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Amazing Exponentials

It all started with Moore's Law. Actually, that isn't remotely accurate. Indications are that it all started with the Big Bang. But Moore's Law is such a handy example of my topic — exponential growth — that I'm going to start there. Kurzweil tells us that Moore's Law

is the prediction that the size of each transistor on an integrated circuit chip will be reduced by 50 percent every twenty-four months. The result is the exponentially growing power of integrated circuit-based computation over time. Moore's Law doubles the number of components on a chip as well as the speed of each component. Both of these aspects double the power of computing, for an effective quadrupling of the power of computation every twenty-four months.

Interesting. But where does all this exponential doubling of computational ability get us? Depends who you ask. There are those who say that it will lead us to nothing less than a new era in human history. But that's a topic for a few dozen other essays on another day. Anyway, as detailed recently in Technology Review, there are many other good examples of technologies that are growing exponentially.

Storage leaps to mind. In 2003, a $400 iPod had 10 gigabytes of memory. By early this year, a $400 iPod had 20 gigabytes of memory. If this annual doubling holds up, then 20 years from now we’ll have portable devices with 20 petabytes of storage—that’s 20 million gigabytes—sitting in our pockets. What might we want to do with all that storage, and what new services might it enable?

The iPod is now big enough to contain the entire personal music collection of today’s average listener. But the immediate consequence of storage growth is that our personal music collections will grow as well. CDs will no longer be a practical way to distribute content; they will go the way of wax cylinders and vinyl platters. That’s why so many companies are rushing in to follow Apple in the music content download and management business.

And consider how iPods might play into one of our favorite scenarios:

Today’s iPod could store 20,000 books. That’s more than most people would read in a lifetime. But just 10 years from now, an iPod might be able to hold 20 million books—more than are in Harvard University’s collection. (If you insist on having the pictures and diagrams in those books, too, perhaps you have to wait until 2017. By then you’ll be able to carry around the complete text for all the volumes in the Library of Congress.) To complete this vision, of course, we’ll need a lightweight, easy-to-read screen to display text. And we’ll need technologies that allow for rapidly digitizing millions of books and other documents, and for extracting text without errors, so the books are searchable.

Of course, not all exponential developments are related to computers:

Finally, the cost of sequencing DNA is diminishing exponentially. By next year, the cost of sequencing a person’s genome is expected to be a mere penny per base pair. Compare that to the $10 it cost in 1990. At that rate, sequencing a person’s 3.2 billion base pairs should cost only $32,000 by 2020. As a practical matter, it’s only necessary to look at 10 million base pairs to cover all the variations in the human genome. Sequencing this number—in order to determine a person’s genetic fingerprint and disease susceptibility—would cost only about one dollar by sometime in the 2020s.

It's likely that gene-based treatments for disease will also increase rapidly, if not exponentially, in line with this drop in price. And speaking of money, economist Robin Hanson has made an interesting observation:

Economists’ best estimates of total world product (average wealth per person times the number of people) show it to have been growing exponentially over the last century, doubling about every fifteen years, or about sixty times faster than under farming. And a model of the whole time series as a transition from a farming exponential mode to an industry exponential mode suggests that the transition is not over yet - we are slowly approaching a real industry doubling time of about six years, or one hundred and fifty times the farming growth rate.

So if we want to be healthy, wealthy, and wise it would appear that all we have to do is sit back and let the exponentials do the work. Of course, nothing is ever quite as simple as that. I'm reminded of the tale (possibly apocryphal) of the New York city planner who, in the 1890's published a report that included dire predictions of a coming ecological disaster for the city. Looking at then-current growth numbers, he predicted that the city would be uninhabitable within fifty years. Interestingly, his population predictions were pretty accurate. What he got wrong was his prediction that, by 1950, Manhattan would be three stories deep in horse manure.

Guess he just didn't see that whole "car" thing coming.

Let that be a lesson to us all. When we base predictions of the future on extrapolations of current trends, we can gain tremendous insights into the world that's coming. Or we may end up peddling thousands of tons of imaginary horse manure. It's a fine line.

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