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 η_{I}=1-(T_{c}/T_{h})

Landauer limit E=K_{b}TLn(2)

Bit rate R=Pη_{I} /E

Relevant values

Boltzmann constant [K_{b}] (J K^{-1}) 1.38E-23

Power output of the sun [P] (W) 3.83E+26

Temperature of the surface of the sun [T_{h}] (K) 5.78E+03

Temperature of cosmic microwave background [T_{c}] (K) 2.73

Calculations

Carnot efficiency η_{I}=1-(T_{c}/T_{h})

η_{I}=1-(2.73/5.78E+03)

η_{I}=1.00

Landauer limit E=K_{b}TLn(2)

E=1.38E-23*2.73*0.693

E= 2.61E-23 Joules per bit

Bit rate R=Pη_{I} /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 R_{humans}=N_{syn}R_{syn}N_{humans}

Comparative rate R_{c}=R_{max}/R_{humans}

Relevant values

Number of synapses in the human brain [N_{syn}] 2.50E+14

Synaptic update rate [R_{syn}] (Hz) 500

Number of humans alive [N_{humans}] 8.07E+09

Theoretical computational limit [R_{max}] (bit s^{-1}) 1.47E+49

Calculation

Bit rate of all humans R_{humans}=N_{syn}R_{syn}N_{humans}

R_{humans}=2.50E+14*500*8.07E+09

R_{humans}= 1.01E+27

Comparative rate R_{c}=R_{max}/R_{humans}

R_{c}=1.47E+49/1.01E+27

R_{c}=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.

If you're trying to maximize computational efficiency, instead of building a Dyson sphere, shouldn't you drop the sun into a black hole and harvest the Hawking radiation?

Hi Robi,

For reference, Anders Sandberg discussed that on The 80,000 Hours Podcast (emphasis mine):

William, I am guessing you would like Anders' episodes! You can find them searching for "Anders Sandberg" here.

Yea, I found him to be a fascinating person when I talked to him at EAGx Warsaw.

I'm initially sceptical of getting 40% of the mass-energy out of, well, anything. Perhaps I would benefit from reading more on black holes.

However I would in principle agree with the idea that if black holes are feasible power outputers, this would increase the theoretical maximum computation rate.

Hi William, interesting post :) Some reactions:

Happy reading :)

Hi Mo, thanks for the feedback.

Yeah, your initial guess was right that more detailed estimations had already been done. I figured the reason you posted your rough BOTEC was to invite others to refer you to those more detailed estimates (saves time on your end via crowdsourcing too), since I've done the same as well in the past, hence the shares :) Happy reading

An efficient idea, good thinking.