection in their need for some external power source that sustains their activities. But the monads are self-sufficient; they are truly automatic, in the sense of self-powered. If they have any dependency, it is only on God.
19. "If we are to give the name of Soul to everything which has perceptions and desires [appetits] in the general sense which I have explained, then all simple substances or created Monads might be called souls; but as feeling [le sentiment] is something more than a bare perception, I think it right that the general name of Monads or Entelechies should suffice for simple substances which have perception only, and that the name of Souls should be given only to those in which perception is more distinct, and is accompanied by memory."
19. We have already seen that our minds are simple substances that are functionally complex; generally speaking, monads are just like our souls. Indeed, insofar as our souls are able to do mathematics, we see that there are simple substances that compute. But to be precise, we should just use the word soul just for those with memory and more powerful perceptual faculties. Monads in general are very simple VR/AI pairs; souls are VR/AI pairs whose AI algorithms are more complex (sharpened perception) and that include memory.
20. "For we experience in ourselves a condition in which we remember nothing and have no distinguishable perception; as when we fall into a swoon or when we are overcome with a profound dreamless sleep. In this state the soul does not perceptibly differ from a bare Monad; but as this state is not lasting, and the soul comes out of it, the soul is something more than a bare Monad. (Theod. 64.)"
20. Our own souls are like bare monads when we are unconscious. But the fact that our souls emerge from this state is evidence for a "master program" in which the VR and AI parts of our souls are embedded. When the soul awakens from sleep, this master program is in fact restarting the AI part of our functionality.
21. "And it does not follow that in this state the simple substance is without any perception. That, indeed, cannot be, for the reasons already given; for it cannot perish, and it cannot continue to exist without being affected in some way, and this affection is nothing but its perception. But when there is a great multitude of little perceptions, in which there is nothing distinct, one is stunned; as when one turns continuously round in the same way several times in succession, whence comes a giddiness which may make us swoon, and which keeps us from distinguishing anything. Death can for a time put animals into this condition."
21. The fact that we are sometimes unconscious (i.e. that our AI functions are turned off) does not imply that our VR program ever ceases to operate. If the VR program were to cease to operate, then we would cease to exist; but monads (including our souls) are not perishable. The VR program operates unconsciously (it is your "subconscious"). In fact, during unconsciousness, the AI program is not entirely shut down; it is still perceiving, but it does not apply much of its functionality to the organization of these perceptions into coherent representations. Death is not the end for monads; it's just a confused state. Dying is like getting dizzy and fainting.
22. "And as every present state of a simple substance is naturally a consequence of its preceding state, in such a way that its present is big with its future; (Theod. 350.)"
22. Each state of a monad's detail is a function of its past state(s). This means that the monadic programs are recursive. Suppose S(t) is the state of a monad at time t, and that F is the monadic program; then S(t+1) = F(S(t)), or S(t+1) = F(S(t), S(t-1)), etc. Cellular automata are recursive, so the VR subprogram of each monad directly satisfies this requirement. In a cellular automaton, each point computes its own local transformation f based on some local state (the state of the point and the states of its neighbors; but the combination of all the f's is a global transformation F applied to the automaton's global state. The global state of a cellular automaton is just a function mapping each point (cell) in the automaton onto its value. Technically, the global transformation F is a function that maps global states onto global states, but the global states are themselves functions, so F is a function that maps functions onto functions. All the activity in a cellular automaton is purely functional! The present state of a cellular automaton is a function of nothing but its past state(s). Cellular automata are deterministic, and in this sense the present of each monad's VR subprogram is pregnant with its future. The life grid gives birth to its future at each moment; it is like a bud that unfolds as it blossoms.
23. "And as, on waking from stupor, we are conscious of our perceptions, we must have had perceptions immediately before we awoke, although we were not at all conscious of them; for one perception can in a natural way come only from another perception, as a motion can in a natural way come only from a motion. (Theod. 401-403.)"
23. The VR functionality of the soul must operate unconsciously and perpetually, since if it did not there would be nothing for the soul to become aware of as it wakes up. But the soul does become aware of something. Information presupposes information (perception comes only from perception). In fact, all AI algorithms in monads are self-aware (though not all are self-conscious, which is sharpened self-awareness). This self-awareness is just the reflexivity of the recursive operation of the monad.
24. "It thus appears that if we had in our perceptions nothing marked and, so to speak, striking and highly-flavoured, we should always be in a state of stupor. And this is the state in which the bare Monads are."
24. The monads we have placed at the cells in the life grid are like bare monads: always unconscious (VRs generating, but AIs very primitive and not capable of sharp perception or apperception). We haven't considered the sophistications of the AI functionality.
25. "We see also that nature has given heightened perceptions to animals, from the care she has taken to provide them with organs, which collect numerous rays of light, or numerous undulations of the air, in order, by uniting them, to make them have greater effect. Something similar to this takes place in smell, in taste and in touch, and perhaps in a number of other senses, which are unknown to us. And I will explain presently how that which takes place in the soul represents what happens in the bodily organs."
25. Specialized sense organs unify materially complex stimuli from the aggregate (from the internal life grid) rendering them into simple informational stimuli fit for computational processing by monads. How this happens will be explained later.
26. "Memory provides the soul with a kind of consecutiveness, which resembles [imite] reason, but which is to be distinguished from it. Thus we see that when animals have a perception of something which strikes them and of which they have formerly had a similar perception, they are led, by means of representation in their memory, to expect what was combined with the thing in this previous perception, and they come to have feelings similar to those they had on the former occasion. For instance, when a stick is shown to dogs, they remember the pain it has caused them, and howl and run away. (Theod. Discours de la Conformite, &c., ss. 65.)"
27. "And the strength of the mental image which impresses and moves them comes either from the magnitude or the number of the preceding perceptions. For often a strong impression produces all at once the same effect as a long-formed habit, or as many and oft-repeated ordinary perceptions."
28. "In so far as the concatenation of their perceptions is due to the principle of memory alone, men act like the lower animals, resembling the empirical physicians, whose methods are those of mere practice without theory. Indeed, in three-fourths of our actions we are nothing but empirics. For instance, when we expect that there will be daylight to-morrow, we do so empirically, because it has always so happened until now. It is only the astronomer who thinks it on rational grounds."
26, 27, 28. Souls (more complex AI programs) are able to learn; they evolve as they observe the appearances generated within them. Of course, this learning is not really the appearance of anything new in the monad (for that would be creation of something from nothing, but nothing comes from nothing); rather, learning is just recollection (the coming into focus of data already implied by the monad's internal functionality). As animals show, souls are affected by the stimuli they receive from their unconscious VR sources. These are not haphazard: there is a mathematical pattern (based on intensity, frequency, and regularity of repetition) that unites affects of the body to those of the soul. This shows that sensation is primarily a mathematical relation, one that transforms the multiplicity of stimuli in the VR program into a simple idea in the AI program. No matter how sophisticated our own human minds might be, we normally operate at an animal level.
29. "But it is the knowledge of necessary and eternal truths that distinguishes us from the mere animals and gives us Reason and the sciences, raising us to the knowledge of ourselves and of God. And it is this in us that is called the rational soul or mind [esprit]."
29. Some monads have AI programs so complex that they are able to comprehend eternal truths via a faculty of reason. Such monads are spirits, and we are spirits. Our rational reflections on what is going on inside our own souls raises us to the knowledge of God. We see God reflected in ourselves.
30. "It is also through the knowledge of necessary truths, and through their abstract expression, that we rise to acts of reflexion, which make us think of what is called I, and observe that this or that is within us: and thus, thinking of ourselves, we think of being, of substance, of the simple and the compound, of the immaterial, and of God Himself, conceiving that what is limited in us is in Him without limits. And these acts of reflexion furnish the chief objects of our reasonings. (Theod. Pref. [E. 469; G. vi. 27].)"
31. "Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false; (Theod. 44, 169.)"
32. "And that of sufficient reason, in virtue of which we hold that there can be no fact real or existing, no statement true, unless there be a sufficient reason, why it should be so and not otherwise, although these reasons usually cannot be known by us. (Theod. 44, 196.)"
33. "There are also two kinds of truths, those of reasoning and those of fact. Truths of reasoning are necessary and their opposite is impossible: truths of fact are contingent and their opposite is possible. When a truth is necessary, its reason can be found by analysis, resolving it into more simple ideas and truths, until we come to those which are primary. (Theod. 170, 174, 189, 280-282, 367. Abrege, Object. 3.)"
34. "It is thus that in Mathematics speculative Theorems and practical Canons are reduced by analysis to Definitions, Axioms and Postulates."
35. "In short, there are simple ideas, of which no definition can be given; there are also axioms and postulates, in a word, primary principles, which cannot be proved, and indeed have no need of proof; and these are identical propositions, whose opposite involves an express contradiction. (Theod. 36, 37, 44, 45, 49, 52, 121-122, 337, 340-344.)"
30-35. The AI programs of spirits are so complexly powerful that their apperception (a reflexive self-relation) is sharpened into Reflexive Acts. Spirits are programs so sophisticated they are able to comprehend themselves and are truly self-conscious (they are able to form theories about themselves, to form representations in their memories concerning what is going on in them). Spirits are able to look at themselves as if in a kind of internal mirror: they are like programs able to figure out their own algorithms and data structures, able to discover that they are monads and to make computational models of themselves. Each spirit mirrors itself. It is as if a country contained a map of itself that is complete down to the smallest detail, including containing a map of itself in this map of itself. This leads to an infinite regress (of maps in maps, nested endlessly), but it is not a vicous regress: it just means that spirits are infinitely complex. This self-mirroring provides rational reflection with its content: it is the source of all mathematical intuitions and constructions. Mathematics is the free play of the mind with itself.