My argument takes the exact same form of Kurzweil’s in the appendix “The Law of Accelerating Returns Revisited” in his book The Singularity is Near (P 491-2).
We are concerned with three variables:
H : the happiness in the world (measured by the Oxford Happiness Inventory or the General Happiness Questionnaire, say)
L: the amount of love in the world as it pertains to happiness
t : time
We observe that happiness is proportional to the amount of love in the world [in a more loving world, people are happier].
(1) H = aL
The rate of change in the amount of love in the world is proportional to the amount of happiness [the amount of love increases more rapidly if people are happier].
(2) dL/dt = bHSubstituting (1) into (2) gives:
(3) dL/dt = abL
The solution to this is:
(4) L = L0eabt
And thus L, the amount of love in the world, grows exponentially with time (e is the base of the natural logarithms).
I have only changed the symbols and a few words. The text above, from “We are concerned with three variables…” onwards, is excerpted from Kurzweil verbatim, with the exception of the glosses in square brackets which are mine. (My glosses have to stand in for the argumentation in large tracts of Kurweil’s book.)
Instead of H, Kurzweil uses V, defined as the “velocity (that is, power) of computation (measured in calculations per second per unit cost).” Instead of L, he has W, defined as “world knowledge as it pertains to designing and building computational devices.” I substituted the constants a and b for his c1 and c2 given the difficulty of writing equations in HTML.
A major flaw in my “proof” is that one can’t measure love; hence, an equation like (2) is utterly meaningless. Consequently, the whole argument is meaningless.
The same flaw applies to Kurzweil’s argument. Since “world knowledge” is nowhere defined, his version of equation (2) (dW/dt = c2V where W is world knowledge and V is velocity of computation) is similarly meaningless.