They defile their studies in regard to the heavenly bodies by circles and figures and very silly characters and very foolish incantations, and irrational speeches.
- Roger Bacon, Opus Majus, pt. 4, dist. 4, ch. xvi
I. BACKGROUNDER. Whenever there has been advancement made in the mathematical or physical sciences, more often than not a “new” philosophy is soon after introduced which piggybacks on the popularity of the “new physics”. It seeks to explain not only natural phenomena, but also man himself - his nature and history, his politics and purpose. After the monumental achievement of Newton’s Principia, some sought to reconstruct his mechanical universe into a newfangled theology, as in the deists who turned God into an indifferent and endistancing "Clockmaker". Recognizing the potentialities of Darwin’s materialism, Herbert Spencer (1820-1903), the Soviets, Nazis and Maoists used a theory of biological evolution to explain societal evolution. After Einstein presented his Theory of Relativity, not a few lesser light philosophers and self-styled cultural commentators voiced that all knowledge and morality is relative, as they still do today. That this piggybacking - namely the introduction of a philosophy based upon the latest scientific picture of the world, germane or bogus - is still commonplace is further evidenced when two fields of mathematics, quite popular today, are considered. These fields are chaos theory and fractal geometry.
II. SYSTEMS OF THE WORLD. These are mentioned for cautionary reasons. When the deterministic laws of science are claimed to be the only way to explain man and society, there is always the hazard of debasing man such that he can fit and lock neatly into the three basic systems of the world exposited from time immemorial. Namely, the cosmos as pure numbers, as a machine, or as an organism.[1] If the fields, say, of statistics, engineering or biology are extrapolated such that they attempt to explain human rationality, then effectively is man respectively deemed to be best characterized as: [i] a mere mind with a self-referencing array of symbols and signs without connection to objective reality, [ii] a mechanism that clanks away through the drudgeries of life which, because of the determinism involved, precludes freewill, or [iii] some pseudo-mystical organismic blob where rational, precise thinking devolves into obfuscating rumination. Today, it is common for popularizers of the “new physics” to combine the symbolical and organismic.
III. SCIENCE OR EPISTEMOLOGY? Let TH2 offer an example of this by quoting a seemingly innocuous statement made in a computer book popularizing fractal geometry:
The universe of fractals is part of a larger issue of understanding of the relationship between humanity and the natural world... What is of critical importance is not the success of the theory but the reorientation of fundamental thinking. This emerging view of nature is more humble, less arrogant. The deepest wonder is for nature itself, not our attempts to model it and understand it.[2]
Is there not a correlation between the mathematics of fractals and human understanding as such? Why should there consequently be a “reorientation of fundamental thinking”? Did not this “fundamental thinking” lead to the discovery of fractals in the first place? Notice in the last sentence: nature should not be understood, but viewed with “wonder”. Now TH2 does not repudiate that nature in itself has beautiful designs and workings. Yet what does this statement have to do with fractal geometry per se? Nothing. This is not science. It is the standard case of shoddy metaphysical speculation by amateurs presuming that the laws of mathematics dictate how man thinks, wills and perceives the world. This is a call for a new epistemology, of how man knows, not for a “new science”.
IV. F. DAVID PEAT: GNOSTIC. Of the three abovementioned worldviews, it is the first (i.e. the world as numbers) to which TH2 will concentrate in this analysis. More specifically, of how chaos theory and fractal geometry have been used by a Canadian physicist who, based on these mathematical fields, calls on humanity to “embrace a new ethic and way of being.”[3] F. David Peat, formerly of Queen’s University and researcher at the National Research Council of Canada, writer for radio and stage, has in TH2's estimation, after reading his book The Philosopher’s Stone, Chaos, Synchronicity, and the Hidden Order of the World, reached a new summit of mathematical obscurantism.[4] As shall be seen below, we have in this text a prime example of how to transform science into gnosis, of how to garner “superior knowledge” from, in this case, fractal geometry and chaos theory. Peat’s book once again authenticates the dictum that the popularizer of science, who is not an expert or leader in the field of his chosen endeavor, is invariably the worst and often the most dangerous of philosophers.
V. CHAOS THEORY. It was introduced in the early 1960s with the publication of a paper by the atmospheric scientist Edward Lorenz (1917-2008).[5] Chaos theory forms one part of the subject known to mathematicians as nonlinear dynamics, pertaining to the analysis of interactions and changes over time of a system of variables. A system is defined as “chaotic” if small changes in initial conditions of the system produce large changes later in time - and this what Lorenz discovered in the unusual numerical outputs generated by a computer model simulation of weather. The simulation used a constant number as an initial condition, and a graph was generated showing changes of a parameter over a certain time frame. However, in other simulations, when the initial constant was changed only minutely, the numerical results produced was not exactly as other simulations (with just slightly differing initial conditions). The hypothesized implication? Small weather disturbances at a particular time can later on generate unexpected and even disordered results. Hence the term “chaos”.[6] This is why we hear of such expressions as the “butterfly effect”. The flap of a butterfly’s wings (a minor atmospheric disturbance) can create an “unpredictable” atmospheric phenomenon at a different place and time. Thus Lorenz could deliver a lecture entitled: “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set off a Tornado in Texas?”[7]
VI. TELECONNECTIONS EXAGGERATED. Now when such catchphrases as the “butterfly effect” and “chaos” are invoked, those who like to jump onto bandwagons are inclined overemphasize or misconstrue chaos theory in three ways: Firstly, in relation to atmospheric phenomena, for example, the case is too often put forward that chaos theory means or suggests extreme or highly unusual conditions. The very word “chaos” itself infers something that is out of control. It is then no surprise that such referent terms for equations that “blow up” or “monsters” have come into being. The teleconnection between a butterfly’s flap in Brazil and a tornado in Texas may be a highly elegant notion. Though in theory is this argument made, popularizers of chaos theory frequently fail to remark that minor atmospheric perturbations can also mitigate extreme conditions. Lorenz:
If the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado... the most they [small atmospheric disturbances] can do is to modify the sequence in which these events occur.[8]
Emphasis is placed on extreme conditions only to generate undue sensationalism. Could it be that the air TH2 exhales can cause a tsunami to ravage the shorelines of Japan? Such cross-correlations are ridiculous, let alone impossible to confirm. The butterfly-tornado analogy was employed by Lorenz for instructive purposes and refers only to the mathematical or formal consideration of initial conditions.
VII. PRECISION VERSUS UNCERTAINTY. Secondly, there is the situation with the initial condition itself. The mistake made here is simple enough. Namely “uncertainty” is convoluted with precision. Since the prediction of a process cannot be exact (theory cannot imitate reality with 100% accuracy, which is obvious, otherwise science would know “everything”) an inference is made that these processes are indeterminable. Thus the belief in chaotic processes (or “noise”) occurring at the smallest level of detail (numerically expressed by many decimal places) or at the smallest physical dimensions. In a prestigious science magazine discussing chaos theory, this remark is found: “There is a sensitive dependence to initial conditions which prevents long-term prediction... due to the uncertainty in our measurements of initial conditions”[9] Could not the word “uncertainty” be substituted with the phrase “lack of finer precision”? Does not word uncertainty indirectly suggest a lack of order in the natural world, of a tendency to purposelessness, of no rational scientific explanation of why such changes in a particular parameter occur over time?
IX. EQUATIONS APPROXIMATE. Take the following sequence of numbers and say that each was an initial condition value used in a computer model simulation: 4, 4.1, 4.17, 4.175, 4.1758, 4.17583. Further, say that in each of the respective simulations that model results increasingly resembled real world conditions. What, then, is happening here? Obviously, precision is being increased. Why is it being increased? Perhaps technological advancements have made it possible to more accurately gauge the phenomenon in question. Or maybe a better numerical scheme has been developed. Lorenz once again: The bulk of our conclusions are based on computer simulation of the atmosphere. The equations to be solved represent our best attempts to approximate the equations actually governing the atmosphere by equations which are compatible with present computer capabilities.[11]
Most importantly, Lorenz mentions “inevitable approximations” which are “not exact forecasts but best forecasts”, “best” meant as in the degree of precision and not as an indicator of chaos.
X. PROTO-CHAOS THEORY. The word chaos is inappropriately used as it is presumes that the finer details of the natural order of existence have not been sensed biologically or cannot be “seen” technologically with whatever kind of instrumentation. The philosophy which undergirds such a view is not dissimilar from that of Lucretis (ca. 99 - 55 BC), himself a subscriber to chaos in nature. An extract from his De Rerum Natura goes:And there you will see how many bodies, set in motion
blind impacts, change their course and bound and rebound
and turn and return this way and that in all directions.
All this activity, of course, comes from the atoms,
for at first these first-beginnings move by themselves,
then the bodies made by the smallest combinations
- the nearest, so to speak, to the impact of the atoms -
are set in motion, driven by blind blows from these,
and they in turn bombard those that are slightly bigger,
and so the motion mounts from the atoms, little by little,
until it emerges to the level of our senses,
so that the motes are moved which we see in the sunbeam,
although the blows that cause their motion are unseen.[12]
The phrase “blind blows” is analogous to what is modernly understood as indeterminacy, uncertainty, chaos, and so forth.
XII. VERHULST EQUATION. F. David peat dispenses with the notion of precision and nature's deterministic laws. He characterizes science as: ...a world of shadows and shadows of shadows. And within that new world, the whole notion of the control of nature assumes a radically different meaning, for our attitude toward the future and its prediction is closer to an intelligible art than to the certainty of a rigid mechanical scheme.[14]
Here we notice the dive into gnosis: “a world of shadows and shadows of shadows”. Obscurum per obscuris. Peat is turning science into obscurantism by making science into an “art”. He further questions truthfulness of the assumed determinism of nature: “Is there, perhaps, an element of the irrational in nature, something fine enough to swim through the net of deterministic chaos theory?”[15] He proposes this idea by reference to the Verhulst equation - a function used by researchers to investigate biological population growth [16]. This equation, which exhibits “chaotic” properties, can be written as:
P = r X (1-X)
where P is the predicted population, X is a population value ranging from 0 to 1 (0=extinction, 1=maximum) and r is the growth rate of that population. If one encodes this formula into a computer program using varying values of r (e.g. 2.7, 2.9, 3.4, 3.5, 3.55, 3.57, 3.58212, 3.58283, 3.584, 4.0) and examines the output, it is found that iterated values of P in respective model runs stabilize to one value, leap to and fro between two values, then four, and then something called “chaos” occurs where numbers exhibit no discernible periodicities or patterns. Now has chaos been demonstrated to occur in the natural world after comparison to real-world data? No. If so, why does Peat so confidently extrapolate chaos theory to be a truth of nature? Chaos theory, as only a theory, indicates that prediction accuracy decreases over time. But does this mean that nature is “irrational” because it cannot be predicted to a prefect level of accuracy? Not at all. Again, the situation of precision and the provisional character of mathematical formulations intrude.
XIII. CIRCUMLOCUTION. To Peat chaos theory is not really mathematics. Even though he claims it to be more so an "art", he is transmogrifying chaos theory into a philosophy, which appears akin to panpsychism [17]:
[Chaos theory]... paints new maps of the world, picturing a universe in which each atom, rock, and star drinks of the same boundless waters of creativity. Nature is a symphony in which new themes, harmonies and structures are ever-unfolding. These structures and processes remain in constant communication with each other and engage in a dance of form. Life swims in an ocean of meaning, in activity and coherence that blur the distinctions between the animate and inanimate, between thought and matter.[18]
Since Peat does not accept nature to be deterministic, he must ascribe to it some innate and self-caused life force, be it “irrational” or otherwise. Moreover, by blurring the distinction between thought and matter, an extrapolation made from a false presupposition of the non-existence of real distinctions between things in the natural world, and thus Peat interlocks man as such into the natural order of existence. Note that that the last quotation comes from a chapter entitled “The Chaotic Universe: Fractals, Intelligence, and Freedom”. What does freedom have to do with mathematics? Other chapters have titles such as “Quantum Theory: From Determinism to Ambiguity”, “The Symphony of Life”, “The Heartbeat of Creation” and “Gentle Action for a Harmonious World”. Science and nature become ambiguous, musical, dulcifying. Again, another sign of crass gnosticism.
XIV. NATURE IS ORDERED. When TH2 looks at the natural world he does not see ambiguity or gentleness. Rather, the hard, specific, impersonal laws of nature are seen to be at work. The roar of a river, a predator devouring its prey, a hurricane battering a coastline, a chimpanzee grooming tics from its progeny - these are rugged and coarse conditions. Consider, for example, the change of an animal’s fur with the seasons: this occurs for a specific reason, namely camouflage. Look at the structural intricacies of a duck's wings, of how its feathers act as a heat insulator and a waterproofing mechanism, including their aerodynamic properties which permit for various types of manoeuvering (gliding, hovering, descending, ascending, flapping, turning) - all of which aeronautical engineers have only crudely reproduced with metals and plastics. Consider that the shape of a hummingbird’s beak is such that it fits perfectly into the flower from which is obtains nectar. Not only this, each species of hummingbird, with their differently contoured beaks, correspond exactly to the exact structure of flower species upon which it feeds. There is no “ambiguity” or disorderliness here, but a biological arrangement with precisely tuned features. By assuming the natural world chaotic Peat, educated as a physicist, fails to realize that science cannot be science unless an order is presupposed. Long ago the mathematician Alfred North Whitehead (1861-1947) wrote: ...there can be no living science unless there is a widespread instinctive conviction in the existence of an Order of Things, and, in particular, of an Order of Nature.[19]
An order must be assumed because if nature is shadowy, chaotic, intangible, and indeterminable, then man loses his grip on reality, with the end result being the conflation of science and gnosis.
XV. FRACTALS. Fractal geometry has been mostly developed by the French mathematician Benoit Mandelbrot (b. 1924), popularized through his 1977 “Essay” thereof, written for a non-technical audience.[20] It concerns itself primarily with the scale of graphically depicted objects in the natural world. In other words, it attempts to use mathematical equations to pictorially delineate the shape (or topology) of physical things at differing scales, from small to large. Many colorfully complex fractal images have been generated for magazine articles and on the internet, of computer-generated clouds, mountains, rivers, cells, crystalline structures, and other biogeophysical phenomena. Like the “butterfly effect” of chaos theory, the graphical productions of fractal geometry are ornate and visually appealing.
XVI. BRITAIN'S COASTLINE. Using Mandelbrot’s now famous example, say that there is polyhedron-like figure consisting of lines and curves that represents the coastline of Britain. Let us also say that we find such figure in the form of a map in the page of an atlas. Looking at the page it is noticed that the figure resembles satellite images of the island taken from space. The page in the atlas also supplies the reader with a legend, showing the map scale. In this example, let us further say that the scale is 1 cm = 200 km, i.e. a distance of 1 cm on the map on the page of the atlas equals a land distance of 200 km in actuality. At this particular scale, and assuming a basic knowledge of geography, we recognize the map figure as the island of Britain. Though, this recognition occurs only at the scale 1 cm = 200 km. If a more detailed (or precise) view of a particular segment of Britain’s coastline is desired, we have to “focus in” as it were. But, then, what happens? The map of Britain’s coastline at the 1 cm:200 km scale is no longer utilizable because as we focus in on the specific segment of coastline the lines and curves of the map are too long and thick to visually capture the higher resolution required. Therefore the scale must be adjusted, more line segments must be added and made smaller and thinner so as to make the sector of the British coastline visually resolvable. In other words, precision is being increased. What is also happening is that the shape of the segmented coastline is moving from regularity to irregularity. A more or less straight line (as viewed far away in space) is changing into zigzag type feature. If even greater precision is required, we might, for instance, want to take that particular segment of coastline and view a few metres of a sandy beach as juxtaposed to the waterline. Again does the scale have to be modified, more lines added, made thinner and shorter, so that a higher definition can be achieved - and it is this process of altering the dimension of lines, planes and three-dimensional objects which the mathematics of fractals emulates. Mandelbrot introduced what he calls a “fractal dimension” to characterize this methodology. It is mathematically represented as:
D > DT
where D is the fractal dimension (not always integer) and DT is the topological dimension (always an integer). In simpler phraseology, D denotes a proportion of irregularity in shape of an object. As D increases, irregularity increases. D, which is the object in its “regular” dimension or shape, must always be greater than DT. Analogically, think of DT as the first, standard, unmodified or assumed object before it is changed by D. In our example, it is the original map of the British coastline before we “focused in” on the segmented shoreline. Also, think of DT as a kind of synthetic, cleanly circumscribed, Euclidean view. It is always an integer. It is an idealized, non-complex “clear view” of the object in question; and think of D as the more intricated, labyrinthine view of the original object (DT) that is modified. Because it is a real number (it has decimal places) it would be presumed that higher value of D would infer a higher amount of precision. However, we run into a problem if the mathematical theory of fractal geometry is used to mimic physical phenomena (objective reality). Mandelbrot stated: “one of the central goals of this work is to establish D in a central position in empirical science.”[21] Though Mandelbrot contradicts himself only a page later. The “effective dimension”, he says, “should not be defined precisely... [it] concerns the relation between mathematical sets and natural objects.”[22] But is not this statement at variance his aim to give the fractal dimension an empirical credibility? As one “focuses in” on the British shoreline, as more details are revealed when D increases, it would be expected that dimensions should be defined more precisely. How is it possible to establish an interrelationship between symbolical-mathematical formulations which re-present “natural objects” (reality) without insisting upon a greater degree of precision in the fractal dimension? The equations must conform to the structure and processes of the natural world and not vice versa. Or, philosophically speaking, the mind, which constructs and collates the symbolic system, cannot dictate how the extrinsic world should operate. Reality comes first, theory second. Science does not create, it discovers.
XVIII. MATHEMATICAL INFINITISM. In opposition to Mandelbrot’s common sense claim, that he does “not consider the fractal point of view a panacea”,[25] Peat, again distorting the situation to give credence to his philosophy, writes in a wishy-washy diction: “There is no end to the Mandelbrot set, and to fly inside is to participate in the unfolding of a mathematical symphony.”[26] Nature becomes a “mathematical symphony” of signs and symbols, a semiotica neurotica if you will, where all distinctions between natural functions and forms transmute into a hazy mire of mathematical vagaries. Nature is not real. It is an “illusion”. Because the fractal dimension of an object forever moves from a state of regularity to irregularity, from simple to intricated, “from determinism to ambiguity”, as we continually “focus in” on the fractal image, we become lost or we “fly inside” infinity, and we do this forever. There are no limits within this picturesque realm. Since lines and curves can be scaled down an infinite number of times, angular differences between these curves and lines disintegrate into a sort of eternalistic nothingness. The supposed implication according to Peat?: “the true circumference of the British coast is the same as that of North and South America combined! It is infinite”. Lines and curves “have no definite slope”, they “cannot be differentiated.”[27] TH2 doubts whether ship navigators and skiers - people who work and recreate in the real world - would agree with such gnostic verbiage.
XVIII. ESOTERICA. F. David Peat's book The Philosopher’s Stone (let alone his other publications) is your typical discourse in obscurantism, cloaked with mathematics to make it appear that the ideas presented form part of the “new science”. In actuality, his science is an old science, though it is not science at all. The fancy graphs, figures and maps given in this book are really no different from the esoteric scribblings of the gnostics of Antiquity. Peat takes the signs and symbols associated with the mathematics of fractal geometry and chaos theory, disengages them from the objective reality which they are supposed to represent and simulate, and then swirls them into poetic descriptions where all meaning is to be found within the mind. Ridiculous.
XIX. SEMIOTICS. The word semiotics is derived from the Greek word semeiousthai, meaning “to interpret signs”. Modern semiotics, influenced by the American logician C.S. Peirce (1839-1914) and popularized by the Italian scholar Umberto Eco (b. 1932), concerns itself with how signs and symbols give meaning in natural and artificially constructed languages. One aspect of semiotics deals with the deciphering of language codes. Eco describes Peirce’s theory on the interpretation of language signs as follows:
...in order to establish what the interpretant of a sign is, it is necessary to name it by means of another sign which in turn has an interpretant to be named by another sign, and so on. At this point begins a process of unlimited semiosis, which, paradoxical as it may be, is the only guarantee for the foundation of a semiotic system capable of checking itself entirely by its own means.[28]
A “semiotic system capable of checking itself entirely by its own means” means that it is resolvable within itself, which, as above, goes against Gödel’s Theorem of Incompleteness. Thus the symbolic free associationism of Peirce and Eco is, of course, a load of crap in the final analysis. Note that the main character is Eco’s best selling novel The Name of the Rose was modelled after William of Ockham (ca. 1288-1348), the notorious Medieval heretic, popularly known for his nominalism. Namely, that all truth and knowledge is bound within the mind. Ockham denied causality in the natural world, by advocating occasionalism, and contended that signs were “mental qualities” without association to the world outside. It is this mentalistic symbolism, this taking of the signs and symbols from chaos theory and fractal geometry to create an infinite playground of illusion, which F. David Peat endorses in his book. Peat may think TH2 incorrect in judgement, though when he writes that “the whole notion of the ‘correct answer’ may itself be a mistake”[29] he simply cancels out his own contention.
XX. DIRT, ROCKS AND WATER. Now back to objective reality. It is time to disprove Peat’s gnostic interpretation of nature by actually encountering the rugged world of empirical reality. Consider the branch of statistics called regression analysis. Regression uses real world observations in conjunction with a mathematical technique to derive an empirical equation. A simple linear regression function is given as:
Y = a + bX
where Y and X are respectively dependent and independent variables, and a and b are constants. In regression analysis, the values of Y and X are measured/observed data, they are the known (or assumed) values in the real world. The unknowns are a and b, derived from a “calibration” technique which allows Y to be computed for other times and places if only X is known. Since a and b are constants, they need not be derived again as they are “universally” applicable. In effect, the constants a and b "secure" the regression equation to concrete reality, providing an objective foundation to the equation. In this context, TH2 came across a very interesting short note in a geological journal[30] demonstrating how various studies in geomorphology, sedimentology and palaeohydrology (dirt, rocks and water) improperly used regression equations. A suite of regression equations, originally calibrated to conform to real world physical properties and processes, were mistakenly rearranged and solved as if they were purely symbolic functions without any connection to concrete reality. These equations, like that given above, were treated as if they were not already "hooked" into reality, so to speak. After they were rearranged and solved for X instead of Y (interchanging the dependent and independent variables) the author of this note discovered, or unearthed if we are to be metaphorical, that the new formulations produced errors on the order of hundred’s of percent. Thus, once again that maxim of realist philosophy is validated: matter is the condition of limitation.
XXI. THE TAO OF CRAP. Though it is the material world itself that is completely overlooked in Peat’s book. He follows in the tradition of Fritjof Capra (b. 1939) and his irrational, anti-material perspective of science. [31] Capra, a gnostic par excellence, is a chief representative of that company of scientist-turned-pseudo-philosophers who are, with popular books sales, nonchalantly duping the general public into thinking that modern science owes its development to the vagaries of Eastern spirituality. Copernicus, Galileo and Newton would rightly cry injustice.
NOTES / REFERENCES
1. For an analysis of these three systems of the world see S.L. Jaki, The Relevance of Physics (Edinburgh: Scottish Academic Press, 1992), pp. 3-137. Originally published in 1970.
2. T. Wegner and M. Peterson, The Waite Group’s Fractal Creations (Mill Valley, CA: Waite Group Press, 1991), p. 15.
3. F.D. Peat, The Philosopher’s Stone, Chaos, Synchronicity, and the Hidden Order of the World (New York: Bantam Books, 1991), p. 206. Hereafter referenced as TPS.
4. All kinds of New Age esoterica is promoted at Peat's web site. LINK
5. E. Lorenz, “Deterministic Nonperiodic Flow”, Journal of the Atmospheric Sciences, 1963, vol. 20, pp. 130-141. Chaos theory was popularized in the late 1980s with a book by the journalist James Gleick, Chaos: Making a New Science (New York: Viking, 1987).
6. This is why Lorenz entitled his paper “Deterministic Nonperiodic Flow”, which is a contradiction in phraseology when logically considered. How can that which is “nonperiodic” (chaotic, indeterminable) be “deterministic” (ordered, discernible pattern) at the same time?
7. The text is given in The Essence of Chaos (Seattle: University Washington Press, 1993), Appendix 1, pp. 181-184. Lecture delivered at the 139th meeting of American Association for the Advancement of Science in Washington, DC on December 29, 1972.
8. Ibid.
9. J. Guckenheimer, “Noise in Chaotic Systems”, Nature, 22 July, 1982, vol. 362, p. 359.
10. H. Kenner, “Computing a Butterfly’s Effect on the Weather”, BYTE Magazine, May 1988, pp. 51-54. BYTE became defunct in 1998.
11. Lorenz, op. cit.
12. On the Nature of the Universe, trans. J.H. Martinbrand (New York: Frederick Ungar Pub. Co., 1968), bk. II, vv. 129-141, pp. 37-38.
13. W.M. Schaffer, “Order and Chaos in Ecological Systems”, Ecology, 1985, vol. 66, p. 104.
14. TPS, p. 154.
15. TPS, p. 197.
16. This function originates from Flemish mathematician Pierre-François Verhulst (1804-1849). Tellingly, he derived it (in 1838) after reading An Essay on the Principle of Population by Rev. Thomas Malthus (1766-1834).
17. Panpsychism comes in varieties, but basically it is a view that says that say some "mind" or consciousness unites and lies behind the totality of all that is (e.g. the universe). An analogy would be "The Force" in the Star Wars film series. It commonly attracts those of a scientific-technological bent, like Alfred North Whitehead (see note 19). Panpsychism is just a more sophisticated version of animism, as pantheism is an emotionalistic version of materialism.
18. TPS, p. 205.
19. A.N. Whitehead, Science and the Modern World (New York: The Free Press, 1967), Lowell Lectures (1925), pp. 3-4. The failure to admit an order in nature is a delusion of the subjectivist philosophy of science advocated by the Copenhagen school.
20. The Fractal Geometry of Nature (New York: W.H. Freeman and Co., 1983 [1977]). Hereafter referenced as FGN. This original scientific paper reference is B.B. Mandelbrot, "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension", Science, 1967, vol. 156, no. 3775, pp. 636-638.
21. FGN, p. 16.
22. FGN, p. 17.
23. FGN, pp. 22, 18.
24. Gödel’s classic paper on the subject, published in 1931, is entitled “Of Formally Undecidable Propositions of Principia Mathematica and Related Systems I”, Collected Works, Kurt Gödel (Oxford University Press, 1986), vol. 1, pp. 145-195. A non-technical description of Gödel’s theorem is given in E. Nagel and J.R. Newman, Gödel’s Proof (New York University Press, 1958). See especially pp. 85-97.
25. FGN, p. 3.
26. TPS, p. 171.
27. TPS, pp. 165, 168.
28. A Theory of Semiotics (Bloomington, IN: Indiana University Press, 1976), p. 68.
29. TPS, p. 209. Authors claiming that truth must be redefined, and that this must be taken as a truth, is a commonplace error found in popularizations of the “new physics”. For instance, P. Davies and J. Gribbin, The Matter Myth, Dramatic Discoveries that Challenge our Understanding of Physical Reality (New York: Simon & Shuster/Touchstone, 1992), p. 18: “the very notion by what we mean by truth and reality must go into the melting pot.” One will notice in such books the Eastern premise of ascribing reality as an illusion. Davies and Gribbin use the neologism “the matter myth”. The physicist David Lindley of Cambridge University even equates cosmology with mythology in his The End of Physics, The Myth of a Unified Theory (New York: Basic Books, 1993), p. 255: “The story of everything will be, in precise terms, a myth. A myth is a story that makes sense within its own terms.” This making “sense within its own terms” further shows that Lindley ignores Gödel’s Incompleteness Theorem.
30. G.P.Williams, “Improper Use of Regression Equations in Earth Sciences”, Geology, 1983, vol. 11, pp. 195-197.
31. An example would be The Tao of Physics, An Explanation of the Parallels Between Modern Physics and Eastern Mysticism (Boston: Shambala, 1991[1975], third edition), p. 81: “In modern physics... the traditional concepts of space and time, of isolated objects, and of cause and effect, lose their meaning. Such an experience, however, is very similar to that of the Eastern mystics. The similarity becomes apparent in quantum and relativity theory, and becomes even stronger in the ‘quantum-relativistic’ models of subatomic physics where both these theories combine to produce the most striking parallels to Eastern mysticism.” Such pseudoscientific quackery is similarly given in a copycat book by G. Zukav, The Dancing Wu Li Masters, An Overview of the New Physics (New York: Bantam Books, 1979), pp. 92-93: “The new physics tells us that an observer cannot observe without altering what he sees. Observer and observed are interrelated in a real and fundamental sense. The exact nature of this interrelation is not clear, but there is a growing body of evidence that the distinction between the ‘in here’ and the ‘out there’ is illusion. The conceptual framework of quantum mechanics... forces contemporary physicists to express themselves in a manner that sounds... like the language of mystics... what we experience is not external reality, but our interaction with it.” The confusion between the “in here” (the mind) and the “out there” (the world) is yet again another incarnation of that Kantianism claiming that the material world is a subjective emanation of the mind.
EPH–5 / SEMIOTICA NEUROTICA
