AI, Futurology

Pocket brains

  • Total iPhone sales between Q4 2017 and Q4 2018: 217.52 million
  • Performance of Neural Engine, component of Apple A11 SoC used in iPhone 8, 8 Plus, and X: 600 billion operations per second
  • Estimated computational power required to simulate a human brain in real time: 36.8×1015
  • Total compute power of all iPhones sold between Q4 2017 and Q4 2018, assuming 50% were A11’s (I’m not looking for more detailed stats right now): 6525.6×1015
  • Number of simultaneous, real-time, simulations of complete human brains that can be supported by 2017-18 sales of iPhones: 177

 

  • Performance of “Next-generation Neural Engine” in Apple A12 SoC used in Phone XR, XS, XS Max: 5 trillion operations per second
  • Assuming next year’s sales are unchanged (and given that all current models use this chip and I therefore shouldn’t discount by 50% the way I did previously) number of simultaneous, real-time, simulations of complete human brains that can be supported by 2018-19 sales of iPhones: 1.30512×1021/36.8×1015 = 35,465

 

  • Speedup required before one iPhone’s Neural Engine is sufficient to simulate a human brain in real time: 36.8×1015/5×1012 = 7,360
  • When this will happen, assuming Moore’s Law continues: log2(7360)×1.5 = 19.268… years = January, 2038
  • Reason to not expect this: A12 feature size is 7nm, silicon diameter is ~0.234nm, size may only reduce by a linear factor of about 30 or an areal factor of about 900 before features are atomic. (Oh no, you’ll have to buy a whole eight iPhones to equal your whole brain).

 

  • Purchase cost of existing hardware to simulate one human brain: <7,360×$749 → <$5,512,640
  • Power requirements of simulating one human brain in real time using existing hardware, assuming the vague estimates of ~5W TDP for an A12 SoC are correct: 7,360×~5W → ~36.8kW
  • Annual electricity bill from simulating one human brain in real time: 36.8kW * 1 year * $0.1/kWh = 32,200 US dollars
  • Reasons to be cautious about previous number: it ignores the cost of hardware failure, and I don’t know the MTBF of an A12 SoC so I can’t even calculate that
  • Fermi estimate of MTBF of Apple SoC: between myself, my coworkers, my friends, and my family, I have experience of at least 10 devices, and none have failed before being upgraded over a year later, so assume hardware replacement <10%/year → <$551,264/year
  • Assuming hardware replacement currently costs $551,264/year, and that Moore’s law continues, then expected date that the annual replacement cost of hardware required to simulate a human brain in real time becomes equal to median personal US annual income in 2016 ($31,099): log2($551,264/$31,099) = 6.22… years = late December, 2024
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