Maybe, but there is another, perhaps simpler hypothesis: Both the transistor count and life expectancy increase with time.
One way to verify one or the other is to look at a linear hypothesis:
States: LifeExp, Transistors, Time
Structural Equation Model [1]:
Model 1:
LifeExp ~ Time + Transistors + noise_exp_1
Transistors ~ Time + noise_trans_1
(The 2nd equation means that:
Transistors(t) = a * t + noise, and you try to estimate "a" from the data.)
vs
Model 2:
LifeExp ~ Time + noise_exp_2
Transistors ~ Time + noise_trans_2
If model 2 has more predictive power of LifeExp than model 2 (i.e., noise_exp_1 is lower than noise_exp_2), then according to _this_ model, Transistors causally affects LifeExp. However, this model is way too simplistic and doesn't incorporate other causal paths, such as the one you describe (Transistors -> Computing -> DiagnosticRate -> ...)
[1] http://en.wikipedia.org/wiki/Structural_equation_modeling