[extropy-chat] Desirability of Singularity (was Are ancestor simulations immoral?)

[Anders Sandberg]

Martin Striz wrote:
> On 6/4/06, Anders Sandberg <asa at nada.kth.se> wrote:
>> Hmm, around 8e14 synapses with an average population of 1-10% neurons
>> firing at 1-100 Hz. That makes 1e9-1e12 firings affecting 8e12-8e15
>> synapses. At a cost of 2.4e-21 - 3.6e-21 J
>
> What is the conversion you're using (i.e. J/spike)?  How do you derive
> it?  Are you taking the total energy demands of a neuron over time
> divided by the average number of spikes over the same time?  Or are
> you counting just the thermodynamics of the axon and boutons?

The Brillouin inequality states that if you erase one bit of information
you have to at least pay an entropy cost of kT ln(2) Joules (where k is
Boltzmann's constant and T is the temperature). This is of course a lower
bound, being the reduction of entropy a bit erasure represents. A synapse
having probability p of failing will on average erase -pln(p)/log(2) bits
of information for each signal. Hence  N synapses receiving f signals per
second will require at least -NfkTp*ln(p) J/s.

I find it rather curious that you have to *pay* energy for having
unreliable synapses. But it really a cleanup bill, where the presynaptic
neuron has to restore itself to its previous state no matter what happens.
Of course, the real processes of neurotransmitter and vesicle recycling
are much more energy demanding than this minimal cost.

>> this is 1.9e-8 - 2.8e-5 W. So I
>> get five-six order of magnitude for this with the most pessimistic
>> calculation.
>
> I'm not sure what you're comparing here, what a neuron could
> accomplish if all of its energy input were used for computation rather
> than metabolism (and minimal loss as heat)?  Or are you suggesting
> that there's energy loss somewhere else?

This would be the energy needed to run a thermodynamically perfect replica
of the brain, with neurons not requiring any energy to run and just
information erasure losses. In reality there are certainly more energy
loss, and even the perfect brain might have a few more entropic losses
(signal summation at the soma seems plausible: ~8000 bits of information
gets turned into one - that is about the same energy demand as from
erasing information at all the synapses).




-- 
Anders Sandberg,
Oxford Uehiro Centre for Practical Ethics
Philosophy Faculty of Oxford University