Footnotes

 

 

*1. We no longer subscribe to the idea of a cosmic vapor from which the universe emerged, but the theory of the big bang holds to a technically identical idea: that the entire universe was once contained within an infinitely dense point (rather than a dense cloud of vapor), a “Singularity,” that through a violent, sudden expansion created our cosmos.

*2. Of course it is true that the sciences sometimes do still reveal undiscovered wonders, but this sense of wonder and awe is usually quickly forgotten in favor of more instrumentalist objectives.

*3. The concept of an “imaginary” is fully explained see here.

*4. The reference to Kantian “faculties” is quite deliberate on Chomsky’s part, I think.

*5. This was mathematician Hadamard’s characterization (in 1912) of the period that saw the appearance of the mathematical and geometrical revelations of Lobachevsky, Riemann, Cantor, Dedekind, and so on. See Mandelbrot, Fractal Geometry of Nature, 415.

*6. Lobachevsky’s (one of the creators of non-euclidean geometry in the nineteenth century) own description of non-euclidean geometry.

*7. Le Goff defines mentalité as “mental outlook as expressed in discourse and artifacts.”

*8. To be quite fair, Le Goff himself divides his extended Middle Ages into several “subsets”: the period from the third to the seventh century he names “Late Antiquity”; the eighth to the tenth century becomes the “High Middle Ages”; the tenth to the middle of the fourteenth century (the latter being the period that most historians refer to as the Renaissance) is the “Central Middle Ages”; the “Late Middle Ages” “began with the great plague (1348) and continued into the sixteenth century, when the Reformation (and nothing so vague as the Renaissance) ended the Church’s monopoly on the Christian religion”; and “Early Modern History” from the Reformation until the Industrial Revolution.

*9. The phrase is Witold Kula’s, and is used by Le Goff to characterize certain anachronisms in any historical period. Le Goff wisely stresses that these periods are a “mere analytical convenience,” not an “ontological reality.” See Le Goff, Medieval Imagination, 12.

*10. Among whom include such varied scholars as Hans Jonas, Moshe Idel, E. R. Dodds, and G. R. S. Mead.

*11. Yates published this paper in 1968, four years after her better known Giordano Bruno and the Hermetic Tradition. This paper in particular focuses on the influence of what she calls the “Rosicrucian phase” of Hermeticism and its formative influence on the development of seventeenth-century science.

*12. In the sense of desiring to conserve old values and ideas rather than the sense of alignment with politically conservative ideas.

*13. One is reminded that the word theory, derived from the Greek theoria, necessarily implies “walking a path” as the term originally referred to an individual’s (the “theorist”) curiosity “such as led Hekataeus or Solon to travel about the world as spectators of its marvels” (see Cornford, From Religion to Philosophy, 200). In terms of early Ionian science, theorists “wandered off to take a closer look” to improve their knowledge of the world, the ancient equivalent of the eighteenth-century Grand Tour. Our contemporary contrast between “theory” and “practice” is derived from the alternative sense in which the term was used by Pythagoras and his followers: theoria meant the contemplation of the heavens, an intellectual pursuit different in kind from any pursuits worked in the mundane world, and superior to them. This latter sense is that generally espoused by Plato; Aristotle clearly holds to the former, Ionian sense.

*14. According to Weeks, German Mysticism. In fact, it is first found in Saint Paul (1 Corinthians 15:28).

*15. Barfield also seems to hold that the “scientific revolution” was hardly an “event” within the seventeenth century. That is why he calls it—with conscious irony—a “prolonged” historical event. Like myself, Barfield does not seem to be convinced of the reality of a revelatory “paradigm shift.”

*16. Two machines (computers or fax machines) must first engage in what is called a “handshake” procedure in order to “recognize” each other in an exchange. Anyone interested in contemporary computer technology will immediately recognize as “computer heroes” the names of John von Neumann or Alan Turing, for example.

*17. GOFAI stands for good old-fashioned artificial intelligence, an initialism invented by Richard Haugeland to sum up just the sort of computer intelligence envisioned by Vinge: a computer (probably in the form of good old-fashioned von Neumann architecture) that is not merely modeling human intelligence (the “weak AI” proposition), but actually is as intelligent—or more so—than any human counterpart.

*18. It is more than likely, of course, that the original author of the Pymander was quite familiar with the biblical text.

*19. In the jargon of AI, “modeling” a mind is called “weak AI” as all that is being attempted is a simulation of mental activity. The aim of “strong AI” is to actually make a mind (as opposed to merely simulating it.)

*20. It was a truism of ancient Hellenic thought that “like knows like” and, as a corollary, that only like could have a causal influence on like. Plato’s division between kinds of stuff (material/nonmaterial) was therefore quite problematic.

†21. A contraction of “binary digits,” a term created by the inventor of information theory, Claude Shannon.

*22. Since 1985, artificial-intelligence research has received well over 60 percent of its funding from the Pentagon and DARPA, the U.S. military defense-research organization.

*23. The “specious present” is defined as the least temporal interval such that two modifications of experience, separated by that interval, may nevertheless seem to the subject to be copresent in consciousness.

*24. Influential in that two of the most important thinkers of the West, Plato and Aristotle, were initiated into the Eleusinian Mysteries, and several lesser thinkers—Marsilio Ficino, for example—were well versed in the mystery tradition. To deny the huge influence of these thinkers on Western thought, and through them the no doubt subtle influence of the mystery tradition, is simply unarguable.

*25. That is, the Platonic/Hellenic idea of chaos as the primary state of the kosmos, before the intercession of the logos.

*26. Bateson is referring to Anton Korzybski’s famous adage, “The map is not the territory.”

*27. In choosing this example, Bateson is drawing attention to the historical link between the development of the concepts of thermodynamics (pioneered by Sadi Carnot) and twentieth-century information and cybernetic theory’s use of such terms as entropy and negentropy.

*28. “To flow together.” Diarrhesis means “to flow through.”

*29. The pleromatic realm that philosopher of science Donna Haraway considers as exhibiting the characteristics of Coyote, the trickster. See chapter 4 of this book.

*30. Quite clearly the world of quantum phenomena is invisible. The fact that scientists can produce photographic plates that purport to reproduce the trajectories of subatomic particles in no way compromises this characterization.

†31. Serres: “All I know, but of this I am certain, is that [the object under observation is] structured around the information-background-noise couple, the chance-program couple or the entropy-negentropy couple.” See Serres, Hermes, 82.

*32. Of course this is an “idealization” of the operation of a logic gate. Such an idealization was explicated by McCulloch and Pitts (for example) when they endeavored to compare the operation of a computer’s logic gate to that of individual neurons. In fact logic gates and neurons only “fire” when a certain degree of voltage is detected.

*33. We can still find etymological traces of this idea in the nineteenth-century spiritualist and Theosophical idea of the “astral body” (Latin, astra, “star”), known to Neoplatonic philosophers of fifth-century Alexandria as the soma astroeides, the “starlike body.”

*34. As Couliano describes it, the Gnostics imagined a manner of “military regime” installed in the heavens, replete with monstrous border guards (the Archons) and passports (the secret “seals” and mysterious words, the knowledge of which the Gnostic mystagogues imparted in secret to their followers). See Couliano’s Psychanodia I.

*35. Centuries later Paracelsus would call this procreative/vitalistic essence the Archaeus, an idea very similar to the Augustinian rendition of the Stoic logon spermatikon as rationes seminales.

†36. See On the Generation of Animals, 736, b. 27 ff. Compare Aristotle’s conception of the pneuma as being transmitted during birth and being common to all animals. In traditional Chinese pneumatology this would be equivalent to the yuanqi, or “congenital” qi transmitted during conception.

*37. In his Advancement of Learning, Francis Bacon summarized this rhetorical model quite succinctly: “Aristotle, after the Ottoman manner, thought he could not reign secure without putting all his brethren to death.” In Aristotle’s De anima alone, the ideas of Heraclitus, Pythagoras, Democritus, Empedocles, and Leucippus are all thoroughly and unapologetically refuted. This model of philosophical discourse as critical commmentary was to hold, or rather, be transmitted through the Arabic translations to the High Latin universities up until, as I say, the first great “systematic” philosophies of the seventeenth century.

*38. E. R. Dodd’s formulation to describe these early “medicine men”: physicians (iatros) and seers (mantis).

†39. I am thinking principally of Jacques Derrida and his followers and the massive oeuvre devoted to a critique of the “Platonic” and “logocentric” origins of Western thought.

*40. The English word influence still preserves its original meaning (if in a very modified form). Originating in English as a medical term, it referred to the pneumatic effects of the stars and planets on the human physiognomy, where said effects “flowed in” (influence) from the heavens.

*41. This lost sense of the term is yet implicit in our contemporary usage of such terms as critical intervention, crisis point, critical, and criticism. Much contemporary “criticism” is an attempt at righting the perceived wrongs, of curing the malaise, of the offending text.

†42. G. R. S. Mead characterizes the soma augoeides (i.e., the subtle body) as the “sensible vehicle of purity and truth,” that is, the vehicle of philosophic validation.

*43. Literally, the “body of bright light.”

*44. That is, the physical comportment of the meditating practitioner.

*45. Intriguingly, the colors red and white are also central to European alchemy (where one encounters the fundamental symbolism of the “red king” and the “white queen”) and to mystical Persian thought. Perhaps the color symbolism has its origin in early Islam, as the first alchemical texts to enter Europe were translations from the Arabic. As to the possible significance of these two transmogrifying hues, one can only guess, but they are usually attributed “male” and “female” correspondences.

*46. The training of batin (spirit) is accomplished through certain breathing exercises in Islamic Indonesian Kebatinan. These exercises are connected with the Muslim practice of dhikr, or the “remembrance of Allah,” which concentrates on the breath as much as it does on the repetition of the names of God. Like the Aristotelian pneuma, the subtle energy of batin is said to derive from the heart.

*47. I am thinking principally of the Hesychastic monks. Eliade notes that the methods of prayer used by the monks “resemble yogic techniques, especially pranayama.” See Eliade, Yoga: Immortality and Freedom, 63.

†48. In Chinese jingluo physiology, the pneumatic system opens at the top of the head at the acupuncture point baihui; in Vedic yoga and Vajrayana Buddhism the system opens at the same cranial site.

*49. The association of the symbol of the serpent and healing goes as far back as Sumer.

†50. Doctors trained in the People’s Republic of China usually study both Western medicine and TCM (traditional Chinese medicine).

*51. I mean radical in the sense of “primary.”

*52. An identification clearly foregrounded in Isaac Newton’s controversial concept of the universe as the sensorium Dei, the “sensorium of God.”

*53. The very name Dominican affords us an exemplary image of how the monks themselves saw the functioning of their order. The Domini Canes (“hounds of God”) were the fierce guard dogs that prowled the spiritual terrain contested by the Cathar heresy.

*54. It must be pointed out that while they function differently on occasion, the circle and the sphere should be regarded as equivalent when one realizes that they share only a difference in dimension. Both circle and sphere derive from the same set of geometrical considerations, and a difference of dimension becomes a negligible difference in terms of the fourth-dimensional vantage point of the vertigral hermeneutic.

†55. This aspect of Bolzano’s work was to have a profound influence on Wittgenstein’s Tractatus Logico-Philosophicus.

*56. The English word gas was invented by J. B. van Helmont (father of F. M. van Helmont, see chapter 5) to describe the “third” state of matter. He coined the word directly from the Greek chaos.

*57. Here we observe a strong resemblance between the Buddhist concept of avidya (ignorance) and Gnostic thinking.

*58. One of the earliest of Euclid’s axioms in his Elements of Geometry: “A point is that of which there is no part.”

*59. In Sanskrit loka—from which we derive our word locus—means “world” or possibly “dimension” (in contemporary scientific parlance.)

†60. Concerning the reception of zero in the West, Spengler says, “This zero, which probably contains a suggestion of the Indian idea of extension—of that spatiality of the world that is treated in the Upanishads and is entirely alien to our space-consciousness—was of course wholly absent in the Classical [consciousness.] By way of Arabian mathematics (which completely transformed its meaning) it reached the West . . . with its sense . . . fundamentally changed, for it became the mean of +1 and –1 as a cut in a linear continuum, i.e., it was assimilated to the Western number-world in a wholly un-Indian sense of relation” (Decline of the West, 1:178). He is, of course, limiting himself to the mathematical concept of relation, as opposed to the (metaphysical) sense in which I have characterized the system of relations in the plenum.

*61. That “self-contained” should imply “spherical” is not immediately obvious to us today. Yet to one schooled in the Platonic and Neoplatonic literature (as was Sendivogius) it would be a natural association.

*62. I am thinking particularly of Foucault’s famous closing statements in Le Mots et les Choses: “As the archaeology of our thought easily shows, man is an invention of recent date. And perhaps one reaching its end.” See Foucault, Order of Things, 387.

*63. Thom uses an elaborate mythology of “capture” and “predation” even when describing higher-level functioning (cognition and language, for example) in organisms such as human beings. Although never mentioned explicitly by Thom, much of his language indicates, in my estimation, the strong influence of sociologist René Giraud on his thinking.

*64. In 1730 Voltaire noted, “If Newton had not used the word attraction, everyone in [the French] Academy would have opened his eyes to the light; but unfortunately he used in London a word to which an idea of ridicule was attached in Paris.” Voltaire, quoted in Mandelbrot, Fractal Geometry of Nature, 5.

*65. Such as Charles Hinton, Claude Bragdon, and Edwin A. Abbot.

*66. I suppose he does not pursue this point for the simple fact that he assumes most readers would be familiar with his assertion that Gnosticism is akin in kind to Heideggerian existentialism. See Jonas, “Gnostic Syndrome,” 268.

*67. Our word planet is derived from the Greek word for “wanderer.”

†68. Complex in the sense of the Medieval/Renaissance use of the word as meaning the particular mixture of humors—themselves determined by celestial influence—that determined physical health: one’s face revealed the particular mixture or complexion of influences.

*69. Harvey’s famous study of the heart and arterial stream, On the Motion of the Heart and Blood in Animals, was instrumental in initiating the post-Galenic medical image of the system of the blood and heart as being simply a case of hydraulic action.

*70. I am using this term figuratively, as Aristotle himself was a keen critic of the philosophy of the atomists.

*71. First articulated by Parmenides and Heraclitus, it was also the opening argument of the Asclepius. This Hermetic truism was thus an aspect of intellectual debate from at least Augustine’s time onward in the West.

*72. This idea was undoubtedly derived from the emanationist account of the origin of the cosmos argued by Plotinus.

*73. Descartes held that the function of the nervous system was to transmit the “animal spirits,” that is, the pneumatic current.

*74. Agrippa claimed to be in communication with Trithemius by “thought transference.”

*75. By which he means a “power” or “force” (virtus, vim, and so on).

*76. An imagery accepted by both Proclus and Plotinus where the spherical soul and heavenly bodies are both described as moving circularly.

*77. I think, therefore I am.

*78. Also Luke 8:11: “The seed is the logos of God.”

*79. An equivalent image, it may be noted in passing, to that of the lotus flower in Buddhist iconography.

*80. And, as I have suggested in this chapter, not only Western initiatic traditions. In the Buddhist Lalita Vistara we find a description of the Buddha attaining samadhi where, “a Ray, called the ‘Ornament of the Light of Gnosis’, proceeding from the opening in the cranial protuberance, plays above his head.” (See Coomaraswamy, Selected Papers: Metaphysics, 154.) These “rays” are found throughout Buddhist iconography, and are always considered signs that a bodhisattva had “matured” through enlightenment or gnosis. For reasons unknown, Robert Fludd uses precisely the same imagery and ideas.

*81. Of course it was not really planetary gravitation as much as siderial gravitation, for the observations were of a solar eclipse.

*82. René Thom usefully translates Heraclitus’s logos as “pattern.”

*83. Or, as is perhaps more appropriate for this section, “from the alone to the Alone” (as it has often been translated).

*84. And not only Gnostic similes. Compare Leibniz’s passage with the Mundaka Upanishad, part 2, chapter 1: “This is the truth: As from a fire aflame thousands of sparks come forth, even so from the Creator an infinity of beings have life and to him return again.” In Mascaró, Upanishads, 77.

*85. Leibniz was fond of the medieval image of the mens as the “mirror of nature”: “Thus one may say that not only is the soul (the mirror of an indestructible universe) itself indestructible, but so also is the animal itself.” See Monadology, in Parkinson, Leibniz: Philosophical Writings, 77, 191.

*86. We should recall Ernst Mach’s conviction that all scientific theories are really only extensions of the psychology of the observing scientist.

*87. In the more accurate sense of one who seeks knowledge of God, rather than a follower of Madame Blavatsky, creator of the Theosophical Society in the late nineteenth century.

*88. “For seventeenth-century corpuscularians generally, it was above all speed and direction of motion that did the explanatory work. As often as not, atoms were thought of as invariant in shape, as spheres.” In Gaukroger, Descartes: An Intellectual Biography, 71; see also Meyerson, Identity and Reality, 71.

*89. A relatively modern example of this is the English occultist Aleister Crowley’s Book 777, a text that presents itself as nothing less than a hyperbolic reworking of Knorr’s original tables and diagrams.

*90. So unknowable is this God that many Kabbalists held that he or she was not even mentioned in the Old Testament texts.

*91. Both Proclus and Plotinus no doubt drew their conclusion from Plato’s Timaeus (34): “The movement suited to his spherical form was assigned to him, being of all the seven that which is most appropriate to mind and intelligence; and he was made to move in the same manner and on the same spot, within his own limits moving in a circle”—that is, a sphere revolving in place.

*92. In regard to the pre-Galilean view, note Leonardo da Vinci on the concept of force: “Force is spiritual essence which by accidental violence is united to weighty bodies. . . . Force I define as an incorporeal agency, an invisible power, which by means of unforeseen external pressure is caused by the movement stored up and diffused within bodies. . . . Force is a spiritual energy, an invisible power which is created and imparted.” In Richter, Notebooks of Leonardo da Vinci, 60, 61, 62.

†93. It was Kepler who first suggested that the word vis be substituted for anima, intending thereby a quantifiable term rather than one which by definition was “ungeometrical.” See Collingwood, Idea of Nature, 101–2.

*94. Meyerson’s Identity and Reality originally appeared in 1908. Rutherford “discovered” the atomic nucleus in the early 1920s.