The Age of Spiritual Machines: When Computers Exceed Human Intelligence (6 page)

Vacuum-Tube Computers

Discrete Transistor Computers

Integrated Circuit Computers

THE EXPONENTIAL GROWTH OF COMPUTING, 1900-1998

In the 1980s, a number of observers, including Carnegie Mellon University professor Hans Moravec, Nippon Electric Company’s David Waltz, and myself, noticed that computers have been growing exponentially in power, long before the invention of the integrated circuit in 1958 or even the transistor in 1947.
²⁰The speed and density of computation have been doubling every three years (at the beginning of the twentieth century) to one year (at the end of the twentieth century), regardless of the type of hardware used. Remarkably, this “Exponential Law of Computing” has held true for at least a century, from the mechanical card-based electrical computing technology used in the 1890 U.S. census, to the relay-based computers that cracked the Nazi Enigma code, to the vacuum-tube-based computers of the 1950s, to the transistor-based machines of the 1960s, and to all of the generations of integrated circuits of the past four decades. Computers are about one hundred million times more powerful for the same unit cost than they were a half century ago. If the automobile industry had made as much progress in the past fifty years, a car today would cost a hundredth of a cent and go faster than the speed of light.

As with any phenomenon of exponential growth, the increases are so slow at first as to be virtually unnoticeable. Despite many decades of progress since the first electrical calculating equipment was used in the 1890 census, it was not until the mid-1960s that this phenomenon was even noticed (although Alan Turing had an inkling of it in 1950). Even then, it was appreciated only by a small community of computer engineers and scientists. Today, you have only to scan the personal computer ads—or the toy ads—in your local newspaper to see the dramatic improvements in the price performance of computation that now arrive on a monthly basis.

So Moore’s Law on Integrated Circuits was not the first, but the fifth paradigm to continue the now one-century-long exponential growth of computing. Each new paradigm came along just when needed. This suggests that exponential growth won’t stop with the end of Moore’s Law. But the answer to our question on the continuation of the exponential growth of computing is critical to our understanding of the twenty-first century. So to gain a deeper understanding of the true nature of this trend, we need to go back to our earlier questions on the exponential nature of time.

THE LAW OF TIME AND CHAOS

Is the flow of time something real, or might our sense of time passing be just an illusion that hides the fact that what is real is only a vast collection of moments?

—Lee Smolin

Time is nature’s way of preventing everything from happening at once.

—Graffito

Things are more like they are now than they ever were before.

.—Dwight Eisenhower

Consider these diverse exponential trends:

• The exponentially
slowing
pace that the Universe followed, with three epochs in the first billionth of a second, with later salient events taking billions of years.

• The exponentially
slowing
pace in the development of an organism. In the first month after conception, we grow a body, a head, even a tail. We grow a brain in the first couple of months. After leaving our maternal confines, our maturation both physically and mentally is rapid at first. In the first year, we learn basic forms of mobility and communication. We experience milestones every month or so. Later on, key events march ever more slowly, taking years and then decades.

• The exponentially
quickening
pace of the evolution of life-forms on Earth.

• The exponentially
quickening
pace of the evolution of human-created technology, which picked up the pace from the evolution of life-forms.

• The exponential growth of computing. Note that exponential growth of a process over time is just another way of expressing an exponentially quickening pace. For example, it took about ninety years to achieve the first MIP (Million Instructions per Second) for a thousand dollars. Now we add an additional MIP per thousand dollars every day. The overall innovation rate is clearly accelerating as well.

• Moore’s Law on Integrated Circuits. As I noted, this was the fifth paradigm to achieve the exponential growth of computing.

Many questions come to mind:

What is the common thread between these varied exponential trends? Why do some of these processes speed up while others slow down? And what does this tell us about the continuation of the exponential growth of computing when Moore’s Law dies?

Is Moore’s Law just a set of industry expectations and goals, as Randy Isaac, head of basic science at IBM, contends? Or is it part of a deeper phenomenon that goes far beyond the photolithography of integrated circuits?

After thinking about the relationship between these apparently diverse trends for several years, the surprising common theme became apparent to me.

What determines whether time speeds up or slows down? The consistent answer is that
time moves in relation to the amount of chaos.
We can state the Law of Time and Chaos as follows:

The Law of Time and Chaos: In a process, the time interval between salient events (that is, events that change the nature of the process, or significantly affect the future of the process) expands or contracts along with the amount of chaos.

When there is a lot of chaos in a process, it takes more time for significant events to occur. Conversely, as order increases, the time periods between salient events decrease.

We have to be careful here in our definition of chaos. It refers to the quantity of disordered (that is, random) events
that are relevant to the process.
If we’re dealing with the random movement of atoms and molecules in a gas or liquid, then heat is an appropriate measure. If we’re dealing with the process of evolution of life-forms, then chaos represents the unpredictable events encountered by organisms, and the random mutations that are introduced in the genetic code.

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