How Not to Be Wrong

02Straight Lines Will Eventually Lie to You

Human beings are naturally obsessed with straight lines, constantly projecting that whatever is happening in the present moment will continue happening in exactly the same way forever. However, the universe rarely moves in a perfectly straight line, and failing to realize this fundamental truth can lead to some truly disastrous assumptions in politics, business, and our personal lives. We have an ingrained cognitive habit called linear thinking. If you see a stock price go up by ten percent this year, your brain automatically assumes it will go up by ten percent next year, and the year after that, stretching infinitely into the future. Mathematics gently taps us on the shoulder and reminds us that curves eventually bend, and lines that shoot straight up almost always level off or crash back down. To understand the immense danger of linear thinking, we can look at one of the most famous economic models in modern political history: the Laffer Curve. The story goes that in 1974, an economist named Arthur Laffer was having dinner at a Washington D.C. restaurant with powerful political figures, including Donald Rumsfeld and Dick Cheney. During the conversation, Laffer grabbed a cloth napkin and sketched a simple curve to illustrate a point about taxation. He explained that if the government sets the income tax rate at zero percent, they will naturally collect zero dollars in revenue. On the other extreme, if the government sets the tax rate at one hundred percent, people will simply stop working entirely, because every single cent they earn would be confiscated. Therefore, at one hundred percent taxation, the government also collects zero dollars. Because the revenue is zero at both extremes, there must be a curve connecting the two points, with a peak somewhere in the middle that represents the absolute maximum amount of revenue the government can collect. The logic of the Laffer Curve is mathematically sound and quite brilliant in its simplicity. It clearly shows that if a country's tax rate is extremely high—say, ninety percent—it sits on the right side of the peak. In that specific scenario, lowering taxes would actually encourage people to work harder, stimulate the economy, and ultimately increase the total amount of tax revenue collected. The problem arose when politicians took this nuanced, non-linear curve and weaponized it into a rigid, straight-line ideology. Politicians began to argue that cutting taxes will always, under all circumstances, increase government revenue. They completely ignored the mathematical reality that if you are already on the left side of the peak, lowering taxes will predictably result in less revenue, not more. They fell in love with a straight line that simply did not exist. This mathematical fallacy of projecting straight lines into infinity shows up everywhere, often with hilarious or terrifying results. Take a moment to think about the growth of a human child. If a baby grows six inches during the first year of its life, a purely linear projection would conclude that the child will continue growing six inches every single year. By the time this child reaches the age of thirty, they would be fifteen feet tall. By the time they retire, they would be towering over a three-story building. Obviously, our common sense tells us this is ridiculous because human biology follows a biological curve that eventually flattens out during adolescence. Yet, when intelligent adults look at financial markets, real estate prices, or the user growth of a new social media application, they frequently abandon their common sense and assume the six-inch growth will continue forever. Jordan Ellenberg points out another classic example regarding public health statistics. In the early 2000s, researchers looked at the rapidly rising rates of obesity in the United States over a period of ten years. The trend line was pointing sharply upward. Some analysts drew a straight line through the data and published alarming reports predicting that by the year 2048, exactly one hundred percent of Americans would be overweight. Even more absurdly, if you extended that exact same straight line just a few years further into the future, you would mathematically conclude that one hundred and nine percent of Americans would be overweight. It is mathematically impossible for more than one hundred percent of a population to possess a trait, yet the straight-line projection blindly marched right past the boundaries of physical reality. How can we protect ourselves from the deception of straight lines? We must learn to actively question the trajectory of every trend we encounter. When a charismatic business leader promises that their company’s profits will double every year indefinitely, you must visualize the curve flattening. When a pessimistic news anchor claims that a temporary rise in inflation means the economy is heading into an endless downward spiral, you must remember that economies operate in complex cycles, not endless plunges. In our own lives, when we start a new diet, a new workout routine, or learn a new language, we often experience rapid, straight-line progress in the first few weeks. When that progress inevitably slows down, we become frustrated and quit, mistakenly believing that the curve is broken. Mathematics teaches us a beautiful lesson in patience: plateaus are not failures; they are simply the natural shape of reality. By embracing non-linear thinking, we align our expectations with the true mathematical nature of the universe.

Continue reading with LeapAhead app

Full summary is waiting for you in the app

Continue reading