Getting Used to Exponential Change

Middle of January 2008

We’re captives of linear thinking because time flows like a river and our lives play out linearly. The closest most of us get to an appreciation of non-linear growth is the wonder of compound interest. Exponential change is so dramatic intuition fails us. We smile at the story of the precocious child who normally gets $10 a week pocket money, but tells her father that she’ll cut him a break but accepting a penny at the beginning of the year and doubling it each week thereafter. Wise fathers decline the offer because the monthly amount will reach $10 in March and instead of $520 they’ll be in for more that the GNP of the world, $45,000,000,000,000 by years’ end.

Some technologies change slowly or improve only marginally. The internal combustion engine is mostly unchanged in a century and the rockets that power the Space Shuttle are close relatives of the chemical rockets that launched Sputnik fifty years ago. Information technology is different. The speed of microprocessors has been doubling every twelve to eighteen months since the mid 1960’s, and Moore’s law is accompanied by shrinkage in size that decreases the power requirement and increases the portability of computers and computational devices. Experts differ on how long this virtuous trend can continue. The fundamental limits of the architecture of integrated circuits are being approached, but by using light instead of electrons Moore’s law might continue for a decade. Beyond that, the famous physicist Richard Feynman pointed out, there’s “room at the bottom.” If bits can flip at the level of individual atoms, the engine of ever-increasing computer power won’t run out of steam, if you’ll pardon the anachronistic metaphor.

Moore’s law is paralleled by two trends equally relevant to information technology. One is the logarithmic or exponential increase in the capacity of memory or storage of digital information. The other is the rapid increase in the bandwidth of most wired and wireless networks. These trends create an extraordinary convergence of benefits for anyone who uses information technology, which is to say: everyone. The manipulation, storage, and transmission of bits are all getting ever-easier and ever-cheaper.

Of course it doesn’t always feel that way. Bloated and Byzantine software seems capable of absorbing all the gains on offer from Moore’s law (for more information, try Googling “Wintel conspiracy.”) Images, music, and particularly, video, can fill the most capacious hard drive, and the sharing of such material within rapidly-growing social networks will tax bandwidth even as it rapidly grows. Despite these teething pains, our digital lives are much richer and more capable than they were a decade ago.

What would happen if we were to anticipate exponential change, rather than just riding it breathlessly? Ironically, if you’re in any business that involves solving problems or doing calculations, you should sit on your hands and do nothing. Procrastination is the logical answer. Why? Because anything you can do right now will be subsumed and superseded in the future. In my field of astronomy, this is the situation of the people who search for radio signals from hypothetical intelligent aliens. They scan the radio spectrum Hertz by Hertz and look at as many stars as possible; the experiment is limited by both bandwidth and computation speed. The survey started last year using the Allen Array will exceed in a year the sum of all surveys that preceded it over fifty years. Such is the power of riding the exponential curve.

Many people do in fact wait on technology. The first cell phones in the 1970’s were the size of a small briefcase, very power-hungry, and served by limited networks. The first PCs of the 1980’s were prone to crashing, and their speed limited them to simple tasks and games. The rapid maturation of technology is a natural byproduct of Moore’s law because a lower price leads to economies of scale in manufacturing and larger potential markets. We sensibly jump into a new technology when it has evolved beyond the first few steps along the exponential curve.

A modest extrapolation of current trends, and technologies currently in the lab, leads to the following prediction. In fifteen, or maybe twenty years, we’ll only dimly remember cursing the slow downloads off the Internet, getting frustrated because we’ve filled our memory stick or iPod, or staring at the hourglass icon (another wonderfully anachronistic metaphor) while our computer chews on some process. Fifteen years of eighteen-monthly doubling is two to the power ten, or a factor of a thousand. Let’s be conservative and say the gain is only a factor of a hundred.

When the average microprocessor runs at 100 GHz, the average memory device holds 1000 Gbytes, and the wireless Internet runs at 10 Gbits per second, the situation will fundamentally change. When your personal computing device holds all the music you could ever listen to or all the photos you could ever take, when you can have instantly delivered to your handheld any web page or video clip, the organization and navigation of information becomes more important that your degree of access to information. The limitations of human sensory input and human processing power will dominate. Without tools to make sense of the cyber-babble, Moore’s law risks turning into a curse of plenty. In this important aspect the Information Age is still in its infancy.

Comments are closed.