Problem solving ability is the pivotal attribute that most organizations need in their brightest recruits. But instead the stipulated requirement is for the hot proprietary skill of the moment in a team player with leadership skills who must hit the ground running (because the project is already late). The more exacting the job specification the less likely one is to fill the vacancy, especially from the pool of talent that is newly entering the workplace from education.
Perhaps the subject specific content and the transient hot skills do not matter as much as the intellectual abilities and contemporary mores gained from the learning experience. As B F Skinner put it, “education is what survives when what has been learned has been forgotten.” In the 21st century it is truer than ever that what matters most is not prescribed content, but developing the generic skills to make connections: the essence of communication, creativity, and collaboration.
The ability to adapt — to learn and to relearn — is more important than the ephemera that are the hot skills. So, should we advise the young to choose any subjects because the outcome will be the same. Or is it possible to recommend a golden set of subjects that optimizes both intellectual rigour (that which survives) as well as prospective utility? Clearly it is rigour — a highly transferable skill — that should be paramount since we live in a complex world replete with metaphor, fantasy, and deceit.
Naturally, as members of the IAP, we would think that instruction in computing (cf IT) is important, but what else might we recommend? Putting my head above the parapet, I have added my favoured six to make a baker’s half-dozen: mathematics, computing, science, economics, accountancy, philosophy, and psychology. For each, I offer a tiny manifesto, by way of a definition, to justify its inclusion. I submit that any subset of four would make a cogent quartet at AS-level.
Subject 0: Mathematics
Mathematics is the design, construction and operation of deductive systems, based on the principles of logic and the patterns of nature. Mathematics is the universal enabling discipline which underpins the physical sciences, modern technology and the global economy.
There is scarcely any aspect of our lives that is not affected by mathematics. Patterns, real and abstract, are the very essence of thought, of communication, of computation, of society, and of life itself. Mathematics helps us understand our perceptions of reality.
“The great book of nature,” said Galileo, “can be read only by those who know the language in which it was written. And this language is mathematics.” John Polkinghorne put it succinctly, “mathematics is the abstract key which turns the lock of the physical universe.”
Mathematics encompasses arithmetic and algebra, geometry and trigonometry, calculus and analysis, statics and dynamics, probability and statistics, and operational (or operations) research. The taught subject now extends to so-called modern topics including sets and groups, vectors and matrices, and topology and non-Euclidean geometry.
Subject 1: Computing
Computing was originally about calculation and its automation, but it has evolved to include information systems and communication technology. This is a current revolution. In a few decades the Internet has wired the global village, and the Web it supports is democratizing information.
The subject is often split into computer science which focuses on software, digital engineering which focuses on hardware, and information theory which focuses on data communication and cryptography. When the subject is titled ‘information technology’ the emphasis is on common applications including Web browsers, text editors, spreadsheets tools, and database systems.
The definitive instrument is the general-purpose stored-program electronic digital computer which, when augmented with devices for sensing and acting, becomes a powerful control system, or a robot. Such an instrument is the realization of a Turing machine, a brilliant concept devised by Alan Mathison Turing to whom we owe so very much.
The essence of computer science is algorithmics: whether it is possible to solve a given problem on a machine, and the cost of so doing in terms of execution time and memory usage. A program is an algorithm (problem solving procedure) written in a machine parsable language. Programming is the art of describing activity in procedural text: dynamic ‘process’ prescribed in a static ‘program’.
Programming languages provide the three elements of process: sequencing (consecution), selection (branching), and iteration (looping) or recursion (spiralling). To develop software is to build a notional machine, simply by describing it in such a language.
Subject 2: Science
Science is the study of the physical universe by means of reproducible observations, measurements, and experiments to establish, verify, or modify general laws which successfully predict its behaviour and explain its nature. “The supreme task,” said Einstein, “is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction.” Alan Sokal points out that science is predicated on two key attitudes: being willing to accept what you find, and being willing to discover that you are wrong.
Organized empirical science is the most impressive result of human rationality. It provides the world frame of modern civilization, and it is the strongest candidate for ‘knowledge’ yet conceived. Indeed, science can be defined as ascertained knowledge plus the techniques whereby such knowledge is tested and extended.
Science, properly co-called, is distinguished by its inductive method, whereby a general law or principle is inferred from observed instances, as distinct from purely logical analysis. However, since a single accredited counterexample is pivotal, falsifiability is arguably the hallmark of science.
Traditionally the three principal sciences are physics, chemistry, and biology. Physics is the study of the properties of matter and energy. Chemistry is the study of the composition and interactions of substances. Biology is the study of living things and what characterizes life.
Subject 3: Economics
Economics is a collection of attempts to understand humanity’s evolving systems of production and distribution. The mainstream focus is on the mechanism whereby scarce resources are allocated to provide goods and services, assuming (usually) that every producer maximizes profit and every consumer optimizes satisfaction.
Whether an economic system is based on capitalism, socialism, or feudalism, economics is founded on the one truism that there is just not enough to go around. And, short of utopia, there never will be — perhaps this in part motivated Thomas Carlyle to dub economics the dismal science.
We are told that we now live in the knowledge economy — in fact we always have. The cavemen had access to the same raw materials as we do but they lacked our technological and organizational knowledge. Indeed, it is arguably the effective application of knowledge, rather than simply access to natural resources, that determines a populations standard of living.
Economics has been described as the physics of the social sciences, but it is not an experimentally verified (falsifiable) discipline like physics, nor does it have the predictive power of physics. However, most politicians and business leaders see the world in terms of orthodox (neoclassical) economic doctrine, and this is reason enough for it to be an important field of study.
Subject 4: Accountancy
Accountancy is the practise of accounting which is based on the twin principles of the accounting equation (assets = liabilities + owners’ equity) and double-entry bookkeeping. Accounting entails the time value of money which leads to the discounted cash flow methods of investment appraisal: nett present value and internal rate of return (breakeven) analysis.
The two principles are usually augmented by six policies. (i) The firm is assumed to be a going concern. (ii) Accruals are recognized on their due-date, and revenues are matched with the expenses incurred in earning them. (iii) Period-to-period consistency is maintained to facilitate comparison over time. (iv) Prudence is exercised by not anticipating profits and by making provision for anticipated losses. (v) Objectivity prevails, as exemplified by the historic cost basis for the valuation or depreciation of assets. (vi) Materiality — non-triviality — is the criterion of inclusion.
Accountancy extends to the auditing of accounts and controls. The fundamental control question is not what decisions are (or were) made but who makes them, and through what process, and under what incentives and constraints. And what feedback mechanism exists to correct decisions if they prove to be wrong — when decision makers are insulated from the forces of feedback, the consequences are often counterproductive and occasionally catastrophic.
Subject 5: Philosophy
Philosophy is the history of ideas and an ongoing inquiry into the nature of things based on abstract reasoning rather than empirical methods. Did the creator create herself? If the barber of Seville shaves all the men of Seville who do not shave themselves, then who shaves the barber? How will we know when the war on terror has been won, and by whom?
What everyone knows is often wrong, and always far from complete. Once, everyone knew that the Earth is at the centre of the Universe, and probably flat. Contrariwise, any nascent idea is always held by a minority of one. So, if we filtered all new ideas by consensus, progress would come to a halt — where all think alike, no one thinks very much.
Philosophy involves examining basic concepts such as truth, existence, reality, causality, and freedom. Philosophy comprises logic, aesthetics, ethics, metaphysics, ontology, and epistemology. And science, which was formerly labelled natural philosophy, but it is now studied separately.
Logic is the system of formal reasoning which deals with those truths that are independent of any particular subject matter. Aesthetics is the study of emotional involvement in regard to the attractiveness of objects. Ethics is the study of the moral consequences of human actions.
Metaphysics is the study of the nature of reality. Ontology is the study of what actually is. Epistemology is the study of how we know what we know about external objects, abstract objects, and minds other than our own.
Subject 6: Psychology
Psychology is the study of the human mind. The objective is to find out why people feel, think and act the way they do. This helps us to understand the self and how we relate to others.
How does the foetal brain give rise to the adult mind? What drives us to seek friends and sexual partners? Why do so many people become depressed and behave in (apparently or actually) self-destructive ways? What causes prejudice, and why is it so widespread? Does language and culture limit the way we think? Does autonomy, mastery and purpose incentivize us more than money?
Psychological phenomena include emotion and motivation, sensation and perception, learning and memory, thinking and language, personality and intelligence. Classic dichotomies include mind and body, love and hate, altruism and selfishness, joy and misery, sleep and wakefulness, remembering and forgetting, mania and depression, obedience and defiance, honesty and deception.
The central methods are, on the one hand, introspection and empathic conversation, and on the other hand, the observation of behaviour and physiological response. The central tension is between innate and learnt capacity. The central yet elusive concept is consciousness.
Stephen Cumbers
London 2014
