On abstraction

Abstraction is central computer science -- theory of computer science to software engineering applies it. Recently I have been involved in a project where I attempted to follow the methods of system engineering and I came across some questions in relation to abstraction.
Although I have some sense of abstraction i.e. a writing instrument is more abstract than a pen but there remains other central mysteries. In particular I went to muse on the following questions

• Is abstraction quantifiable as we can quantify speed, for example, but then before I try to measure abstraction what is meant by "quantifying something"? Which quantities are fundamentally quantifiable and which quantities are not quantifiable?
  

While musing on the above question I could make up the following line of reasoning ( on haunch and no correctness is implied ) if something has to be quantifiable then a measurement has to exist for the quantity. Since measurement is a process -- physical process and questions about a physical process can be answered with respect to Quantum Turing machines. This means only those measurements are plausible which can be simulated on a Quantum Turing machine (QTM) and other measurements are implausible. Hence the question of measurement and quantification might be resolvable by the study of QTM's, however it still does not answer if abstraction is quantifiable.
It appears that there must be some relationship between a concept/idea, like abstraction and its property of being quantifiable. Since I don't have any go from now on I leave these questions here. However, I must note that when I think of trying to measure abstraction some quantities do come to mind like entropy but then it also appears that the quantity (if it exists) might be similar to entropy but not exactly the same.
Another question that has propped up in my musings is the following

• Is abstraction a fundamental concept in the same sense that momentum is a fundamental quantity?

Conclusion
Quantification of abstraction would be interesting, for quantification might indicate the more levels of abstraction that is yet to be traversed. And what could be better if we can still quantify the degrees of abstraction.
I am not sure of the validity of my questions or line of reasoning but I have written it because it all appeared very cogent to haunch.