The Half-Life of Facts

The Half-Life of Facts by Samuel Arbesman Page A

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Authors: Samuel Arbesman
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a postdoctoral fellow Heebyung Koh, decided to examine the progress we’ve made in our ability to calculate, or what they termed
information transformation
. They compiled a vast data set of all the different instances of information transformation that have occurred throughout history. Their dataset, which goes back to the nineteenth century, is close to exhaustive: It begins with calculations done by hand in 1892 that clocked in at a little under one calculation a minute. Following that came: an IBM Hollerith Tabulator in 1919 that was only about four times faster; the ENIAC, which is often thought of as the world’s first computer, that used vacuum tubes to complete about fourthousand calculations per second in 1946; the Apple II, which could perform twenty thousand calculations every second, in 1977; and, of course, many more modern and extremely fast machines.
    By lining up one technology after another, one thing becomes clear: Despite the differences among all of these technologies—human brains, punch cards, vacuum tubes, integrated circuits—the overall increase in humanity’s ability to perform calculations has progressed quite smoothly and extremely quickly. Put together, there has been a roughly exponential increase in our information transformation abilities over time.
    But how does this happen? Isn’t it true that when a new technology or innovation is developed it is often far ahead of what is currently in use? And if a new technology’s not that much better, shouldn’t it simply not be adopted? How can all of these combined technologies yield such a smooth and regular curve? Actually, the truth is far messier but much more exciting.
    In fact, when someone develops a new innovation, it is often largely untested. It might be better than what is currently in use, but it is clearly a work in progress. This means that the new technology is initially only a little bit better. As its developers improve and refine it (this is the part that often distinguishes engineering and practical application from basic science), they begin to realize the potential of this new innovation. Its capabilities begin to grow exponentially.
    But then a limit is reached. And when that limit is reached there is the opportunity to bring in a new technology, even if it’s still tentative, untested, and buggy. This progression of refinement and plateau for each successive innovation is in fact described in the mathematical world as a series of steadily rising
logistic curves.
    This is a variation on the theme of the exponential curve. Imagine bacteria growing in a petri dish. At first, as they gobble the nutrients in the dish, they obey the doubling and rapid growth of the exponential curve. One bacterium divides into two bacteria, two bacteria become four, and eventually, one million becomes two million. But soon enough these bacteria bump up against certainlimits. They begin to run out of space, literally bumping up against each other, since the size of the petri dish, though very large in the eyes of each individual bacterium, is far from infinite relative to the entire colony.
    Soon the growth slows, and eventually it approaches a certain steady number of bacteria, the number that can be safely held in the petri dish over a long period of time. This amount is known as the
carrying capacity
. The mathematical function that explains how something can quickly begin to grow exponentially, only to slow down until it reaches a carrying capacity, is known as a logistic curve.
    Of course, the logistic curve describes lots more than bacteria. It can explain everything from how deer populate a forest to how the fraction of the world population with access to the Internet changes over time. It can also explain how people adopt something new.
    When a tech gadget is new, its potential for growth is huge. No one has it yet, so its usage can only grow. As people begin to buy the newest Apple device, for example, each additional user is gained

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