Amazing correspondence

I always wondered looking at the facts that sometimes different disciplines in science/engineering have striking similarity in the final result : no matter what principles you are studying, the final equations look similar across multiple disciplines. One such example is the Arrhenius type dependence of many processes (generally if you have to overcome some energy barrier to do something then it is highly likely that you will end up getting an Arrhenius dependence). I just came across a simple relation called Amdahl's Law (https://computing.llnl.gov/tutorials/parallel_comp/) which states that if you are parallelizing a computer program/code, the potential program speedup (x) can be defined by the fraction of code (p) that can be parallelized or,

          1
x = ------------;
         1 - p

Now while taking the polymer engineering class, I learned about the special case of Carother's equation (http://en.wikipedia.org/wiki/Carothers_equation) where the degree of polymerization (x_n) is related to the conversion (p) as follows:


              1
x_n = ------------
             1 - p

You need to have a very high amount of conversion (~ 99%) in order to get a really long polymer chain. What amazes me is the striking similarity between these two simple equations which are from two unrelated fields, but still analogous. Nature surely has only a few main principles or rules --  everything else can just be explained through analogy. We just have to unravel those simple rules -- are we there yet?