|This essay by Robert R. Prechter, Jr. originally appeared in The Elliott Wave Theorist in August 1999 and was republished in the MTA Journal, Summer-Fall 2000. It was reprinted in:
Prechter, Robert R. (2003). Pioneering Studies in Socionomics. Gainesville, Georgia: New Classics Library, pp. 294-308 (Note: The book is also available for purchase as part of a two-volume set.)
It is one thing to say that the Wave Principle makes sense in the context of nature and its growth forms. It is another to postulate a hypothesis about its mechanism. The biological and behavioral sciences have produced enough relevant work to make a case that unconscious paleomentational processes produce a herding impulse with Fibonacci-related tendencies in both individuals and collectives. Man’s unconscious mind, in conjunction with others, is thus disposed toward producing a pattern having the properties of the Wave Principle.
The Paleomentational Herding Impulse
Over a lifetime of work, Paul MacLean, former head of the Laboratory for Brain Evolution at the National Institute of Mental Health, has developed a mass of evidence supporting the concept of a “triune” brain, i.e., one that is divided into three basic parts. The primitive brain stem, called the basal ganglia, which we share with animal forms as low as reptiles, controls impulses essential to survival. The limbic system, which we share with mammals, controls emotions. The neocortex, which is significantly developed only in humans, is the seat of reason. Thus, we actually have three connected minds: primal, emotional and rational. Figure 1, from MacLean’s book, The Triune Brain in Evolution,1 roughly shows their physical locations.
The neocortex is involved in the preservation of the individual by processing ideas using reason. It derives its information from the external world, and its convictions are malleable thereby. In contrast, the styles of mentation outside the cerebral cortex are unreasoning, impulsive and very rigid. The “thinking” done by the brain stem and limbic system is primitive and pre-rational, exactly as in animals that rely exclusively upon them.
The basal ganglia control brain functions that are often termed instinctive: the desire for security, the reaction to fear, the desire to acquire, the desire for pleasure, fighting, fleeing, territorialism, migration, hoarding, grooming, choosing a mate, breeding, the establishment of social hierarchy and the selection of leaders. More pertinent to our discussion, this bunch of nerves also controls coordinated behavior such as flocking, schooling and herding. All these brain functions insure life-saving or life-enhancing action under most circumstances and are fundamental to animal motivation. Due to our evolutionary background, they are integral to human motivation as well. In effect, then, portions of the brain are “hardwired for certain emotional and physical patterns of reaction”2 to insure survival of the species. Presumably, herding behavior, which derives from the same primitive portion of the brain, is similarly hardwired and impulsive. As one of its primitive tools of survival, then, emotional impulses from the limbic system impel a desire among individuals to seek signals from others in matters of knowledge and behavior and therefore to align their feelings and convictions with those of the group.
There is not only a physical distinction between the neocortex and the primitive brain but a functional dissociation between them. The intellect of the neocortex and the emotional mentation of the limbic system are so independent that “the limbic system has the capacity to generate out-of-context, affective feelings of conviction that we attach to our beliefs regardless of whether they are true or false.”3 Feelings of certainty can be so overwhelming that they stand fast in the face of logic and contradiction. They can attach themselves to a political doctrine, a social plan, the verity of a religion, the surety of winning on the next spin of the roulette wheel, the presumed path of a financial market or any other idea.4 This tendency is so powerful that Robert Thatcher, a neuroscientist at the University of South Florida College of Medicine in Tampa, says, “The limbic system is where we live, and the cortex is basically a slave to that.”5 While this may be an overstatement, a soft version of that depiction, which appears to be a minimum statement of the facts, is that most people live in the limbic system with respect to fields of knowledge and activity about which they lack either expertise or wisdom.
This tendency is marked in financial markets, where most people feel lost and buffeted by forces that they cannot control or foresee. In the 1920s, Cambridge economist A.C. Pigou connected cooperative social dynamics to booms and depression.6 His idea is that individuals routinely correct their own errors of thought when operating alone but abdicate their responsibility to do so in matters that have strong social agreement, regardless of the egregiousness of the ideational error. In Pigou’s words:
Apart altogether from the financial ties by which different businessmen are bound together, there exists among them a certain measure of psychological interdependence. A change of tone in one part of the business world diffuses itself, in a quite unreasoning manner, over other and wholly disconnected parts.7
“Wall Street” certainly shares aspects of a crowd, and there is abundant evidence that herding behavior exists among stock market participants. Myriad measures of market optimism and pessimism8 show that in the aggregate, such sentiments among both the public and financial professionals wax and wane concurrently with the trend and level of the market. This tendency is not simply fairly common; it is ubiquitous. Most people get virtually all of their ideas about financial markets from other people, through newspapers, television, tipsters and analysts, without checking a thing. They think, “Who am I to check? These other people are supposed to be experts.” The unconscious mind says: You have too little basis upon which to exercise reason; your only alternative is to assume that the herd knows where it is going.
In 1987, three researchers from the University of Arizona and Indiana University conducted sixty laboratory market simulations using as few as a dozen volunteers, typically economics students but also, in some experiments, professional businessmen. Despite giving all the participants the same perfect knowledge of coming dividend prospects and then an actual declared dividend at the end of the simulated trading day, which could vary more or less randomly but which would average a certain amount, the subjects in these experiments repeatedly created a boom-and-bust market profile. The extremity of that profile was a function of the participants’ lack of experience in the speculative arena. Head research economist Vernon L. Smith came to this conclusion: “We find that inexperienced traders never trade consistently near fundamental value, and most commonly generate a boom followed by a crash….”9 Groups that have experienced one crash “continue to bubble and crash, but at reduced volume. Groups brought back for a third trading session tend to trade near fundamental dividend value.” In the real world, “these bubbles and crashes would be a lot less likely if the same traders were in the market all the time,” but novices are always entering the market.
While these experiments were conducted as if participants could actually possess true knowledge of coming events and so-called fundamental value, no such knowledge is available in the real world. The fact that participants create a boom-bust pattern anyway is overwhelming evidence of the power of the herding impulse.
It is not only novices who fall in line. It is a lesser-known fact that the vast majority of professionals herd just like the naive majority. Figure 2 shows the percentage of cash held at institutions as it relates to the level of the S&P 500 Composite index. As you can see, the two data series move roughly together, showing that professional fund managers herd right along with the market just as the public does.
Apparent expressions of cold reason by professionals follow herding patterns as well. Finance professor Robert Olsen recently conducted a study of 4000 corporate earnings estimates by company analysts and reached this conclusion:
Experts’ earnings predictions exhibit positive bias and disappointing accuracy. These shortcomings are usually attributed to some combination of incomplete knowledge, incompetence, and/or misrepresentation. This article suggests that the human desire for consensus leads to herding behavior among earnings forecasters.10
Olsen’s study shows that the more analysts are wrong, which is another source of stress, the more their herding behavior increases.11
How can seemingly rational professionals be so utterly seduced by the opinion of their peers that they will not only hold, but change opinions collectively? Recall that the neocortex is to a significant degree functionally dissociated from the limbic system. This means not only that feelings of conviction may attach to utterly contradictory ideas in different people, but that they can do so in the same person at different times. In other words, the same brain can support opposite views with equally intense emotion, depending upon the demands of survival perceived by the limbic system. This fact relates directly to the behavior of financial market participants, who can be flushed with confidence one day and in a state of utter panic the next. As Yale economist Robert Schiller puts it, “You would think enlightened people would not have firm opinions” about markets, “but they do, and it changes all the time.”12 Throughout the herding process, whether the markets are real or simulated, and whether the participants are novices or professionals, the general conviction of therightness of stock valuation at each price level is powerful, emotional and impervious to argument.
Falling into line with others for self-preservation involves not only the pursuit of positive values but also the avoidance of negative values, in which case the reinforcing emotions are even stronger. Reptiles and birds harass strangers. A flock of poultry will peck to death any individual bird that has wounds or blemishes. Likewise, humans can be a threat to each other if there are perceived differences between them. It is an advantage to survival, then, to avoid rejection by revealing your sameness. D.C. Gajdusek researched a long-hidden Stone Age tribe that had never seen Western people and soon noticed that they mimicked his behavior; whenever he scratched his head or put his hand on his hip, the whole tribe did the same thing.13 Says MacLean, “It has been suggested that such imitation may have some protective value by signifying, ‘I am like you.'” He adds, “This form of behavior is phylogenetically deeply ingrained.”14
The limbic system bluntly assumes that all expressions of “I am not like you” are infused with danger. Thus, herding and mimicking are preservative behavior. They are powerful because they are impelled, regardless of reasoning, by a primitive system of mentation that, however uninformed, is trying to save your life.
As with so many useful paleomentational tools, herding behavior is counterproductive with respect to success in the world of modern financial speculation. If a financial market is soaring or crashing, the limbic system senses an opportunity or a threat and orders you to join the herd so that your chances for success or survival will improve. The limbic system produces emotions that support those impulses, including hope, euphoria, cautiousness and panic. The actions thus impelled lead one inevitably to the opposite of survival and success, which is why the vast majority of people lose when they speculate.15 In a great number of situations, hoping and herding can contribute to your well-being. Not in financial markets. In many cases, panicking and fleeing when others do cuts your risk. Not in financial markets. The important point with respect to this aspect of financial markets is that for many people, repeated failure does little to deter the behavior. If repeated loss and agony cannot overcome the limbic system’s impulses, then it certainly must have free rein in comparatively benign social settings.
Regardless of their inappropriateness to financial markets, these impulses are not irrational because they have a purpose, no matter how ill-applied in modern life. Yet neither are they rational, as they are within men’s unconscious minds, i.e., their basal ganglia and limbic system, which are equipped to operate without and to override the conscious input of reason. These impulses, then, serve rational general goals but are irrationally applied to too many specific situations.
Phi in the Unconscious Mentational Patterns of Individuals and Groups
At this point, we have identified unconscious, impulsive mental processes in individual human beings that are involved in governing behavior with respect to one’s fellows in a social setting. Is it logical to expect such impulses to be patterned? When the unconscious mind operates, it could hardly do so randomly, as that would mean no thought at all. It must operate in patterns peculiar to it. Indeed, the limbic systems of individuals produce the same patterns of behavior over and over when those individuals are in groups. The interesting observation is how the behavior is patterned. When we investigate statistical and scientific material on the subject, rare as it is, we find that our Fibonacci-structured neurons and microtubules participate in Fibonacci patterns of mentation.
Perhaps the most rigorous work in this area has been performed by psychologists in a series of studies on choice. G.A. Kelly proposed in 1955 that every person evaluates the world around him using a system of bipolar constructs.16 When judging others, for instance, one end of each pole represents a maximum positive trait and the other a maximum negative trait, such as honest/dishonest, strong/weak, etc. Kelly had assumed that average responses in value-neutral situations would be 0.50. He was wrong. Experiments show a human bent toward favor or optimism that results in a response ratio in value-neutral situations of 0.62, which is phi. Numerous binary-choice experiments have reproduced this finding, regardless of the type of constructs or the age, nationality or background of the subjects. To name just a few, the ratio of 62/38 results when choosing “and” over “but” to link character traits, when evaluating factors in the work environment, and in the frequency of cooperative choices in the prisoner’s dilemma.17
Psychologist Vladimir Lefebvre of the School of Social Sciences at the University of California in Irvine and Jack Adams-Webber of Brock University corroborate these findings. When Lefebvre asks subjects to choose between two options about which they have no strong feelings and/or little knowledge, answers tend to divide into Fibonacci proportion: 62% to 38%. When he asks subjects to sort indistinguishable objects into two piles, they tend to divide them into a 62/38 ratio. When subjects are asked to judge the “lightness” of gray paper against solid white and solid black, they persistently mark it either 62% or 38% light,18 favoring the former. (See Figure 3.) When Adams-Webber asks subjects to evaluate their friends and acquaintances in terms of bipolar attributes, they choose the positive pole 62% of the time on average.19 When he asks a subject to decide how many of his own attributes another shares, the average commonality assigned is 0.625.20 When subjects are given scenarios that require a moral action and asked what percentage of people would take good actions vs. bad actions, their answers average 62%.21 “When people say they feel 50/50 on a subject,” Lefebvre says, “chances are it’s more like 62/38.”22
Lefebvre concludes from these findings, “We may suppose that in a human being, there is a special algorithm for working with codes independent of particular objects.”23 This language fits MacLean’s conclusion and LeDoux’s confirmation that the limbic system can produce emotions and attitudes that are independent of objective referents in the cortex. If these statistics reveal something about human thought, they suggest that in many, perhaps all, individual humans, and certainly in an aggregate average, opinion is predisposed to a 62/38 inclination. With respect to each individual decision, the availability of pertinent data, the influence of prior experiences and/or learned biases can modify that ratio in any given instance. However, phi is what the mind starts with. It defaults to phi whenever parameters are unclear or information insufficient for an utterly objective assessment.
This is important data because it shows a Fibonacci decision-based mentational tendency in individuals. If individual decision-making reflects phi, then it is less of a leap to accept that the Wave Principle, which also reflects phi, is one of its collective products. To narrow that step even further, we must be satisfied that phi appears in group mentation in the real world. Does Fibonacci-patterned decision-making mentation in individuals result in a Fibonacci-patterned decision-making mentation in collectives? Data from the 1930s and the 1990s suggests that it does.
Lefebvre and Adams-Webber’s experiments show unequivocally that the more individuals’ decisions are summed, the smaller is the variance from phi. In other words, while individuals may vary somewhat in the phi-based bias of their bipolar decision-making, a large sum of such decisions reflects phi quite precisely. In a real-world social context, Lefebvre notes by example that the median voting margin in California ballot initiatives over 100 years is 62%. The same ratio holds true in a study of all referenda in America over a decade24 as well as referenda in Switzerland from 1886 to 1978.25
In the early 1930s, before any such experiments were conducted or models proposed, stock market analyst Robert Rhea undertook a statistical study of bull and bear markets from 1896 to 1932. He knew nothing of Fibonacci, as his work in financial markets predated R.N. Elliott’s discovery of their Fibonacci connection by eight years. Thankfully, he published the results despite, as he put it, seeing no immediate practical value for the data. Here is his summary:
Bull markets were in progress 8143 days, while the remaining 4972 days were in bear markets. The relationship between these figures tends to show that bear markets run61.1 percent of the time required for bull periods…. The bull market[‘s]…net advance was 46.40 points. [It] was staged in four primary swings of 14.44, 17.33, 18.97 and 24.48 points respectively. The sum of these advances is 75.22. If the net advance, 46.40, is divided into the sum of advances, 75.22, the result is 1.621. The total of secondary reactions retraced 62.1 percent of the net advance.26
To generalize his findings, the stock market on average advances by 1s and retreats by .618s, in both price and time.
Lefebvre and others’ work showing that people have a natural tendency to make choices that are 61.8%optimistic and 38.2% pessimistic directly reflects Robert Rhea’s data indicating that bull markets tend both to move prices and to endure 62% relative to bear markets’ 38%. Bull markets and bear markets are the quintessential expressions of optimism and pessimism in an overall net-neutral environment for judgment. Moreover, they are created by a very large number of people, whose individual differences in decision-making style cancel each other out to leave a picture of pure Fibonacci expression, the same result produced in the aggregate in bipolar decision-making experiments. As rational cogitation would never produce such mathematical consistency, this picture must come from another source, which is likely the impulsive paleomentation of the limbic system, the part of the brain that induces herding.
While Rhea’s data need to be confirmed by more statistical studies, prospects for their confirmation appears bright. For example, in their 1996 study on log-periodic structures in stock market data, Sornette and Johansen investigate successive oscillation periods around the time of the 1987 crash and find that each period (tn) equals a value (l) to the power of the period’s place in the sequence (n), so that tn= ln. They then state outright the significance of the Fibonacci ratio that they find for l:
The “Elliott wave” technique…describes the time series of a stock price as made of different “waves.” These different waves are in relation with each other through the Fibonacci series, [whose numbers] converge to a constant (the so-called golden mean, 1.618), implying an approximate geometrical series of time scales in the underlying waves. [This idea is] compatible with our above estimate for the ratio l @ 1.5-1.7$.27
This phenomenon of time is the same as the one that R.N. Elliott described for price swings in the 1930-1939 period, as recounted in Chapter 5 of The Wave Principle of Human Social Behavior.
In the past three years, modern researchers have conducted experiments that further demonstrate Elliott’s observation that phi and the stock market are connected. The October 1997 New Scientist reports on a study that concludes that the stock market’s Hurst exponent,28 which characterizes its fractal dimension, is 0.65.29 This number is quite close to the Fibonacci ratio. However, since that time, the figure for financial auction-market activity has gotten even closer. Europhysics Letters has just published the results of a market simulation study by European physicists Caldarelli, Marsili and Zhang. Although the simulation involves only a dozen or so subjects at a time trading a supposed currency relationship, the resulting price fluctuations mimic those in the stock market. Upon measuring the fractal persistence of those patterns, the authors come to this conclusion:
The scaling behavior of the price “returns”…is very similar to that observed in a real economy. These distributions [of price differences] satisfy the scaling hypothesis…with an exponent of H = 0.62.30
The Hurst exponent of this group dynamic, then, is 0.62. Although the authors do not mention the fact, this is the Fibonacci ratio. Recall that the fractal dimension of our neurons is phi. These two studies show that the fractal dimension of the stock market is related to phi. The stock market, then, has the same fractal dimensional factor as our neurons, and both of them are the Fibonacci ratio. This is powerful evidence that our neurophysiology is compatible with, and therefore intimately involved in, the generation of the Wave Principle.
Lefebvre explains why scientists are finding phi in every aspect of both average individual mentation and collective mentation:
The golden section results from the iterative process…. Such a process must appear [in mentation] when two conditions are satisfied: (a) alternatives are polarized, that is, one alternative plays the role of the positive pole and the other one that of thenegative pole; and (b) there is no criterion for the utilitarian preference of one alternative over the other.31
This description fits people’s mental struggle with the stock market, it fits people’s participation in social life in general, and it fits the Wave Principle.
It is particularly intriguing that the study by Caldarelli et al. purposely excludes all external input of news or “fundamentals.” In other words, it purely records “all the infighting and ingenuity of the players in trying to outguess the others.”32 As Lefebvre’s work anticipates, participants in such a subjective environment should default to phi, which Elliott’s model and the latest studies show is exactly the number to which they default in real-world financial markets.
R.N. Elliott discovered before any of the above was known, that the form of mankind’s evaluation of his own productive enterprise, i.e., the stock market, has Fibonacci properties. These studies and statistics say that the mechanism that generates the Wave Principle, man’s unconscious mind, has countless Fibonacci-related properties. These findings are compatible with Elliott’s hypothesis.■
1 MacLean, P. (1990). The Triune Brain in Evolution: Role in Paleocerebral Functions. New York: Plenum Press.
2 Scuoteguazza, H. (1997, September/October). “Handling Emotional Intelligence.” The Objective American.
3 MacLean, P. (1990). The Triune Brain in Evolution, p. 17.
4 Chapters 15 through 19 of The Wave Principle of Human Social Behavior explore this point further.
5 Wright, K. (1997, October). “Babies, Bonds and Brains.” Discover, p. 78.
6 Pigou, A.C. (1927). Industrial Fluctuations. London: F. Cass.
7 Pigou, A.C. (1920). The Economics of Welfare. London: F. Cass.
8 Among others, such measures include put and call volume ratios, cash holdings by institutions, index futures premiums, the activity of margined investors, and reports of market opinion from brokers, traders, newsletter writers and investors.
9 Bishop, J.E. (1987, November 17). “Stock market experiment suggests inevitability of booms and busts.” The Wall Street Journal.
10 Olsen, R. (1996, July/August). “Implications of Herding Behavior for Earnings Estimation, Risk Assessment, and Stock Returns.” Financial Analysts Journal, pp. 37-41.
11 Just about any source of stress can induce a herding response. MacLean humorously references the tendency of governments and universities to respond to tension by forming ad hoc committees.
12 Passell, P. (1989, August 25). “Dow and reason: Distant cousins?” The New York Times.
13 Gajdusek, D.C. (1970). “Physiological and Psychological Characteristics of Stone Age Man.” Symposium on Biological Bases of Human Behavior, Engineering and Science 33, pp. 26-33, 56-62.
14 MacLean, P. (1990). The Triune Brain in Evolution, p. 239.
15 There is a myth, held by nearly all people outside of back-office employees of brokerage firms and the IRS, that many people do well in financial speculation. Actually, almost everyone loses at the game eventually. The head of a futures brokerage firm once confided to me that never in the firm’s history had customers in the aggregate had a winning year. Even in the stock market, when the public or even most professionals win, it is a temporary, albeit sometimes prolonged, phenomenon. The next big bear market usually wipes them out if they live long enough, and if they do not, it wipes out their successors. This is true regardless of today’s accepted wisdom that the stock market always goes to new highs eventually and that today’s investors are “wise.” Aside from the fact that the “new highs forever” conviction is false (Where was the Roman stock market during the Dark Ages?), what counts is when people act, and that is what ruins them.
16 Kelly, G.A. (1955). The Psychology of Personal Constructs, Vols. 1 and 2.
17 Osgood, C.E. and Richards, M.M. (1973). Language, 49, pp. 380-412; Shalit, B. (1960). British Journal of Psychology, 71, pp. 39-42; Rapoport, A. and Chammah, A.M. (1965). Prisoner’s Dilemma. University of Michigan Press.
18 Poulton, E.C., Simmonds, D.C.V. and Warren, R.M. (1968). “Response Bias in Very First Judgments of the Reflectance of Grays: Numerical Versus Linear Estimates.” Perception and Psychophysics, Vol. 3, pp. 112-114.
19 Adams-Webber, J. and Benjafield, J. (1973). “The Relation Between Lexical Marking and Rating Extremity in Interpersonal Judgment.” Canadian Journal of Behavioral Science, Vol. 5, pp. 234-241.
20 Adams-Webber, J. (1997, Winter). “Self-Reflexion in Evaluating Others.” American Journal of Psychology, Vol. 110, No. 4, pp. 527-541.
21 McGraw, K.M. (1985). “Subjective Probabilities and Moral Judgments.” Journal of Experimental and Biological Structures, No. 10, pp. 501-518.
22 Washburn, J. (1993, March 31). “The human equation.” Los Angeles Times.
23 Lefebvre, V.A. (1987, October). “The Fundamental Structures of Human Reflexion.” Journal of Social Biological Structure, Vol. 10, pp. 129-175.
24 Lefebvre, V.A. (1992). A Psychological Theory of Bipolarity and Reflexivity. Lewinston, NY: The Edwin Mellen Press. And (1997). The Cosmic Subject. Moscow: Russian Academy of Sciences Institute of Psychology Press.
25 Butler, D. and Ranney, A. (1978). Referendums. Washington, D.C.: American Enterprise Institute for Public Policy Research.
26 Rhea, R. (1936). The Story of Averages: A Retrospective Study of the Forecasting Value of Dow’s Theory as Applied to the Daily Movements of the Dow-Jones Industrial & Railroad Stock Averages. Republished January 1990. Omnigraphi. (See discussion in Chapter 4 of Elliott Wave Principle by Frost and Prechter.)
27 Sornette, D., Johansen, A. and Bouchaud, J.P. (1996). “Stock Market Crashes, Precursors and Replicas.” Journal de Physique I France 6, No. 1, pp. 167-175.
28 The Hurst exponent (H), named for its developer, Harold Edwin Hurst [ref: Hurst, H.E. et al. (1951). Long-Term Storage: An Experimental Study] is related to the fractal, or Hausdorff dimension (D) by the following formula, where E is the embedding Euclidean dimension (2 in the case of a plane, 3 in the case of a space): D=E-H. It may also be stated as D=E+1-H if E is the generating Euclidean dimension (1 in the case of a line, 2 in the case of a plane). Thus, if the Hurst exponent of a line graph is .38, or Φ-2, then the fractal dimension is 1.62, or Φ; if the Hurst exponent is .62, or Φ-1, then the fractal dimension is 1.38, or 1+ Φ-2. [source: Schroeder, M. (1991). Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise. New York: W.H. Freeman & Co.] Thus, if H is related to Φ, so is D.
29 Brooks, M. (1997, October 18). “Boom to Bust.” New Scientist.
30 Caldarelli, G. et al. (1997). “A Prototype Model of Stock Exchange.” Europhysics Letters, 40 (5), pp. 479-484.
31 Lefebvre, V.A. (1998, August 18-20). “Sketch of the Reflexive Game Theory,” from the proceedings of The Workshop on Multi-Reflexive Models of Agent Behavior conducted by the Army Research Laboratory.
32 See endnote 30.
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events of history—such as investment booms and busts, political events,
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