The problem is not with the accuracy of Moore's law or other laws. The problem is with your misinterpretation of the word. A "law" is not a fundamental of nature. It is simply a statement or formula. It can be completely wrong and still be a law.
What's interesting is of course that Moore's law predicts a doubling every 22 months, not 18 months. I heard it from the man directly at a talk back in 2005 at the computer history museum. He was being interviewed by Carver Mead. Google the following "Computer History Museum Presents The 40th Anniversary of Moore's Law with Gordon Moore and Carver Mead." There is a video of the interview somewhere too.
If memory serves he explained that originally he had said it would double every two years but a few years later scaled it back by two months to doubling every 22 months. A few years later, Intel's marketing started a campaign in which they were saying that processor performance would double every 18 months (likely from refinements and jumps to half-step processes). In the talk, Moore explained the two numbers got confused and thus most folks wrongly say Moore's law predicts a capacity doubling every 18 mos. It is actually every 22.
That said, what does it mean for this study?
You can take the reporter out of the investigation, but you can't take the investigation out of the reporter.
It's possible that Moore's law may even be applicable into the future, aided of course by Necessity is the Mother of Invention Law. How many nanometer interations are left in silicon, and what will happen after that?
We need another 'Law', that tracks the media's obsession with the 'sound-bite', and desire to appear educated, to try to disguise the vacuous fluff they write about.
Thus there is an increasing divergence of the claims from reality.
My Physics teacher, always pointed out that extrapolation was dangerous.
Moor's law is based on a short term and totally unustainable condition that market demand drives technological advances. We are begining to hit the limits of they physics, but have not yet even come close to the limits of the marketed hardware. The hard question is whether there can be any breakthroughs the equivalent of phase shift masks and the like. Crystaline like quantum logic structures appear to be a long long ways off.
What do you mean by exact science? Exact like in Newton's equation for gravity or Einstein's later revised one?
Nothing in life is exact science. Not even ohm's law. But it works well enough today to be a useful tool for getting work done. Moore's law does the same thing and for whatever observable reason it may be.