Increasing Returns and Path Dependence in the Economy by Brian Arthur

The Rabbit Hole is written by Blas Moros. To support, sign up for the newsletter, become a patron, and/or join The Latticework. Original Design by Thilo Konzok.


  1. The idea of increasing returns has come up every few decades but Brian Arthur’s precise and fully-modeled papers caused us to clearly understand what kinds of models have what kinds of implications. One outstanding characteristic of Arthur’s viewpoint is emphatically dynamic in nature. Learning by using or doing plays an essential role, as opposed to static examples of returns to scale (those based on volume-area relations). The object of study is a history. Another distinctive feature of most of the work is its stochastic character. This permits emphasis on the importance of random deviations for long-run tendencies. Other tendencies include the multiplicity of possible long-run states, depending on initial conditions and on random fluctuations over time, and the specialization (in terms of process or geographical location) in an outcome achieved. Increasing returns may also serve as a reinforcement for early leading positions and so act in a manner parallel to more standard forms of increasing returns. A similar phenomenon occurs even in individual learning, where again successes reinforce some courses of action and inhibit others, thereby causing the first to be used more intensively, and so forth. There are in all of these models opposing tendencies, some toward achieving an optimum, some toward locking in on inefficient forms of behavior. 

 Key Takeaways

  1. The papers here reflect two convictions I have held since I started work in this area. The first is that increasing returns problems tend to show common properties and raise similar difficulties and issues wherever they occur in economics. The second is that the key obstacle to an increasing returns economics has been the “selection problem” – determining how an equilibrium comes to be selected over time when there are multiple equilibria to choose from. Thus the papers here explore these common properties – common themes – of increasing returns in depth. And several of them develop methods, mostly probabilistic, to solve the crucial problem of equilibrium selection. 
  2. Arthur studied electrical engineering so was vaguely familiar with positive feedback already and became more intrigued when he read about the history of the discovery of the structure of DNA and read whatever he could about molecular biology and enzyme reactions and followed these threads back to the domain of physics. In this work, outcomes were not predictable, problems might have more than one solution, and chance events might determine the future rather than be average away. The key to this work, I realized, lay not in the domain of the science it was dealing with, whether laser theory, or thermodynamics, or enzyme kinetics. It lay in the fact that these were processes driven by some form of self-reinforcement, or positive feedback, or cumulative causation – processes, in economics terms that were driven by nonconvexities. Here was a framework that could handle increasing returns. 
    1. Great discoveries tend to come from outside the field 
  3. Polya Process – path-dependent  process in probability theory 
  4. In looking back on the difficulties in publishing these papers, I realize that I was naive in expecting that they would be welcomed immediately in the journals. The field of economics is notoriously slow to open itself to ideas that are different. The problem, I believe is not that journal editors are hostile to new ideas. The lack of openness stems instead from a belief embedded deep within our profession that economics consists of rigorous deductions based on a fixed set of foundational assumptions about human behavior and economic institutions. If the assumptions that mirror reality are indeed etched in marble somewhere, and apply uniformly to all economics problems, and we know what they are, there is of course no need to explore the consequences of others. But this is not the case. The assumptions economists need to use vary with the context of the problem and cannot be reduced to a standard set. Yet, at any time in the profession, a standard set seems to dominate. I am sure this state of affairs is unhealthy. It deters many economists, especially younger ones, from attempting approaches or problems that are different. It encourages use of the standard assumptions in applications where they are not appropriate. And it leaves us open to the charge that economics is rigorous deduction based upon faulty assumptions. At this stage of its development economics does not need orthodoxy and narrowness; it needs openness and courage. 
  5. I did not set out with an intended direction but if I have had a constant purpose it is to show that transformation, change, and messiness are natural in the economy. The increasing-returns world in economics is a world where dynamics, not statics, are natural; a world of evolution rather than equilibrium; a world or probability and chance events. Above all, it is a world of process and pattern change
  6. Positive Feedbacks in the Economy
    1. Diminishing returns, what conventional economic theory is built around, imply a single economic equilibrium point for the economy, but positive feedback – increasing returns – makes for many possible equilibrium points. There is no guarantee that the particular economic outcome selected from among the many alternatives will be the “best” one. Furthermore, once random economic events select a particular path, the choice may become locked-in regardless of the advantages of the alternatives
    2. Increasing returns do not apply across the board – agriculture and mining (resource-based portions) – are subject to diminishing returns caused by limited amounts of fertile land or high quality deposits. However, areas of the economy which are knowledge-based are largely subject to increasing returns. Even the production of aircraft is subject to increasing returns – it takes a large initial investment but each plane after that is only a fraction of the initial cost. In addition, producing more units means gaining more experience in the manufacturing process and achieving greater understanding of how to produce additional units even more cheaply. Moreover, experience gained with one product or technology can make it easier to produce new products incorporating similar or related technologies. Not only do the costs of producing high-technology products fall as a company makes more of them, but the benefits of using them increase. Many items such as computers or telecommunications equipment work in networks that require compatibility; when one brand gains a significant market share, people have a strong incentive to buy more of the same product so as to be able to exchange information with those using it already. 
    3. Timing is important too in the sense that getting into an industry that is close to being locked in makes little sense. However, early superiority does not correlate with long term fitness 
    4. Like punctuated equilibrium, most of the time the perturbations are averaged away but once in a while they become all important in tilting parts of the economy into new structures and patterns that are then preserved and built on in a fresh layer of development 
  7. Competing technologies, increasing returns, and lock-in by historical events 
    1. There is an indeterminacy of outcome, nonergodicity (path dependence where small events cumulate to cause the systems to gravitate towards that outcome rather than others). There may be potential inefficiency and nonpredictability. Although individual choices are rational, there is no guarantee that the side selected is, from any long term viewpoint, the better of the two. The dynamics thus take on an evolutionary flavor with a “founder effect” mechanism akin to that in genetics 
  8. Path dependent processes and the emergence of macrostructure 
    1. Many situations dominated by increasing returns are most usefully modeled as dynamic processes with random events and natural positive feedbacks or nonlinearities. We call these nonlinear Polya processes and show that they can model a wide variety of increasing returns and positive feedback problems. In the presence of increasing returns or self reinforcement, a nonlinear Polya process typically displays a multiplicity if possible asymptotic outcomes. Early random fluctuations cumulate and are magnified or attenuated by the inherent nonlinearities of the process. By studying how these build up as the dynamics of the process unfold over time, we can observe how an asymptotic outcomes becomes “selected” over time 
    2. Very often individual technologies show increasing returns to adoption – the more they are adopted the more is learned about them; in then the more they are improved, and the more attractive they become. Very often, too, there are several technologies that compete for shares of a “market” of potential adopters 
  9. Industry location patterns and the importance of history 
    1. This study indeed shows that it is possible to put a theoretical basis under the historical-accident-plus-agglomeration argument (mostly arbitrary location for determining where a city is established but then more people flock to it, it receives more investment, more buildings come up, etc. which leads to agglomeration and increasing returns).
  10. Information Contagion
    1. When a prospective buyer is making purchasing decisions among several available technically-based products, choosing among different computer workstations, say, they often augment whatever publicly available information they can find by asking previous purchasers about their experiences – which product they chose, and how it is working for them. This is a natural and reasonable procedure; it adds information that is hard to come by otherwise. But it also introduces an “information feedback” into the process whereby products compete for market share. The products new purchasers learn about depend on which products the previous purchasers “polled” or sampled and decided to buy. They are therefore likely to learn more about a commonly purchased product than one with few previous users. Hence, where buyers are risk-averse and tend to favor products they know more about, products that by chance win market share early on gain an information-feedback advantage. Under certain circumstances a product may come to dominate by this advantage alone. This is the information contagion phenomenon
  11. Self-Reinforcing Mechanisms in Economics
    1. Dynamical systems of the self-reinforcing or autocatalytic type – systems with local positive feedbacks – in physics, chemical kinetics, and theoretical biology tend to possess a multiplicity of asymptotic states or possible “emergent structures”. The initial starting state combined with early random events or fluctuations acts to push the dynamics into the domain of one of these asymptotic states and thus to “select” the structure that the system eventually “locks into”. 
    2. Self-reinforcing mechanisms are variants of or derive from four generic sources:
      1. Large set up or fixed costs (which give the advantage of falling unit costs to increased output)
      2. Learning effects (which act to improve products or lower their cost as their prevalence increases)
      3. Coordination effects (which confer advantages to “going along” with other economic agents taking similar action)
      4. Self-reinforcing expectations (where increased prevalence on the market enhances beliefs of further prevalence)
    3. Besides these 4 properties, we might note other analogies with physical and biological systems. The market starts out even symmetric, yet it ends up asymmetric: there is “symmetry breaking.” An “order” or pattern in market shares “emerges” through initial market “fluctuations.” The two technologies compete to occupy one “niche” and the one that gets ahead exercises “competitive exclusion” on its rival. And if one technology is inherently superior and appeals to a larger proportion of purchasers, it is more likely to persist: it possesses “selectional advantage.”
    4. Some more characteristics: multiple equilibria (multiple “solutions” are possible but the outcome is indeterminate, not unique and predictable); possible inefficiency, lock-in, path dependence
    5. We can say that the particular equilibrium is locked in to a degree measurable by the minimum cost to effect changeover to an alternative equilibrium. In many economic systems, lock-in happens dynamically, as sequential decisions “groove” out an advantage that the system finds it hard to escape from. Exiting lock-in is difficult and depends on the degree to which the advantages accrued by the inferior “equilibrium” are reversible or transferable to an alternative one. It is difficult when learning effects and specialized fixed costs are the source of reinforcement. Where coordination effects are the source of lock-in, often advantages are transferable. As long as each user has certainty that the others also prefer the alternative, each will decide independently to “switch”. Inertia must be overcome though because few individuals dare change in case others do not follow
  12. Path Dependence, Self-Reinforcement, and Human Learning
    1. There is a strong connection between increasing returns mechanisms and learning problems. Learning can be viewed as competition among beliefs or actions, with some reinforced and others weakened as fresh evidence and data are obtained. But as such, the learning process may then lock-in to actions that are not necessarily optimal nor predictable, by the influence of small events
    2. What makes this iterated-choice problem interesting is the tension between exploitation of knowledge gained and exploration of poorly understood actions. At the beginning many actions will be explored or tried out in an attempt to gain information on their consequences. But in the desire to gain payoff, the agent will begin to emphasize or exploit the “better” ones as they come to the fore. This reinforcement of “good” actions is both natural and economically realistic in this iterated-choice context; and any reasonable algorithm will be forced to take account of it. 
  13. Strategic Pricing in Markets and Increasing Returns
    1. Overall, we find that producers’ discount rates are crucial in determining whether the market structure is stable or unstable. High discount rates damp the effect of self-reinforcement and lead to a balanced market, while low discount rates enhance it and destabilize the market. Under high discount rates, firms that achieve a large market share quickly lose it again by pricing high to exploit their position for near-term profit. And so, in this case the market stabilizes. Under low discount rates, firms price aggressively as they struggle to lock in a future dominant position; and when the market is close to balanced shares, each drops its price heavily in the hope of reaping future monopoly rents. The result is a strong effort by each firm to “tilt” the market in its favor, and to hold it in an asymmetric position if successful. And so, in this case strategic pricing destabilizes the market
    2. The simple dynamics and stochastic model of market competition analyzed in this paper reveals striking properties. First, positive feedback or self-reinforcement to market share may result in bistable stationary distributions with higher probabilities assigned to asymmetric market shares. The stronger the positive feedback, the lower the probability of passing from the region of relative prevalence of one product to that of the other. Second, when producers can influence purchase probabilities by prices, in the presence of positive feedback, optimal pricing is highly state-dependent. The producers struggle for market shares by lowering prices, especially near pivot states with balanced shares. 

 What I got out of it

  1. Influential read discussing self-reinforcement, lock-in, increasing returns in knowledge-based economies/industries, path dependence, and more. Extremely applicable for business, investing, economics, learning, and more. A great mental model to have in your toolbox

Ice Age by John and Mary Gribbin

The Rabbit Hole is written by Blas Moros. To support, sign up for the newsletter, become a patron, and/or join The Latticework. Original Design by Thilo Konzok.

  1. “As we mentioned earlier, given the present day geography of our planet—the distribution of the continents and oceans—the natural state of the Earth is in a full Ice Age. Koppen was correct in highlighting the importance of summer warmth in influencing the advance and retreat of the ice in the Northern Hemisphere. But, in a sense, he, too, got the argument backwards. It isn’t so much that Ice Ages occur when the astronomical influences conspire to produce particularly cool summers; rather, what matters is that Interglacials only occur when the astronomical influences conspire to produce unusually warm summers, encouraging the ice to retreat. Without all three of the astronomical rhythms working in step in this way, the Earth stays in a deep freeze. And that is why the actual pattern of climate over the past few million years has been one of long Ice Ages (in fact, a single long Ice Epoch) interrupted by short-lived Interglacials, like the one we are living in now…Without the astronomical rhythms of the Ice Ages, we would probably still be tree-apes. It was the repeated drying out and recovery of the East African forests that pushed our ancestors out on to the plains, forced them to become more versatile, encouraged them to walk upright rather than climbing on branches, and, almost as an afterthought, made us intelligent. Fully modern humans, Homo sapiens sapiens, emerged during the previous Interglacial to our own, by about 100,000 years ago, and had just one more Ice Age to endure before they began to build civilization. We are the product of the latest Ice Epoch, in a way that Agassiz, Croll and Milankovitch could never have guessed, and that realization is the ultimate triumph of the theory of Ice Ages.”
Key Takeaways
  1. “Our perspective (the entire history of human civilization) embraces only a short-lived, temporary retreat of the ice, an Interglacial. The succession of relatively long-lived Ice Ages and relatively short-lived Interglacials is now known as an Ice Epoch, and lasts for several million years…We think that it is normal to have ice at both poles of our planet. After all, there has been ice there for longer than there has been human civilization. But in the long history of the Earth, polar ice caps are rare, and having two polar ice caps at the same time may be unique. Indeed, it may be the presence of those polar ice caps which has made us human. And although we associate weather with the movement of masses of air around the globe, with high pressure systems bringing settled, dry conditions and low pressure systems bringing wind and rain or snow, as far as climate is concerned great ocean currents are much more important.”
  2. The changes resulting from Arctic warming would be bigger than you might expect at first sight, and would in many ways be unpredictable, because of the effect of positive feedback. Today, the shiny white surface of the ice covering the Arctic Ocean reflects away incoming solar energy, and helps to keep the polar region cool. Once the ice starts to melt, however, it exposes dark water, which absorbs the incoming solar energy and warms the region still further. If the world cooled for any reason, the feedback would operate in reverse, with dark ocean being covered by shiny ice that reflects away incoming solar energy and helps to keep things cold. But you can’t have half the north polar icecap; the feedbacks make it an all or nothing choice.
  3. This fact alone tells you that our distance from the Sun is not the cause of the seasons; in the Northern Hemisphere, we have summer when we are furthest from the Sun. But maybe the elliptical orbit produces other, more subtle effects on climate.
  4. In order to understand a given law, I was generally obliged to make myself acquainted with the preceding law or condition on which it depended. I remember well that, before I could make headway in physical astronomy… I had to go back and study the laws of motion and the fundamental principles of mechanics. In like manner I studied pneumatics, hydrostatics, light, heat, electricity and magnetism. I obtained assistance from no one.
  5. The environment suited him down to the ground. ‘I have never been in any place so congenial to me as that institution,’ he wrote. ‘My salary was small, it is true, little more than sufficient to enable me to subsist; but this was compensated by advantages for me of another kind.’ He meant the library, and the peace and quiet, allowing him to give rein to his ‘strong and almost irresistible propensity towards study’.
  6. The change in eccentricity is measured in terms of the distance between the two foci of the ellipse, as a percentage of the long axis of the ellipse. For a perfect circle, the two foci merge to become one, with no distance between them, so the eccentricity is zero. Today, the eccentricity of the Earth’s orbit is about 1 per cent, but Leverrier showed that at its most extreme the Earth’s orbit has an eccentricity of roughly 6 per cent. Because Leverrier’s calculations showed that the Earth’s orbit was in a more highly eccentric state 100,000 years ago, while for the past 10,000 years or so it has been in a low eccentricity state, and since the world is warmer now than it was in the past, Croll speculated that some effect associated with high eccentricity must be responsible for Ice Ages.
  7. Leverrier’s calculations had already shown that whatever kind of orbit the Earth is in at any particular epoch, the amount of heat received from the Sun over the course of an entire year stays the same; but Croll followed up the idea that it might be the way the heat is distributed between the seasons which matters, since this is undoubtedly affected by the eccentricity. When the orbital eccentricity is low, and the orbit is circular, the amount of heat received by the whole planet from the Sun each week is the same throughout the year; but when the orbit is more elliptical, with high eccentricity, the Earth receives more heat in a week at one end of its orbit, closest to the Sun, and correspondingly less heat in a week at the other end of its orbit, farthest from the Sun. Depending on which hemisphere you live in, this may mean that when the orbit is more eccentric there is more difference between the seasons, with cold winters when the Earth is farthest from the Sun and hot summers when it is closest to the Sun; or (in the other hemisphere) it may mean that the eccentricity effect smooths out the difference between the seasons, keeping summers cool and winters mild.
  8. Croll argued that what was needed to build an Ice Age was a series of very cold winters, so that there would be more snowfall, building up white snowfields and ice sheets which would reflect away the summer heat from the Sun to keep the hemisphere cool. He was one of the first scientists to develop the idea of feedback in any context, and although it happens that he got the detail of this influence backwards, his model would be important historically for that reason alone.
  9. Croll was one of the first people to appreciate the major influence of the great ocean currents on climate, and was the first person to work out the link between the trade winds (essentially driven by convection in the atmosphere stirred up by the Sun heating the surface of the Earth) and the flow of these currents, pushed by the winds. He reasoned that the change in the balance of heat between the hemispheres when one polar region cooled would increase the strength of the trade winds, blowing from the hotter part of the world to the colder region in an attempt to even out the temperature, and also change their direction somewhat. This would change the pattern of the ocean currents. In particular, he noted that a relatively small shift in the westward flowing current of the equatorial Atlantic Ocean could make it flow either northward past the bulge of Brazil and up past North America, or southward past the bulge of Brazil, and down past South America. The potential climatic consequences of such a shift, which could be triggered by a relatively small outside influence, are clear from the Prologue. Once again, Croll was at the forefront of thinking about feedbacks, and the way in which they can magnify small initial disturbances.
  10. Finally, in Climate and Time he pointed out that there is yet a third astronomical influence on climate, which really ought to be taken into account. The tilt of the Earth’s axis (the amount it leans out of the vertical) also varies as time passes,
  11. In his own words, he was ‘under the spell of infinity’. Milankovitch was based in Belgrade for the rest of his working life, and within two years he had found the problem that would occupy him for the next thirty years—but always, strictly speaking as a hobby, worked on at home, alongside his day job as a teacher and engineer.
  12. Milankovitch reckoned that he started out on the task, when he was thirty-two years old, at exactly the right time: Had I been somewhat younger I would not have possessed the necessary knowledge and experience… Had I been older I would not have had enough of that self-confidence that only youth can offer.
  13. Coffee (black) was served by Milankovitch’s wife promptly at ten o’clock, and occupied just ten minutes before it was back to work. Lunch at one was followed by a short siesta and a cigar, then more calculations until six, when work ceased for the day. A stroll before dinner, which was a leisurely meal taken at eight, where the family discussed the topics of the day, was followed by an early night, with bed at ten providing time to read (never anything related to work) for an hour before settling down, usually to think for a considerable time before sleeping. I was always intrigued by his method of work—never rushing nor delegating anything, including even drawing and translating into French or German. He always made thorough preparations by outlining relevant points before precisely detailing the body of the article, then rewriting prior to typing the final copy himself. A simple reply to any correspondence would be treated in the same personal manner.
    1. NOTE: cool study schedule
  14. It was while watching the fighting that he suddenly had a flash of insight which showed him the way around the mathematical logjam that had been holding him up. It was a classic example of the way the answer to a problem you have been struggling with can pop into your head once you stop looking for the solution.
  15. But it was Koppen who pointed out that it is always cold enough for snow to fall in the Arctic in winter, even today, and that the reason that the Northern Hemisphere is not in the grip of a full Ice Age at present is because the ‘extra’ snow melts away again in summer. He reasoned that the way to encourage the ice to spread would be to have a reduction in summer warmth, because then less of the winter snowfall would melt. If less snow melted in summer than fell in winter, the ice sheets would grow—and once they had started to grow, the feedback effect of the way the ice and snow reflect away incoming solar energy would enhance the process.
  16. The best place to find out what the climate of the Earth was like in the past is at the bottom of the deep ocean. Different kinds of sea creatures flourish under different climates, and in particular at different ocean temperatures. Layer by layer, the mud of the sea bed builds up, and each layer contains the remains of the creatures best suited to the climate at the time that layer was being laid down. The solution was to drop hollow steel pipes vertically into the sea bed, so that their weight would drive them into the mud. When the pipes were hauled back on board ship, the mud inside the pipe could be extracted as a cylindrical core, with its layered structure intact. Unfortunately, because of the resistance of the water, which stops the pipes building up any great speed as they fall, this kind of ‘gravity coring’ can only extract cores about a metre long—the pipes just won’t penetrate any deeper into the ooze. This was better than nothing, and provided the first evidence, in the 1930s, for three distinct layers in this top metre of mud in cores from the tropical Atlantic—two layers containing remains corresponding to warm conditions like those in the region today, sandwiching a layer containing remains corresponding to a colder climate.
  17. The obvious candidate for that something else was the way water gets locked up in great ice sheets during an Ice Age. When water evaporates, it is easier for the lighter molecules to escape into the air, so the water left behind tends to have a higher proportion of oxygen-18; much of the evaporated water, relatively rich in oxygen-16 compared with the water left behind (exactly how rich also depends on the temperature), falls as snow during an Ice Age, and gets locked up as ice instead of being recycled back into the sea. So the proportion of oxygen-18 available in the oceans is higher during an Ice Age, even before you take account of the way the proportion of oxygen-18 in their shells is enhanced by the way plankton take up the water.
  18. The isotope technique, it was now clear, gave you, in effect, a measure of the global average temperature, no matter where in the oceans the core had been drilled. But they still needed a way to date accurately the temperature fluctuations that were now clearly apparent in the cores covering the entire Pleistocene Epoch.
  19. When more water is locked up in ice, the sea level falls; but when the ice sheets melt, sea level rises.
  20. Kukla had not invented this technique, although he was one of the first people to apply it to the study of past climates. It depended upon the discovery that the Earth’s magnetic field is not constant, but sometimes (seemingly at random) reverses itself entirely, first fading away to nothing and then building up again in the opposite sense, so that what is now the North magnetic pole becomes the South magnetic pole, and vice versa. The details of exactly how and why this happens are still not known, but it is clearly a result of the way the Earth’s magnetic field is generated, by swirling currents of fluid, electrically-conducting, iron-rich material in the deep interior of our planet.
  21. When reversals happen, they take place in less than 10,000 years (perhaps much less), so they show up sharply in the geological record; but once a particular orientation of the field is established, it may last for millions of years, or only for a few tens of thousands of years. The most recent reversal happened about 780,000 years ago, but the Earth’s magnetic field is weakening at the moment, so we may be living through the early stages of the next reversal.
  22. Since the temperature at the bottom of the sea hardly changes, even during the switch from an Ice Age to an Interglacial, this was the definitive proof that the main influence on the oxygen isotope composition was indeed the advance and retreat of the ice sheets on land, and that the isotopes were recording the pulsebeat of global climate change.
  23. It is concluded that changes in the Earth’s orbital geometry are the fundamental cause of Quaternary ice ages. A model of future climate based on the observed orbital-climate relationships… predicts that the long-term trend over the next several thousand years is towards extensive northern-hemisphere glaciation.
  24. They depend simply on the amount of heat which is required to turn ice at 0°C into water at the same temperature—the latent heat of fusion, which is (in the units used by Mason) 80 calories for every gram of ice melted. Since one calorie is defined as the amount of heat needed to raise the temperature of one gram of water by one degree Celsius, this means that the heat required to melt one gram of water at the freezing point is enough to heat that same gram of liquid water all the way from 0°C to 80°C. When you are melting glaciers, that adds up to a lot of heat, which is why Mason started the calculation expecting to prove that the change in heat balance of the Northern Hemisphere caused by the astronomical rhythms would not be sufficient for the task. A similar process operates in reverse when water vapour condenses into liquid or water freezes into ice. In each case, latent heat is given out by the water, rather than being taken up. When the vapour condenses into water at the same temperature, 595 calories of heat are released for each gram involved; so when the vapour goes all the way to the solid form and falls as snow, it liberates 675 calories for every gram of snow that falls. This heat goes into warming the surrounding air and the globe generally, while the need for heat to be absorbed in melting snow and ice tends to keep regions covered by winter snow cool well into early summer. Each year, we see the Ice Age cycle repeated in miniature.
  25. In the most extreme example of this chauvinistic approach, geologists set the start of the present epoch, the Holocene, at the beginning of the present Interglacial, 10,000 years ago. This is completely unjustified, since there is no evidence that the present Interglacial marks the end of the Ice Epoch that has persisted for the past few million years; the boundary is really chosen to mark the emergence of human civilization, as much out of hubris as chauvinism. But we will not be concerned here with anything that happened as recently as 10,000 years ago.
  26. South America, moving northward, gradually caught up with North America, so that by about 3 Myr BP the gap between them was closed, and ocean currents that used to flow westward through that gap were being diverted northward as the Gulf Stream, setting up the pattern of circulating ocean currents that we see today. But the drifting continents were also closing the gaps around the Arctic Ocean, so that this northward flow of warm water could not penetrate all the way into the polar sea. The first Northern Hemisphere glaciation of the present Ice Epoch, dated using the radioactive potassium method, occurred about 3.6 million years ago. This was a particularly significant event in the evolution of humankind, because fossil remains show that our ancestors lived in East Africa at that time. It wasn’t so much the cooling itself that affected them, as the fact that, during an Ice Age, with lowered temperatures there is less evaporation from the oceans, and therefore less rainfall. Together with changes in the pattern of circulation of the atmosphere caused by the presence of ice sheets at higher latitudes, this means that with the present geography of the globe when Europe experiences an Ice Age, East Africa experiences a drought. So the forest in which our ancestors lived shrank when the ice advanced. Put all of the evidence together, and it tells us that a forest-dwelling East African proto-ape line gave rise to three separate lines, leading to ourselves, the chimpanzees and the gorillas, between about 3.5 and 4 million years ago, exactly when the climate was changing dramatically. Since both the Ice Ages and the evolutionary changes are tied to the same absolute timescale (ultimately, through radioactive potassium), there is no doubt that the evolutionary changes and the environmental changes occurred at the same time. Conceivably (but highly improbably!) the geological timescale might be adjusted once again; but if it is, the evolutionary timescale will change in step with it. It is hard to escape the conclusion that the changes in the environment in which our ancestors lived were responsible for the three-way split
  27. The distinguishing characteristic of human beings is versatility. Some animals run faster, some are better swimmers, some have better teeth and claws for killing and eating meat, some have better teeth and digestive systems for eating plants, and so on. But people do a little bit of everything quite well.
  28. Without the astronomical rhythms of the Ice Ages, we would probably still be tree-apes. It was the repeated drying out and recovery of the East African forests that pushed our ancestors out on to the plains, forced them to become more versatile, encouraged them to walk upright rather than climbing on branches, and, almost as an afterthought, made us intelligent. Fully modern humans, Homo sapiens sapiens, emerged during the previous Interglacial to our own, by about 100,000 years ago, and had just one more Ice Age to endure before they began to build civilization. We are the product of the latest Ice Epoch, in a way that Agassiz, Croll and Milankovitch could never have guessed, and that realization is the ultimate triumph of the theory of Ice Ages.
What I got out of it
  1. Interesting to learn more about positive and negative feedback loops as they relate to climate. More mild summers in which less snow melts would allow glaciers to grow, reflecting more light and absorbing less heat, allowing the glaciers to grow further, and on and on…Also didn’t know that the natural state of the Earth is in what we call an Ice Age. Without unusually warm summers to melt the ice caps, the Earth would revert back to a deep freeze

Gödel, Escher and Bach: An Eternal Golden Braid by Douglas Hofstadter

The Rabbit Hole is written by Blas Moros. To support, sign up for the newsletter, become a patron, and/or join The Latticework. Original Design by Thilo Konzok.

  1. Douglas Hofstadter sets out to show that if life can evolve out of simple chemicals and cells and consciousness out of neurons, it is not a far cry to believe that computers will some day gain human intelligence. He explores an amazing array of topics including self-recursion and reduction; all within the structure of the works of Gödel, Escher and Bach. The book follows a unique layout in that he creates a dialogue between fictitious characters which is meant to set the stage for the lesson he is discussing the the following chapter. 
Key Takeaways:
  1. I cannot do this book justice in trying to summarize and distill the lessons throughout. I know when I am out of my league and implore you to watch the following videos taught at MIT around GEB. Also found here, on YouTube if you want to watch at double speed.
What I got out of it:
  1. An absolutely fascinating and thought-provoking book. Hofstadter discusses so many topics which were new to me and out of my general area of knowledge and comfort zone. It is refreshing to read about an area that I knew so little about and it gave me a much deeper insight into the beauty of mathematics, art and music than I had ever understood. 

Read GEB

Interested in seeing some of M.C. Escher’s amazing works? Artsy is a beautiful website which aims to make the world’s art accessible to everyone. They have hundreds of pieces from some of the world’s most renowned artists. Definitely check them out