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Mathematical Structures of Natural Intelligence 1st Edition Yair Neuman (Auth.)
Complex Systems Design Management Proceedings of the Fourth International Conference on Complex Systems Design Management CSD M 2013 1st Edition John Fitzgerald
Complex Systems Design Management Proceedings of the Fifth International Conference on Complex Systems Design Management CSD M 2014 1st Edition Frédéric Boulanger
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This book is dedicated to my friend S. Gozlan, who played twice with Lady Fortuna and won.
Preface
Knowing is not understanding. There is a great difference between knowing and understanding: you can know a lot about something and not really understand it.
—Charles F. Kettering
There is an unexplained and shocking gap between our knowledge and our understanding. We all know this, but we are surprised each time we realize it, an experience that recursively supports the existence of this gap. I am no exception. When Netanyahu’s government was established, I knew its components were not the bread and butter of a democratic government. However, it came to me as a total surprise that the coalition of these components is actually striving to destroy Israel’s democracy at any cost.
In a deep sense, my surprise was similar to what people feel when they unexpectedly come under a violent attack. We know these things happen, but we don’t get any deep understanding until we experience them at first hand. In his book, Miller (2008, p. 55) describes four basic truths of violent assault: “Assaults happen closer, faster, more suddenly, and with more power than most people believe.” Most people are not trained to handle this kind of violence. They may be talented martial “artists,” big athletic guys, or just the tough guys in their high school, but as Miller explains, they are not prepared for this kind of attack, and may therefore be surprised and shocked to the extent of being totally destroyed.
While I feel unable to fully determine my motivations for writing the present book, I am convinced that the situation in Israel was an important trigger. Moreover, in October 2023, the radical Islamists of Hamas launched the most devastating terror attack Israel has ever experienced. Before the attack, I completed a research paper analyzing the Palestinian–Israeli conflict and explaining how poorly prepared we were for a bombshell of these proportions.
Being hit so hard and so suddenly teaches us another important lesson. This book draws on my scientific work and presents an attempt to understand the dynamics of crowds. Through this scientific understanding, it aims to identify the individual’s place within the collective and point out ways she can bet against the crowd. Asserting one’s individuality within the crowd is possible, but as will be explained, it is a never-ending challenge. For such a challenge, it is better to be well prepared.
This is where it is useful to build up a toolkit of ideas and lessons gained by studying non-linear and complex systems. This book provides just such a toolkit and applies it in different contexts, from politics to sport and finance. The reader won’t find recipes for betting against the crowd, but rather a toolkit of ideas illustrated through experiment, theory, common sense, and humor.
Beersheba, Israel
Reference
Yair Neuman
Miller, R. (2008). Meditations on violence. USA: YMAA Publication Center.
Acknowledgments I thank Yochai Cohen for his indispensable support in my work. I also thank Grzegorz Wilk for commenting on previous papers and my editor, Angela Lahee, for her support and trust in my academic ventures.
Summary
Crowds are misleading in both their simplicity and their complexity. On the one hand, they behave according to expected trends, and on the other hand, they present sudden shifts and frantic, unexpected behavior. Therefore, “betting against the crowd,” whether in politics, sports, or finance, requires a deep understanding of crowd dynamics. In this book, Prof. Neuman addresses this challenge by delving into the complexity of crowds. The book exposes foundational issues and presents novel ideas, such as why our understanding of crowds decays exponentially, how to use short-term prediction to bet against the crowd in financial markets, and why the long tail of fatalities in armed conflicts leaves us surprised by the blitz attack of violent mobs. The book combines scientific knowledge, experiments, and friendly, humoristic exposition that will interest anyone who seeks to understand crowds and sometimes wishes to act within and against them.
Part I
Foundations of Crowd’s Dynamics
1
Navigating the Collective: Insights into Crowd Behavior and Strategies for the Individual
From the Painted Bird to the Celebrating Crowd
… an agglomeration of men presents new characteristics very different from those of the individuals composing it. (Bon, 1895,p.2)
Human beings group into various “agglomerations,” from the coalition of Iranian women struggling against the Ayatollahs’ oppression to the mob of football hooligans violating public order and the crowd celebrating the carnival in Rio. Understanding the behavior of these agglomerates is an old challenge, and the mind of the collective has been expressed and studied in numerous scientific and artistic works. For example, “The Painted Bird” (Kosi ´ nski, 1965) is a novel that provides a powerful artistic description of the exclusion and painful destiny of social outsiders, and Bakhtin (1984)gaveus important insights into the mind of the collective celebrating the carnival. It would seem that nothing new could be added to this vast literature. However, as Le Bon (1895) observed in his classic, the agglomeration of people is a whole different from the sum of its parts. A group may be composed of good citizens. Each and every individual may be of good character, but when put together under the leadership of a charismatic person, they may turn into a murderous mob. One may then doubt the human quality of these good Samaritans, arguing that each and every individual comprising the murderous mob must actually be a hidden murderer and that our failure to understand the emerging behavior of the mob is a failure to understand the dark side of
its components. For the outside observer, like Le Bon, what is inside any individual’s mind is less important when observing the crowd’s behavior. Most of those making up the mob just mentioned may never have carried out a deadly deed. But within the mob, they may do so. To understand this point, watch Dogville 1 by Lars von Trier is a tantalizing film showing how ultimate evil emerges from a collective of good American citizens. Watch it if you have your own doubts about the complexity of social wholes and the evil that human beings can impose on their fellow men and women.
In this context of a whole different from the sum of its parts, we are in the realm of non-linear systems, where uncertainty and surprise may have the upper hand. For instance, imagine two different societies of equal size. One is a collective of hunter–gatherers where the distribution of “wealth” is almost equal. The other is one where the distribution of wealth is unequal, in fact, a Pareto-style distribution where 10% of the population holds 90% of the wealth. What happens if, through some malicious experiment, we mix the two populations? What would the new society look like in terms of its wealth distribution? A naïve hypothesis might be that the new distribution of wealth will simply be the sum of the two previous distributions. This hypothesis is grounded on the assumption of additivity . However, we would not scientifically bet on this result for a simple reason: interactions . As nicely explained by Rovelli (2019), we are biased to think about the “essence” of things, where sometimes the most important thing to look at is change and dynamics taking place through interactions.
An event , such as a kiss, explains Rovelli, is not a thing. It does not persist in time and space like my kitchen table. The vicious behavior of Dogville’s citizens is grounded in group dynamics. In interactions. Some information exists in-between the interacting components (Neuman, 2021), and this information cannot be reduced to the psychology of each and every individual who is a part of this “wonderful” community of good Americans. However, sometimes, a reduction is possible. A group of notorious South American gang members is probably composed of violent individuals with violent group behavior. As we can see, the agglomerate discussed by Le Bon may come in different forms.
1 https://en.wikipedia.org/wiki/dogville.
The Importance of Interactions
The interactions between “human particles” are not the same as those between gas particles. In fact, all living systems, from the cell to the snail, exhibit the miracle of emerging behaviors irreducible to the simple behavior or sum of their components. Something miraculous happens when things interact and produce, on a higher level of analysis, a behavior that cannot be trivially explained by reduction to the lowest level of the aggregate; this miracle also holds for human collectives. Simple explanations of crowd behavior sometimes ignore this fact realized by Le Bon long ago. For example, Rosner and Ritchie (2018) present the results of their optimism opinion survey covering 26,489 people across 28 countries.2 Their results are presented in terms of simple percentages. For example, 41% of the Chinese respondents “think the world is getting better.” This result is significantly higher than the 3% of French respondents who think the same. These results might be taken to imply that Chinese optimism is 14 times greater (!) than French optimism. Chinese and French optimism seem to be on a different scale. For comparison, the ratio between Chinese and French optimism is almost the same as the ratio between the heights of the Eiffel Tower and a giraffe. We may imagine 41% of the current 1,425,572,821 people living today in China starting their day with a smile, reminding themselves that the future under the eternal leadership of Xi Jinping is more promising than ever, while 97% of the French begin their day by dipping a butter-saturated croissant in coffee and gazing depressively into the future. Is it the case that the Chinese collective is more optimistic than the French one? And if so, in what sense, except for the trivial sense that a greater portion of the Chinese respondents answered the optimism question positively? There is a fact: 41% of the specific sample of respondents agreed with the specific optimism item. However, jumping to the conclusion that the Chinese collective, whatever it is, is optimistic requires a leap of inference. The Chinese collective may behave differently from the sum, or some of the sum, of individuals comprising it. This lesson has not been sufficiently built into our understanding, although it has been pointed out by people from Le Bon to Bateson (Bateson, 2000).
So far, I have emphasized two points. First, a collective of human beings is a whole different from the sum of its parts. Second, it is the outcome of interactions. The first point urges us to examine the behavior of collectives by avoiding the naïve assumption that they are the sum of their parts
or that their behavior scales linearly with the size of the system. Crowds do not behave like a single individual multiplied by 10,000. The second point urges us to examine the collective as an event constituted through microlevel interactions, with possibly surprising and unexpected results. Again, this understanding is important to avoid poor explanations which merely attribute some kind of “essence” to the collective. Le Bon made this mistake by discussing race as an innate explanation of a crowd’s behavior. Today, with the exception of anti-scientific and zealous racists, this essentialist explanation had been rejected. Therefore, we are left with complex wholes and the challenge of understanding them while maintaining a delicate balance between authentically representing their complexity and our need to simplify in order to understand. This is also an important point. Human beings cannot represent the full complexity of events and form simple models. However, simplicity may have an enormous cost if we cross some delicate boundary of oversimplification. This is why I repeatedly advocate a critical and cautious approach, supported but not limited by simple models.
The Individual and the Collective
The failure to acknowledge the unique behavior of the aggregate entails fallacies of understanding and prediction. Although we may retrospectively explain the behavior of collectives, narratives can always be given post-factum. Our ability to tell stories weaving together the elements of reality and fantasy is no less than impressive. Bruner (2004) observed that human beings are gifted storytellers. However, in a complex world that West (2016) described as uncertain, unfair, and unequal, stories are no substitute for scientific representations. Commentators on China’s foreign policy can provide us with narratives to frame our understanding of China, but who can predict whether and when the Chinese superpower will hit a tipping point of growth or turn against Taiwan?
Telling stories is a part of human nature, whatever that may be. However, telling stories and interpreting the world are no substitute for pragmatically motivated understanding . The phrase “the proof of the pudding is in the eating” explains this approach. It means that true value or quality can only be judged when something is put to use or tested. Pragmatically motivated understanding means that reality is the ultimate judge of our models. And when we face this judge, we will not be assessed on the aesthetic value of our stories, but on the practical consequences of our models. Therefore,
a pragmatically oriented understanding refers to an approach or interpretation focused on practicality and real-world application. In this context, “pragmatic” relates to a practical, hands-on, and results-driven perspective, as opposed to one that is purely theoretical or abstract. A pragmatically oriented understanding emphasizes the importance of considering how concepts, ideas, or theories can be applied effectively in practical situations. It involves lookingatthe tangible outcomes and consequences of a particular approach or concept.
To better understand this approach, consider a recent trend where traditional martial artists are challenged and empirically “tested.”3 Those who have watched action movies as teenagers may have been impressed by the secret power of old Chinese Kung Fu masters to beat their opponents with ease, grace, and mastery, using hidden sources of “energy.” When tested in reality against the brutal force of MMA fighters, these fraudulent masters are squashed like flies. Their “theory” does not stand up to the brutal reality. This pragmatically oriented approach is not limited to martial arts, of course. One should read Mandelbrot’s “The (mis)behavior of markets” (Mandelbrot & Hudson, 2007) to understand how economic models did not survive the brutal realities of financial markets.
Luckily, we have gained much knowledge about the dynamics of nonlinear systems that can guide us, at least negatively , to a modest understanding of crowds. The main focus of the present book is not this form of understanding, though, but rather the question of how the individual within the collective can act non-stupidly in the face of the madding crowd. This challenge involves some deep questions concerning uncertainty and the degrees of freedom within the collective. To address this challenge, we must understand that there is an inherent difficulty in the scientific modeling of uncertainty.
Uncertainty is defined only for a large collective of particles (Lawrence, 2019). It is not defined for a single particle, and talking about the uncertainty of a single particle as decontextualized from the collective is meaningless. Adopting this perspective, the human particle, striving to understand himself within the collective, can only use the Copernican principle , according to which he has no unique position in existence and can reflect on himself only through the eyes of the collective. On the other hand, our understanding of ourselves as individuals who strive to have some control of our lives leaves us frustrated, not to say pessimistic and depressed, when our ignorance is conceptualized at the macro level alone. This tension is expressed through the tension between the individual and the crowd and the degrees of freedom
3 https://en.wikipedia.org/wiki/xu_xiaodong.
and choice one has within a collective. Are we a part of the system that we observe? We may use statistical mechanics to model the system if the answer is negative. However, we may use quantum mechanics to model ourselves within the crowd if the answer is positive. And good luck to us if we do … Dealing with our uncertainty as individuals through a concept that describes the collective seems paradoxical. Why should someone consider himself a particle among particles when he only wants to celebrate his individuality? How can someone’s free will be expressed through the logic of the collective? The idea of free will is one of the traps facing us when we try to understand the individual within the collective. As explained by Rovelli (2022, p. 626), “failing to distinguish a rigid (mistaken) understanding of a concept from the actual (fluid) role that it plays within our overall conceptual structure” is a repeated fallacy.
In this book, I propose nothing contradicting our scientific understanding of uncertainty. However, I suggest that collectives have their Achilles heels and that individuals can study and use them to bet against the crowd. Our freedom is, therefore, expressed by playing on the outskirts of the main mass of the distribution while exploiting the variability of complex systems. This proposal reframes our understanding, reminding us that “we are all unique but never alone” (Holquist, in Bakhtin, 1990, p. xxvi). Understanding the distribution of which we are a part is the first step in understanding what it means to be different. As variability and change are inherent in all living systems, betting against the crowd means playing dynamically to change our position and exploiting “pockets” of potential freedom within and against the crowd. In this book, I use the expression “betting against the crowd” to describe the individual’s attempt to adopt a contrarian approach by adopting this dynamic form of play.
Constraints and Opportunities
Betting against the crowd is a tricky business. The default is to bet with the crowd, as the crowd dictates our reality. Betting against the crowd pushing the stock market upward is a mistake, as it is better to ride on the wave than to bet on the exact timing of its collapse. Joining the regime is opportunistically better than fighting against it. However, in some contexts, we may want to express our individuality and gain some edge by betting against the crowd. In these contexts, we must understand the system’s constraints to identify the best timing and context to take action. Constraints are limitations reducing
the degrees of freedom available to the system. But constraints do not necessarily tell us where the system is heading. Negatively, and as discussed in the next section, they may mark out the system’s boundary, telling us where it cannot go.
Let me use the Brazil nut paradox to illustrate the meaning of constraints. The paradox, also known as “granular convection” or “muesli effect,” is observed in mixed granular materials. It describes the tendency of larger particles to rise to the top of a container filled with a mixture of particles of different sizes when the container is shaken. When you shake a jar of granola, you may notice that the Brazil nuts rise to the top, although they are larger and heavier than other components like raisins. At the same time, smaller particles settle towards the bottom. This is a counterintuitive effect because one might expect that the larger and heavier particles would sink rather than rise.
I am fascinated by this paradox, as it shows how a nontrivial pattern emerges by simply shaking a system. This emerging pattern has also fascinated physicists (Aranson & Tsimring, 2006). When you think about it, the Brazil nut paradox involves two important processes. First, the jar is shaken. No part of the action is intended to move the nuts to the top. On the contrary, the interaction between the shaking hand and the jar aims to mix the granola and increase the homogeneity of the distribution so that each bite will represent a variety of tastes. The order produced by the shaking is unintentional and even contradicts our intention to mix the components. The various particles have degrees of freedom to move in the jar. Therefore, shaking the jar should have led to a perfect mixture, maximizing the particles’ entropy (i.e., variability).
This is where constraints get into the picture—size constraints. When they have been thrown up in the air and are falling back down again, the small particles sneak in between the bigger ones. Given their size, the Brazil nuts do not display the same behavior. Therefore, it is not the case that the Brazil nuts rise to the top. Rather, the smaller particles sneak to the bottom because of size constraints. The constraints present differential restrictions on the particles’ degrees of freedom. Order is produced when some unconstrained potential is restricted in a law-like way, given constraints formed through interactions .The shaking hand inserts energy into the jar. The collective of particles has no intention or “essence” directing it to the formation of order. Order is generated when the energy-driven movement of the particles is constrained in a law-like way.
Considerations about constraints may be used to bet against the crowd. In Chap. 4, I explain how the identification of short time frames where hidden regularity is expressed may be important for short-term prediction. Similarly,
the identification of time frames where constraints are loosened may also be important to spot when the collective starts moving away from a given trend, and to exploit this situation to bet against the crowd. In both cases, context and timing are crucial.
A contextual representation is built into living systems, from the immune system (Cohen, 2000) to human personality (Mischel, 2004) and state-ofthe-art large language models (LLM) such as GPT. The point here is that humans do not respond to stimuli using general and automatic patterns. We respond with sensitivity to the context. Most people, for instance, are not pure introverts or extroverts. Some contexts may turn our gaze inside, while others may orient us toward the outside. As Mischel (2004) explains, personality is not an underlying essence hidden in our skull, but a pattern of relatively stable person–context relationships. A highly verbal individual may respond as an extrovert to contexts where he feels secure in expressing himself. However, in other contexts where he feels insecure, he may withdraw and appear as an introvert.
Contextual representation allows us to respond adaptively , rather than mechanically, to changes in our external and internal environment. Without contextual representation, we cannot have the variability of response which is necessary for adaptive behavior. However, variability must be constrained in a law-like manner to avoid ending up in a fully disordered state. In other words, between fully rigid and fully disordered behaviors, there is an optimal level of variability that uniquely characterizes each living system (Neuman, 2021). Adopting this perspective, we may make the following definition: Context is the set of signals that support constrained variability in a law-like way.
Given our shortcomings in providing exact pointwise predictions of crowd behavior, an important idea that I would like to present in this book is that our analysis should focus on identifying informative cues or signals. These signals are contextual cues that may support our adaptive behavior. By recognizing these signs in time, an individual may use them to gain an edge, as explained in Chap. 2.
The Importance of Learned Ignorance
In such complex businesses, you almost have no other way. You have to start with the simplest probabilities and hope to get less and less tangled later on. After all, Ariadne does not always wait for you at the entrance of the labyrinth, handing you the end of the thread. (Meiran, 1990, p. 89)
Complex behaviors do not easily lend themselves to prediction and control. In fact, this is the very thing that defines complexity, so we need to think about it differently. Years ago, I visited a leading university where the head of the institute presented a new and highly expensive predictive system sponsored by the government. I do not remember the exact details, but he tried to impress us by saying that the system predicted the second Lebanon war between Israel and the terror organization Hizballah with a 0.60 probability. I explained to him that, for the Israel Defense Forces (IDF), the working assumption is that a war is more probable than not probable, so a single pointwise probability of 0.6 would be of little help to decision-makers. After all, what does it mean to say that there is a 0.60 probability that a war is expected? That a war is more probable than getting heads when you flip a coin? What is the margin of error in this prediction? Moreover, what does it mean to the people with their boots on the ground who have to make practical decisions about things like recruitment of reserve forces?
I realized then that it is much easier to learn what to avoid than what to actually do in many real-world and complex situations, and that academic research is sometimes so blind to its shortcomings that it becomes meaningless. Saying something positive about the behavior of a complex system is not trivial, and few warriors of academia would survive if tested in the sparring ring of reality.
Theideaofvia negativa originated from theology, where it was argued that we could say nothing positive about God. Nicholas of Cusa (b. 1401) is a scholar I still remember from my undergraduate studies in philosophy. He introduced the idea of docta ignorantia (‘learned ignorance’), emphasizing the importance of being aware of our limitations. Knowing our limits and avoiding stupidity may be the first step in understanding collectives and our own role within the collective. Knowing the system’s limits means understanding the constraints operating on the system. By understanding some of these constraints, we may incrementally and modestly reduce our ignorance. The above quote from Meiran’s novel “South of Antarctica” exemplifies this understanding, albeit in a different context. It describes some real-life situations where complexity dominates the situation. This complexity is portrayed as a maze from which there is no simple way to escape.
In Greek mythology, Ariadne was the daughter of King Minos of Crete. She fell in love with the hero Theseus. Theseus decided to kill the Minotaur, remembered in Picasso’s paintings as a monster, half man and half beast. The monster that excited the imagination of Picasso lived in a labyrinth, so Ariadne gave Theseus a ball of yarn, which he unwound as he entered the
labyrinth. After killing the monster, the hero used Ariadne’s thread to find hisway out of themazeand back to hislover.Evenifweare Greek heroes, we must seek assistance to get out of a maze.
Similarly, when studying complex systems, such as crowds, we are forced to start with simple assumptions and should “hope to get less and less tangled later on.” The notion of docta ignorantia is important primarily for its didactic value as a guiding principle. Suppose we do not really understand the “essence” of the collective. In that case, we can only approach it negatively, accepting that we cannot provide a precise prediction of how far the stock market would fall under the rush and roar of the madding crowd. Is there a way in which we can say something positive about what to do? This is the challenge that will be discussed throughout this book.
The Dancing Crowd
I played and replayed the scenes … trying to find some order, pattern. I found none. (Didion, 1971,p.12)
When I dance with my two-year-old granddaughters, we dance in a circle or a straight line, pretending to be a train. We sing and move symmetrically, either through rotation or translation. These dances express simple and predictable order, which is adaptive to my granddaughters’ developmental level and my limited dancing skills. Dance patterns range from the highly ordered to the highly disordered, where the madding crowd behaves like gas particles (Silverberg et al., 2013). My dance with my granddaughters is fully ordered. Rave dance and moshing are total chaos. Modern dance, as epitomized in the choreography of Alonzo King, is non-simple, complex, and unpredictable. So, which form of dance would be best for a metaphorical description of crowd behavior?
The kinds of dance described here represent three prototypical forms of behavior: chaotic, ordered, and non-simple. In a deep sense, both chaotic/ random behavior and ordered behavior are simple to model. In the first case, we can model the dancers’ behavior as an example of Brownian motion, where the particles are pushed around randomly by gas particles, joyfully boosted as the temperature gets higher. In the second case, we can model the behavior of the particles by analyzing the identity-preserving transformation of their structure. If you have watched the military marches of fascist regimes like North Korea, you can easily identify the structure and dynamics of the soldiers’ movements. Dictators are fond of order and predictability and
have no patience with the expression of variability. Simplicity and complexity are two extremes that are easy to identify. We all recognize the difference between the ordered march of soldiers and the disordered movements of free dancers at a rock festival. Interestingly, at some music festivals organized by neo-Nazis, the crowds dance in a totally disordered way. Extreme order and total disorder seem to have something in common: they do not like life as it is. In contrast with these two extreme forms, deciphering the thinking behind Alonzo King’s “Meyer” is challenging. Collectives may present all three forms of behavior. However, for the individual participating in the dance of the collective, the important question is not what the pattern is, but how variability in the pattern may be used as an opportunity for betting against the crowd.
Dance is a nice metaphor, but human behavior differs from dance. Like the Brazil nut paradox, it may display non-trivial behavior when subject to changing constraints. Dancing with a crowd is much more challenging than dancing on stage. For the individual dancer in King’s Meir, there is a welldefined choreography that is opaque to the audience. She cannot simply make her own moves. For the observer, the complexity in work is not the same as the complexity for the performing dancers. Whether choreography underlies our collective behavior is an interesting question. Complex social systems, like crowds, seem to express different forms of order.
Scientific Thinking in the Absence of
Truth
Fortunately, in the absence of truth, facts take its place, and it is difficult to contend with them. (Meiran, 1990, p. 74)
A naïve conception of science presents it as lifting the veil to uncover nature’s true face. This may be true of physics and biology. However, “truth” is an idea that is much more difficult to understand than facts. Facts are generally considered more concrete and less subject to interpretation or personal belief. They are often based on empirical evidence and can be supported by data or observations. In contrast, truth can sometimes be relative or influenced by individual perspectives. Facts are typically objective and can be objectively demonstrated or proven. For example, the statement “The Earth orbits the Sun” is supported by scientific evidence and observations. However, a statement like “chocolate is the best ice cream flavor” may be true for someone who particularly enjoys chocolate. But it is not a fact, because it is based on personal preference and not universally verifiable.
The difficulty in gaining access to “truth” is not a barrier for knowledge seekers. Maybe this is why the legendary John von Neumann said that science does not try to explain or interpret, but places models above all else. This is especially relevant when modeling collectives and the individuals within them. The “truth” underlying the behavior of a collective may be hard to decipher, but there are facts, measurable and proven behaviors, that can be used to model the collective. We use facts as the building blocks for a model which is always a simple representation of the complex behavior we seek to understand.
Jorge Luis Borges wrote a short story titled “On Exactitude in Science” (Borges, 1999). It’s a brief but thought-provoking tale. In Borges’ story, he describes an empire where the art of cartography has reached an extreme level of perfection. The mapmakers of this empire have created a map so detailed and accurate that it is an exact 1:1 scale replica of the entire territory it represents. In other words, the map covers every square inch of the land it represents, leaving no room for gaps or discrepancies. This colossal map is so large and unwieldy that it cannot be used for navigation. In fact, it is so immense that it lies in tatters across the empire, with people using various portions of it for different purposes. Some people live on sections of the map, others study it as a scholarly pursuit, and some even use it as a flag.
The tale is often interpreted as a parable about the nature of knowledge and representation. It raises questions about the relationship between reality and our attempts to represent it, suggesting that perfect representation is impractical and perhaps even impossible. The map, intended to represent reality, merely becomes a burden and a symbol of the hubris of those seeking to create a perfect world model.
Science is about models, explained von Neumann, and a model is an abstract, simple, and clear representation aiming to improve prediction and control over the best practice . The last point is highly important for a pragmatic approach. As argued by Zilliak (2019, p. 283):
Whatever the purpose of the experiment, best practice research compares a novel treatment or variable with best practice and/or prevailing wisdom, not with an assumed-to-be-true null hypothesis or blank placebo.
To prove the relevance of our model, we must compare it with the “best practice,” whatever that may be. When betting against the crowd, we may consult the “best practice” we know of. Being able to model the crowd’s behavior provides the individual with an edge over the best practice, but not with access to the “truth.”
The Rebel’s Perspective
I must emphasize that this book is not a philosophical treatise. It attempts to understand some foundational scientific aspects of crowds and describe how the empowered individual may find his way within such a collective by understanding the underlying dynamics. The book thus combines a scientific attempt to model collectives in a way that may be useful for the individual to find his way within, and largely against, the crowd. In this sense, it is a scientific contemplation for the rebel who strives to gain individuality while confronting the madding crowd. And it is no coincidence that the book is being written at a time when Israeli democracy is facing its most difficult challenge. The interaction of dark political forces has formed a soliton, moving forward against the only democracy in the Middle East and the history of the Jewish people. This wave, which has surprised most Israelis, including myself, is nothing less than the perfect context for the current book.
Several words should be said about the general approach used in the book and the audience for which it is intended. The book is scientific. However, it is written as a self-contained book for the educated reader. It aims at a wide audience interested in understanding the dynamics of crowds. Moreover, it specifically focuses on the way individuality may be empowered within such collectives by adopting a scientific and reflective approach. No recipes are given, just guidelines which are supported by a certain amount of scientific evidence.
Monty Python’s “Life of Brian”4 includes a hilarious scene in which a poor individual is to be stoned to death. The bloodthirsty crowd includes women wearing fake beards because women are forbidden to watch such an event. The humor in this scene does not hide the fact that the crowd, as observed by Le Bon (Le Bon, 1895, p. 17), “is guided almost exclusively by unconscious motives” (some of which may be dark and dangerous). The empowerment and emancipation of the individual is a process that must vanquish the barrier of the unconscious. I invite the reader on a journey of contemplation where she will meet different crowds, from Hungarian political parties to groups of gamblers and stock market traders. These are cases where a lesson could be learned and hopefully empower the individual in the face of the madding crowd.
The book draws on some of my previous more technical papers (Neuman & Cohen, 2022, 2023;Neumanetal., 2021), but the themes presented are original and mostly appear in the first, more general part of the book. In fact, there are two parts. Part I is introductory and aims to present general ideas. Part II is more specific and technical and aims to analyze different examples and aspects of crowd behavior and to deepen our understanding of how the individual may find her place within and in opposition to the crowd. The reader may find these two parts quite different in their orientation. However, he may benefit from reading the more technical aspects of the book as these are the places where ideas are made explicit. Speaking about technicalities, I must conclude by apologizing for any technical errors. Throughout my academic career, I have noticed that regardless of careful and repeated reading of the manuscript, it is almost inevitable that some error will slip into the text. Given the thesis presented in the book, such surprises are inevitable and almost a normal part of any natural system that is not artificially designed for mass production.
References
Aranson, I. S., & Tsimring, L. S. (2006). Patterns and collective behavior in granular media: Theoretical concepts. Reviews of Modern Physics, 78 (2), 641.
Bakhtin, M. M. (1990). Art and answerability: Early philosophical essays .University of Texas Press.
Bakhtin, M. M. (1984). Rabelais and his world (Vol. 341). Indiana University Press. Bateson, G. (2000). Steps to an ecology of mind . University of Chicago Press. Borges, J. L. (1999). On Exactitude in Science. Borges JL Collected Fictions (trans. Andrew Hurley).
Bruner, J. (2004). Life as narrative. Social Research: An International Quarterly, 71 (3), 691–710.
Cohen, I. (2000). Tending Adam’s garden: Evolving the cognitive immune self .Elsevier. Didion, J. (1971). Play it as it lays . Bantam Books.
Kosi ´ nski, J. (1965). The Painted Bird. Houghton Mifflin.
Lawrence, A. (2019). Probability in physics. In Undergraduate lecture notes in physics . Springer, https://doi.org/10.1007/978-3-030-04544-9.
Le Bon, G. (1895). The crowd: A study of the popular mind . T. Fisher Unwin. Mandelbrot, B., & Hudson, R. L. (2007). The misbehavior of markets: A fractal view of financial turbulence . Basic books.
Meiran, R. (1990). South of Antarctica . Keter. (in Hebrew).
Mischel, W. (2004). Toward an integrative science of the person. Annual Review of Psychology, 55 , 1–22.
Neuman, Y. (2021). How small social systems work: from soccer teams to jazz trios and families . Springer Nature.
Neuman, Y., & Cohen, Y. (2023). Unveiling herd behavior in financial markets. Journal of Statistical Mechanics: Theory and Experiment, 2023 (8), 083407.
Neuman, Y., Cohen, Y., & Tamir, B. (2021). Short-term prediction through ordinal patterns. Royal Society Open Science, 8 (1), 201011.
Neuman, Y., & Cohen, Y. (2022). A permutation-based heuristic for buy low, Sell High. arXiv preprint arXiv:2207.01245.
Roser, M., & Ritchie, H. (2018) Optimism and pessimism. Published online at OurWorldInData.org. Retrieved from: https://ourworldindata.org/optimismand-pessimism [Online Resource] https://ourworldindata.org/optimism-and-pes simism
Rovelli, C. (2019). The order of time . Penguin.
Rovelli, C. (2022). The old fisherman’s mistake. Metaphilosophy, 53 (5), 623–631.
Silverberg, J. L., Bierbaum, M., Sethna, J. P., & Cohen, I. (2013). Collective motion of humans in mosh and circle pits at heavy metal concerts. Physical Review Letters, 110 (22), 228701.
West, B. J. (2016). Simplifying complexity: Life is uncertain, unfair and unequal . Bentham Science Publishers.
Ziliak, S. T. (2019). How large are your G-values? Try Gosset’s Guinnessometrics when a little “p” is not enough. The American Statistician, 73 (sup1), 281–290.
2
Signs of Collective Dynamics: Insights from the Stock Market Collapse
Introduction
From the early’20s, the New York stock market and its main performance index, the Dow Jones, showed unprecedented growth. “From 1920 to 1929, stocks more than quadrupled in value,”1 meaning that investors increased their wealth fourfold. For example, if an investor bought a stock for $100, it would be worth $400 nine years later. Selling his stock at this point would leave the investor with a profit of $300. Such an increase in wealth would have been considered unthinkable by most Americans living at that time. For a better understanding of the excitement this inspired, take a look at Fig. 2.1 showing the increase of the Dow Jones index from 1 January 1920 to 1 September 1929. The X-axis shows the timeline, and the Y-axis the Dow Jones index.
Y. Neuman, Betting Against the Crowd, https://doi.org/10.1007/978-3-031-52019-8_2
Another random document with no related content on Scribd:
The Aftonian stage was followed by the Kansan glaciation, when the ice-sheets reached their maximum area over the greater part of North America. The chief centre of glaciation at this stage was the Keewatin, west of Hudson Bay. While it is certain that the Keewatin centre reached its maximum later than the Cordilleran, geological opinion in America is divided as to whether or no the two ice-sheets ever coalesced, but it is difficult to understand how an independent ice-sheet could have grown up on the comparatively low ground of the Keewatin centre. Most probably the course of events here was an exact parallel of that in the better-known Scandinavian region— the Cordilleran ice-sheet extended eastwards over the lower ground until a glacial anticyclone developed east of the Rockies. When this happened the supply of moisture to the western part of the ice-sheet fell off somewhat, and the eastern part took on an independent life, ultimately becoming the main centre of glaciation. It was while these changes were in progress that the southern limit of the ice retreated northwards and the “Aftonian” deposits were formed.
The next stage (Kansan) occurred when the ice from the Keewatin centre spread outwards in all directions, and in the south reached the maximum limits of glaciation in America. In the west this sheet overlapped on to the ground-moraine of the former Cordilleran ice, but the Rocky Mountains were too far away and too high for Keewatin ice to dominate them and overflow them from east to west. Instead these mountains must have maintained an extensive glaciation of their own.
With the growth of the Keewatin centre the Labradorean also decreased, but more slowly, and this change was not associated with a retreat of the southern ice-edge, so that there was no corresponding “interglacial” in the east of the United States. The moraines of these older glaciations resemble those of the early icesheets of Europe in presenting only featureless level surfaces of boulder-clay without morainic ridges, lakes and the other characteristics of ice-bearing surface detritus, and there is no doubt that conditions at the southern edge were similar—the climate was severe in winter, but not insupportable in summer. At the same time it was decidedly more severe than the present, even as far south as
Florida, where there are colonies of northern plants, which migrated southwards during the Ice Age, still living on local cold slopes with a northerly aspect. After the maximum of glaciation the disappearance of the ice took place gradually and chiefly by ablation, for there are none of the extensive river gravels and flood terraces which we should find had the melting been rapid. It is only in the valleys of the Rocky Mountains that such deposits occur, testifying to conditions such as obtained in the Alps.
The succeeding Yarmouth stage of deglaciation was very long, corresponding in this respect to the Mindel-Riss interglacial of Europe. The Kansan moraine was weathered to a depth of ten or twenty feet, and four-fifths of its surface was removed by the erosion of streams and rivers. In the mountain districts the side streams which had been left occupying “hanging valleys” by the overdeepening of the heavily glaciated main valleys, had time to cut out uniformly graded broad V-shaped valleys descending to the level of the main stream. In the Great Basin also, where the periods of high water-level are considered to correspond to the main glaciations, the interval of low water corresponding to the Yarmouth stage was very long. A rough estimate of its length is about 200,000 years— somewhat shorter than the Mindel-Riss. Actually, though the Kansan and Mindelian glaciations were approximately contemporaneous, the subsequent recurrence of glaciation in America appears to have preceded slightly that in Europe.
Of the climate of this stage we have unfortunately little evidence. Old land surfaces of this age are known, containing deposits of peat and bones of the wood rabbit and common skunk, but both of these animals have a wide range Perhaps the climate resembled the present during most of the period; there is no evidence that it was ever warmer, and it appears quite likely that ice-sheets maintained their existence in the far north through the whole of this stage.
After this interglacial there set in a period of renewed elevation in the Rocky Mountains and in the Labrador-Newfoundland centres, which brought about a recurrence of the glaciation. In the Rocky Mountains the ice was not so thick as in the preceding stage, but all the valleys were occupied to a considerable depth and the ice
spread out to the eastward. The Labrador ice-sheets also developed again, forming the Illinoian glaciation, the moraines of which are found as far west as Illinois, but no moraines are known of this age due to the Keewatin ice-sheet. The latter developed later, and is classed by some American geologists as a separate glaciation, the Iowan, which is only certainly found in northern Iowa, but may be represented further east by a thin sheet of boulder-clay overlapping the Illinoian moraine. The supposed interglacial between the Illinoian and Iowan, the “Sangamon Stage,” is represented only by land surfaces formed of the Illinoian moraine and covered by the loess or locally by the equivalent of the Iowan moraine, and there is no evidence that the ice-edge retreated far. Other American geologists, including F. Leverett, do not recognize the existence of a separate Iowan glaciation, and as the amount of weathering and denudation undergone by the two moraines differs very little, this seems the more natural view. The natural explanation seems to be that this was another case of “glacial piracy,” the Keewatin ice-sheet, owing to its lesser snowfall, developing more gradually, and finally diverting the supply of moisture from the Labradorean ice-sheet, until it reached a maximum after the latter was already on the wane. Both these sheets of drift present similar flat features to the Kansan sheet, without morainic ridges.
Leverett’s interpretation of the succession is as follows: The third (Illinoian-Iowan) glaciation was followed by a period of moist climate, when peat-bogs were formed on level poorly-drained surfaces, while elsewhere coniferous forests developed. This was followed by a period of dry steppe-like conditions with a cold temperate climate, when the great American loess sheet was deposited. This loess sheet extends northwards, overlapping the Iowan moraine, and in places passing under the Wisconsin drift. The material has come from the west, and probably most largely from the dry plains east of the Rocky Mountains, from which it diminishes in thickness eastwards. But unlike Europe this phase of steppe conditions was followed in America by a definite interglacial, when the climate seems to have become rather warmer than the present. In the northern States an old land-surface formed on the loess, and, termed the Peorian stage, is overlain by the Wisconsin drift; but near
Toronto, on the shores of Lake Ontario and in the Don valley, the gap represented by this land-surface is partly filled by a remarkable series of lacustrine deposits known as the Toronto stage. The Lake Ontario beds indicate a climate slightly colder than the present, but the Don valley beds contain plants and animals living in the central States, and refer to conditions more favourable than those now found in the district.
The duration of this interglacial has been worked out in a remarkable way by A. P. Coleman, who on the basis of wave-action estimated it as 62,000 years, which agrees very closely with the 60,000 years found by Penck and Brückner in the Alps. This period was not long enough for streams in the “hanging valleys” to cut out uniformly graded valleys down to the main rivers, and was consequently much shorter than the preceding interglacial.
The last glaciation of North America was the Wisconsin, which closely resembles the Wurmian of Europe both in its relations to the older glaciations and in the rough topography and unworn character of its moraines. It extended within the limits of the Kansan drift across fully two-thirds of the continent, from Nantucket and Cape Cod through Long Island, northern New Jersey, Pennsylvania, southern New York, Ohio, Indiana, Illinois, Michigan, Wisconsin, Minnesota, Iowa and the Dakotas, Manitoba, Saskatchewan and Alberta. At the same time the Cordilleran centre probably bore increased local valley glaciers.
Like the Wurm glaciation, the Wisconsin was double. The older moraines are well-marked, and in places are covered by a foot or two of loess, though this deposit reaches nothing like the thickness of that overlying the moraines of the earlier glaciations. The moraine under this loess is very little weathered, so that the time interval was very short; possibly this loess is redistributed older loess associated with glacial east winds. The ice of the first glaciation melted very slowly and there is very little gravel outwash to the moraines. But “after the Wisconsin ice-sheet had reached a position a little outside the limits of the Great Lakes the retreat became much more rapid, and large outwash aprons were formed from which valley trains of
gravel led far down the drainage lines. From this position the moraines are practically free from loess-like silts.”[4]
From this point onwards the glacial history of America is one of irregular retreat, with occasional halts or even readvances resembling those of the Scandinavian ice. Banded clays are found similar to those used so successfully by Baron de Geer in dating the retreat stages of Scandinavia, and this geologist has recently been investigating them, but until his results are worked out no correlation with Europe can be attempted.
A natural clock of another type is provided by Niagara Falls, which are cutting their way back up the gorge at a rate which has been definitely ascertained. Taking into account the varying amounts of water which have passed over the falls at different stages of postglacial geography, the duration since the region became free of ice has been calculated at about 20,000 years, which agrees closely with the time elapsed since the Scandinavian ice-sheet left the North German coast.
Before leaving North America it is necessary to give a brief account of the phenomena outside the main centres of glaciation, and especially of the history of the Great Basin between the Sierra Nevada and Wasatch Mountains. The lowest levels of this basin are at present occupied by several salt lakes without outflow, of which the largest is the Great Salt Lake, the level of the water being determined by the balance between inflow of the rivers and evaporation from the surface. Twice in the past this balance has been decidedly more favourable, and then the lakes grew to many times their present size. The two greatest of these old lakes have been fully described under the names of Lake Bonneville (of which the Great Salt Lake is a vestige) and Lake Lahontan, further to the west. The investigations have shown that before the Glacial period, and extending back into an unknown past, there was a period of great aridity. To this succeeded a long period of high water, during which, however, neither of the lakes overflowed. This stage was followed by a very long period of great aridity, during which the lakes dried up completely, and all their soluble matter was deposited and buried by alluvial material. This period was followed by a return of
moist conditions, during which the water reached a higher level than before, and in the case of Lake Bonneville actually overflowed into the Snake river, cutting a deep gorge. This period, however, was shorter than the preceding moist period. It was followed by an irregular fall interspersed with occasional slight rises, but ultimately both lakes descended below their present level and probably again dried up completely. Both lakes suggest that this low level was followed by a third rise to a height very slightly above the present level, followed by a slow fall in recent years.
The relations of the periods of high water to the glaciations are not clear in these large lakes, but in the Mono Basin, a small basin further west, there is no doubt that the two were almost contemporaneous, high water accompanying the maxima of glaciation and extending some way into the retreat phase. The very long interval between the first and second period of high water, several times that since the second period, agrees with this correlation. We find then that south-west of the main glaciated area there was a district of greater precipitation or less evaporation, or more probably both. This is confirmed by the valley moraines of all this region—Sierra Nevada, Uinta and Wasatch mountains, Medicine Bow Range of northern Colorado, etc., all of which indicate two glaciations, of which the first was the greater, separated by a very long interval. In several ranges the moraines of the second glaciation are double, and some geologists consider that there were three Glacial periods in these regions.
In the extremely arid region of Arizona, on the other hand, which is considerably further south, the evidence of the Gila conglomerates indicates that while frost was very active, the increase of precipitation, though undoubtedly present, was comparatively slight. This shows that the climatic balance was not greatly disturbed, the chief effect being an important lowering of temperature, probably due to cold northerly winds. The Gila conglomerates are double, separated by a period representing present-day conditions.
Summing up the evidences of glacial climate in North America, we find a striking similarity to Europe. In the north elevation and increased land area caused the development of large ice-sheets,
which appeared first in the mountainous regions with a heavy snowfall, and later spread over the drier plains and plateaux of the interior. This first glaciation was long and complex. Owing to the anticyclonic conditions which formed over the ice, the rain- and snow-bearing depressions were forced to pass further southward, causing greater snowfall on the mountains and high water-level in the lake basins. This greater snowfall, together with the cold conditions due to the existence of the ice-sheets to the north, caused the development of mountain glaciers south of the main glaciated region. In the east there were cold northerly winds which carried a severe climate as far south as Florida. This Glacial period was followed by subsidence, and a long spell of dry, moderately warm climate lasting perhaps 200,000 years, after which elevation and glacial conditions again set in. These conditions were not so severe as the first, and their duration was much less, while they were broken up by several intervals of temporary recession of the ice, one of which, corresponding to the Riss-Wurm period, lasted for 60,000 years, and perhaps should be considered as an “interglacial.” This period was marked in its early stages by the deposition of the curious æolian deposit known as “loess,” indicating steppe conditions. After the last glaciation there set in a stage of irregular retreat.
BIBLIOGRAPHY
Leverett, F “Comparison of North American and European glacial deposits ” Zs f Gletscherkünde 4, 1910, pp 280, 323
Wright, W. B. “The Quaternary Ice Age.” London, 1914, Chs. 8-9.
Attwood, W. W. “The glaciation of the Uinta Mountains.” J. Geol., 15, 1907, p. 790.
Henderson, J. “Extinct glaciers of Colorado.” Colo. Univ. Studies, 3, 1905, p. 39.
Gilbert, G K “Lake Bonneville ” Washington, U S Geol Survey Monograph I, 1890.
Russell, I. C. “The geological history of Lake Lahontan.” Washington, U.S. Geol. Survey Monograph XI, 1885
Coleman, A. P. “An estimate of post-Glacial and interglacial time in North America.” Rep. 12 Internat. Congr. Geol., 1913, p. 435.
CHAPTER IX
The scarcity of data which was bewailed in dealing with Asia is still more marked in the case of South America, and it will be necessary to present the glacial history of that continent in the barest outline only. This is the more unfortunate as the chain of the Andes, extending from north of the equator to high southern latitudes, is of enormous importance in glacial theory, and especially in the question of simultaneity of glaciation in the two hemispheres.
The beginnings of glaciation in South America are obscure. The distribution of animals shows that towards the close of the Tertiary the Falkland Islands were greatly elevated and were united to Tierra del Fuego and Patagonia, and this enlarged land area was connected in some way with Australia and Tasmania, but the mode of this latter connexion is not definitely known. This question will be discussed more fully in Chapter XI; it is sufficient to say here that the amount of elevation may have reached 12,000 feet in Tierra del Fuego. Equatorwards the elevation diminished, and near the equator the land probably lay somewhat lower than now.
In South Georgia the present glaciers greatly expanded, until practically the whole island was buried in ice, and the same is true of the Falkland Islands and Tierra del Fuego, only the highest peaks remaining above the ice. In the latter district there is some evidence of two glaciations separated by an interglacial, the earlier glaciation being due to a regional ice-sheet and the later to smaller valley glaciers. The intricate coast-line of the Falkland Islands and Tierra del Fuego points to fiord erosion by ice which extended well beyond the present limits of the land, and can only have occurred during considerable elevation. As to the character of the interglacial, little is
known. In the Falklands there is a bed of black vegetable soil full of tree-trunks, indicating the existence of luxuriant forests and a temperate climate. This deposit is overlain by boulder-clay, and may be either interglacial or pre-glacial, but since it was formed when the land stood at a comparatively low level, while we have reason to believe (see Chapter XII) that during the close of the Tertiary period these islands were greatly elevated, it is probably an interglacial formation, and indicates a great amelioration of climate. In Gable Island, Tierra del Fuego, Halle found beneath boulder-clay a Quaternary fauna of barnacles and marine mollusca indicating a climate slightly warmer than the present, and this probably belongs to the same period. To the concluding stages of the Glacial period in the Falklands belong the curious “stone rivers,” great streams of moss-grown boulders which fill the valleys, and under the influence of temperature changes are probably still slowly advancing.
Passing further north to the Andes, between 39° and 44° south latitude, the glaciation was not so severe, and its records are therefore clearer. The first result of elevation was the cutting of deep canyons by the rivers. This was followed, possibly without much further elevation, by a fall of temperature, which in this connexion may be attributed to the extension of the Antarctic and Tierra del Fuego ice-sheets. Glaciers now developed and spread down the canyons, leaving moraines of great volume and height, associated with all the other criteria of glaciation. The snow-fields from which these glaciers originated lay between 5000 and 6000 feet above the sea, and the snow-line lay at about 3000 feet instead of above 6000 as at present.
This glaciation was followed by a long interglacial, during which the glaciers retreated to the highest summits of the Andes. The length of this period is indicated by the fact that the earlier moraines have been eroded to such an extent that they no longer present distinctly the typical features of glacial topography, while the materials of which they are composed are decayed to somewhat the same extent as the older moraines of North America, the granite boulders especially being rotten and friable. This interglacial was followed by a re-development of the glaciers, but to nothing like the
same extent as formerly; their moraines are smaller and freshlooking, indicating that this glaciation was comparatively recent.
Still further north, in latitude 20°-25° S., we come to a region of very slight snowfall, where the snow-line lies higher than anywhere else on the face of the earth. The glaciation here was comparatively unimportant, the snow-line descending only 1600 to 2500 feet. Here Keidel found moraines of three glacial advances, and from his description it appears probable that the earliest and greatest was separated by a considerable interval from the two younger, the interglacial between which was short and not characterized by a return to present-day climatic conditions, since during this interval there was very little weathering. Probably we have here to do with two glaciations, of which the second was double. In fact, some writers have described no less than five glacial advances in the Argentine Andes, but most of these are probably merely retreat stadia.
In Peru, W. Sievers reports the existence of two glaciations separated by a considerable interval. The present limit of the glaciers is about 15,200 feet; during the first glaciation they descended to about 11,000 feet, and during the second to 12,800 feet. The evidence is very complete. In Ecuador, H. Meyer records a similar bipartition. The oldest glaciation is represented by trough-like valleys, enormous gravel terraces, and old moraines much weathered; the limits are far below the present limits of glaciers, but have been much obscured by subsequent erosion. This glaciation was followed by a long period of steppe climate resembling the present, during which the loess-like Cangagua formation was deposited. This in turn was followed by a readvance of the glaciers to a level about 2700 feet below the present limit. This glaciation is associated with crescent-shaped moraines, corrie lakes, hanging valleys and gravel terraces, covered with vegetation, but otherwise fresh-looking. The snow-line lay about 1600 feet below the present. Probably during the first glaciation the Andes were invaded by numerous mountain plants and animals related to North American forms—a valuable piece of evidence which indicates that the glaciation was contemporaneous with that in North America. In
Columbia and Venezuela there are traces of Glacial periods, but these have not yet been studied in detail. The most northerly evidence of a Glacial period comes from the Sierra Nevada de Santa Maria, near the north coast of Venezuela in 11° N.
Except in Tierra del Fuego and Patagonia the ice did not extend far from the mountains. But in the eastern Argentine there is a great series of Quaternary deposits known as the Pampean. This formation covers 200,000 square miles, and consists of at least ninety feet of fine loam without a single pebble (except for a few thin calcareous layers), but containing large numbers of complete skeletons of mammals. It raises several interesting problems. Apparently it represents the whole course of the Glacial period. By some geologists it is considered to be a delta deposit of the combined Parana and Paraguay rivers, but the absence of mollusca, except in a marine intercalation near its summit, is against this view, and Steinmann attributes it to æolian agencies and compares it to the loess of Europe and North America. If this view is correct the Pampean represents steppe conditions prevailing on the equatorial side of the Patagonia-Falkland Islands ice-sheet. Apparently before the incoming of the greatest cold the Pampas were in part at least forest-clad, for in the older beds are found peculiar forms of groundsloths which were adapted for forest life and have been found also in cave-deposits of Brazil. At the maximum of glacial conditions the Pampas probably had a steppe climate, but the disappearance of the forests is to be attributed rather to drought than to cold. Elevated glacier-bearing Andes to the west and ice-sheets to the south would render the Argentine extremely arid, and this accounts for the gradual extinction of so many giant forms whose remains are found in the Pampean deposits. Conditions ultimately became too severe even for the horse, which died out in South America. The marine transgression which left its mark near the top of the Pampean is probably post-glacial.
In Brazil, on the other hand, there is no evidence that the climate has ever been drier than the present, and in the semi-arid regions of the north-east it is even probable that during the Glacial period the climate was moister, presumably owing to the greater strength of the
rain-bearing east and north-east winds. Further west in the Andes the existence of this wet period is borne out by the former greater size of Lake Titicaca, and there seems to be additional evidence to the same effect in the Chilian deserts.
BIBLIOGRAPHY
Steinmann, J “Diluvium in Südamerika ” Zs d D Geol Gesellsch , 58, 1906, p 215.
Meyer, H. “In den Hochanden von Ekuador.” Berlin, 1907.
Sievers, W. “Reise in Peru und Ecuador, ausgeführt 1909.” München und Leipzig, 1914.
Keidel, H “Ueber den Anteil der Quartaren Klimaschwankungen an der Gestaltung der Gebirgsoberfläche in dem Trockengebiete der mittleren und nördlichen Argentinischen Anden ” Congr Geol Internat , 12, Canada, 1913, p 757
Willis, Bailey. “Physiography of the Cordillera de los Andes between latitudes 39° and 44° S.” Congr. Geol. Internat., 12, Canada, 1913, P. 733.
Halle, T G “On Quaternary deposits and changes of level in Patagonia and Tierra del Fuego ” Bull Geol Inst , Upsala, 9, 1908-9, p 93
CHAPTER X
A F R I C A
The Quaternary history of Africa can unfortunately be dismissed in a very few words. The glaciation of the Atlas Mountains has already been referred to in connexion with the Mediterranean region. Further south we have no great mountain chain such as the Andes extending above the snow-line over the whole extent of the country, but merely a few isolated peaks. Three of these, all close to the equator, are known to show traces of a greatly extended glaciation in the past: Ruwenzori, just north of the equator, on the borders of Uganda and the Congo, reaching an elevation of 16,794 feet, with the present snow-line at 15,000 feet, and glaciers extending to 10,000 feet, formerly bore glaciers extending down as far as 5200 feet; Kenya, on the equator in Kenya Colony, height 17,040 feet, present snow-line about 15,000 feet, past snow-line 12,000 feet, and old moraines at 10,000 feet; finally, Kilimanjaro, 3° S., on the borders of Tanganyika territory, height 19,320 feet, present limit of glaciers 13,650 feet, past limit 4870 feet. Further south, the Drakensberg Mountains, between Basutoland and Natal, were glaciated on their higher summits. In none of these cases have the remains of more than one glaciation been described, but the mountains are still very little known and this negative evidence is not conclusive. In the neighbourhood of Ruwenzori there are several peaks, which approach 12,000 feet, but these were not glaciated, pointing to a snow-line above this level. Unfortunately the latter piece of evidence is of doubtful validity since these mountains are volcanic and possibly of post-glacial age; we may consider, however, that the glaciation of the central African mountains was characterized by a great increase in the length of the glaciers with only a slight
depression of the snow-line, conditions showing that the glaciation was due chiefly to an increase of snowfall, and only in a minor degree to a fall of temperature. This conclusion is borne out by the low-level beds, which nowhere show an appreciably lower temperature, but abound in indications of a former greatly increased rainfall. The first of these is the former greater size of the African great lakes.
Abyssinia, as we have seen, was probably drier than at present, but further south the rainfall must have been considerably greater. Lake Kioga stood 600 feet above its present level and was connected with Lake Victoria. Lake Victoria and the smaller lakes were twice their present size, and most of the broad valleys were filled with water. Lake Magadi is the attenuated relic of a vast sheet of water, and other great lakes have disappeared entirely. One of these, in the Rift valley, south of Lake Naivasha, has been mapped by Professor Gregory and named after Professor Suess. Part of this decrease of the lakes has undoubtedly taken place within historic times, and part may be attributed to changes in the drainage, but there remains enough evidence to show that some time in the Ice Age the great lakes were very much larger than the present.
Mr. E. J. Wayland, the Government Geologist of Uganda, informs me that in the old basin of Victoria Nyanza there are masses of gravel which may be two or three miles in breadth, the surface of which forms two terraces at different levels. Above the level of these is an old peneplain with ancient beach gravels. Mr. Wayland considers that this peneplain was formed probably during the Pliocene by the first Victoria Nyanza occupying a basin between folds. The initial high level was due to the want of an outlet, but may have been amplified by other causes. The level of the lake then sank gradually to a considerably lower level, after which it rose again nearly to its old level and remained there for a considerable time. During this period the great gravel deposits were formed; they contain flood deposits, especially near their base. The level of the lake then sank again and this part of the basin was converted into a valley occupied by a river. Subsequently the level rose again sufficiently to carve out the lower terrace in the gravels. Mr. Wayland
considers that the upper terrace may also represent a stage distinct from that in which the gravels were actually deposited, but the upper terrace may be the original surface of the gravels. Thus there is evidence of two Pluvial periods in central Africa, of which the first, probably corresponding with the great extension of the mountain glaciers, was the greater. From the archæological evidence it appears to correspond with the Mindelian glaciation of Europe.
A second line of evidence has been pointed out by C. W. Hobley. At the entrance to Kilindi Harbour, Mombasa, there is a gap in the coral barrier through which the fresh water from the river finds its way. These gaps are always found opposite the mouths of rivers, and are due to the inability of the coral polyp to live in fresh or brackish water. In Pleistocene times the land stood some seventy feet lower relatively to the sea, and the old channel through the reef at this height is almost double the width of the present channel, showing that the river then had a greater volume, i.e. the rainfall in its basin was greater.
But Africa is noteworthy chiefly for its deserts, and the most important evidence of climatic change is found in the deserts of Sahara and Kalahari. From the time of the ancient Greeks it had been believed that the Sahara was formerly the site of a great inland sea, and the presence of this sea had even been suggested as the cause of the Ice Age in Europe, but recent investigations have shown that this is not so; the Sahara has been land at least throughout the Tertiary period. There is, however, abundant evidence that during the Quaternary the rainfall was considerably greater than the present. The presence of numerous animals closely associated with water, such as the hippopotamus and even the crocodile, in oases now entirely isolated, shows that these oases were formerly connected with the big rivers. The most definite evidence, however, comes from Lake Tchad. This was formerly of much greater area, but Chudeau and Freydenberg have made out a whole series of changes from desert conditions in the Tertiary through pluvial conditions in the Quaternary back to desert conditions of the present. The sequence is as follows:
1. A regime of dunes.
2. A slow transgression causing a long marshy period, during which numerous plants whose remains are found lived in the period.
3. A slow regression.
4. A rapid transgression (grey loam).
5. A slow regression (clayey white loam with traces of roots).
6. A transgression (white loam).
7. Establishment of a new dune regime.
In the Chari basin east of Lake Tchad are the remains of fish and shells, and also small pebbles of sandstone and chalcedony, which are not local, but must have been brought from the mountains of Tibesti by the rivers Egnei and Toro when their current was much stronger than at present. In Senegal, south of the 15th parallel, the present dune sands are underlain by an alluvial soil, indicating moister conditions preceding the present climate. There is no means of dating the moist periods indicated by these phenomena, but it is reasonable to correlate them with the former extension of the central African lakes.
Passing south to the Kalahari, we find evidence of a number of moist stages separated by drier intervals, but they can apparently be grouped into two main Pluvial periods, separated by a long interpluvial with steppe-like conditions. One at least of these Pluvial periods must be correlated with the former immense extension of Lake Ngami and the Etosha Pan.
From Cape Colony, there is some evidence of moister conditions in the past, but the Quaternary variations cannot be separated from those of historic times.
Before leaving Africa some reference must be made to an interesting suggestion by C. W. Hobley, as to the mechanism of climatic change in tropical countries. He notes that the north-east and south-west monsoons extend to a height of only a few thousand feet. Above them are the very steady “trade winds” connected with the general circulation of the atmosphere. In Kenya Colony these
blow from east or a little south of east. “Their effect is very marked on the high mountains of the interior, such as Kenya, Kilimanjaro and Elgon; in the early morning they are generally quite clear, but about 10 a.m. the clouds sweep up from the S.S.E. and collect on the mountains and blot them out from view for the rest of the day. These are believed to be clouds borne inland by the trade winds, and the moisture they carry is precipitated mainly on the south and southeast sides of the mountains.” Hobley suggests that there was formerly a nearly continuous ridge of high land extending north and south, and this caught the moisture from the trade winds, so causing the Pluvial period, the evidence for this ridge being the distribution of alpine plants on the now isolated high mountains. An alternative explanation is that the greater strength of the earth’s circulation during glacial times caused the trade winds to be much stronger and also to extend to a lower level at the expense of the monsoons, just as the west winds extended to a lower level in northern Egypt. This would bring a great deal more moisture to be precipitated on the mountains, increasing the length of the glaciers and also the volume of the rivers.
BIBLIOGRAPHY
Scott Elliott, G. F. “The geology of Mount Ruwenzori and some adjoining regions of tropical Africa.” Q.J.G.S., 51, 1895, p. 669.
Hobley, C W “The alleged desiccation of East Africa ” Geogr Journ , 44, 1914, p 467
Freydenberg, H. “Le Tchad et le Bassin du Chari.” Diss. Paris, 1908.
Passarge, H “Die Kalahari ”
CHAPTER XI
The continent of Australia has a relatively low relief, only rising above the snow-line in Mount Kosciusko, and glacial traces have a relatively unimportant development. The history of the region appears to be as follows:
In late Tertiary times the shore-line lay some distance to the east towards New Zealand, this being a relic of a much earlier connexion between the two lands. Towards the close of the Tertiary earthmovements set in, which elevated the mountain belt of eastern Australia and formed a land connexion with Tasmania and the Antarctic continent. At the same time the land to the east and the closed basins of central Australia were also probably developed about this time. The climate was then somewhat warmer than the present, at least on the east coast, for the Australian barrier reef extended further south. Probably at this time the Antarctic ice-sheet did not reach the sea, and there was none of the floating ice which is such an important factor in cooling the Southern Ocean.
The next stage was the lowering snow-line on Kosciusko to about 3000 feet below the present and the development of extensive glaciers, which descended to 5500 feet above the sea, and attained an area of 80 to 100 square miles and a thickness of at least 1000 feet. Tasmania was also extensively ice-covered, probably by glaciers which coalesced at low levels, forming what is known as a “piedmont” ice-sheet, which possibly reached the sea. The lowering of the snow-line in Tasmania is estimated as 6000 feet, corresponding to a fall in temperature of 18° F. Probably a large part of this fall is accounted for by the increased elevation, which may have been several thousand feet in Tasmania and more than a
thousand feet even in New South Wales. This glaciation, which was probably dependent on the growth of the Antarctic ice-sheet, was followed by a very long interglacial, the duration of which has been estimated by Professor David as 100,000 to 200,000 years. The old moraines are much weathered and denuded, resembling in this respect the older moraines of Europe. No information is available as to the climate of this interglacial period. Possibly some of the Quaternary raised beaches with warmth-loving mollusca found in unglaciated parts of Australia belong to this period, and if so the climate was warmer than the present for at least part of the time.
The interglacial was followed by uplift and a second much less severe Glacial period, characterized by valley glaciers on Kosciusko and in Tasmania, reaching the sea in places on the latter island. It was at the close of this Glacial period that man reached Tasmania; its conclusion is dated by Prof. David at about 10,000 years ago. It was terminated by a period of depression below the present level with a warm climate.
In the dry interior of Australia there is evidence that at one time, probably during the maximum glaciation, the rainfall was heavier than the present, and numerous lakes were developed which have now been dry for a very long time. It is possible that the artesian water supply of Australia, which Gregory considers to be “fossil water” accumulated under different conditions from the present, is a vestige of the rainfall of this period. Further north, in Java, the beds in which the famous Pithecanthropus skeleton was found, believed to be lower glacial, contain also plant remains similar to those now found in the Khassian mountains of Assam, one of the rainiest climates in the world. The climate of Java during the maximum glaciation was thus decidedly rainier, and probably somewhat cooler than the present.
An extraordinary find which may be referred to here is that of Professor Neuhauss, who discovered giant erratics, scratched and polished, and moraines at sea-level at the western end of Huon Gulf, New Guinea. The region is very unstable, and is known to have stood at a very much higher level, perhaps 10,000 feet or more, in Quaternary times, and if the moraines indicate glaciers terminating at
10,000 feet above the sea they are explicable by a slight fall of temperature and increase of snowfall.
Turning now to New Zealand, we find extensive glacial remains on South Island, though not on North Island. As in so many other countries, the Quaternary opened with great elevation, which reached at least 1500 feet over the whole group. North and South Islands were united with each other, with Stewart Island and probably also the outlying islands, even including the Chatham Islands, forming a great land-mass several times the present area of New Zealand. On the southern part of this land-mass extensive glaciers were formed; on the east these did not reach the present sea-level, but on the snowy south-west they extended far below it, so that the terminal moraines are now completely submerged; possibly they were never formed, but the debris was floated away seaward on icebergs. Further north moraines are found near the present shoreline at many places between Milford Sound and Hokitika, and morainic mounds cover a large part of the low ground. Still further north they retreat inland, and in the Nelson Province are not found below a level of 2000 feet at the foot of Lake Rotoiti.
In the south-east a great moraine has been described at the south end of Lake Wakatipu and others at the north-east ends of Lakes Manapouri and Te Anau, but none are found nearer the sea-coast. The glaciated area of New Zealand was at least ten times the present ice-covered area, and the Tasman, the longest glacier in New Zealand, was expanded from its present length of 16 miles to at least 30 miles. Much of the apparent fall of temperature shown by this glaciation was probably due to the great elevation, but apart from this the ice had a marked influence on climate. Outside the limits of glaciation on the east is a thick deposit of typical loess, which extends up to a level of 1000 feet on the flanks of the hills. The occurrence of this loess points to a steppe climate with dry, cold, southerly winds on the lee side of the glaciated mountains, and is probably also connected with the increase of land area. Further north, north of Auckland in North Island, the present treeless plains were covered by forests; for Kauri gum, apparently very old, has been found. The sub-antarctic islands—Campbell, Antipodes, etc.—
