As we all know, computer chips have been getting smaller, faster, and cheaper year-by-year for decades now. Today, some $10 pocket calculators pack more power than the most sophisticated, multi-million-dollar mainframe computer of the mid-1950s.

As pointed out in the Los Angeles Times, if the same rate of performance improvement versus cost held for airlines, a flight from New York to Paris would cost one cent and last less than a second.

This has been made possible by ever denser and more complex integrated circuits.

• In 1971, Intel’s first microprocessor chip had 2,300 transistors.

• By 1978, the 8086 processor had 29,000 transistors.

• Less than a decade later, the 486 housed 1.2 million transistors.

• Last year, the Pentium 4 reached 410 million.

• The Itanium 2, due this year, will run big servers with its astounding 1.7 billion transistors — all on something the size of a postage stamp.

At the same time, manufacturing has been improving at an astonishing rate, with micro-lithography taking only one second to lay down all those transistors.

As a result of these converging trends, the cost of a transistor fell by a factor of more than 10 million between the 1950s and today, according to a report in the Daily Telegraph.

In 2004, more transistors were produced than grains of rice — and they cost less. There were 10 quintillion transistors shipped in 2003 — that’s a “10” with 18 zeroes after it, or 100 times the number of ants in the world.

These astonishing numbers — and the improvements in computer chips — were achieved by building transistors closer and closer together on smaller and smaller bits of silicon. And when it comes to chips, smaller is faster and even cheaper — up to a point.

But when they run that fast, fully half the electricity is wasted as heat — they run hot enough to cook an egg. Moreover, a factory to build these chips costs $2 billion and covers four football fields — the most expensive factory ever built on a per-acre basis. Even in a $213 billion industry, that cost is getting too high to pay.

With almost two billion transistors on a half-inch-square chip, the technology is reaching its limits. For example, back in 2003,...