Part 1
The limit is based on a computer operating at the Landauer Limit, at the temperature of the cosmic microwave background, powered by a Dyson sphere operating at the efficiency of a Carnot engine. [EDIT: this proposed limit is too low, as the Landauer Limit can be broken, it is now just a lower bound.]
Relevant equations
Carnot efficiency ηI=1-(Tc/Th)
Landauer limit E=KbTLn(2)
Bit rate R=PηI /E
Relevant values
Boltzmann constant [Kb] (J K-1) 1.38E-23
Power output of the sun [P] (W) 3.83E+26
Temperature of the surface of the sun [Th] (K) 5.78E+03
Temperature of cosmic microwave background [Tc] (K) 2.73
Calculations
Carnot efficiency ηI=1-(Tc/Th)
ηI=1-(2.73/5.78E+03)
ηI=1.00
Landauer limit E=KbTLn(2)
E=1.38E-23*2.73*0.693
E= 2.61E-23 Joules per bit
Bit rate R=PηI /E
R=3.83E+26*1.00/2.61E-23
R=1.47E+49 bits per second
Notes
Numbers are shown rounded to 3 significant figures, full values were used in calculations.
Part 2
The theoretical computational limit of the solar system is 22 orders of magnitude above the estimated computational ability of all alive humans. This is based on estimates of the number of synapses in the human brain, the update rate of those synapses, and the number of humans alive. This estimate is only an approximation and should be used with caution.
The purpose of this post was to show the limit of computation, and therefore intelligence, is far above all humans combined.
Relevant equations
Bit rate of all humans Rhumans=NsynRsynNhumans
Comparative rate Rc=Rmax/Rhumans
Relevant values
Number of synapses in the human brain [Nsyn] 2.50E+14
Synaptic update rate [Rsyn] (Hz) 500
Number of humans alive [Nhumans] 8.07E+09
Theoretical computational limit [Rmax] (bit s-1) 1.47E+49
Calculation
Bit rate of all humans Rhumans=NsynRsynNhumans
Rhumans=2.50E+14*500*8.07E+09
Rhumans= 1.01E+27
Comparative rate Rc=Rmax/Rhumans
Rc=1.47E+49/1.01E+27
Rc=1E22
Notes
Numbers are shown rounded to 3 significant figures, full values were used in calculations, final result rounded to one significant figure due to low confidence in synaptic update rate.
Synaptic update rate estimated based on a 2 millisecond refractory time of a neuron.
Hi William, interesting post :) Some reactions:
Happy reading :)
An efficient idea, good thinking.