Microsoft Word Kurzweil, Ray The Singularity Is Near doc

Epilogue 
1.
As quoted in James Gardner, "Selfish Biocosm," 
Complexity
5.3 (January–February 2000): 34–45. 
2.
In the function 
y
= 1/
x
, if 
x
= 0, then the function is literally undefined, but we can show that the 
value of 
y
exceeds any finite number. We can transform 
y
= 1/
x
into 
x
= 1/
y
by flipping the 
nominator and denominator of both sides of the equation. So if we set y to a large finite number, 
then we can see that 
x
becomes very small but not zero, no matter how big 
y
gets. So the value of 
y
in 
y
= 1/
x
can be seen to exceed any finite value for 
y
if 
x
= 0. Another way to express this is that 
we can exceed any possible finite value of 
y
by setting 
x
to be greater than 0 but smaller than 1 
divided by that value. 
3.
With estimates of 10
16
cps for functional simulation of the human brain (see chapter 3) and about 
10
10
(under ten billion) human brains, that's 10
26
cps for all biological human brains. So 10
90
cps 
exceeds this by a factor of 10
64
. If we use the more conservative figure of 10
19
cps, which I 
estimated was necessary to simulate each nonlinearity in each neuron component (dendrite, axon, 
and so on), we get a factor of 10
61
. A trillion trillion trillion trillion trillion is 10
60
. 
4.
See the estimates in the preceding note; 10
42
cps exceeds this by a factor of ten thousand trillion 
(10
16
). 

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5.
Stephen Jay Gould, "Jove's Thunderbolts," 
Natural History
103.10 (October 1994): 6–12; chapter 
13 in 
Dinosaur in a Haystack: Reflections in Natural History
(New York: Harmony Books, 1995). 

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[Index omitted] 
 

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