A concrete illustration of practical running time vs big-O notation

Big Oh is simply a mathematical tool that is helpful to abstract away uninteresting details. But what people do not realize is that by using this tool, they perform some abstraction of their own -- it can be used to count anything, and the most important thing to establish is what you count. Most importantly, you want to count time & space used by an algorithm. But you don't always want to count the time used by an algorithm as the number of instruction performed. For example, we may compare comparison-based sorting procedures by the number of comparisons they perform. Why? Because we are smart and realize that this (# of comparisons) is a good way to compare such algorithms.

For some algorithms, you might want to count the number of memory accesses you make. Or the number of level-i memory accesses in a memory hierarchy. Or the number of network packets. Get it?