Read more to find out what convexity is and how it relates to antifragility.<\/p>\n\n\n\n\n\n\n\n
Exponential Benefit or Harm<\/strong><\/h2>\n\n\n\nWe start with a graphical representation of fragility and antifragility. Using that simple illustration as a guide, we revisit exactly why fragile systems<\/a> hate random events while antifragile systems love them.<\/strong><\/p>\n\n\n\nAfter that, we return to the discussion of how size causes fragility, now with an added dimension: concentration. A centralized system is much more fragile than a decentralized one, even if they add up to the same size. For example, a single large bank is more vulnerable to mistakes and bad deals than 10 banks that are each a 10th the size; the simple reason is that the large bank has more resources, and therefore has more to lose. <\/p>\n\n\n\n
We\u2019ll also touch on the idea that large, influential systems can cause damage even outside of themselves.<\/strong> When that large bank got itself into trouble, the global stock market took close to a 10% hit\u2014one of the 10 hypothetical smaller banks doing something similar would have caused a much smaller shock to the market, if any at all. <\/p>\n\n\n\nThen we expand on the fragility of size, and how large systems like banks cause harm to those who rely on them. It also explores how we could mitigate the damage by dividing up our investments and our consumption. For example, large tuna fisheries cause harm to the environment by overfishing, but they only do so because people keep demanding tuna. If we returned to a more natural method of consuming what\u2019s readily available, our large systems wouldn\u2019t cause as much damage.<\/p>\n\n\n\n
Concavity and Convexity<\/strong><\/h3>\n\n\n\nBoth fragility and antifragility have exponential effects. In other words, as the significance of an event increases, the effect of that event increases even faster.<\/strong> For example, if you punched a window you could easily break it; however, you could drum your fingers on the glass all day without damaging it. The thousands of tiny impacts from your fingers wouldn\u2019t add up to the same effect as one large impact from your fist. <\/p>\n\n\n\nAs we\u2019ve previously discussed, when those significant events have negative effects, the situation is fragile. When they have positive effects, the situation is antifragile. We can roughly sketch this general concept as seen below: <\/p>\n\n\n\n![\"\"\/](\"https:\/\/lh4.googleusercontent.com\/2_tsibnSSHzLYllcmQibc7d2ahgAidEMEFjS21DpLfp2OHmYiHWSfhIYCrV-NdQ5LH4kb1NQzoq1Q9nzxUHNzCRF5UfTM9X_uttFhfHQltTGr2r0Cl9zjFeOVZxl9K9KXKMvOqXf\")
<\/figure>\n\n\n\nA fragile situation has a limit to how good an outcome can be, but no limit (or almost no limit) to how bad an outcome can be. A graph of the situation has a concave <\/em>shape: it flexes outward in the middle. An antifragile situation is exactly the opposite, and the graph has a convex <\/em>shape: it flexes inward in the middle. An easy way to remember this is that fragility makes a frown, and antifragility makes a smile. <\/strong><\/p>\n\n\n\nThe two graphs also illustrate why fragility dislikes randomness, and antifragility loves it. Imagine picking random points on each of the graphs; depending on where the point falls on the significance <\/em>axis, it may have a positive or negative outcome<\/em>. Now imagine that you keep picking such random points over and over again. Eventually you\u2019re going to land on a point with enough significance that the outcome is either hugely negative (for the fragility graph) or hugely positive (for the antifragility graph). <\/p>\n\n\n\nA side note: Any line on a graph can be represented by an equation. Putting a negative sign in front of that equation will result in the same graph, but upside-down. This also holds true for our graphs of fragility and antifragility; the opposite of concavity is convexity. Fat Tony made his fortune in the oil slump by putting a minus sign in front of the banks\u2019 equation, so that whenever they lost a dollar, he made one. <\/p>\n\n\n\n
Acceleration of Harm or Benefit<\/strong><\/h3>\n\n\n\nAn intrinsic property of concave and convex graphs is that, the farther along the horizontal axis you go, the steeper the slope becomes. In other words, the outcome changes by greater amounts over the same horizontal distance. <\/p>\n\n\n\n
This gives us an easy way to check systems for fragility (or antifragility). Take, for example, travel time from point A to point B on the thruway. If there\u2019s no traffic, you\u2019ll drive from A to B quickly and easily. Now let\u2019s say, hypothetically, you note that when there are 10,000 cars on the thruway, travel time increases by 10 minutes. If traffic increases by another <\/em>10,000 cars, your travel time now increases by 30 minutes. Add another 10,000 and you may be stuck in traffic for hours. <\/p>\n\n\n\nThough the increases in traffic are the same, the increases in travel time get bigger and bigger. <\/strong>Since the change is undesirable, we would say that the degree of harm is accelerating. This is a fragile system. If more traffic meant you somehow got to your destination sooner, then it would be an antifragile system; it would have accelerating benefits as the amount of cars on the road increases. <\/p>\n\n\n\nWe\u2019ve talked before about the fragility of relying on forecasting. Whether in finances, weather, votes, or anything else, trying to predict the future<\/a> is notoriously unreliable. However, these forecast models could be made a great deal more accurate\u2014and the decisions based on them made much less fragile\u2014by subjecting them to a simple acceleration of harm test. <\/p>\n\n\n\n
After that, we return to the discussion of how size causes fragility, now with an added dimension: concentration. A centralized system is much more fragile than a decentralized one, even if they add up to the same size. For example, a single large bank is more vulnerable to mistakes and bad deals than 10 banks that are each a 10th the size; the simple reason is that the large bank has more resources, and therefore has more to lose. <\/p>\n\n\n\n
We\u2019ll also touch on the idea that large, influential systems can cause damage even outside of themselves.<\/strong> When that large bank got itself into trouble, the global stock market took close to a 10% hit\u2014one of the 10 hypothetical smaller banks doing something similar would have caused a much smaller shock to the market, if any at all. <\/p>\n\n\n\n Then we expand on the fragility of size, and how large systems like banks cause harm to those who rely on them. It also explores how we could mitigate the damage by dividing up our investments and our consumption. For example, large tuna fisheries cause harm to the environment by overfishing, but they only do so because people keep demanding tuna. If we returned to a more natural method of consuming what\u2019s readily available, our large systems wouldn\u2019t cause as much damage.<\/p>\n\n\n\n Both fragility and antifragility have exponential effects. In other words, as the significance of an event increases, the effect of that event increases even faster.<\/strong> For example, if you punched a window you could easily break it; however, you could drum your fingers on the glass all day without damaging it. The thousands of tiny impacts from your fingers wouldn\u2019t add up to the same effect as one large impact from your fist. <\/p>\n\n\n\n As we\u2019ve previously discussed, when those significant events have negative effects, the situation is fragile. When they have positive effects, the situation is antifragile. We can roughly sketch this general concept as seen below: <\/p>\n\n\n\n A fragile situation has a limit to how good an outcome can be, but no limit (or almost no limit) to how bad an outcome can be. A graph of the situation has a concave <\/em>shape: it flexes outward in the middle. An antifragile situation is exactly the opposite, and the graph has a convex <\/em>shape: it flexes inward in the middle. An easy way to remember this is that fragility makes a frown, and antifragility makes a smile. <\/strong><\/p>\n\n\n\n The two graphs also illustrate why fragility dislikes randomness, and antifragility loves it. Imagine picking random points on each of the graphs; depending on where the point falls on the significance <\/em>axis, it may have a positive or negative outcome<\/em>. Now imagine that you keep picking such random points over and over again. Eventually you\u2019re going to land on a point with enough significance that the outcome is either hugely negative (for the fragility graph) or hugely positive (for the antifragility graph). <\/p>\n\n\n\n A side note: Any line on a graph can be represented by an equation. Putting a negative sign in front of that equation will result in the same graph, but upside-down. This also holds true for our graphs of fragility and antifragility; the opposite of concavity is convexity. Fat Tony made his fortune in the oil slump by putting a minus sign in front of the banks\u2019 equation, so that whenever they lost a dollar, he made one. <\/p>\n\n\n\n An intrinsic property of concave and convex graphs is that, the farther along the horizontal axis you go, the steeper the slope becomes. In other words, the outcome changes by greater amounts over the same horizontal distance. <\/p>\n\n\n\n This gives us an easy way to check systems for fragility (or antifragility). Take, for example, travel time from point A to point B on the thruway. If there\u2019s no traffic, you\u2019ll drive from A to B quickly and easily. Now let\u2019s say, hypothetically, you note that when there are 10,000 cars on the thruway, travel time increases by 10 minutes. If traffic increases by another <\/em>10,000 cars, your travel time now increases by 30 minutes. Add another 10,000 and you may be stuck in traffic for hours. <\/p>\n\n\n\n Though the increases in traffic are the same, the increases in travel time get bigger and bigger. <\/strong>Since the change is undesirable, we would say that the degree of harm is accelerating. This is a fragile system. If more traffic meant you somehow got to your destination sooner, then it would be an antifragile system; it would have accelerating benefits as the amount of cars on the road increases. <\/p>\n\n\n\n We\u2019ve talked before about the fragility of relying on forecasting. Whether in finances, weather, votes, or anything else, trying to predict the future<\/a> is notoriously unreliable. However, these forecast models could be made a great deal more accurate\u2014and the decisions based on them made much less fragile\u2014by subjecting them to a simple acceleration of harm test. <\/p>\n\n\n\nConcavity and Convexity<\/strong><\/h3>\n\n\n\n
Acceleration of Harm or Benefit<\/strong><\/h3>\n\n\n\n