[math-fun] The amount of computation required to evolve or simulate human-level intelligence naively
The atoms on or slightly below Earth surface can be regarded as performing experiments. If we re-express (4.4 gigayears) * (surface area of earth) * (1 meter deep) = 7 * 10^31 * meter^3 * sec in Hartree atomic time and length units, then we get 2 * 10^79 as the total number of such experiments performed so far. Now, of course, if you were going to redo that inside a computer, you could save time. The total amount of biomass on Earth is estimated to be (7+-1)*10^14 kg of carbon (and biomass is about 12 atomic percent carbon). http://www.pnas.org/content/109/40/16213 If we only simulated the biomass, with the nonliving matter being dealt with via some cheap model, that'd be only 1.5 * 10^73 experiments. OK, what if we decided, to hell with all that atom-level simulation, we are just going to propose a cheesy model of an entire cell (e.g. neuron) and simulate the interaction of those, 1 interaction per millisecond, with everything else in the world handled via some cheap model, and only some fixed set of possible interaction behaviors/rules, which can evolve. The same paper estimates total cell count on Earth is 5 * 10^31 which brings us down to 6 * 10^51 experiments. Of course, this all is well beyond what today's computers could reproduce. But suppose all you wanted to do was to simulate a single human brain (whose "wiring diagram" and neuron behaviors assumed 100% pre-known and the latter assumed pretty simple). Total energy use by brain is about 20 watts. If each synapse "firing" consumes about 24000 ATP molecules worth of energy per bit transmitted [Julia J. Harris, Renaud Jolivet, and David Attwell: Synaptic Energy Use and Supply, http://discovery.ucl.ac.uk/1368741/1/1368741.pdf] and ATP provides 40 kJoule/mole, then we would find the brain is transmitting at most about 10^16 bits/second inside. (Cells tend to fire all their synapses simultaneously, which would greatly lower simulation costs per bit.) Probably only 10-50% of that since brain cells also consume energy when they do nothing. Meanwhile a 64-bit processor chip would be transmitting 2*10^11 bits/sec on its bus if all 64 bits of the bus were continuously transmitting at 3 GHz. If you instead counted all the wires inside the chip, whenever they change logic state, what would the logic-event count per second be? I am guessing 10^12 / sec? Here the fact the human brain has 1.5*10^14 synapses [http://www.dana.org/News/Details.aspx?id=43512], and 9*10^10 neurons, is largely irrelevant to the time-cost, but does affect the memory usage, of the simulation. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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Warren D Smith