Douglas Adams on Technology, Zoology and the Future

Biomimetics Technology imitates nature

ISSUES IN TECHNOLOGY(3 N.O.T)2

The Social System Imposes Some Restrictions on Openness in Technology

For the most part, the professional values of engineering are very similar to those of science, including the advantages seen in the open sharing of knowledge. Because of the economic value of technology, however, there are often constraints on the openness of science and engineering that are relevant to technological innovation. A large investment of time and money and considerable commercial risk are often required to develop a new technology and bring it to market. That investment might well be jeopardized if competitors had access to the new technology without making a similar investment, and hence companies are often reluctant to share technological knowledge. But no scientific or technological knowledge is likely to remain secret for very long. Secrecy most often provides only an advantage in terms of time—a head start, not absolute control of knowledge. Patent laws encourage openness by giving individuals and companies control over the use of any new technology they develop; however, to promote technological competition, such control is only for a limited period of time.

Commercial advantage is not the only motivation for secrecy and control. Much technological development occurs in settings, such as government agencies, in which commercial concerns are minimal but national security concerns may lead to secrecy. Any technology that has potential military applications can arguably be subject to restrictions imposed by the federal government, which may limit the sharing of engineering knowledge—or even the exportation of products from which engineering knowledge could be inferred. Because the connections between science and technology are so close in some fields, secrecy inevitably begins to restrict some of the free flow of information in science as well. Some scientists and engineers are very uncomfortable with what they perceive as a compromise of the scientific ideal, and some refuse to work on projects that impose secrecy. Others, however, view the restrictions as appropriate.

Decisions About the Use of Technology Are Complex

Most technological innovations spread or disappear on the basis of free-market forces—that is, on the basis of how people and companies respond to such innovations. Occasionally, however, the use of some technology becomes an issue subject to public debate and possibly formal regulation. One way in which technology becomes such an issue is when a person, group, or business proposes to test or introduce a new technology—as has been the case with contour plowing, vaccination, genetic engineering, and nuclear power plants. Another way is when a technology already in widespread use is called into question—as, for example, when people are told (by individuals, organizations, or agencies) that it is essential to stop or reduce the use of a particular technology or technological product that has been discovered to have, or that may possibly have, adverse effects. In such instances, the proposed solution may be to ban the burial of toxic wastes in community dumps, or to prohibit the use of leaded gasoline and asbestos insulation.

Rarely are technology-related issues simple and one-sided. Relevant technical facts alone, even when known and available (which often they are not), usually do not settle matters entirely in favor of one side or the other. The chances of reaching good personal or collective decisions about technology depend on having information that neither enthusiasts nor skeptics are always ready to volunteer. The long-term interests of society are best served, therefore, by having processes for ensuring that key questions concerning proposals to curtail or introduce technology are raised and that as much relevant knowledge as possible is brought to bear on them. Considering these questions does not ensure that the best decision will always be made, but the failure to raise key questions will almost certainly result in poor decisions. The key questions concerning any proposed new technology should include the following:

• What are alternative ways to accomplish the same ends? What advantages and disadvantages are there to the alternatives? What trade-offs would be necessary between positive and negative side effects of each?
• Who are the main beneficiaries? Who will receive few or no benefits? Who will suffer as a result of the proposed new technology? How long will the benefits last? Will the technology have other applications? Whom will they benefit?
• What will the proposed new technology cost to build and operate? How does that compare to the cost of alternatives? Will people other than the beneficiaries have to bear the costs? Who should underwrite the development costs of a proposed new technology? How will the costs change over time? What will the social costs be?
• What risks are associated with the proposed new technology? What risks are associated with not using it? Who will be in greatest danger? What risk will the technology present to other species of life and to the environment? In the worst possible case, what trouble could it cause? Who would be held responsible? How could the trouble be undone or limited?
• What people, materials, tools, knowledge, and know-how will be needed to build, install, and operate the proposed new technology? Are they available? If not, how will they be obtained, and from where? What energy sources will be needed for construction or manufacture, and also for operation? What resources will be needed to maintain, update, and repair the new technology?
• What will be done to dispose safely of the new technology's waste materials? As it becomes obsolete or worn out, how will it be replaced? And finally, what will become of the material of which it was made and the people whose jobs depended on it?

Individual citizens may seldom be in a position to ask or demand answers for these questions on a public level, but their knowledge of the relevance and importance of answers increases the attention given to the questions by private enterprise, interest groups, and public officials. Furthermore, individuals may ask the same questions with regard to their own use of technology—for instance, their own use of efficient household appliances, of substances that contribute to pollution, of foods and fabrics. The cumulative effect of individual decisions can have as great an impact on the large-scale use of technology as pressure on public decisions can.

Not all such questions can be answered readily. Most technological decisions have to be made on the basis of incomplete information, and political factors are likely to have as much influence as technical ones, and sometimes more. But scientists, mathematicians, and engineers have a special role in looking as far ahead and as far afield as is practical to estimate benefits, side effects, and risks. They can also assist by designing adequate detection devices and monitoring techniques, and by setting up procedures for the collection and statistical analysis of relevant data

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ISSUES IN TECHNOLOGY

The Human Presence

The earth's population has already doubled three times during the past century. Even at that, the human presence, which is evident almost everywhere on the earth, has had a greater impact than sheer numbers alone would indicate. We have developed the capacity to dominate most plant and animal species—far more than any other species can—and the ability to shape the future rather than merely respond to it.

Use of that capacity has both advantages and disadvantages. On the one hand, developments in technology have brought enormous benefits to almost all people. Most people today have access to goods and services that were once luxuries enjoyed only by the wealthy—in transportation, communication, nutrition, sanitation, health care, entertainment, and so on. On the other hand, the very behavior that made it possible for the human species to prosper so rapidly has put us and the earth's other living organisms at new kinds of risk. The growth of agricultural technology has made possible a very large population but has put enormous strain on the soil and water systems that are needed to continue sufficient production. Our antibiotics cure bacterial infection, but may continue to work only if we invent new ones faster than resistant bacterial strains emerge.

Our access to and use of vast stores of fossil fuels have made us dependent on a nonrenewable resource. In our present numbers, we will not be able to sustain our way of living on the energy that current technology provides, and alternative technologies may be inadequate or may present unacceptable hazards. Our vast mining and manufacturing efforts produce our goods, but they also dangerously pollute our rivers and oceans, soil, and atmosphere. Already, by-products of industrialization in the atmosphere may be depleting the ozone layer, which screens the planet's surface from harmful ultraviolet rays, and may be creating a buildup of carbon dioxide, which traps heat and could raise the planet's average temperatures significantly. The environmental consequences of a nuclear war, among its other disasters, could alter crucial aspects of all life on earth.

From the standpoint of other species, the human presence has reduced the amount of the earth's surface available to them by clearing large areas of vegetation; has interfered with their food sources; has changed their habitats by changing the temperature and chemical composition of large parts of the world environment; has destabilized their ecosystems by introducing foreign species, deliberately or accidentally; has reduced the number of living species; and in some instances has actually altered the characteristics of certain plants and animals by selective breeding and more recently by genetic engineering.

What the future holds for life on earth, barring some immense natural catastrophe, will be determined largely by the human species. The same intelligence that got us where we are—improving many aspects of human existence and introducing new risks into the world—is also our main resource for survival.

Technological and Social Systems Interact Strongly

Individual inventiveness is essential to technological innovation. Nonetheless, social and economic forces strongly influence what technologies will be undertaken, paid attention to, invested in, and used. Such decisions occur directly as a matter of government policy and indirectly as a consequence of the circumstances and values of a society at any particular time. In the United States, decisions about which technological options will prevail are influenced by many factors, such as consumer acceptance, patent laws, the availability of risk capital, the federal budget process, local and national regulations, media attention, economic competition, tax incentives, and scientific discoveries. The balance of such incentives and regulations usually bears differently on different technological systems, encouraging some and discouraging others.

Technology has strongly influenced the course of history and the nature of human society, and it continues to do so. The great revolutions in agricultural technology, for example, have probably had more influence on how people live than political revolutions; changes in sanitation and preventive medicine have contributed to the population explosion (and to its control); bows and arrows, gunpowder, and nuclear explosives have in their turn changed how war is waged; and the microprocessor is changing how people write, compute, bank, operate businesses, conduct research, and communicate with one another. Technology is largely responsible for such large-scale changes as the increased urbanization of society and the dramatically growing economic interdependence of communities worldwide.

Historically, some social theorists have believed that technological change (such as industrialization and mass production) causes social change, whereas others have believed that social change (such as political or religious changes) leads to technological change. However, it is clear that because of the web of connections between technological and other social systems, many influences act in both directions.

DESIGN AND SYSTEMS(2 N.O.T)2

Technologies Always Have Side Effects

In addition to its intended benefits, every design is likely to have unintended side effects in its production and application. On the one hand, there may be unexpected benefits. For example, working conditions may become safer when materials are molded rather than stamped, and materials designed for space satellites may prove useful in consumer products. On the other hand, substances or processes involved in production may harm production workers or the public in general; for example, sitting in front of a computer may strain the user's eyes and lead to isolation from other workers. And jobs may be affected—by increasing employment for people involved in the new technology, decreasing employment for others involved in the old technology, and changing the nature of the work people must do in their jobs.

It is not only large technologies—nuclear reactors or agriculture—that are prone to side effects, but also the small, everyday ones. The effects of ordinary technologies may be individually small but collectively significant. Refrigerators, for example, have had a predictably favorable impact on diet and on food distribution systems. Because there are so many refrigerators, however, the tiny leakage of a gas used in their cooling systems may have substantial adverse effects on the earth's atmosphere.

Some side effects are unexpected because of a lack of interest or resources to predict them. But many are not predictable even in principle because of the sheer complexity of technological systems and the inventiveness of people in finding new applications. Some unexpected side effects may turn out to be ethically, aesthetically, or economically unacceptable to a substantial fraction of the population, resulting in conflict between groups in the community. To minimize such side effects, planners are turning to systematic risk analysis. For example, many communities require by law that environmental impact studies be made before they will consider giving approval for the introduction of a new hospital, factory, highway, waste-disposal system, shopping mall, or other structure.

Risk analysis, however, can be complicated. Because the risk associated with a particular course of action can never be reduced to zero, acceptability may have to be determined by comparison to the risks of alternative courses of action, or to other, more familiar risks. People's psychological reactions to risk do not necessarily match straightforward mathematical models of benefits and costs. People tend to perceive a risk as higher if they have no control over it (smog versus smoking) or if the bad events tend to come in dreadful peaks (many deaths at once in an airplane crash versus only a few at a time in car crashes). Personal interpretation of risks can be strongly influenced by how the risk is stated—for example, comparing the probability of dying versus the probability of surviving, the dreaded risks versus the readily acceptable risks, the total costs versus the costs per person per day, or the actual number of people affected versus the proportion of affected people.

All Technological Systems Can Fail

Most modern technological systems, from transistor radios to airliners, have been engineered and produced to be remarkably reliable. Failure is rare enough to be surprising. Yet the larger and more complex a system is, the more ways there are in which it can go wrong—and the more widespread the possible effects of failure. A system or device may fail for different reasons: because some part fails, because some part is not well matched to some other, or because the design of the system is not adequate for all the conditions under which it is used. One hedge against failure is overdesign—that is, for example, making something stronger or bigger than is likely to be necessary. Another hedge is redundancy—that is, building in one backup system or more to take over in case the primary one fails.

If failure of a system would have very costly consequences, the system may be designed so that its most likely way of failing would do the least harm. Examples of such "fail-safe" designs are bombs that cannot explode when the fuse malfunctions; automobile windows that shatter into blunt, connected chunks rather than into sharp, flying fragments; and a legal system in which uncertainty leads to acquittal rather than conviction. Other means of reducing the likelihood of failure include improving the design by collecting more data, accommodating more variables, building more realistic working models, running computer simulations of the design longer, imposing tighter quality control, and building in controls to sense and correct problems as they develop.

All of the means of preventing or minimizing failure are likely to increase cost. But no matter what precautions are taken or resources invested, risk of technological failure can never be reduced to zero. Analysis of risk, therefore, involves estimating a probability of occurrence for every undesirable outcome that can be foreseen—and also estimating a measure of the harm that would be done if it did occur. The expected importance of each risk is then estimated by combining its probability and its measure of harm. The relative risk of different designs can then be compared in terms of the combined probable harm resulting from each.

DESIGN AND SYSTEMS(2 N.O.T)1

DESIGN AND SYSTEMS

The Essence of Engineering Is Design Under Constraint

Every engineering design operates within constraints that must be identified and taken into account. One type of constraint is absolute—for example, physical laws such as the conservation of energy or physical properties such as limits of flexibility, electrical conductivity, and friction. Other types have some flexibility: economic (only so much money is available for this purpose), political (local, state, and national regulations), social (public opposition), ecological (likely disruption of the natural environment), and ethical (disadvantages to some people, risk to subsequent generations). An optimum design takes into account all the constraints and strikes some reasonable compromise among them. Reaching such design compromises—including, sometimes, the decision not to develop a particular technology further—requires taking personal and social values into account. Although design may sometimes require only routine decisions about the combining of familiar components, often it involves great creativity in inventing new approaches to problems, new components, and new combinations—and great innovation in seeing new problems or new possibilities.

But there is no perfect design. Accommodating one constraint well can often lead to conflict with others. For example, the lightest material may not be the strongest, or the most efficient shape may not be the safest or the most aesthetically pleasing. Therefore every design problem lends itself to many alternative solutions, depending on what values people place on the various constraints. For example, is strength more desirable than lightness, and is appearance more important than safety? The task is to arrive at a design that reasonably balances the many trade-offs, with the understanding that no single design is ever simultaneously the safest, the most reliable, the most efficient, the most inexpensive, and so on.

It is seldom practical to design an isolated object or process without considering the broad context in which it will be used. Most products of technology have to be operated, maintained, occasionally repaired, and ultimately replaced. Because all these related activities bear costs, they too have to be considered. A similar issue that is becoming increasingly important with more complex technologies is the need to train personnel to sell, operate, maintain, and repair them. Particularly when technology changes quickly, training can be a major cost. Thus, keeping down demands on personnel may be another design constraint.

Designs almost always require testing, especially when the design is unusual or complicated, when the final product or process is likely to be expensive or dangerous, or when failure has a very high cost. Performance tests of a design may be conducted by using complete products, but doing so may be prohibitively difficult or expensive. So testing is often done by using small-scale physical models, computer simulations, analysis of analogous systems (for example, laboratory animals standing in for humans, earthquake disasters for nuclear disasters), or testing of separate components only.

All Technologies Involve Control

All systems, from the simplest to the most complex, require control to keep them operating properly. The essence of control is comparing information about what is happening with what we want to happen and then making appropriate adjustments. Control typically requires feedback (from sensors or other sources of information) and logical comparisons of that information to instructions (and perhaps to other data input)—and a means for activating changes. For example, a baking oven is a fairly simple system that compares the information from a temperature sensor to a control setting and turns the heating element up or down to keep the temperature within a small range. An automobile is a more complex system, made up of subsystems for controlling engine temperature, combustion rate, direction, speed, and so forth, and for changing them when the immediate circumstances or instructions change. Miniaturized electronics makes possible logical control in a great variety of technical systems. Almost all but the simplest household appliances used today include microprocessors to control their performance.

As controls increase in complexity, they too require coordination, which means additional layers of control. Improvement in rapid communication and rapid processing of information makes possible very elaborate systems of control. Yet all technological systems include human as well as mechanical or electronic components. Even the most automatic system requires human control at some point—to program the built-in control elements, monitor them, take over from them when they malfunction, and change them when the purposes of the system change. The ultimate control lies with people who understand in some depth what the purpose and nature of the control process are and the context within which the process operates.

TECHNOLOGY AND SCIENCE(1 N.O.T)

TECHNOLOGY AND SCIENCE

! Technology Draws on Science and Contributes to It

In earlier times, technology grew out of personal experience with the properties of things and with the techniques for manipulating them, out of know-how handed down from experts to apprentices over many generations. The know-how handed down today is not only the craft of single practitioners but also a vast literature of words, numbers, and pictures that describe and give directions. But just as important as accumulated practical knowledge is the contribution to technology that comes from understanding the principles that underlie how things behave—that is, from scientific understanding.
Engineering, the systematic application of scientific knowledge in developing and applying technology, has grown from a craft to become a science in itself. Scientific knowledge provides a means of estimating what the behavior of things will be even before we make them or observe them. Moreover, science often suggests new kinds of behavior that had not even been imagined before, and so leads to new technologies. Engineers use knowledge of science and technology, together with strategies of design, to solve practical problems.
In return, technology provides the eyes and ears of science—and some of the muscle, too. The electronic computer, for example, has led to substantial progress in the study of weather systems, demographic patterns, gene structure, and other complex systems that would not have been possible otherwise. Technology is essential to science for purposes of measurement, data collection, treatment of samples, computation, transportation to research sites (such as Antarctica, the moon, and the ocean floor), sample collection, protection from hazardous materials, and communication. More and more, new instruments and techniques are being developed through technology that make it possible to advance various lines of scientific research.
Technology does not just provide tools for science, however; it also may provide motivation and direction for theory and research. The theory of the conservation of energy, for example, was developed in large part because of the technological problem of increasing the efficiency of commercial steam engines. The mapping of the locations of the entire set of genes in human DNA has been motivated by the technology of genetic engineering, which both makes such mapping possible and provides a reason for doing so.
As technologies become more sophisticated, their links to science become stronger. In some fields, such as solid-state physics (which involves transistors and superconductors), the ability to make something and the ability to study it are so interdependent that science and engineering can scarcely be separated. New technology often requires new understanding; new investigations often require new technology.

! Engineering Combines Scientific Inquiry and Practical Values

The component of technology most closely allied to scientific inquiry and to mathematical modeling is engineering. In its broadest sense, engineering consists of construing a problem and designing a solution for it. The basic method is to first devise a general approach and then work out the technical details of the construction of requisite objects (such as an automobile engine, a computer chip, or a mechanical toy) or processes (such as irrigation, opinion polling, or product testing).
Much of what has been said about the nature of science applies to engineering as well, particularly the use of mathematics, the interplay of creativity and logic, the eagerness to be original, the variety of people involved, the professional specialties, public responsibility, and so on. Indeed, there are more people called engineers than people called scientists, and many scientists are doing work that could be described as engineering as well as science. Similarly, many engineers are engaged in science.
Scientists see patterns in phenomena as making the world understandable; engineers also see them as making the world manipulable. Scientists seek to show that theories fit the data; mathematicians seek to show logical proof of abstract connections; engineers seek to demonstrate that designs work. Scientists cannot provide answers to all questions; mathematicians cannot prove all possible connections; engineers cannot design solutions for all problems.
But engineering affects the social system and culture more directly than scientific research, with immediate implications for the success or failure of human enterprises and for personal benefit and harm. Engineering decisions, whether in designing an airplane bolt or an irrigation system, inevitably involve social and personal values as well as scientific judgments.

THE NATURE OF TECHNOLOGY

Chapter 3: THE NATURE OF TECHNOLOGY

As long as there have been people, there has been technology. Indeed, the techniques of shaping tools are taken as the chief evidence of the beginning of human culture. On the whole, technology has been a powerful force in the development of civilization, all the more so as its link with science has been forged. Technology—like language, ritual, values, commerce, and the arts—is an intrinsic part of a cultural system and it both shapes and reflects the system's values. In today's world, technology is a complex social enterprise that includes not only research, design, and crafts but also finance, manufacturing, management, labor, marketing, and maintenance.
In the broadest sense, technology extends our abilities to change the world: to cut, shape, or put together materials; to move things from one place to another; to reach farther with our hands, voices, and senses. We use technology to try to change the world to suit us better. The changes may relate to survival needs such as food, shelter, or defense, or they may relate to human aspirations such as knowledge, art, or control. But the results of changing the world are often complicated and unpredictable. They can include unexpected benefits, unexpected costs, and unexpected risks—any of which may fall on different social groups at different times. Anticipating the effects of technology is therefore as important as advancing its capabilities.

This chapter presents recommendations on what knowledge about the nature of technology is required for scientific literacy and emphasizes ways of thinking about technology that can contribute to using it wisely. The ideas are sorted into three sections: the connection of science and technology, the principles of technology itself, and the connection of technology and society. Chapter 8, The Designed World, presents principles relevant to some of the key technologies of today's world. Chapter 10, Historical Perspectives, includes a discussion of the Industrial Revolution. Chapter 12, Habits of Mind, includes some skills relevant to participating in a technological world.

MATHEMATICAL INQUIRY(3 N.O.S)

MATHEMATICAL INQUIRY

Using mathematics to express ideas or to solve problems involves at least three phases: (1) representing some aspects of things abstractly, (2) manipulating the abstractions by rules of logic to find new relationships between them, and (3) seeing whether the new relationships say something useful about the original things.

 ! Abstraction and Symbolic Representation

Mathematical thinking often begins with the process of abstraction—that is, noticing a similarity between two or more objects or events. Aspects that they have in common, whether concrete or hypothetical, can be represented by symbols such as numbers, letters, other marks, diagrams, geometrical constructions, or even words. Whole numbers are abstractions that represent the size of sets of things and events or the order of things within a set. The circle as a concept is an abstraction derived from human faces, flowers, wheels, or spreading ripples; the letter A may be an abstraction for the surface area of objects of any shape, for the acceleration of all moving objects, or for all objects having some specified property; the symbol + represents a process of addition, whether one is adding apples or oranges, hours, or miles per hour. And abstractions are made not only from concrete objects or processes; they can also be made from other abstractions, such as kinds of numbers (the even numbers, for instance).

Such abstraction enables mathematicians to concentrate on some features of things and relieves them of the need to keep other features continually in mind. As far as mathematics is concerned, it does not matter whether a triangle represents the surface area of a sail or the convergence of two lines of sight on a star; mathematicians can work with either concept in the same way. The resulting economy of effort is very useful—provided that in making an abstraction, care is taken not to ignore features that play a significant role in determining the outcome of the events being studied.

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Manipulating Mathematical Statements

After abstractions have been made and symbolic representations of them have been selected, those symbols can be combined and recombined in various ways according to precisely defined rules. Sometimes that is done with a fixed goal in mind; at other times it is done in the context of experiment or play to see what happens. Sometimes an appropriate manipulation can be identified easily from the intuitive meaning of the constituent words and symbols; at other times a useful series of manipulations has to be worked out by trial and error.

Typically, strings of symbols are combined into statements that express ideas or propositions. For example, the symbol A for the area of any square may be used with the symbol s for the length of the square's side to form the proposition A = s². This equation specifies how the area is related to the side—and also implies that it depends on nothing else. The rules of ordinary algebra can then be used to discover that if the length of the sides of a square is doubled, the square's area becomes four times as great. More generally, this knowledge makes it possible to find out what happens to the area of a square no matter how the length of its sides is changed, and conversely, how any change in the area affects the sides.

Mathematical insights into abstract relationships have grown over thousands of years, and they are still being extended—and sometimes revised. Although they began in the concrete experience of counting and measuring, they have come through many layers of abstraction and now depend much more on internal logic than on mechanical demonstration. In a sense, then, the manipulation of abstractions is much like a game: Start with some basic rules, then make any moves that fit those rules—which includes inventing additional rules and finding new connections between old rules. The test for the validity of new ideas is whether they are consistent and whether they relate logically to the other rules.

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Mathematical processes can lead to a kind of model of a thing, from which insights can be gained about the thing itself. Any mathematical relationships arrived at by manipulating abstract statements may or may not convey something truthful about the thing being modeled. For example, if 2 cups of water are added to 3 cups of water and the abstract mathematical operation 2+3 = 5 is used to calculate the total, the correct answer is 5 cups of water. However, if 2 cups of sugar are added to 3 cups of hot tea and the same operation is used, 5 is an incorrect answer, for such an addition actually results in only slightly more than 4 cups of very sweet tea. The simple addition of volumes is appropriate to the first situation but not to the second—something that could have been predicted only by knowing something of the physical differences in the two situations. To be able to use and interpret mathematics well, therefore, it is necessary to be concerned with more than the mathematical validity of abstract operations and to also take into account how well they correspond to the properties of the things represented.

Sometimes common sense is enough to enable one to decide whether the results of the mathematics are appropriate. For example, to estimate the height 20 years from now of a girl who is 5' 5" tall and growing at the rate of an inch per year, common sense suggests rejecting the simple "rate times time" answer of 7' 1" as highly unlikely, and turning instead to some other mathematical model, such as curves that approach limiting values. Sometimes, however, it may be difficult to know just how appropriate mathematical results are—for example, when trying to predict stock-market prices or earthquakes.

Often a single round of mathematical reasoning does not produce satisfactory conclusions, and changes are tried in how the representation is made or in the operations themselves. Indeed, jumps are commonly made back and forth between steps, and there are no rules that determine how to proceed. The process typically proceeds in fits and starts, with many wrong turns and dead ends. This process continues until the results are good enough.

But what degree of accuracy is good enough? The answer depends on how the result will be used, on the consequences of error, and on the likely cost of modeling and computing a more accurate answer. For example, an error of 1 percent in calculating the amount of sugar in a cake recipe could be unimportant, whereas a similar degree of error in computing the trajectory for a space probe could be disastrous. The importance of the "good enough" question has led, however, to the development of mathematical processes for estimating how far off results might be and how much computation would be required to obtain the desired degree of accuracy.

MATHEMATICS, SCIENCE, AND TECHNOLOGY(2 N.O.M)

MATHEMATICS, SCIENCE, AND TECHNOLOGY

Because of its abstractness, mathematics is universal in a sense that other fields of human thought are not. It finds useful applications in business, industry, music, historical scholarship, politics, sports, medicine, agriculture, engineering, and the social and natural sciences. The relationship between mathematics and the other fields of basic and applied science is especially strong. This is so for several reasons, including the following:

• The alliance between science and mathematics has a long history, dating back many centuries. Science provides mathematics with interesting problems to investigate, and mathematics provides science with powerful tools to use in analyzing data. Often, abstract patterns that have been studied for their own sake by mathematicians have turned out much later to be very useful in science. Science and mathematics are both trying to discover general patterns and relationships, and in this sense they are part of the same endeavor.

• Mathematics is the chief language of science. The symbolic language of mathematics has turned out to be extremely valuable for expressing scientific ideas unambiguously. The statement that a=F/m is not simply a shorthand way of saying that the acceleration of an object depends on the force applied to it and its mass; rather, it is a precise statement of the quantitative relationship among those variables. More important, mathematics provides the grammar of science—the rules for analyzing scientific ideas and data rigorously.

• Mathematics and science have many features in common. These include a belief in understandable order; an interplay of imagination and rigorous logic; ideals of honesty and openness; the critical importance of peer criticism; the value placed on being the first to make a key discovery; being international in scope; and even, with the development of powerful electronic computers, being able to use technology to open up new fields of investigation.

• Mathematics and technology have also developed a fruitful relationship with each other. The mathematics of connections and logical chains, for example, has contributed greatly to the design of computer hardware and programming techniques. Mathematics also contributes more generally to engineering, as in describing complex systems whose behavior can then be simulated by computer. In those simulations, design features and operating conditions can be varied as a means of finding optimum designs. For its part, computer technology has opened up whole new areas in mathematics, even in the very nature of proof, and it also continues to help solve previously daunting problems.

PATTERNS AND RELATIONSHIPS(1 N.O.M)1

PATTERNS AND RELATIONSHIPS

Mathematics is the science of patterns and relationships. As a theoretical discipline, mathematics explores the possible relationships among abstractions without concern for whether those abstractions have counterparts in the real world. The abstractions can be anything from strings of numbers to geometric figures to sets of equations. In addressing, say, "Does the interval between prime numbers form a pattern?" as a theoretical question, mathematicians are interested only in finding a pattern or proving that there is none, but not in what use such knowledge might have. In deriving, for instance, an expression for the change in the surface area of any regular solid as its volume approaches zero, mathematicians have no interest in any correspondence between geometric solids and physical objects in the real world.

A central line of investigation in theoretical mathematics is identifying in each field of study a small set of basic ideas and rules from which all other interesting ideas and rules in that field can be logically deduced. Mathematicians, like other scientists, are particularly pleased when previously unrelated parts of mathematics are found to be derivable from one another, or from some more general theory. Part of the sense of beauty that many people have perceived in mathematics lies not in finding the greatest elaborateness or complexity but on the contrary, in finding the greatest economy and simplicity of representation and proof. As mathematics has progressed, more and more relationships have been found between parts of it that have been developed separately—for example, between the symbolic representations of algebra and the spatial representations of geometry. These cross-connections enable insights to be developed into the various parts; together, they strengthen belief in the correctness and underlying unity of the whole structure.

Mathematics is also an applied science. Many mathematicians focus their attention on solving problems that originate in the world of experience. They too search for patterns and relationships, and in the process they use techniques that are similar to those used in doing purely theoretical mathematics. The difference is largely one of intent. In contrast to theoretical mathematicians, applied mathematicians, in the examples given above, might study the interval pattern of prime numbers to develop a new system for coding numerical information, rather than as an abstract problem. Or they might tackle the area/volume problem as a step in producing a model for the study of crystal behavior.

The results of theoretical and applied mathematics often influence each other. The discoveries of theoretical mathematicians frequently turn out—sometimes decades later—to have unanticipated practical value. Studies on the mathematical properties of random events, for example, led to knowledge that later made it possible to improve the design of experiments in the social and natural sciences. Conversely, in trying to solve the problem of billing long-distance telephone users fairly, mathematicians made fundamental discoveries about the mathematics of complex networks. Theoretical mathematics, unlike the other sciences, is not constrained by the real world, but in the long run it contributes to a better understanding of that world.

THE NATURE OF MATHEMATICS

Chapter 2: THE NATURE OF MATHEMATICS

Mathematics relies on both logic and creativity, and it is pursued both for a variety of practical purposes and for its intrinsic interest. For some people, and not only professional mathematicians, the essence of mathematics lies in its beauty and its intellectual challenge. For others, including many scientists and engineers, the chief value of mathematics is how it applies to their own work. Because mathematics plays such a central role in modern culture, some basic understanding of the nature of mathematics is requisite for scientific literacy. To achieve this, students need to perceive mathematics as part of the scientific endeavor, comprehend the nature of mathematical thinking, and become familiar with key mathematical ideas and skills.

This chapter focuses on mathematics as part of the scientific endeavor and then on mathematics as a process, or way of thinking. Recommendations related to mathematical ideas are presented in Chapter 9, The Mathematical World, and those on mathematical skills are included in Chapter 12, Habits of Mind.

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! Science Is Organized Into Content Disciplines and Is Conducted in Various Institutions

Organizationally, science can be thought of as the collection of all of the different scientific fields, or content disciplines. From anthropology through zoology, there are dozens of such disciplines. They differ from one another in many ways, including history, phenomena studied, techniques and language used, and kinds of outcomes desired. With respect to purpose and philosophy, however, all are equally scientific and together make up the same scientific endeavor. The advantage of having disciplines is that they provide a conceptual structure for organizing research and research findings. The disadvantage is that their divisions do not necessarily match the way the world works, and they can make communication difficult. In any case, scientific disciplines do not have fixed borders. Physics shades into chemistry, astronomy, and geology, as does chemistry into biology and psychology, and so on. New scientific disciplines (astrophysics and sociobiology, for instance) are continually being formed at the boundaries of others. Some disciplines grow and break into subdisciplines, which then become disciplines in their own right.

Universities, industry, and government are also part of the structure of the scientific endeavor. University research usually emphasizes knowledge for its own sake, although much of it is also directed toward practical problems. Universities, of course, are also particularly committed to educating successive generations of scientists, mathematicians, and engineers. Industries and businesses usually emphasize research directed to practical ends, but many also sponsor research that has no immediately obvious applications, partly on the premise that it will be applied fruitfully in the long run. The federal government funds much of the research in universities and in industry but also supports and conducts research in its many national laboratories and research centers. Private foundations, public-interest groups, and state governments also support research.

Funding agencies influence the direction of science by virtue of the decisions they make on which research to support. Other deliberate controls on science result from federal (and sometimes local) government regulations on research practices that are deemed to be dangerous and on the treatment of the human and animal subjects used in experiments.

! There Are Generally Accepted Ethical Principles in the Conduct of Science

Most scientists conduct themselves according to the ethical norms of science. The strongly held traditions of accurate recordkeeping, openness, and replication, buttressed by the critical review of one's work by peers, serve to keep the vast majority of scientists well within the bounds of ethical professional behavior. Sometimes, however, the pressure to get credit for being the first to publish an idea or observation leads some scientists to withhold information or even to falsify their findings. Such a violation of the very nature of science impedes science. When discovered, it is strongly condemned by the scientific community and the agencies that fund research.

Another domain of scientific ethics relates to possible harm that could result from scientific experiments. One aspect is the treatment of live experimental subjects. Modern scientific ethics require that due regard must be given to the health, comfort, and well-being of animal subjects. Moreover, research involving human subjects may be conducted only with the informed consent of the subjects, even if this constraint limits some kinds of potentially important research or influences the results. Informed consent entails full disclosure of the risks and intended benefits of the research and the right to refuse to participate. In addition, scientists must not knowingly subject coworkers, students, the neighborhood, or the community to health or property risks without their knowledge and consent.

The ethics of science also relates to the possible harmful effects of applying the results of research. The long-term effects of science may be unpredictable, but some idea of what applications are expected from scientific work can be ascertained by knowing who is interested in funding it. If, for example, the Department of Defense offers contracts for working on a line of theoretical mathematics, mathematicians may infer that it has application to new military technology and therefore would likely be subject to secrecy measures. Military or industrial secrecy is acceptable to some scientists but not to others. Whether a scientist chooses to work on research of great potential risk to humanity, such as nuclear weapons or germ warfare, is considered by many scientists to be a matter of personal ethics, not one of professional ethics.

! Scientists Participate in Public Affairs Both as Specialists and as Citizens

Scientists can bring information, insights, and analytical skills to bear on matters of public concern. Often they can help the public and its representatives to understand the likely causes of events (such as natural and technological disasters) and to estimate the possible effects of projected policies (such as ecological effects of various farming methods). Often they can testify to what is not possible. In playing this advisory role, scientists are expected to be especially careful in trying to distinguish fact from interpretation, and research findings from speculation and opinion; that is, they are expected to make full use of the principles of scientific inquiry.

Even so, scientists can seldom bring definitive answers to matters of public debate. Some issues are too complex to fit within the current scope of science, or there may be little reliable information available, or the values involved may lie outside of science. Moreover, although there may be at any one time a broad consensus on the bulk of scientific knowledge, the agreement does not extend to all scientific issues, let alone to all science-related social issues. And of course, on issues outside of their expertise, the opinions of scientists should enjoy no special credibility.

In their work, scientists go to great lengths to avoid bias—their own as well as that of others. But in matters of public interest, scientists, like other people, can be expected to be biased where their own personal, corporate, institutional, or community interests are at stake. For example, because of their commitment to science, many scientists may understandably be less than objective in their beliefs on how science is to be funded in comparison to other social needs

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THE SCIENTIFIC ENTERPRISE

Science as an enterprise has individual, social, and institutional dimensions. Scientific activity is one of the main features of the contemporary world and, perhaps more than any other, distinguishes our times from earlier centuries.

Science Is a Complex Social Activity

Scientific work involves many individuals doing many different kinds of work and goes on to some degree in all nations of the world. Men and women of all ethnic and national backgrounds participate in science and its applications. These people—scientists and engineers, mathematicians, physicians, technicians, computer programmers, librarians, and others—may focus on scientific knowledge either for its own sake or for a particular practical purpose, and they may be concerned with data gathering, theory building, instrument building, or communicating.

As a social activity, science inevitably reflects social values and viewpoints. The history of economic theory, for example, has paralleled the development of ideas of social justice—at one time, economists considered the optimum wage for workers to be no more than what would just barely allow the workers to survive. Before the twentieth century, and well into it, women and people of color were essentially excluded from most of science by restrictions on their education and employment opportunities; the remarkable few who overcame those obstacles were even then likely to have their work belittled by the science establishment.

The direction of scientific research is affected by informal influences within the culture of science itself, such as prevailing opinion on what questions are most interesting or what methods of investigation are most likely to be fruitful. Elaborate processes involving scientists themselves have been developed to decide which research proposals receive funding, and committees of scientists regularly review progress in various disciplines to recommend general priorities for funding.

Science goes on in many different settings. Scientists are employed by universities, hospitals, business and industry, government, independent research organizations, and scientific associations. They may work alone, in small groups, or as members of large research teams. Their places of work include classrooms, offices, laboratories, and natural field settings from space to the bottom of the sea.

Because of the social nature of science, the dissemination of scientific information is crucial to its progress. Some scientists present their findings and theories in papers that are delivered at meetings or published in scientific journals. Those papers enable scientists to inform others about their work, to expose their ideas to criticism by other scientists, and, of course, to stay abreast of scientific developments around the world. The advancement of information science (knowledge of the nature of information and its manipulation) and the development of information technologies (especially computer systems) affect all sciences. Those technologies speed up data collection, compilation, and analysis; make new kinds of analysis practical; and shorten the time between discovery and application.

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Science Explains and Predicts

Scientists strive to make sense of observations of phenomena by constructing explanations for them that use, or are consistent with, currently accepted scientific principles. Such explanations—theories—may be either sweeping or restricted, but they must be logically sound and incorporate a significant body of scientifically valid observations. The credibility of scientific theories often comes from their ability to show relationships among phenomena that previously seemed unrelated. The theory of moving continents, for example, has grown in credibility as it has shown relationships among such diverse phenomena as earthquakes, volcanoes, the match between types of fossils on different continents, the shapes of continents, and the contours of the ocean floors.

The essence of science is validation by observation. But it is not enough for scientific theories to fit only the observations that are already known. Theories should also fit additional observations that were not used in formulating the theories in the first place; that is, theories should have predictive power. Demonstrating the predictive power of a theory does not necessarily require the prediction of events in the future. The predictions may be about evidence from the past that has not yet been found or studied. A theory about the origins of human beings, for example, can be tested by new discoveries of human-like fossil remains. This approach is clearly necessary for reconstructing the events in the history of the earth or of the life forms on it. It is also necessary for the study of processes that usually occur very slowly, such as the building of mountains or the aging of stars. Stars, for example, evolve more slowly than we can usually observe. Theories of the evolution of stars, however, may predict unsuspected relationships between features of starlight that can then be sought in existing collections of data about stars.

Scientists Try to Identify and Avoid Bias

When faced with a claim that something is true, scientists respond by asking what evidence supports it. But scientific evidence can be biased in how the data are interpreted, in the recording or reporting of the data, or even in the choice of what data to consider in the first place. Scientists' nationality, sex, ethnic origin, age, political convictions, and so on may incline them to look for or emphasize one or another kind of evidence or interpretation. For example, for many years the study of primates—by male scientists—focused on the competitive social behavior of males. Not until female scientists entered the field was the importance of female primates' community-building behavior recognized.

Bias attributable to the investigator, the sample, the method, or the instrument may not be completely avoidable in every instance, but scientists want to know the possible sources of bias and how bias is likely to influence evidence. Scientists want, and are expected, to be as alert to possible bias in their own work as in that of other scientists, although such objectivity is not always achieved. One safeguard against undetected bias in an area of study is to have many different investigators or groups of investigators working in it.

Science Is Not Authoritarian

It is appropriate in science, as elsewhere, to turn to knowledgeable sources of information and opinion, usually people who specialize in relevant disciplines. But esteemed authorities have been wrong many times in the history of science. In the long run, no scientist, however famous or highly placed, is empowered to decide for other scientists what is true, for none are believed by other scientists to have special access to the truth. There are no preestablished conclusions that scientists must reach on the basis of their investigations.

In the short run, new ideas that do not mesh well with mainstream ideas may encounter vigorous criticism, and scientists investigating such ideas may have difficulty obtaining support for their research. Indeed, challenges to new ideas are the legitimate business of science in building valid knowledge. Even the most prestigious scientists have occasionally refused to accept new theories despite there being enough accumulated evidence to convince others. In the long run, however, theories are judged by their results: When someone comes up with a new or improved version that explains more phenomena or answers more important questions than the previous version, the new one eventually takes its place.

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SCIENTIFIC INQUIRY

Fundamentally, the various scientific disciplines are alike in their reliance on evidence, the use of hypothesis and theories, the kinds of logic used, and much more. Nevertheless, scientists differ greatly from one another in what phenomena they investigate and in how they go about their work; in the reliance they place on historical data or on experimental findings and on qualitative or quantitative methods; in their recourse to fundamental principles; and in how much they draw on the findings of other sciences. Still, the exchange of techniques, information, and concepts goes on all the time among scientists, and there are common understandings among them about what constitutes an investigation that is scientifically valid.

Scientific inquiry is not easily described apart from the context of particular investigations. There simply is no fixed set of steps that scientists always follow, no one path that leads them unerringly to scientific knowledge. There are, however, certain features of science that give it a distinctive character as a mode of inquiry. Although those features are especially characteristic of the work of professional scientists, everyone can exercise them in thinking scientifically about many matters of interest in everyday life.

! Science Demands Evidence

Sooner or later, the validity of scientific claims is settled by referring to observations of phenomena. Hence, scientists concentrate on getting accurate data. Such evidence is obtained by observations and measurements taken in situations that range from natural settings (such as a forest) to completely contrived ones (such as the laboratory). To make their observations, scientists use their own senses, instruments (such as microscopes) that enhance those senses, and instruments that tap characteristics quite different from what humans can sense (such as magnetic fields). Scientists observe passively (earthquakes, bird migrations), make collections (rocks, shells), and actively probe the world (as by boring into the earth's crust or administering experimental medicines).

In some circumstances, scientists can control conditions deliberately and precisely to obtain their evidence. They may, for example, control the temperature, change the concentration of chemicals, or choose which organisms mate with which others. By varying just one condition at a time, they can hope to identify its exclusive effects on what happens, uncomplicated by changes in other conditions. Often, however, control of conditions may be impractical (as in studying stars), or unethical (as in studying people), or likely to distort the natural phenomena (as in studying wild animals in captivity). In such cases, observations have to be made over a sufficiently wide range of naturally occurring conditions to infer what the influence of various factors might be. Because of this reliance on evidence, great value is placed on the development of better instruments and techniques of observation, and the findings of any one investigator or group are usually checked by others.

Science Is a Blend of Logic and Imagination

Although all sorts of imagination and thought may be used in coming up with hypotheses and theories, sooner or later scientific arguments must conform to the principles of logical reasoning—that is, to testing the validity of arguments by applying certain criteria of inference, demonstration, and common sense. Scientists may often disagree about the value of a particular piece of evidence, or about the appropriateness of particular assumptions that are made—and therefore disagree about what conclusions are justified. But they tend to agree about the principles of logical reasoning that connect evidence and assumptions with conclusions.

Scientists do not work only with data and well-developed theories. Often, they have only tentative hypotheses about the way things may be. Such hypotheses are widely used in science for choosing what data to pay attention to and what additional data to seek, and for guiding the interpretation of data. In fact, the process of formulating and testing hypotheses is one of the core activities of scientists. To be useful, a hypothesis should suggest what evidence would support it and what evidence would refute it. A hypothesis that cannot in principle be put to the test of evidence may be interesting, but it is not likely to be scientifically useful.

The use of logic and the close examination of evidence are necessary but not usually sufficient for the advancement of science. Scientific concepts do not emerge automatically from data or from any amount of analysis alone. Inventing hypotheses or theories to imagine how the world works and then figuring out how they can be put to the test of reality is as creative as writing poetry, composing music, or designing skyscrapers. Sometimes discoveries in science are made unexpectedly, even by accident. But knowledge and creative insight are usually required to recognize the meaning of the unexpected. Aspects of data that have been ignored by one scientist may lead to new discoveries by another.

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! Scientific Ideas Are Subject To Change

Science is a process for producing knowledge. The process depends both on making careful observations of phenomena and on inventing theories for making sense out of those observations. Change in knowledge is inevitable because new observations may challenge prevailing theories. No matter how well one theory explains a set of observations, it is possible that another theory may fit just as well or better, or may fit a still wider range of observations. In science, the testing and improving and occasional discarding of theories, whether new or old, go on all the time. Scientists assume that even if there is no way to secure complete and absolute truth, increasingly accurate approximations can be made to account for the world and how it works.

! Scientific Knowledge Is Durable

Although scientists reject the notion of attaining absolute truth and accept some uncertainty as part of nature, most scientific knowledge is durable. The modification of ideas, rather than their outright rejection, is the norm in science, as powerful constructs tend to survive and grow more precise and to become widely accepted. For example, in formulating the theory of relativity, Albert Einstein did not discard the Newtonian laws of motion but rather showed them to be only an approximation of limited application within a more general concept. (The National Aeronautics and Space Administration uses Newtonian mechanics, for instance, in calculating satellite trajectories.) Moreover, the growing ability of scientists to make accurate predictions about natural phenomena provides convincing evidence that we really are gaining in our understanding of how the world works. Continuity and stability are as characteristic of science as change is, and confidence is as prevalent as tentativeness.

! Science Cannot Provide Complete Answers to All Questions

There are many matters that cannot usefully be examined in a scientific way. There are, for instance, beliefs that—by their very nature—cannot be proved or disproved (such as the existence of supernatural powers and beings, or the true purposes of life). In other cases, a scientific approach that may be valid is likely to be rejected as irrelevant by people who hold to certain beliefs (such as in miracles, fortune-telling, astrology, and superstition). Nor do scientists have the means to settle issues concerning good and evil, although they can sometimes contribute to the discussion of such issues by identifying the likely consequences of particular actions, which may be helpful in weighing alternatives.

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THE SCIENTIFIC WORLD VIEW(2 N.0.S)

Scientists share certain basic beliefs and attitudes about what they do and how they view their work. These have to do with the nature of the world and what can be learned about it.

! The World Is Understandable

Science presumes that the things and events in the universe occur in consistent patterns that are comprehensible through careful, systematic study. Scientists believe that through the use of the intellect, and with the aid of instruments that extend the senses, people can discover patterns in all of nature.

Science also assumes that the universe is, as its name implies, a vast single system in which the basic rules are everywhere the same. Knowledge gained from studying one part of the universe is applicable to other parts. For instance, the same principles of motion and gravitation that explain the motion of falling objects on the surface of the earth also explain the motion of the moon and the planets. With some modifications over the years, the same principles of motion have applied to other forces—and to the motion of everything, from the smallest nuclear particles to the most massive stars, from sailboats to space vehicles, from bullets to light rays.

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Over the course of human history, people have developed many interconnected and validated ideas about the physical, biological, psychological, and social worlds. Those ideas have enabled successive generations to achieve an increasingly comprehensive and reliable understanding of the human species and its environment. The means used to develop these ideas are particular ways of observing, thinking, experimenting, and validating. These ways represent a fundamental aspect of the nature of science and reflect how science tends to differ from other modes of knowing.

It is the union of science, mathematics, and technology that forms the scientific endeavor and that makes it so successful. Although each of these human enterprises has a character and history of its own, each is dependent on and reinforces the others. Accordingly, the first three chapters of recommendations draw portraits of science, mathematics, and technology that emphasize their roles in the scientific endeavor and reveal some of the similarities and connections among them.

This chapter lays out recommendations for what knowledge of the way science works is requisite for scientific literacy. The chapter focuses on three principal subjects: the scientific world view, scientific methods of inquiry, and the nature of the scientific enterprise. Chapters 2 and 3 consider ways in which mathematics and technology differ from science in general. Chapters 4 through 9 present views of the world as depicted by current science; Chapter 10, Historical Perspectives, covers key episodes in the development of science; and Chapter 11, Common Themes, pulls together ideas that cut across all these views of the world.<(T j)>