Free The Half-Life of Facts by Samuel Arbesman

it is accelerating.
    If this acceleration continues, something curious will happen at a certain point. When we begin adding more than one year to the expected life span—a simple shift from less than one to greater than one—we get what is called
actuarial escape velocity
. What this means is that when we are adding more than one year per year, we can effectively live forever. Let me stress this again: A slight change of the underlying state of affairs in our technological and medical abilities—facts about the world around us—can allow people to be essentially immortal. The phrase
actuarial escape velocity
was popularized by Aubrey de Grey, a magnificently bearded scientist obsessed with immortality. Aubrey de Grey has made the realization of this actuarial escape velocity his life’s work.
    We’re at least several decades from this, according to even the most optimistic and starry-eyed of estimates. And it might very well never happen. But this sort of simple back-of-the-envelope calculation can teach us something: Not only can knowledge changerapidly based on technology, but it can happen so rapidly that it can produce other drastically rapid changes in knowledge. In this case, life spans go from short to long to very long to effectively infinite. Discontinuous jumps in knowledge, and how they occur, are discussed in more detail in chapter 7 . But the message is clear: Technological change can affect many other facts, sometimes with the potential for profound change around us.
    But what about the opposite direction? Rather than being overly optimistic and assuming massive positive changes in the world based on technology, what about a quantified pessimism? Will we ever reach the end of technology? And are there mathematical regularities here, too?
    Just as with science, where naysayers have prognosticated the end of scientific progress, others have done the same with innovation more generally. There is the well-known story of the head of the United States Patent and Trademark Office who said there was nothing more to invent, and a similar story about a patent clerk who even resigned because he felt this to be true.
    But there is actually no truth to these stories. In the first case, U.S. Patent Office commissioner Henry Ellsworth, in a report to Congress in 1943, wrote the following: “The advancement of the arts, from year to year, taxes our credulity and seems to presage the arrival of that period when human improvement must end.” But Ellsworth wrote this to contrast it with the fact of continuous growth. Essentially, he was arguing that the fact that things continue to grow exponentially, despite the constant feeling that we have reached some sort of plateau, is something startling and worth marveling at. In the other case, the statement by the head of the U.S. Patent Office—that new inventions were things of the past—simply never happened.
    However, these stories, and how we use them to laugh at our own ignorance, are indicative of a viewpoint in our society: Not only will innovation continue, but anyone who foresees an end to the growth in technological knowledge is bound to be proven wrong. Technological development, and the changes in facts that go along with it, doesn’t seem to be ending anytime soon. Ofcourse, these things must end eventually. The physicist Tom Murphy has shown, in a reductio ad absurdum style of argument, that based on certain fundamental ideas about energy constraints, we will exhaust all the energy in our entire galaxy in less than three millennia. So a logistic curve, with its slow saturation to some sort of upper limit, might be more useful in the long term than a simple exponential with never-ending growth.
    In the meantime, technology and science are growing incredibly rapidly and systematically. But there are still questions that need to be addressed: Why do these fields continue to grow? And why do they grow in such a regular manner, with mathematical shapes that are so