Let’s start with some basic assumptions. Let the grain of sand be a 1 mm cube (i.e. 10^-3 m on a side). Assume the molecules in the sand have a cubic dimension of 1 nm on a side (i.e. 10^-9 m). Let each molecule consist of 10 atoms (for the purposes of an “order of magnitude” calculation). Assume the grain of sand has been nanoteched such that each atom can switch its state usefully in a femto-second (i.e. 10^-15 of a second). Assume the computational capacity of the human brain is 10^16 bits per second (i.e. 100 billion neurons in the human brain, times 10,000, the average number of connections between neurons, times 10, the maximum number of bits per second firing rate at each interneuronal (synaptic) connection = 10^11*10^4 *10^1 = 10^16. I will now show that the nanoteched grain of sand has a total bit switching (computational) rate that is a factor of a quintillion (a million trillion) times larger than the brain’s 10^16 bits per second. How many sand molecules in the cubic mm? Answer:– a million cubed, i.e. 10^18, with each of the 10 atoms per molecule switching 10^15 times per second, so a total switching (bits per second) rate of 10^18 times 10^15 times 10^1 = 10^34. This is 10^34/10^16 = 10^18 times greater, i.e. a million trillion, or a quintillion.

OK, but that’s coarse sand …

Ben Goertzel chips in:

According to the Bekenstein bound the number of bits possibly storable in the matter comprising a human brain is around 10^42. Factoring in the smaller diameter and mass of a grain of sand, one decreases this number by a few powers of ten, arriving at an estimate around 10^35 or so for the sand grain. Compare this to estimates in the range 10^13 – 10^20 for the human brain, based on our current understanding of psychology and neuroscience [http://www.merkle.com/humanMemory.html]. Of course, a human brain cannot approach the Bekenstein bound without being restructured so as to constitute some very non-human-brain-like strange matter. A cyborg combining a human brain with a grain of “sand” composed of strange matter that approaches the Bekenstein bound, would potentially contain 10^35 bits in the femtotech sand grain component, and 10^21 bits or so bits in the legacy-human-brain component.

Much follows …