The Great Mental Models Volume 3: Systems and Mathematics
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Read between December 5 - December 11, 2021
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Termite mounds exhibit emergent properties. A single termite is powerless, but a million or two working together can build a complex mound up to 17 feet tall, requiring the movement of a ton of soil and several tons of water each year.3 Without a leader orchestrating their movements, termites build ventilation and cooling systems, storage chambers, fungal gardens, and specialized housing for the queen.
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Weak emergence occurs in systems in which functions are based on identifiable rules. We can model weak emergence by identifying the underlying rules. Strong emergence does not have identifiable rules behind it, so we cannot model it. So it’s possible to construct a computer simulation of the flocking behavior of a group of birds (weak emergence) but not of the interplay of cells in our brains that creates consciousness (strong emergence).
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One of the primary features of emergence is self-organization. The parts of a system may appear to interact in chaotic ways, but the whole can seem orderly. This occurs without centralized control—the parts organize themselves from the bottom up.
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Emergence is not synonymous with complexity. Some complex systems exhibit emergent properties, some only resultant properties. Some simple systems have complex emergent properties.
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The rules governing how pieces can move are basic, but they lead to complex, high-level strategies, and the outcomes of games are unpredictable. The rules don’t tell you how a game will end.
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Finally, the story can teach us that you don’t always need to plan things all the way to the end. If you have a simple starting point on the right trajectory, surprising things can pan out through the power of emergence.
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Knowledge sharing can often produce unexpected results. We start to work together; I bring an understanding of x, and you contribute experience with y. Combining our knowledge means we have x and y covered, but sometimes we are also able to create z.
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We don’t need to reinvent the wheel each generation. We have evolved social networks that allow us to learn from our elders and to pass on that knowledge to our children. What is important for humans, though, is that we all don’t need to know everything. Look around and you will see many items that you cannot build but that you can use. Cultural learning produces products that are emergent properties of human collective organization.
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“the striking technologies that characterize our species, from the kayaks and compound bows used by hunter-gatherers to the antibiotics and airplanes of the modern world, emerge not from singular geniuses but from the flow and recombination of ideas, practices, lucky errors, and chance insights among interconnected minds and across generations.”16 Basically humans create things as a group that no one person is capable of.
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Cultural learning has produced a cultural mind: an emergent property allowing human knowledge to be far beyond the scope of any individual.
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Relatively small improvements are easier than large ones, so most successful innovations will lead to small changes. These modest attempts at improvement give behaviors a nudge in an adaptive direction, on average. Cultural transmission preserves the nudges, and exposes the modified traditions to another round of nudging.
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Humans are generally very good at sharing our improvements and insights with those around us. Furthermore, we find it natural to learn from other people. Thus, although innovating is important in terms of adaptability and survival, what makes humans unique is our social networks that encourage the sharing and uptake of innovation.
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“once individuals evolve to learn from one another with sufficient accuracy (fidelity), social groups of individuals develop what might be called collective brains.”21 It is these collective brains—products of large, interconnected groups with strong social norms—that have the potential to generate emergent properties and propel a society to increased sophistication in technological complexity.
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Henrich explains how cultural learning has put selection pressures on humans, changing both our bodies and our instincts. Thus, we start out in life not as a total blank slate but with a huge amount of cumulative cultural evolution behind us.
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“Culture allows us to evolve over timescales that are normally accessible only to short-lived species, while at the same time allowing us to enjoy the benefits of having a long life history, such as a large brain, an extended juvenile period, and long life span.”
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culturally inherited knowhow and practices.”24 People specialize because no one can know everything. Then they interact. And in that system in which the interaction occurs, something happens that otherwise wouldn’t. He argues that “innovation does not take a genius or a village; it takes a big network of freely interacting minds.”25 Innovation then is not the product of one-off smarts but is the result of the emergent property that our cultural learning has produced.
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Using this mental model is not about trying to predict emergent properties but rather acknowledging they are possible. So don’t always stick with what you know. Learn new skills, interact with new people. Working and sharing with others can create unexpected possibilities.
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« Most systems behave linearly only when they are close to equilibrium, and only when we don’t push them too hard. » Steven Strogatz1
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In 1814, the mathematician Pierre-Simon Laplace declared Newton’s laws would enable us, should we know the position and velocity of every particle in the universe, to predict anything, forever. Over a century later, computers made it seem as though we could put Laplace’s prediction to the test.4 The butterfly effect suggests otherwise. Even when we can identify deterministic rules, we cannot make perfect predictions. In the face of chaos, we should expect to be surprised. We may know the rules governing a chaotic system’s behavior, but we cannot know its precise initial conditions. When we ...more
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The image of a butterfly flapping its wings and causing a typhoon is a vivid one, and it’s no surprise it went on to inspire endless films, books, songs, and motivational quotes. It’s unusual for a mathematical idea to become so mainstream. The idea of a tiny thing having a big impact on the world is powerful.
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It’s not that the wing flap causes the typhoon; it’s that the difference in starting conditions between a world where the butterfly flaps its wings and one where it doesn’t is sufficient to mean a typhoon in one and not the other. Chaotic systems are so sensitive to starting conditions that the minutest differences can lead to highly divergent outcomes.
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Some systems are very sensitive to their starting conditions, so that the tiny difference in the initial push you give them causes a big difference in where they end up. And there is feedback, so that what a system does affects its own behavior. —John Gribbin2
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Albert Einstein’s idea was that it is possible to reduce any theory down to a certain level that makes it as understandable as possible to as many people as feasible, but past a certain point, it would lose its meaning. That point is where a theory is irreducible.
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Irreducibility is about finding the point beyond which you will inevitably change the fundamentals so that you can recognize when you are changing the system to something different.
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There are certain irreducible limits to any system past which the system ceases to function as intended. One of the challenges is being able to identify those limits and not get sidetracked by what you think ought to be there.
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In communications, to get to the essence of the thing is important because simple communications are easier to understand.
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They contain less ambiguity and give fewer options for interpretation. Wartime propaganda posters are an excellent example of using few words and images to convey complicated information. Poster artists sought the minimum number of words and images they needed to depict their message.
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Like Plato's idea of forms, there are certain elements that a thing must possess in order to be considered that thing. We only need to see these minimum elements to be able to identify the object.
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“Always keen to derive maximum meaning from minimum means, his use of clever symbolic devices and simplified forms resulted in some of the most arresting and powerful posters of the era.”
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The images may have been uncomplicated, but the message was clear. His posters were an effective means of communicating complex topics. They were not so simple as to introduce ambiguity or confusion.
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The use of symbols is a critical component of being able to simplify the message. The less you have to explain, the more you can communicate in any one poster.
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Simplicity can convey a powerful meaning. But too much simplicity conveys no meaning at all.
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There are limits to how much we can reduce while maintaining the important qualities making a thing what it is. Being aware of those limits allows for experimentation and creativity.
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Understanding the irreducible components of a system means you won’t waste your time trying to change what is unchangeable. You can master the minimum elements, then explore. Using irreducibility as a lens helps you shed the nonessential, giving you options for adjusting or pivoting.
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Using the law of diminishing returns as a model shows us that the relationship between inputs and outputs in systems is not always linear. Past a certain point, diminishing returns almost always set in.
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In economics, it is a specific term for the fact that increasing inputs, like materials and labor in production processes, increases outputs, but not indefinitely. Past a certain level, more inputs will lead to lower increases in outputs, until the inputs start to become a hindrance.
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The advantage to understanding the law of diminishing returns is being able to calculate where that point is for different systems so we know how best to interact with them.
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New opinions are always suspected, and usually opposed, without any other reason but because they are not already common. —John Locke3
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A film that kept someone awake at night when they were a teenager might end up being something they show their kids on a weeknight. A powerful advertising campaign might seem quaint after it becomes a convention. By looking at the history of exploitation films, we can see how the mental model of diminishing returns makes us nonchalant about things that used to provoke a reaction.
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Advertising materials were fair game too. After Color Me Blood Red (1965) used the tagline “You must keep reminding yourself it’s only a motion picture!” on posters, similar sentiments followed for films lacking the clout to warrant it. Last House on the Left (1972) advised viewers, “To avoid fainting keep repeating, it’s only a movie…only a movie…only a movie…” Hallmark then reused essentially the same marketing for Don’t Look in the Basement (1973) and The Horrible House on the Hill (1974).26 Makers of exploitation films had to keep coming up with new ideas to get a response. Any part of a ...more
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Writing around 300 BCE, he came after Plato and Aristotle and was a contemporary of the early Stoics. One of his core ideas centered around the value of pleasure. Epicurus argued that pleasure is the only realistic measure we have of evaluating our lives. When we experience pleasure, things are good, and thus the pursuit of pleasure ought to be the driving force behind our choices.
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At first glance, his philosophy seems to promote a life of selfish indulgence. Criticized for promoting a hedonism that would lead to the breakdown of society, Epicurean philosophy has endured much maligning over the millennia. However, a complete read of his philosophy reveals how pursuing the Epicurean ideal of pleasure actually leads to a very sedate, mindful life. Using the lens of a normal distribution curve helps us understand why and thus suggests modern uses for this ancient philosophy.
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In his Letter to Menoeceus, Epicurus writes that “no pleasure is a bad thing in itself. But the things which produce certain pleasures bring troubles many times greater than the pleasures.”1 These latter types of pleasures are the ones we should avoid, because what positive feeling ...
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The ideal state is one of neither pleasure nor pain. As Daniel Klein writes, for Epicurus, “happiness is tranquility.”2 The state we should aim to be in is at the top of a normal distribution curve—a life free from pain and also free from the negative consequences of excess pleasure.
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For Epicurus, paying attention to the knowledge we gain from our experiences is critical for achieving a pain-free life. We need to be in tune with ourselves, noticing how our actions impact our bodies and psychological states. We also need to actively perform second-order thinking, considering the effects of the effects of our actions.
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Epicurus believed close human relationships to be the greatest source of pleasure in life.”7 Pleasure is not then about the attainment of things, status, and stuff, but the interactions we have and the knowledge we gain from them. It is a philosophy of experience rather than consumption.
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Knowledge, experience, and relationships compound. When it comes to our personal capabilities, there are few limits to the possibilities suggested by this model.
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An apparently trivial indulgence in lust or anger today is the loss of a ridge or railway line or bridgehead from which the enemy may launch an attack otherwise impossible. » C. S. Lewis3
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To gain insight and eventually wisdom, we need to reinvest our knowledge and let it compound. One way to do that is to be more deliberate about identifying how our past experiences can improve our chances of success in future ones.
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It suggests to us that continual reinvestment of what we learn and in the people around us is the best way to set ourselves up for reliable, steady gains. The majority of success doesn’t happen by accident, and the lens of compounding illuminates the investments we need to make to get there.