Lloyd shows how the potential computing capacity of a kilogram of matter equals pi times energy divided by Planck’s constant. Since the energy is such a large number and Planck’s constant is so small, this equation generates an extremely large number: about 5 × 1050 operations per second.
[Note: π × maximum energy (1017 kg × meter2/second2) / (6.6 × 10–34) joule-seconds) = ~ 5 × 1050 operations/second.]
If we relate that figure to the most conservative estimate of human brain capacity (1019 cps and 1010 humans), it represents the equivalent of about 5 billion trillion human civilizations.
[Note: 5 × 1050 cps is equivalent to 5 × 1021 (5 billion trillion) human civilizations (each requiring 1029 cps).]
If we use the figure of 1016 cps that I believe will be sufficient for functional emulation of human intelligence, the ultimate laptop would function at the equivalent brain power of 5 trillion trillion human civilizations.
[Note: Ten billion (1010) humans at 1016 cps each is 1026 cps for human civilization. So 5 × 1050 cps is equivalent to 5 × 1024 (5 trillion trillion) human civilizations.]
Such a laptop could perform the equivalent of all human thought over the last ten thousand years (that is, ten billion human brains operating for ten thousand years) in one ten-thousandth of a nanosecond.
[Note: This estimate makes the conservative assumption that we’ve had ten billion humans for the past ten thousand years, which is obviously not the case. The actual number of humans has been increasing gradually over the past to reach about 6.1 billion in 2000. There are 3 × 107 seconds in a year, and 3 × 1011 seconds in ten thousand years. So, using the estimate of 1026 cps for human civilization, human thought over ten thousand years is equivalent to certainly no more than 3 × 1037 calculations. The ultimate laptop performs 5 × 1050 calculations in one second. So simulating ten thousand years of ten billion humans’ thoughts would take it about 10–13 seconds, which is one ten-thousandth of a nanosecond.]
Again, a few caveats are in order. Converting all of the mass of our 2.2-pound laptop into energy is essentially what happens in a thermonuclear explosion. Of course, we don’t want the laptop to explode but to stay within its one-liter dimension. So this will require some careful packaging, to say the least. By analyzing the maximum entropy (degrees of freedom represented by the state of all the particles) in such a device, Lloyd shows that such a computer would have a theoretical memory capacity of 1031 bits. It’s difficult to imagine technologies that would go all the way in achieving these limits. But we can readily envision technologies that come reasonably close to doing so. As the University of Oklahoma project shows, we already demonstrated the ability to store at least fifty bits of information per atom (although only on a small number of atoms, so far). Storing 1027 bits of memory in the 1025 atoms in a kilogram of matter should therefore be eventually achievable.
But because many properties of each atom could be exploited to store information—such as the precise position, spin, and quantum state of all of its particles—we can probably do somewhat better than 1027 bits. Neuroscientist Anders Sandberg estimates the potential storage capacity of a hydrogen atom at about four million bits. These densities have not yet been demonstrated, however, so we’ll use the more conservative estimate.
[Note: Anders Sandberg, “The Physics of the Information Processing Superobjects: Daily Life Among the Jupiter Brains,” Journal of Evolution and Technology 5 (December 22, 1999), http://www.transhumanist.com/volume5/Brains2.pdf.]
As discussed above, 1042 calculations per second could be achieved without producing significant heat. By fully deploying reversible computing techniques, using designs that generate low levels of errors, and allowing for reasonable amounts of energy dissipation, we should end up somewhere between 1042 and 1050 calculations per second.
The design terrain between these two limits is complex. Examining the technical issues that arise as we advance from 1042 to 1050 is beyond the scope of this chapter. We should keep in mind, however, that the way this will play out is not by starting with the ultimate limit of 1050 and working backward based on various practical considerations. Rather, technology will continue to ramp up, always using its latest prowess to progress to the next level. So once we get to a civilization with 1042 cps (for every 2.2 pounds), the scientists and engineers of that day will use their essentially vast nonbiological intelligence to figure out how to get 1043, then 1044, and so on. My expectation is that we will get very close to the ultimate limits.
Even at 1042 cps, a 2.2-pound “ultimate portable computer” would be able to perform the equivalent of all human thought over the last ten thousand years (assumed at ten billion human brains for ten thousand years) in ten microseconds.
[Note: See note above. 1042 cps is a factor of 10–8 less than 1050 cps, so one ten-thousandth of a nanosecond becomes 10 microseconds.]
If we examine the Exponential Growth of Computing chart (chapter 2), we see that this amount of computing is estimated to be available for one thousand dollars by 2080.