Methodology of Computer Science

Abstract

ion in Computer Science Computer scientists are often thought to labor exclusively in a world of bits, logic circuits and microprocessors. Indeed, the foundational concepts of computer science are described in the language of binary arithmetic and logic gates, but it is a fascinating aspect of the discipline that the levels of abstraction that one can lay upon this foundational layer are limitless, and make possible to model familiar objects and processes of every day life entirely within a digital world. When digital models are sufficiently realistic, the environments they inhabit are called virtual worlds. So today, of course, there are virtual libraries, virtual shopping malls, virtual communities, and even virtual persons, like the digital version of actor Alan Alda created in an episode of PBS’s Scientific American Frontiers. Complex virtual worlds such as these are made possible by computer scientists’ ability to distance themselves from the mundane and tedious level of bits and processors through tools of abstraction. To abstract is to describe something at a more general level than the level of detail seen from another point of view. For example, an architect may describe a house by specifying the height of the basement foundation, the location of load-bearing walls and partitions, the R-factor of the insulation, the size of the window and door rough openings, and so on. A realtor, however, may describe the same house as having a certain number of square feet, a certain number of bedrooms, whether the bathrooms are full or half, and so on. The realtor’s description leaves out architectural detail but describes the same entity at a more general level, and so it is an abstraction of the architect’s description. But abstraction is relative. For example, the architect’s description is itself an abstraction when compared to a metallurgist’s description of the nails, screws, and other fasteners making up the house, and the botanist’s description of the various cellular properties of the wood it contains. The computer scientist’s world is a world of nothing but abstractions. It would not be possible to create the complex virtual worlds described above if the only things computer scientists could talk about were bits, bytes, and microcircuits. One can give an accurate idea of what computer scientists do by describing the abstraction tools they use. Now to characterize computer science as involved with abstractions seems to claim for it a place alongside mathematics as a purely formal endeavor. But the general trends in all programming are toward higher-quality software by abstracting away from the lower-level concepts in computer science and toward the objects and information that make up the real world. This is a kind of abstraction that is fundamentally different from that which takes place in mathematics. Understanding the difference is crucial in avoiding the persistent misconception by some that computer science is just a branch of pure mathematics. Both mathematics and computer science are marked by the introduction of abstract objects into the realm of discourse, but they differ fundamentally in the nature of these objects. The difference has to do with the abstraction of form versus the abstraction of content. Traditionally, mathematics, as a formal science, has been contrasted with the factual sciences such as physics or biology. As natural sciences, the latter are not concerned with abstraction beyond that offered by mathematics as an analytical tool. The literature is full of