1.3 Science, engineering, and the liberal arts

Much ink and many bits have been spent debating whether computer science is an art, an engineering discipline, or a science. The confusion stems from the nature of computing as a new field that does not fit well into existing silos. In fact, computer science fits into all three kingdoms, and it is useful to approach computing from all three perspectives.

Science. Traditional science is about understanding nature through observation. The goal of science is to develop general and predictive theories that allow us to understand aspects of nature deeply enough to make accurate quantitative predications. For example, Newton’s law of universal gravitation makes predictions about how masses will move.Newton, Isaac The more general a theory is the better. A key, as yet unachieved, goal of science is to find a universal law that can describe all physical behavior at scales from the smallest subparticle to the entire universe, and all the bosons, muons, dark matter, black holes, and galaxies in between. Science deals with real things (like bowling balls, planets, and electrons) and attempts to make progress toward theories that predict increasingly precisely how these real things will behave in different situations.

Computer science focuses on artificial things like numbers, graphs, functions, and lists. Instead of dealing with physical things in the real world, computer science concerns abstract things in a virtual world. The numbers we use in computations often represent properties of physical things in the real world, and with enough bits we can model real things with arbitrary precision. But, since our focus is on abstract, artificial things rather than physical things, computer science is not a traditional natural science but a more abstract field like mathematics. Like mathematics, computing is an essential tool for modern science, but when we study computing on artificial things it is not a natural science itself.

In a deeper sense, computing pervades all of nature. A long term goal of computer science is to develop theories that explain how nature computes. One example of computing in nature comes from biology. Complex life exists because nature can perform sophisticated computing. People sometimes describe DNA as a “blueprint”, but it is really much better thought of as a program. Whereas a blueprint describes what a building should be when it is finished, giving the dimensions of walls and how they fit together, the DNA of an organism encodes a process for growing that organism. A human genome is not a blueprint that describes the body plan of a human, it is a program that turns a single cell into a complex human given the appropriate environment. The process of evolution (which itself is an information process) produces new programs, and hence new species, through the process of natural selection on mutated DNA sequences. Understanding how both these processes work is one of the most interesting and important open scientific questions, and it involves deep questions in computer science, as well as biology, chemistry, and physics.

The questions we consider in this book focus on the question of what can and cannot be computed. This is both a theoretical question (what can be computed by a given theoretical model of a computer) and a pragmatic one (what can be computed by physical machines we can build today, as well as by anything possible in our universe).

Scientists study the world as it is; engineers create the world that never has been. Theodore von Kármán

von Kármán, Theodore Engineering. Engineering is about making useful things. Engineering is often distinguished from crafts in that engineers use scientific principles to create their designs, and focus on designing under practical constraints. As William Wulf and George Fisher put it:1

  1. Whereas science is analytic in that it strives to understand nature, or what is, engineering is synthetic in that it strives to create. Our own favorite description of what engineers do is “design under constraint”. Engineering is creativity constrained by nature, by cost, by concerns of safety, environmental impact, ergonomics, reliability, manufacturability, maintainability–the whole long list of such “ilities”. To be sure, the realities of nature is one of the constraint sets we work under, but it is far from the only one, it is seldom the hardest one, and almost never the limiting one.

Computer scientists do not typically face the natural constraints faced by civil and mechanical engineers—computer programs are massless and not exposed to the weather, so programmers do not face the kinds of physical constraints like gravity that impose limits on bridge designers. As we saw from the Apollo Guidance Computer comparison, practical constraints on computing power change rapidly — the one billion times improvement in computing power is unlike any change in physical materials2. Although we may need to worry about manufacturability and maintainability of storage media (such as the disk we use to store a program), our focus as computer scientists is on the abstract bits themselves, not how they are stored.

Computer scientists, however, do face many constraints. A primary constraint is the capacity of the human mind—there is a limit to how much information a human can keep in mind at one time. As computing systems get more complex, there is no way for a human to understand the entire system at once. To build complex systems, we need techniques for managing complexity. The primary tool computer scientists use to manage complexity is abstraction. Abstraction is a way of giving a name to something in a way that allows us to hide unnecessary details. By using carefully designed abstractions, we can construct complex systems with reliable properties while limiting the amount of information a human designer needs to keep in mind at any one time.

Liberal Arts.

I must study politics and war that my sons may have liberty to study mathematics and philosophy. My sons ought to study mathematics and philosophy, geography, natural history, naval architecture, navigation, commerce, and agriculture, in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry, and porcelain. John Adams, 1780

The notion of the liberal arts emerged during the middle ages to distinguish education for the purpose of expanding the intellects of free people from the illiberal arts such as medicine and carpentry that were pursued for economic purposes. The liberal arts were intended for people who did not need to learn an art to make a living, but instead had the luxury to pursue purely intellectual activities for their own sake. The traditional seven liberal arts started with the Trivium (three roads), focused on language:3

  • Grammar — “the art of inventing symbols and combining them to express thought”

  • Rhetoric — “the art of communicating thought from one mind to another, the adaptation of language to circumstance”

  • Logic — “the art of thinking”

The Trivium was followed by the Quadrivium, focused on numbers:

  • Arithmetic — “theory of number”

  • Geometry — “theory of space”

  • Music — “application of the theory of number”

  • Astronomy — “application of the theory of space”

All of these have strong connections to computer science, and we will touch on each of them to some degree in this book.

Language is essential to computing since we use the tools of language to describe information processes. The next chapter discusses the structure of language and throughout this book we consider how to efficiently use and combine symbols to express meanings. Rhetoric encompasses communicating thoughts between minds. In computing, we are not typically communicating directly between minds, but we see many forms of communication between entities: interfaces between components of a program, as well as protocols used to enable multiple computing systems to communicate (for example, the HTTP protocol defines how a web browser and web server interact), and communication between computer programs and human users. The primary tool for understanding what computer programs mean, and hence, for constructing programs with particular meanings, is logic. Hence, the traditional trivium liberal arts of language and logic permeate computer science.

The connections between computing and the quadrivium arts are also pervasive. We have already seen how computers use sequences of bits to represent numbers.Chapter 6 examines how machines can perform basic arithmetic operations. Geometry is essential for computer graphics, and graph theory is also important for computer networking. The harmonic structures in music have strong connections to the recursive definitions introduced in Chapter 4 and recurring throughout this book.4 Unlike the other six liberal arts, astronomy is not directly connected to computing, but computing is an essential tool for doing modern astronomy.

Although learning about computing qualifies as an illiberal art (that is, it can have substantial economic benefits for those who learn it well), computer science also covers at least six of the traditional seven liberal arts.


  1. William Wulf and George Fisher, A Makeover for Engineering Education, Issues in Science and Technology, Spring 2002 (http://www.issues.org/18.3/p_wulf.html). 

  2. For example, the highest strength density material available today, carbon nanotubes, are perhaps 300 times stronger than the best material available 50 years ago. 

  3. The quotes defining each liberal art are from Miriam Joseph (edited by Marguerite McGlinn), The Trivium: The Liberal Arts of Logic, Grammar, and Rhetoric, Paul Dry Books, 2002. 

  4. See Douglas Hofstadter’s Gödel, Escher, Bach for lots of interesting examples of connections between computing and music.