Microsoft Word Kurzweil, Ray The Singularity Is Near doc

Memory and Computational Efficiency:
A Rock Versus a Human Brain. With the limits of matter and energy to 
perform computation in mind, two useful metrics are the memory efficiency and computational efficiency of an object. 
These are defined as the fractions of memory and computation taking place in an object that are actually useful. Also, 
we need to consider the equivalence principle: even if computation is useful, if a simpler method produces equivalent 
results, then we should evaluate the computation against the simpler algorithm. In other words, if two methods achieve 
the same result but one uses more computation than the other, the more computationally intensive method will be 
considered to use only the amount of computation of the less intensive method.
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The purpose of these comparisons is to assess just how far biological evolution has been able to go from systems 
with essentially no intelligence (that is, an ordinary rock, which performs no useful computation) to the ultimate ability 
of matter to perform purposeful computation. Biological evolution took us part of the way, and technological evolution 
(which, as I pointed out earlier, represents a continuation of biological evolution) will take us very close to those 
limits. 
Recall that a 2.2-pound rock has on the order of 10
27
bits of information encoded in the state of its atoms and 
about 10
42
cps represented by the activity of its particles. Since we are talking about an ordinary stone, assuming that 
I set the date for 
the Singularity—
representing a 
profound and 
disruptive trans-
formation in 
human capability—
as 2045. 
The nonbiological 
intelligence 
created in that year 
will be one billion 
times more 
powerful than all 
human intelligence 
today. 

---

its surface could store about one thousand bits is a perhaps arbitrary but generous estimate.
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This represents 10
–24
of 
its theoretical capacity, or a memory efficiency of 10
–24
.
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We can also use a stone to do computation. For example, by dropping the stone from a particular height, we can 
compute the amount of time it takes to drop an object from that height. Of course, this represents very little 
computation: perhaps 1 cps, meaning its computational efficiency is 10
–42
.
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In comparison, what can we say about the efficiency of the human brain? Earlier in this chapter we discussed how 
each of the approximately 10
14
interneuronal connections can store an estimated 10
4
bits in the connection's 
neurotransmitter concentrations and synaptic and dendritic nonlinearities (specific shapes), for a total of 10
18
bits. The 
human brain weighs about the same as our stone (actually closer to 3 pounds than 2.2, but since we're dealing with 
orders of magnitude, the measurements are close enough). It runs warmer than a cold stone, but we can still use the 
same estimate of about 10
27
bits of theoretical memory capacity (estimating that we can store one bit in each atom). 
This results in a memory efficiency of 10
–9
. However, by the equivalence principle, we should not use the brain's 
inefficient coding methods to rate its memory efficiency. Using our functional memory estimate above of 10
13
bits, we 
get a memory efficiency of 10
–14
. That's about halfway between the stone and the ultimate cold laptop on a logarithmic 
scale. However, even though technology progresses exponentially, our experiences are in a linear world, and on a 
linear scale the human brain is far closer to the stone than to the ultimate cold computer. 
So what is the brain's computational efficiency? Again, we need to consider the equivalence principle and use the 
estimate of 10
16
cps required to emulate the brain's functionality, rather than the higher estimate (10
19
cps) required to 
emulate all of the nonlinearities in every neuron. With the theoretical capacity of the brain's atoms estimated at 10
42
cps, this gives us a computational efficiency of 10
–26
. Again, that's closer to a rock than to the laptop, even on a 
logarithmic scale. 
Our brains have evolved significantly in their memory and computational efficiency from pre-biology objects 
such as stones. But we clearly have many orders of magnitude of improvement to take advantage of during the first 
half of this century.