Jacob’s analysis in that section also fails to adjust for how, by his own model in the previous section, power consumption scales linearly with system size (and also scales linearly with temperature).
If we fix the neuron/synapse/etc count (and just spread them out evenly across the volume) then length and thus power consumption of interconnect linearly scale with radius R, but the power consumption of compute units (synapses) doesn’t scale at all. Surface power density scales with R2.
First key observation: all the R’s cancel out. If we scale down by a factor of 2, the power consumption is halved (since every wire is half as long), the area is quartered (so power density over the surface is doubled), and the temperature gradient is doubled since the surface is half as thick
This seems rather obviously incorrect to me:
There is simply a maximum amount of heat/entropy any particle of coolant fluid can extract, based on the temperature difference between the coolant particle and the compute medium
The maximum flow of coolant particles scales with the surface area.
Given a fixed compute temperature limit, coolant temp, and coolant pump rate thus results in a limit on the device radius
But obviously I do agree the brain is nowhere near the technological limits of active cooling in terms of entropy removed per unit surface area per unit time, but that’s also mostly irrelevant because you expend energy to move the heat and the brain has a small energy budget of 20W. Its coolant budget is proportional to it’s compute budget.
Moreover as you scale the volume down the coolant travels a shorter distance and has less time to reach equilibrium temp with the compute volume and thus extract the max entropy (but not sure how relevant that is at brain size scales).
If we fix the neuron/synapse/etc count (and just spread them out evenly across the volume) then length and thus power consumption of interconnect linearly scale with radius R, but the power consumption of compute units (synapses) doesn’t scale at all. Surface power density scales with R2.
This seems rather obviously incorrect to me:
There is simply a maximum amount of heat/entropy any particle of coolant fluid can extract, based on the temperature difference between the coolant particle and the compute medium
The maximum flow of coolant particles scales with the surface area.
Given a fixed compute temperature limit, coolant temp, and coolant pump rate thus results in a limit on the device radius
But obviously I do agree the brain is nowhere near the technological limits of active cooling in terms of entropy removed per unit surface area per unit time, but that’s also mostly irrelevant because you expend energy to move the heat and the brain has a small energy budget of 20W. Its coolant budget is proportional to it’s compute budget.
Moreover as you scale the volume down the coolant travels a shorter distance and has less time to reach equilibrium temp with the compute volume and thus extract the max entropy (but not sure how relevant that is at brain size scales).