The Half-Life of Facts Read Free

spearhead an entirely new way of looking at science. But his plans to continue research in physics and mathematics were altered by the construction on the college library. Since Raffles was a small university, the library was actually giving books out to students and faculty to store in their dormitories and apartments while the construction was under way.
    Price ended up with a complete set of
Philosophical Transactions
of the Royal Society of London, a British scientific journal that dates back to 1665. Once home, he stacked the journals chronologically against the walls in his apartment: Each pile was published later than the one before it, and they were all lined up one after another. One day, while idly looking at this large collection of books that the library had foisted upon him, he realized that the heights of the piles of these bound volumes weren’t all the same. But their heights weren’t random either. Instead, he realized, the heights of the volumes fit a specific mathematical shape: an exponential curve. Price’s simple observation was the origin of a sophisticated quantitative theory for how scientific knowledge advances.
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    MOST of our everyday lives revolve around linear growth, or changes that can be fit onto a line. When something increases by the same amount each year, when the rate is constant, we get linear growth. When we drive somewhere, and go at the same speed the entire way, a chart showing the distance we’ve traveled over time follows a straight line. And if we have a machine that builds widgets at a constant rate of three per hour, the number of widgets after a given number of hours grows linearly with the number of hours we’re considering.
    Due to how easy it is to imagine (and our brains seem particularly well suited to this type of thinking), we often think in terms of linear growth. If the temperature was sixty-five degrees yesterday, and sixty degrees the day before that, it is not surprising if we expect it to be about seventy degrees today.
    But there are many examples of change that occur differently. If you were watching when the sun set over the course of a few days early in the summer, it wouldn’t be unreasonable to expect the sunset’s timing to follow a nice linear curve: Each day the sun sets the same number of minutes later than it did the day before. But it turns out that sunsets at a specific location adhere to a sine curve—a wavelike shape that looks like a rope being shaken up and down, a shape that we aren’t particularly intuitive about. During the solstices—the shortest and longest days of the year—we are at the top or bottom of the wave, when the sunset only varies by a small amount each day; during the equinoxes (spring and fall), we are in the steep parts of the wave, and each day the sunset time is many minutes different from the day before. This is far from a curve that we can think about easily.
    We are just as ill suited when it comes to noticing the many changes that adhere to exponential growth. When we encounter exponential curves all around us, we often don’t think about it this way at all, because it is harder to picture. Exponential growth is when something increases by the same fraction or percentage,rather than the same amount, each second or minute or hour. If bacteria double every hour, that’s exponential growth, because they’re growing at a constant rate of 200 percent an hour. Compound interest is the same sort of thing: If our money grows by a certain percentage each year, we can describe this growth by an exponential curve.

    Figure 1. A linear (black) versus exponential (gray) curve versus sine (dotted) curve.
    As you might have realized, exponential growth is very rapid. Even if we are initially adding only a small amount to some quantity each hour or day, that quantity can become very big very quickly. Imagine we are given a penny and begin doubling it each day. After a week we would be receiving less than a $1.50