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Moore's Law is generating a lot of animated discussion these days. Described first in a 1965 paper written by Intel Corp. co-founder Gordon Moore, the axiom predicts that the number of transistors that can be squeezed onto a computer's integrated circuit board doubles every two years or so. Moore said that computing power would expand at that pace for a decade.

He was right and then some. Moore's Law has held true in chip manufacture for 45 years. The newest models at Intel , IBM and Qualcomm , in fact, are threatening to blow past Moore's Law, with size and power improvements that exceed even the blistering pace he predicted. Among the latest doodads: a 3-D chip unveiled by Intel in May that has conducting channels that stick up slightly, allowing electrons to move up and down, as well as left and right.

Yet silicon is a physical thing, governed by physical laws. At some point, when transistors have shrunk to the size of atoms, it will be impossible to make them any smaller. That physical limit suggests that the growth rate of computing power will slow and hit the wall. Depending on which theorist you ask, Moore's Law will likely hit its expiry date between 2015 and 2020.

Should we care? Absolutely, argues Michio Kaku in his latest book, The Physics of the Future. An esteemed American physicist and co-founder of string field theory, Kaku writes that our future economic prosperity will pivot on the discovery of a suitable replacement for silicon. This is where much of the recent animated discussion comes from. It's focused on new research out of Cavendish Laboratories, the department of physics at Cambridge University. A study published in July provided new insights into "spintronics," a potentially revolutionary new way of transferring information. Conventional electronics rely on harnessing the charge of electrons. Spintronics depends, instead, on manipulating an electron's spin, and transforming it into a so-called spin current, which can then be used to store and transfer information in a way that generates little or no heat.

Obstacles remain, including harnessing enough spin current to meet the electricity requirements of existing computers and devices. There's also work to be done to integrate spin current with existing semiconductor technology. Still, the idea is intriguing and would, if commercialized, offer a way of climbing back on Moore's exponential growth curve even after reaching silicon's limits.

Of course, if the idea of computers operating without electricity or batteries seems like science fiction, it's nothing compared to what some theorists foresee if computing power keeps growing exponentially for decades. One concern is that we will develop computers that are more intelligent than humans. This is called "technological singularity," where we pass a point beyond which the future may become impossible to understand.

Supercomputers could enable an "intelligence explosion," says futurist Ray Kurzweil. Once those computers learn to evolve, they may choose a future not at all to our liking—cyborgs and all. As artificial intelligence theorist Eliezer Yudkowsky memorably put it: "The AI does not hate you, nor does it love you, but you are made out of atoms which it can use for something else."

Perhaps our best hope is that 25-year Silicon Valley veteran Martin Ford is right. In his book The Lights in the Tunnel: Automation, Accelerating Technology and the Economy of the Future, Ford predicts a "technology paradox" that might precede singularity: So many jobs in the economy are automated that consumer demand plummets, destroying the incentive to invest in the technologies necessary to bring the singularity about.

Not a great outcome, but better than choosing between technological stagnation via Moore's expiry or potential human extinction via its continuance.

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