Computer Science

WHAT IS “COMPUTER SCIENCE”?

It turns out that there are philosophical or at least conceptual issues arising in about just what is included under the label “Computer Science.”

At various universities and other institutions the units that house at least some computer scientists have many variations in their name and structure. Variants include Computing Science, Computer Engineering, Informatics, Information Science, Information Systems, Information Technology (IT), and various combinations of these and other names, e.g., Computer and Information Science, Library and Information Science, Information and Communications Technology (ICT), Bioinformatics, Medical Informatics, Legal Informatics, etc. This keeps you on your toes in getting the names right.

The exact boundaries of “computer science” are clearly difficult to define, but I take it from the above that it can include the study of computing, not just computing machines, and that it can also include the study of information, at least in digital form. This is not just an accident of institutional nomenclature, or even of technology. As we shall see below, because of the von Neumann notion of a “stored program,” the very distinction in a “computer” between computation and information becomes subtle and there is in fact a kind of duality between the two.

3.1 Computer science: its nature, scope and methods

One of the fundamental questions for a philosophy of computer science concerns the nature and scientific status of computer science. We will discuss four prominent accounts of computer science as an academic field and discuss some of their limitations. The first account that is sometimes given may be called the deflationary account. It holds that computer science is such a diverse field that no unified definition can be given that would underscore its status as a science or even as a coherent academic field. Paul Graham [2004], for example, has claimed that “computer science is a grab bag of tenuously related areas thrown together by an accident of history”, and Paul Abrahams has claimed that “computer science is that which is taught in computer science departments” [Abrahams, 1987, p. 1].

An objection to deflationary accounts is that they do not explain how computer science is capable of functioning as a recognized academic field, nor do they address its scientific or academic credentials. Rejecting a deflationary account, others have attempted to characterize computer science as either a science, a form of engineering, or a branch of mathematics [Wegner, 1976; Eden, 2007]. On the mathematical conception of computer science, computer science is a branch of mathematics, its methods are aprioristic and deductive, and its aims are to develop useful algorithms and to realize these in computer programs. Theoretical computer science is defended as the core of the field of computer science. A mathematical conception has been defended, amongst others, by Knuth [1974a], who claims that computer science centrally consists of the writing and evaluation of programs, and that computer programs are mere representations of algorithms that can be realized in computers. Knuth defines an algorithm as a “precisely-defined sequence of rules telling how to produce specified output information from given input information in a finite number of steps” [Knuth, 1974a, p. 2]. Since algorithms are mathematical expressions, Knuth argues, it follows that computer science is a branch of applied mathematics. A similar position is taken by Hoare [1986].

The scientific conception of computer science holds that the apriorism of the mathematical conception is incorrect, and that computer science is an ordinary empirical science. The aim of computer science is to explain, model, understand and predict the behavior of computer programs, and its methods include deduction and empirical validation. This conception has been defended by Allen Newell and Herbert Simon, who have defined computer science as “the study of the phenomena surrounding computers” and who have claimed that it is a branch of natural (empirical) sciences, on a par with “astronomy, economics, and geology” [1976, pp. 113-114]. A computer is both software and hardware, both algorithm and machinery. Indeed, it is inherently difficult to make a distinction between the two [Suber, 1988]. The workings of computers are therefore complex causal-physical processes that can be studied experimentally like ordinary physical phenomena. Eden claims that the scientific conception seems to make a good fit with various branches of computer science that involve scientific experiments, including “artificial intelligence, machine learning, evolutionary programming, artificial neural networks, artificial life, robotics, and modern formal methods” [2007, p. 138].

An objection to the scientific conception has been raised by Mahoney [2002], who argues that computers and programs cannot be the subject of scientific phenomena because they are not natural phenomena. They are human-made artifacts, and science does not study artifacts but natural phenomena. Newell and Simon have anticipated this objection in their 1976 paper, where they acknowledge that programs are indeed contingent artefacts. However, they maintain that they are nonetheless appropriate subjects for scientific experiments, albeit of a novel sort. They argue that computers, although artificial, are part of the physical world and can be experimentally studied just like natural parts of the world (see also [Simon, 1996]). Eden [2007] adds that analytical methods fall short in the study of many programs, and that the properties of such programs can only be properly understood using experimental methods.

The engineering conception of computer science, finally, conceives of computer science as a branch of engineering concerned with the development of computer systems and software that meet relevant design specifications (see e.g. [Loui, 1987]). The methodology of computer science is an engineering methodology for the design and testing of computer systems. Theoretical computer science does not constitute the core of the field and has only limited applicability. The engineering conception is supported by the fact that most computer scientists do not conduct experiments but are rather involved in the design and testing of computer systems and software. The testing that is involved is usually not aimed at validating scientific hypotheses, but rather at establishing the reliability of the systems that is being developed and in making further improvements in its design.

Eden [2007] has argued that the engineering conception of computer science seems to have won out in recent decades, both in theory and in practice. The mathematical conception has difficulties accounting for complex software systems, and the scientific conception does not make a good fit with the contemporary emphasis on design. A worrisome aspect of this development, Eden argues, is that the field seems to have developed an anti-theoretical and even anti-scientific attitude. Theoretical computer science is regarded to be of little value, and students are not taught basic science and the development of a scientific attitude. The danger is that computer science students are only taught to build short-lived technologies for short-term commercial gain. Eden argues that computer science has gone too far in jettisoning theoretical computer science and scientific approaches, and that the standards of the field have suffered, resulting in the development of poorly designed and unreliable computer systems and software. For computer science (and especially software engineering) to mature as a field, Eden argues, it should embrace again theoretical computer science and scientific methods and incorporate them into methods for design and testing.

2.33.5.1.2 Computer science research

Computer science has made and continues to make significant contributions to research in the life sciences. From the early days of the human genome project when base calling and assembly programs converted sequence trace files into reliable contiguous regions of cDNA and genomic sequence to today’s active research in areas such as image processing, computer science continues to be a critical component of life science research. Also, within this domain are the technologies that utilize the internet for exchange and analysis of large, multidimensional datasets. Although the technologies, such as web services that support the exchange of this type of information have become more conventional, methods and techniques that can improve our ability to store, disseminate, retrieve, view, and mine both locally and remotely stored datasets are still areas of active research.

2.1 Computer science and complexity

Computer science is the study of algorithms and their complexity. Here, the term “complexity” means the amount of effort (that is, physical resources such as time, space, and energy) required to solve a given mathematical problem, as a function of the size of the problem.

For example, the problem of adding two n-digit numbers together has O(n) complexity, meaning that the time (or space) required to add the two numbers grows linearly with n. There is some cleverness involved in bounding complexity, however. One might think that the problem of multiplying two n × n matrices together would require O(n³) time, since there are n² numbers to compute, andeach takes O(n) multiplications with straightforward matrix multiplication methods. But there is a better way to multiply matrices, discovered by Strassen, which requires only $O\left(n^{{\log }_2{}^7}\right)$ resources. Since log₂ 7 ≈ 2.8, this is better.

Complexity is defined by the best possible time, or minimum resources required, and this can often be hard to define. But there are different classes of complexity which are easier to identify than specific complexities. For example, consider the question of identifying whether or not two graphs G₁ and G₂, each with n nodes, are equivalent to each other under relabeling of their nodes; this problem of graph isomorphism is believed to have complexity $O\left(2^n\right)$, but that has never been proven. Likewise, the problem of factoring a number $x=pq$, the product of two prime numbers p and q, is believed to have complexity O(2^n1/3) (that is roughly the minimum resources with which the best known algorithm can solve the problem today). But there is no proof of this today.

Nevertheless, Computer Science has successfully crafted great insight in to the nature of mathematical problems, by relating the complexities of various mathematical problems to each other. Consider a boolean function f(x) which is the logical OR of many terms, each of which depend on no more than three bits of the n-bit number x; for example, $f(x)=x_1{x}_2+x_2{\overline{x}}_3+x_1{\overline{x}}_4{x}_7+\cdots$, where x_k is the k^th bit of x, + represents OR, and multiplication AND. Does there exist x such that f(x) = 1?

The complexity of this 3-SAT problem is believed to be O(2ⁿ), but more interestingly, the ability to easily solve 3-SAT implies the ability to easily solve any other problem in a wide class of problems known as NP, short for “nondeterministic polynomial time.” NP problems are characterized by having answers that are easy to check, but difficult to find, typically requiring time that is exponential in the problem size. These hard problems sit in contrast to P, or “polynomial” problems like addition, which are considered easy; defining the boundary between such problems is an art at the heart of computer science. We also define efficient as meaning that no exponential resources are required.

Of course, the boundary between easy and hard problems depends upon the model of computation being adopted. For example, how does one represent a real number (such as π) with error ∈? Using a unary representation, this is a hard problem, but with a binary (or any digital) representation, this is easy.

The importance of quantum computation is that it violates this thesis! Quantum computers can solve certain mathematical problems faster than is possible using classical resources alone, and moreover, classical computers cannot efficiently simulate quantum computations! Thus, physics makes its entree into computer science, and vice versa. Each of these fields has something to contribute to the other, as we shall see.

Introduction

With the explosion of new knowledge and the expansion of global linkages, it has become essential to learn new techniques and skills for this technology dominated world. Computers are being used by people of all ages and in every profession, in their work as well as in their leisure. Many of the routine activities in today's society are performed by computers. Computers and software can also play a major role in improving the educational skills of our youth and in preparing them for the future. Our work has just begun. With computers, software, and people working together, the possibilities are endless.

The computer is becoming almost invisible and omnipresent. Washing machines, microwave ovens, cars, and televisions have already been computerized. This is the beginning of the invisible computer, which will result in virtually every electronic device known, or to be invented, being similarly computerized. Computer technology also represents access to new worlds. Computers provide information – text, audio and graphic-based – about new areas of learning, new places, new shapes, and new worlds. They stimulate new ways of thinking and analyzing problems. With computers, people are free to manipulate the information and look at facts and ideas in different ways. With increased storage capabilities, the computer is able to take on even more critical roles as ‘information grabbers’ and organizers for individuals, schools, and businesses.

Hamza and Alhalabi anticipated that the ‘virtual world’ grows stronger and, hopefully, smarter and wiser as educators, engineers, computer scientists, and researchers of diverse disciplines attempt to locate better, more powerful ways to synthesize ‘Artificial Intelligence’ on the Net in order to increase productivity and efficiency in meeting future demands. Technology is in essence a manifestation of human creativity. Thus, an important way in which students can come to understand it would be by engaging in acts of technological creation. Lewis opines that technology as a context for creativity is an important area of research. Romeike emphasizes that everyday life requires creativity – and so does Computer Science.

Publisher Summary

This chapter reviews current research from computer science and related fields into memory, reasoning and learning. The potential synergies with cognitive neuroscience and related disciplines over 5- and 20-year horizons, linked with wider trends in computing are discussed. The aim is to uncover research themes in the area of cognitive science or neuroscience that are important for the development of computer science. Such themes may be problems that have to be solved, or potential opportunities for progress. Thus it looks into the scope of research, the assumptions that underlie it, and some of the important distinctions to bear in mind while considering these issues. This chapter further focuses on memory, reasoning and learning and also discusses there interrelationships. These interrelate in interesting ways. A position on one issue affects the possibilities on others. Orthogonal to these interrelationships are a number of key distinctions. This includes human and artificial neural computing, top-down and bottom-up approaches, and physical and digital.

2.1.2 Location

Our discussion is concerned with computer science and the potential for development in the UK. This will, however, be understood in the context of the worldwide discipline, and the market forces that will privilege particular lines of development over others.

Abstract

In cognitive science, computers can be used in three ways: to simulate cognition for artificial intelligence (AI), to enhance cognition by assisting human intellectual activity, and to help scientists understand cognition by testing theories on large amounts of data. These three approaches are not mutually exclusive, since specialists in any of these areas frequently adopt techniques designed for the others. This chapter surveys theories of categorization and reasoning in cognitive science that have been implemented and tested in computer systems. Most of the ideas originated long before modern computers were invented, but computers provide an opportunity for developing them in greater detail than was previously possible. Section 1 presents early work in the field of computation in cognitive science. Section 2 surveys top-down and bottom-up approaches to categorization; Section 3 analyzes the implications of structure, context, and purpose on the choice of categories and the methods for recognizing individuals that belong to those categories; and Section 4 considers the interactions of categorization and reasoning. The concluding Section 5 discusses the levels of cognition and some successes and failures in simulating those levels by AI.

2 Fundamentals: quantum mechanics and computer science

This lecture reviews the foundations of computer science and of quantum mechanics. We begin with the notion of complexity, turn to a quick summary of the current state of the theory of quantum computation, then a summary of the four fundamental postulates of quantum mechanics, then conclude with a simple mathematical example, superdense coding, illustrating some surprises hidden within quantum mechanics.