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The Limits of Computation?

Seth Lloyd (b. 1960)

“Each generation of technology has seen faster computations, larger storage systems, and improved communications bandwidth. Nevertheless, physics may impose fundamental limits on computing systems that cannot be overcome. The most obvious limit is the speed of light: a computer in New York City will never be able to request a web page from a server in London and download the results with a latency of less than 0.01 seconds, because light takes 0.0186 seconds to travel the 5,585 kilometers each direction, consistent with Einstein’s Theory of Special Relativity. On the other hand, recently some scientists have claimed that they can send information without sending light particles by using quantum entanglement, something Einstein dismissively called spooky action at a distance. Indeed, in 2013, scientists in China measured the speed of information propagation due to quantum entanglement and found that it was at least 10,000 times faster than the speed of light.

Computation itself may also have a fundamental limit, according to Seth Lloyd, a professor of mechanical engineering and physics at MIT. In 2000, Lloyd showed that the ultimate speed of a computer was limited by the energy that it had available for calculations. Assuming that the computations would be performed at the scale of individual atoms, a central processor of 1 kilogram occupying the volume of 1 liter has a maximum speed of 5.4258 × 1050 operations per second—roughly 1041, or a billion billion billion billion times faster than today’s laptops.

Such speeds may seem unfathomable today, but Lloyd notes that if computers double in speed every two years, then this is only 250 years of technological progress. Lloyd thinks that such technological progress is unlikely. On the other hand, in 1767, the fastest computers were humans.

Because AI is increasingly able to teach and train itself across all technological and scientific domains—doing so at an exponential rate while sucking in staggering amounts of data from an increasingly networked and instrumented world—perhaps it is appropriate that a question mark be the closing punctuation for the title of this entry.”

SEE ALSO Sumerian Abacus (c. 2500 BCE), Slide Rule (1621), The Difference Engine (1822), ENIAC (1943), Quantum Cryptography (1984)

Based on our current understanding of theoretical physics, a computer operating at the maximum speed possible would not be physically recognizable by today’s standards. It would probably appear as a sphere of highly organized mass and energy.

Lloyd, Seth. “Ultimate Physical Limits to Computation.” Nature 406, no. 8 (August 2000): 1047–54.

Yin, Juan, et al. “Bounding the Speed of ‘Spooky Action at a Distance.’” Physical Review Letters 110, no. 26 (2013).