Category: Experimental Research

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Attempts to define the word “science” offer many variations, none of which may be complete or fully satisfactory. The word “science,” a derivative from the Latin scientia, simply means knowledge. We know that any person with great knowledge is not necessarily a scientist, as we currently use the word. On the other hand, the word “philosophy,” a derivative from Greek, means love of wisdom. When combined with the word “nature” to form “Natural Philosophy,” the phrase seems to refer to the knowledge of nature; it is more specific. Until fairly recently, sci­ence was, indeed, referred to as natural philosophy. The full title of Isaac Newton’s monumental work is Mathematical Principles of Natural Philosophy.

For reasons not easy to trace, the name natural philosophy was dropped for the preferred name, science. The intellectual dis­tance between science and philosophy, for a time, increased, until about the early part of the twentieth century, when some of the best known scientists started philosophizing on such concepts as space, time, matter, and energy. Philosophers, in turn, found a new topic ripe with possibilities: the philosophy of science.

Returning to the phrase “natural philosophy,” the word “natu­ral” simply signifies nature. Thus, science may be understood to indicate curiosity about or knowledge, even love, of nature. If sci­ence is the study and knowledge of nature, we mean nature minus man. Man and nature are thus placed as dipoles, with man at one polarity taking a position from which he can study nature for play, curiosity, admiration, or even exploitation and gain. Nature, on the other hand, “just lies there,” like an animal caged in a zoo, or worse, like a cadaver for a student’s study by dissection.

As if to protest such harsh statements, in nature we have not just the inanimate part, but the animate part as well, and the above statement may be justified only for the inanimate part. The study of the animate part is broadly covered under biology with various specialties. The medical sciences, as a group, are a good example of where the polarity of man and nature gets blurred, since man himself—with life—is the subject of study, combining other sciences, such as physics, chemistry, and biol­ogy. What about technology? Much of the admiration accorded to science is derived from its accomplishments through its deriv­ative, technology. Like a full-grown son beside his aging father, technology stands tall and broad, dependent yet defiant. With this attempt to define science broadly, we may briefly look at some definitions available:

• “Comprehension or understanding of the truths or facts of any subject” (Webster’s Dictionary).
• “The progressive improvement of man’s understanding of Nature” (Encyclopedia Britannica).
• “[T]he study of those judgments concerning which univer­sal agreement can be obtained” (Norman Campbell, What Is Science? (New York, NY, Dover, 1953).
• “[E]ssentially a purposive continuation of . . . what I have called common knowledge, but carried out in a more sys­tematic manner, and to a much higher degree of exactitude and refinement” (E. W. Hobson, The Domain of Natural Science (New York, NY, Dover, 1968).

These being only a few of the many definitions offered for sci­ence, we venture to add one more: Science is the activity directed toward a systematic search for, or confirmation of, the relations between events of nature.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

Apart from the definition(s), it is to be understood that science, per se, is not the theme of this book. There are many books and articles devoted to the definition, delineation, and explanation of what science is, to discussing what its aims and activities should be, and even to philosophizing about what its limitations are. The relevance, however, of science to this book is that science, unlike subjects known as “liberal arts,” is very much associated with experimental research.

In terms of experiments, scientific research may be broadly classified into two categories with a slight overlap: (1) theoretical research and (2) experimental research. Some of the greatest works in physics, for example, quantum mechanics, are the out­come of theoretical research. The work of great theoretical scien­tists not only solve many scientific puzzles but also create new visions through which hitherto unknown relations between events can be predicted, leading to new experiments.

Several raw materials, heaped together or scattered here and there, do not make a house. It is the work of a builder to create a house out of these raw materials. In terms of science, theories are like finished houses, and experimental findings leading to some generalizations are more like house-building materials. Whereas the works of Michael Faraday are experimental, those of James Maxwell are theoretical. Some of the greatest figures in physics have been theoretical scientists: Ludwig Boltzman, Neils Bohr, Werner Heisenberg. Scientist of that caliber, who also happen to be great experimental researchers, are rather few: Isaac Newton, Errico Fermi, Henry and Lawrence Bragg. But a large number of researchers, not only in physics but in other areas of science as well, are experimental researchers.

This is not to belittle the value of experiments. In fact, no the­ory is valid until it passes one or more crucial tests of experi­ments. In engineering and technology also, some works lay claim to being theoretical; however, considering their limited domains, albeit extensive applications, they are more in the nature of gen­eralizations based on empirical data.

As a side issue, is the work of Charles Darwin theoretical or experimental? It is true, Darwin spent time “in the field” collect­ing a lot of new “data” on his well-known expedition to the Galapagos Islands. But his work, embodied in writing, consisted of fitting together the many pieces of the puzzle to form a fin­ished picture, which came to be known as the Theory of Evolu­tion. Experimental? Maybe. Theoretical? Yes.

This far we have looked at science as an activity. Looking at the actors in this drama known as science is even more interest­ing. Leonardo da Vinci is acclaimed as a great scientist; yet, his fame rests on many unfinished works. His dependence on experi­ment and observation rather than preconceived ideas marks him as the precursor of the experimental researcher. Curiosity led him into many fields of inquiry: mechanics, anatomy, optics, astron­omy. Being primarily an artist, possibly he did not depend for his living on scientific activities.

Galileo Galilei’s interest in mechanics and astronomy, Johannes Kepler’s in planets, Gregor Mendel’s in mutation of plant seeds, Ivan Pavlov’s in conditioning dogs: all have something in com­mon, namely curiosity to observe the way these segments of nature operate. These men, quite likely, did not earn their livings by means of their scientific interests either. It is in this sense that Ervin Schrodinger, in his book Science, Theory and Man (1957), equates science with the arts, dance, play—even card games, board games, dominos, and riddles—asserting that these activities are the result of surplus energy, in the same way that a dog in play is eager to catch the ball thrown by his master. “Play, art and science are the spheres of human activity where action and aim are not as a rule determined by the aims imposed by the necessities of life.”

The activity of science has changed considerably since the times of Pavlov or Mendel, even since the times of Schrodinger. He writes, “What is operating here is a surplus force remaining at our disposal beyond the bare struggle for existence; art and sci­ence are thus luxuries like sport and play, a view more acceptable to the beliefs of former centuries than to the present age.” In the present age, the activity of science is no more a luxury; it has become a need, though more collectively than individually. An individual, even in a scientifically advanced country, may not be cognizant of the results of science in his or her daily life; nonethe­less, his way of life, even relative to bare necessities, is vastly dif­ferent from that of humans even 200 years ago. The difference, more than anything else, is attributable to the fruits borne by sci­ence. The percentage of people now involved in activities that can be considered scientific is very large compared to that of 200 years ago. Further, science, which was more or less the activity of isolated, private individuals, is now more the activity of an “orga­nization man.” An individual privately working out a theory or conducting an experiment or inventing a device is a rare excep­tion. Thomas Edison is said to have taken many patents before establishing the General Electric lab. But since his time, about a century ago, the so-called scientist now belongs to an organiza­tion. In this way, science is neither a luxury nor an activity of sur­plus energy. It is a full-time job, a professional career for many persons; it is no longer play.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

The word “research,” like many others, has acquired a wide cur­rency over the past several decades. Relatively few people con­ducted research in the first half of the twentieth century. Those who were known to be doing research were looked upon as belonging to an elite class, often shrouded in mystery, not unlike the FBI agents portrayed in popular movies. In the imagination of the common person, researchers belonged to a secret society, the initiation into and the ideal of which were guarded secrets. Not any more. Elementary school children now ask their parents for rides to libraries or museums because they have to “do some research” on a project given by their teacher. If we need a book from the library and that particular book is not found in the list or on the rack, the librarian says, on your request for help, that she or he “needs to do some research.” Finding a particular poem needs research; so does finding a music album, or a particular brand, style, or size of shoes.

With the expanding influence of consumer goods on the lives of common people, market research has acquired great power. Firstly, the products that members of society consume, be they houses, cars, items of clothing, or sunglasses, are the outcomes of research. Secondly, the various subtle and sophisticated processes of persuasion—the brand names by which a product is called, the faces that flash, the music that plays during a commercial, the pictures of heroes, stars, or muscle men on packaging-are all subject to market research.

The service industry is just as much shaped and controlled by research. The kind of plays, movies, or TV shows that are likely to become popular (hence, profitable) are not guessed and gam­bled on any more. Entrepreneurs intending to start a new prod­uct a few decades ago needed to do the familiar “market survey.” Now, they go to specialty companies that “do research” to find the answer to fit the client’s requirement. Lawyers searching for precedents, doctors looking for case histories, accountants look­ing for loopholes to minimize taxes: all engage in matters of research. Though one may question the accuracy of the word “research” in these contexts, the word, of course, is free for all. But we want to point out that research, as discussed in this book, is meant to be scientific research in its broadest sense. Accord­ingly, ornithologists observing the nesting habits of the peregrine falcon, pharmacologists trying to reduce the side effects of a drug, zoologists planning to clone a camel: all these, besides hun­dreds of other activities, may be considered academic, technical, or scientific research.

Further effort calls for a bifurcation, somewhat overlapping, between research activities that are scientific in nature and those that are not; this site deals only with the former, meaning, research in those areas that are conventionally considered “science.” Thus, although several thousand Ph.D. dissertations being written throughout the world in the areas of philosophy, political science, literature, and so forth, are research efforts, these, for our purpose, offer mar­ginal interest. And even within science, this book deals only with those research works that are experimental in nature. This distinction requires that we clarify the phrase “experimental research” even further.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

To experiment is to try, to look for, to confirm. A familiar exam­ple may make the meaning clear. After getting ready in the morn­ing to go to the office, I look for the keys. I can’t find them. I am mildly agitated. Thoughts of not getting to the office, of not get­ting the notes I wrote yesterday, of going late or empty-handed to class, and so forth, run quickly through my mind. But I know the first thing I need to do is look for my keys. I run up again to my bedroom and look in the same chest of drawers where I keep them every night. Not there. I look in the next drawer. Not there either. Then, I recollect that I was watching TV last night. I go into the TV room and look on the TV table and places near about. Not there. Then, I think of the clothes I wore yesterday. I go to the closet, recollect what I wore, and search the pockets. Not there. Did I, by any chance, leave them in the car when I got out of it yesterday? I look through the locked door of the car. Not there. Then, I remember that I needed the keys to lock the door; so, I decide, because the doors are locked now, there is no chance that the keys are inside the car. I go back into the house and ask others in the family if any of them have seen my keys. They start, half-heartedly, looking for them. In the meanwhile, I go up to the bedroom, rehearse in my mind—even partly, physically and orally—how I came into the house yesterday, where and how I keep my briefcase, where and how I removed my jacket and shoes, how I was called to eat dinner soon after, how I did not fully change my clothes before going to the table, and so forth. I go through the places involved, look at all surfaces on which I could have placed the keys, step by step in sequence. I even open the refrigerator and look inside—just in case. My frustration, of course, is mounting steadily.

At this stage, the reader may object that this is all searching; where is the experiment? Indeed, it is searching, but searching with a difference. The difference is that the search is not haphaz­ard; it is not arbitrary. Frantic though it appears, it is systematic; it is organized. It was done with one question in mind all the time: Can my keys be here? The search is not extended every­where: to the bathrooms, the attic, the basement, the backyard, or even to other bedrooms. It is done only in places where the keys are likely to be. The circumstances that could cause them to be in selected places are thought about. To use a more precise lan­guage, it is a search directed by one or more hypotheses.

If my boy wants to collect seashells, I will take him to the sea­shore, not to the zoo. If he wants to collect pinecones, I advise him to wait until late fall, then to go and look under pine trees, not under any tree in the park. Every parent, with some sense, does the same. Primitive as they seem, these are logical decisions: to search with a question in mind and to do so at a time and place and under the circumstances likely to yield a favorable answer.

I am aware that these examples are not adequate in strength to reach the textbook definition of “experiment,” but these are experiments, nonetheless. Very famous scientific works, like the discovery of the planet Neptune in 1846, which was hailed as one of the greatest achievements of mathematical astronomy, not­withstanding all the work it involved in mathematics and astron­omy, is eventually a search. Many theoretical calculations were obviously needed to direct the search at a particular location in the vast sky at a particular time. But is it far-fetched to call the search for the object itself an experiment?

If the above is an example of a deliberate search, backed by an expectation, there are instances in the world of science in which unexpected happenings led to discoveries of monumental scale. Wilhelm Roentgen’s discovery of X-rays and Alexander Fleming’s discovery of antibiotics are, to outsiders, just accidents. But such accidents can happen only to those who are prepared to perceive things that most of us do not. The culture of the mind of those scientists was such that they could decipher meaning in these “accidents”; they could expect answers to questions they were prepared to ask, even if they had not consciously asked them yet. The preparation of their minds embodies the question; the acci­dents, the answers. The accidental discoveries, subject to further confirmation or variation, become part of science.

The training of athletes is another example of experiment. Several timed runs of a sprinter, several shots to the hoop of the basketball player, under repetitive conditions and often with intentional variations, are answers to the combined questions, Can I do it again? Can I do it better? The housewife’s cookies, the chef’s old and new dishes, the old and new styles of dress items, new creations in art, music, and literature: all are, in a sense, experiments backed by hypotheses. Logic is implied, if not expressed, in each. That the word “research” ends with “search” is, quite likely, purposive.

Even the zest of the gambler—with various games, combina­tions, and numbers—is not devoid of logic, though often, when it comes to detail and when it is too late, he recognizes that logic worked, not for, but against him.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

The most typical and common experimental works of our times, are the works of

• Research scientists and technologists employed in a career in private or government-supported institutions and orga­nizations, including the military
• Thousands of scientists and engineers in the making, namely registered graduate students working toward uni­versity degrees, such as an M.S. or Ph.D.
• Thousands of inventors, some affiliated with organizations and some private, working for patent rights on materials, processes, and devices.

State governments in which a ministry (or department) of sci­ence and technology does not exist are exceptions. Most coun­tries spend a considerable part of their revenue on research work. Almost all countries have military establishments, a considerable part of whose resources are directed to defense research.

The following are some common features among researchers in such a wide variety of research fields:

• Most of them work either individually or in groups, under the supervision of a guide or a director.
• They work for a short or long term or for promotion in the form of a degree or other enhancement of profes­sional status.
• They have the intellectual support, the library, and a field of work, the laboratory.
• Last, but by no means least, they have “the problems.” Their efforts are directed toward finding answers to ques­tions posed by individuals or organizations.

This last aspect, namely, the existence of questions and the efforts toward answers, is to us the significant part of experimen­tal research.

I have had the unpleasant experience of having registered in a prestigious institution to do research for my Ph.D. without hav­ing identified a research problem. And this, as I now under­stand, is not a rare incident, particularly in developing countries. That institution, at that time, was devoted to research, as well as to teaching engineering at the graduate level, but it was devoted to research only in the physical and biological sciences. Students were registered for research positions, mostly for Ph.D’s, the main attraction being the availability of federal funds for schol­arships and research assistantships. The institution requisitioned a yearly grant and was awarded a certain percentage of requested, based on the prestige and politics exercised by the people involved.

I cite this example to illustrate the situation of putting the “Ph.D. before the problem,” the cart before the horse, in that the student, the would-be Ph.D., knows that he is working for a doctorate, but he doesn’t know what his topic of investigation, his “problem,” will be. In my case, the situation continued for more than a year and was likely to continue indefinitely. Luckily for me, I came up with a problem for myself after a year or so. That situation is far from ideal. I invented a problem through literature search not because the solution to that problem was a pressing need, but solely for the purpose of getting a Ph.D.

In an ideal situation, on the other hand, the “problem,” at least in outline, should be available, and a certain amount of funding should be earmarked in the budget for the effort of find­ing the solution. That effort should be assigned to a suitable stu­dent, with compensation coming from the funds. A healthy and desirable situation exists when the problem(s), along with the funds come from those who face the problem, whether it is an agency of the local or federal government or a manufacturing (or service) company. This is what, in principle, is happening in developed countries, for example, in the United States. In devel­oping countries, in view of the limited availability of funds, it is even more desirable that this model should prevail.

This brings us to the last and most idealistic kind of research: research done in the same spirit as playing a game, creating a piece of music, or painting a picture, not for gain of any kind, but simply out of exuberance and energy, just for enjoyment, for its own sake. Certainly such a situation is very desirable to the cause of science, as well as to the enjoyment of the people involved. There have been many such people in earlier times whose contributions to science have been significant, but they are now a vanishing species, if not endangered as well.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

The following is a segment from the Dialogues of Plato¹:

Socrates: “What I asked you, my friend, was, What is piety? and you have not explained to me, to my satisfaction. You only tell me that what you are doing now, namely, prosecuting your father for murder, is a pious act.”

After some cajoling from Socrates, Euthyphro offers this definition:

“What is pleasing to the gods is pious, and what is not pleas­ing to them is impious.”

Socrates effectively shows Euthyphro—in fact he gets a “con­fession” from him—that gods may differ among themselves, may even quarrel, with some gods accepting certain acts as pious and others coming hard on the same act as impious. So bringing “gods” into the definition does not help in defining piety. The dialog continues,

Socrates: “[P]iety and impiety cannot be defined in that way; for we have seen that what is displeasing to the gods is also pleas­ing to them. So I will let you off in this point Euthyphro; and all the gods shall agree in thinking your father’s deed wrong and in hating it, if you like. But shall we correct our definition and say that whatever all the gods hate is impious and whatever they all love is pious: while whatever some of them love and others hate, is either both or neither? Do you wish us now to define piety or impiety in this manner?”

Euthyphro: “Why not Socrates?”

Socrates: “There is no reason why I should not Euthyphro. It is for you to consider whether that definition will help you to teach me what you promised.”

Euthyphro: “Well I should say that piety is what “all the gods love and that impiety is what they all hate.” [emphasis mine]

The dialog, of course, goes further. There are two points wor­thy of note. Firstly, Socrates insists on defining a quality, piety, so that in any further discussion, he and Euthyphro shall have a common ground. And secondly, he is, in fact, defining what a definition should be. If some gods agree that a certain act is pious, and some other gods disagree, holding the opinion that the same act is impious, then the word “piety,” based on that act, is not defined satisfactorily. If, instead, all the gods agree that a certain act is pious, then that act serves the purpose of being an example, and the word “piety” can be attached to it. So, a definition should be such that it helps avoid disputes or disagreements. In the situ­ation quoted, it is the dispute, the disagreements among gods, that is evidenced. In our context, in place of gods for the ancient Greeks, we find other researchers, each of whom is a self-appointed judge and the harbinger of truth in his little corner of the world. And to make the situation worse, these earthly gods are usually scattered over wide stretches of space and time. Any word or combination of words, including symbols, that a researcher employs in his discourse, needs to be clear beyond the possibility of being mistaken by any other researchers in his field; that is how definitions become relevant.

Definition is the domain of logicians and philosophers. But it is necessary that the experimental researcher should have some familiarity to build on, in case he needs either to use definitions in his own work or to understand definitions in the works of oth­ers. To that extent, we will review, in brief outline, some impor­tant aspects of definitions. In addition, this chapter aims to impress upon the experimental researcher that the process of defining, when required, should not be done casually.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

How do we define “definition”? It is somewhat disappointing to learn that there is no one definition, acceptable to most, if not all, logicians. This surprise will soon disappear when we notice that several functions performed as a way of clarifying expressions (or statements), either completely with words or with combinations of words and symbols, have all been considered legitimate acts of defining. Consequently, there are many variations of the meaning of “definition.”

Having accepted this situation, we will mention (rather, quote somewhat freely) a few variations, meant to give the breadth of the word “definition,” though not its depth.

• A real definition involves two sets of expressions, each with a meaning of its own, and these mean­ings are equivalent if the definition is true.²
• A definition is a phrase signifying a thing’s essence. (Furthermore,) A definition contains two terms as components, the genus and the A genus is what is predicated in the category of essence of a number of things exhibiting differences in kind, and the differentia is that part of the essence that distinguishes the species from the other species in the same genus.

—Attributed to Aristotle³

Four of the following definitions, (C) through (F), appear within a span of six pages in one book.⁴ The rest are taken from other sources.

• A definition is a way of restricting the meaning of a term that has several meanings to prevent ambi­guity and equivocation.
• A definition is true . . . if the defining term has the same designation as the term to be defined.
• Definition is a rule of substitution.
• “Definition” = statement that one term has the same designation as another term.
• A definition is the statement of the meaning of a word, etc.
• A definition is a brief description of a thing by its properties.
• A definition is an explanation of the meaning of a word or expression.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

Though the word “definition” itself defies definition, the com­ponents that constitute a definition are delimited fairly well as follows:

Term,: Word or group of words, such as phrases, clauses, or one or more assertive sentences. To the extent that terms are defined, when need be, communication between or among researchers becomes precise. In the Socratic dialog cited earlier, the term to be defined was the word “piety.” In dictionaries or books of syn­onyms, we may find several alternate meanings for a given word to be defined. Out of these alternatives, the one that best explains the term and—this is important—best fits the context may serve the purpose of being the definition of the word. There may be occasions when the term is a group of related words, a phrase,

wherein it is not the literal meaning of individual words that is significant, but that of the bunch of words as a whole, such as “shadow boxing,” “end of the tunnel”; these are often referred to as idioms. In such cases, we need to go to books of idioms, which, though not as common as dictionaries, are available in most well- developed languages like English. The language of science is usu­ally sober; there is little room for idioms like those above or for other figurative words or word combinations.

The need to define a term when the term is a whole sentence is less often encountered; when it is, the definition usually takes the form of an explanation, often with illustrative example(s). It is worthy of note that in his great work, the Principia, Isaac New­ton starts with definitions, covering the first dozen or so pages, before even mentioning the problems addressed therein. One of the twelve definitions, as an example, is quoted below:

“Definition VII: The accelerative quantity of a centripetal force is the measure of the same, proportional to the velocity which it generates in a given time.

Thus the force of the same loadstone is greater at a less dis­tance, and less at a greater: also the force of gravity is greater in valleys, less on tops of exceeding high mountains; and yet less (as shall hereafter be shown), at greater distances from the body of the earth; but at equal distances, it is the same everywhere; because (taking away, or allowing for, the resistance of the air), it equally accelerates all falling bodies, whether heavy or light, great or small.”⁵

Definiendum and Definienst These names are given, respec­tively, to the term to be defined and the term that does the defin­ing. One or both of these terms may be one or more words, or even, as we have just seen Newton do, one or more sentences.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

1. Direct and B. Indirect Definitions

Direct definitions are explicit in nature; hence, the definiens can replace the definiendum without any further need for elaboration or explanation. If a definition forms a part of a whole statement, and if after replacing the definiendum with the definiens, the

statement can be repeated without any loss or alteration in the original meaning, it is also a case of direct definition. In contrast, indirect definitions are such that by replacing the definiendum with definiens, both of these being either isolated or part of a statement, the meaning of the statement remains open to further relevant questions. There are two variations within this. Firstly, when a word or a combination of words conveys meaning far beyond what a usual-length definiens can clarify, because the definiendum may have several aspects, some of which are implied and cannot be demonstrated, the definition is referred to as an implied definition: “religion,” “democracy,” and “honesty” are some examples. It is often the case that such definitions have emotional overtones. Secondly, ify is the descendent (the word to be defined) of x, then y may be a son, a grandson, or many more generations removed, and yet be the descendent of x. The defini­tion then for “descendent,” the definiendum, is uncertain and open to further question, in this case, as to how many genera­tions removed or recurring. The definition, whichever way it is offered, needs to be qualified; this is often referred to as a recur­sive definition.

2. Informal and D. Formal Definitions

In most cases of human discourse, definitions are blended so nicely that we do not notice them as such. In a sense, every word of every language, either spoken or written, may be considered a definition. We live with these without needing to be conscious of their definitional nature. Most experimental scientists, most of the time, enjoy the same privilege. But occasions may arise unno­ticed, though rare, when additional effort may be necessary to highlight the aspect of “definition” in their discourse. The degree of highlighting required and the amount of clarity intended, among other circumstances, decide the degree of formality that is desirable in the process of defining. Defining done with a low degree of formality is usually referred to as informal definition. Suppose I were writing for a tennis magazine on the advantages and disadvantages of “bubbleballing.” I might write something like this: “Some players are likely to return the balls to the oppo­nent intentionally and repeatedly, hitting the ball high above the net, making the ball drop to their opponent almost vertically near the baseline. For our purpose we may call this ‘bubble-balling.’ Here are some advantages of bubbleballing.” I would proceed to write on, using bubbleballing instead of the rather long definiendum mentioned above. This is an example of infor­mal definition.

Informal definitions can be stated in several different ways, using different sets of words; a few variations follow:

1. Bubbleballing is the act of returning balls, the path of which to the opponent resembles a bubble.
2. The word “bubbleballing” is applied to the way a tennis player returns the ball to his opponent with a big upswing, followed by a big downswing.
3. A player who does “bubbleballing” is understood to be returning the ball to his opponent in tennis, deliberately hit high into the sky.

So long as the sense in the expression is conveyed, some resid­ual vagueness or ambiguity is not frowned upon. However, we require formal definition most often in research, and it needs to be done with a tighter grip on the words. One possible way is, “‘Brainwashing’ has the same designation as ‘Changing the other person’s opinion by subtle repetitions of slogans.’” Even more for­mal definitions avoid the words altogether between the definien- dum (x) and the definiens (y) and connect the two with the “=” sign in the form “x = y”; the “=” does not have the same meaning as in mathematics. Originating from Principia Mathematica by Alfred Whitehead and Bertrand Russell, a formal way of defining has come to be widely accepted. It has the following form:

Beauty . = . that which is pleasing to look at. Df.

The term on the left-hand side is the definiendum and that on the right-hand side is the definiens, ending with “Df.” to denote that this is a definition.

3. Lexical and F. Stipulated Definitions

Lexical definitions, obviously, are the meanings as listed in the dic­tionaries. As such, we find the current and established meaning(s) of a word. For instance, in the United States, currently, the word “suck” has acquired a meaning that has sexual connotation, unlike in other English-speaking societies or in the past. It is rea­sonable that in the near future, we will see this new usage reflected in American dictionaries. Also, dictionaries list more than one meaning for many words. It is then left to the individ­ual to find the appropriate meaning by context.

Stipulated definitions assign special or restrictive meanings to words (or combinations of words) that otherwise have a collo­quial usage, which is most often obvious. “Stress,” for instance, is a word commonly used to connote that someone is mentally tired, but engineers take the same word, define it as “load per unit area,” and assign to it a mathematical format:

σ = P + A

where σ stands for stress, P for load, and A for area.

A variation of the stipulated definition will occur when a word (or a combination of words) is improvised to describe a certain thing or phenomenon within a limited and exclusive domain. The use of the word “bubbleballing” within the game of tennis is an example. In such circumstances, the definition is known as an impromptu definition. It is obvious that such definitions should not have currency outside the particular domain, in this case, the game of tennis.

4. Nominal and H. Real Definitions

A nominal definition is most often a common understanding of what a certain word or group of words should mean for the users. In this sense, the dictionary meanings of words in any language have this characteristic. The entire human discourse depends on words, though we seldom have occasions to notice these as defi­nitions. In mathematics and the sciences, we depend on a large number of symbols. That “3” stands for “three” and “23” stands for “the sum of two tens and three ones” is so much a part of our routine that we do not think of them as definitions. In addition to the economy of space and time, both in writing and reading, such symbols are instrumental for the clear thinking needed for further development. What distinguishes a nominal definition is that it is neither true nor false and, hence, cannot be a proposi­tion. No Briton can charge an American with being “untrue” if the latter writes “center” where it ought to be, according to the Briton, “centre.” The same is true for symbols; for instance, the current symbol for gold (in chemistry) is “Au.” If there is a move in some future time among chemists, who agree to do so, it may be changed to “Go,” or any other letter or group of letters, with­out rendering any statement made thus far “false.”

In contrast, a real definition can serve as a proposition, which means that it is either true or false, not by itself, but as decided by individual people. If “music” is defined as “a series of sound variations, capable of producing a pleasing sensation,” then there is plenty of room to dispute whether some of modern music is music or something else, to be defined using different words as definiens.

5. Definitions by Denotation

Denotation is a way of further clarifying the meaning of a term by means of examples or instances, which most often follow, but may precede, the formal part of the definition. A good example is Newton’s definition that we quoted earlier, wherein the passage “the force of the same loadstone is greater at less distance” is used to substantiate “the accelerative quantity of a centripetal force” that he is defining.

6. Ostensive Definitions

Ostensive definitions cannot be described exhaustively by words alone but can be demonstrated or pointed to easily to obtain complete satisfaction. If a painter is asked to describe (or define) yellow ochre as a color, the one way most suitable to him is to squeeze on his palette a thread of paint from his tube of yellow ochre and ask the other person to look at it.

7. Definitions by Genus and Difference

Attributed to Aristotle, such a method of definition depends on showing a particular entity as belonging to a set and nonetheless being different from all other elements of the set. The famous example is “Man is a rational animal”; in all respects, man is another animal, with the difference that he alone is endowed with rationality.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

We opened this chapter quoting the dialog of Socrates on defini­tion as a way of showing how definitions are created. The need for definition, according to many modern logicians, arises because of the possible effects of what are meant by the two words most often mentioned: “vagueness” and “ambiguity.”

“Vagueness” itself may be understood as “the quality of not being clearly stated (or understood),” and ambiguity as “the quality of an expression whose meaning can be taken in two or more ways.” No language is perfectly free of vagueness or ambi­guity; English is no exception. An experimental scientist, in his profession, needs to express his findings, be it for the benefit or the judgment of others. His expressions, as interpreted by oth­ers, should have a one-to-one correspondence with what he meant to express. Ideally, there should be no occasion for him to say, “No, that is not what I meant”; there should be no such excuse because, as we pointed out earlier, many of his potential judges or benefactors, as the case may be, will be scattered far and wide, in both space and time. Slackness in definitions may lead researchers elsewhere, or those yet to come, into mistaken tracks of investigation.

Fortunately for the experimental researcher, most of his or her work can be expressed with close-to-ordinary words and symbols, there being less need for strict and formal definitions. But when the need arises, definitions should be considered as tools, and if the researcher is not familiar with the use of these, his or her job may become difficult, if not impossible.

The motivation for definition can also be either the need for economy of words, or contrarily, the need for elaboration or clar­ification as shown following:

Abbreviation:

My father’s father’s other son’s son . = . my cousin. Df.

Elaboration:

Here is an instance of ambiguity. My cousin could be either:

my father’s brother’s son or daughter, or

my father’s sister’s son or daughter, or

my mother’s brother’s son or daughter, or

my mother’s sister’s son or daughter. In way of specifying:

My (this) cousin . = . My father’s father’s other son’s son. Df.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

Even among logicians, there is no unanimity as to what ought to be called “definitions.” Having said this, we mention below briefly, without the constraints of quotation, some of the desir­able and some of the undesirable traits of definitions, as expressed by logicians.

A definition should

1. Make communication possible when it is impossi­ble without it, or make communication clear when it would be fuzzy without it
2. Have two terms: (a) the term to be defined (the meaning of which, in the context, is doubtful), and (b) the term that does the defining (the mean­ing of which is expected to be understood)

Example: Painter . = . one who paints pictures. Df.

3. Distinguish between things and words

Example: In “Anger is harmful,” we are talking about the thing (emotion) “anger.” In contrast, in “‘Anger’ has five letters,” we are talking about the word “anger” (not about the emotion “anger”).

The means of making this distinction is to use the quotation marks judiciously.

4. Distinguish between the noun and verb forms of some words, which can be used in both forms.

Example: “I am writing this passage,” versus “This writing is done well.”

5. Give the essence of that which is to be defined. The definiens must be equivalent to the definien- dum—it must be applicable to everything of which the definiendum can be predicated, and applicable to nothing else.
6. Be so selected that, whether explicit or implicit, the attributes known to belong to the thing defined must be formally derivable from the definition.

A definition should not

1. Use examples as the sole means of defining, though examples may supplement a given defini­tion. We have seen this done, as it should be, in the definition quoted from Newton’s
2. Use description as the sole means of defining. Here again, the definition quoted from Newton’s Principia, done as it should be, may be considered as containing a supplementary description.
3. Use exaggeration (as a form of definition)

Example: “Definition” by Bernard Shaw:

Teacher: He who can, does. He who cannot, teaches.

4. Be circular; it must not, directly or indirectly, con­tain the subject to be defined (some times referred to as tautology)

Examples:

• Hinduism . = . the religion followed by the Hindus. Df.

This is obviously and completely circular.

• Hinduism . = . the religious and social doc­trines and rites of the Hindus. Df.

This is from a respectable dictionary; the circu­larity is obvious, though not direct.

• Hinduism . = . the religious and social system of the Hindus, a development of ancient Brah­manism. Df.

This is from another respectable dictionary. The addition of the phrase “a development of ancient Brahmanism” is an improvement, but not in the direction of reducing the circularity.

Instead, use the form:

• Hinduism . = . religious and social rites and doctrines that are a development of ancient Brah­manism. Df.

The circularity is completely avoided, though the new word introduced, “Brahmanism,” needs to be defined, in turn.

5. Be phrased in the negative when it can be phrased in the positive

Example:

1. Night . = . part of the day wherein there is no sunlight. Df.
2. Night . = . the time from sunset to sunrise. Df.

Though (a) may be literally correct, (b) fulfills the logical requirement better.

However, there are legitimate exceptions.

Example:

• Orphan . = . child who has no parents. Df.

This is acceptable, though it is possible to remove “no” by defining the word differently as

• Orphan . = . one who is bereaved of parents. Df.

6. Contain obscure term(s)

This pertains to the purpose of definition, namely, to clarify, not to complicate, confuse, or lead astray. The earlier example, in which “Brah­manism” was used to define “Hinduism,” is an instance.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

One can think of several cases in which the distinctive feature that separates the scientific from the nonscientific is quantifica­tion, which means expressing laws or relations in terms of quanti­ties combined with qualities rather than by qualities alone. To mention that New York city is full of criminals is a nonscientific expression in contrast to providing the data about how many criminals, decided by such and such criteria, are in the custody of the New York City Police Department. In the latter case, two items render the statement scientific:

1. The criteria needed to decide how to identify the criminals
2. The enumeration of those who fulfill such criteria

The first of these is a matter of definition (see Chapter 2); the second, namely, the enumeration involved, is a matter of quanti­fication. Even in terms of our previous discussion relative to the function of science, we may think of the relation between those identified as criminals and the number of those who constitute such a group as a law. In such statements, which are quantitative and thereby can be claimed to be scientific, the relation is not between two events; it is between a certain defined quality and the number of those who have such quality. In such statements, there is need for a definition and to count those entities that ful­fill that definition. There is no room left to make arbitrary, biased, and unconfirmed statements. If it is one’s hypothesis to brand New York as a place full of criminals, the hypothesis needs to be confirmed by experimentation, in this case done by check­ing the definition of “criminal” and further by enumeration of the criminals. The process of enumeration, better known as counting, is done by means of numbers.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

Recognition of the importance of numbers, the basis of all quan­tification, dates back to Pythagoras (572—500 BC). One of the first steps ever taken toward the formation of science was count­ing, using numbers. Otherwise, it is hardly possible to express anything with at least some degree of the precision needed for science. Whether the statement is about an extensive quality, like the “hugeness” of a building, or an intensive quality, like the “hotness” of a summer day, we need to count by numbers.

But numbers are known to serve many purposes. Firstly, num­bers are used as tags, as in the case of the route of a city transport bus or house numbers on a street. Numbers may also stand for names, as in the case of patients in a hospital ward or a private in a military regiment. In both these cases, the numbers have no sig­nificant quantitative values. Route 61 may have no relation what­soever relative to any conceivable quantity. The patient in bed number seven may very well be treated without the hospital staff knowing his name. He can be moved to another bed and given another number, which becomes his new “name.” Such numbers have, besides identification, no significance in science. Then, there is the “ordinal” use of numbers, which denotes the order of a cer­tain attribute or quantity or even a quality, but without quantita­tive values. For instance, if three cities in a state are numbered according to their size based on population, city number two may be smaller than city number one by a million, and city number three may be smaller than city number two by only a few hun­dred. Here the significant relation is (in terms of population)

City number 1 > city number 2 > city number 3

If another city’s population, hitherto unknown, is newly determined, it is possible to place it in the appropriate slot rela­tive to the three cities. If this idea is extended to a large group of items, into which hitherto unknown items, newly found, need to be added, any new item can be assigned its appropriate relative spot in the series of all items of its kind. This is an important rela­tion often used in science, as in the case of the identification of elements in the periodic table. Another important relation made more explicit in mathematics is that

If A > B, and B > C, then A > C

This law, known as transitivity, is often used in scientific rela­tions. The ordinal numbers, though related to quantities, as above, do not directly denote quantities. For instance, consider a series of twenty different solids in order of increasing density as S1, S2, S3, . . . S20. In this, S18 is known to be denser than S1, S3, . . . S17 and to be less dense than S19 and It does not imply, however, that S18 is two times as dense as S9, the “two times” coming from dividing 18 by 9.

Such denotative significance is assigned to the so-called cardinal numbers, which are meant to answer the question, How many?

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

Counting requires that the group within which it is done be sep­arable. If it is said that there are more people in Chicago than in New York, it is understood that the areas that are officially demarcated as Chicago and New York are known without ambi­guity, relative to their various suburbs, that only people living within the respective areas are counted, and that the number of people so counted within Chicago is more than the number of people so counted in New York. An assumption made is that the entities counted—in this case, men, women, and children—are discrete. (A pregnant woman due to deliver a baby in a moment is counted as one, not two.)

The theory of numbers involved in counting, done by rote by most civilized persons, has been found worthy of analysis by some of the greatest mathematicians. Suffice it for our purpose to record the three basic rules involved:

1. If a set A of discrete entities and another set B of discrete entities are both counted against a third set C of discrete entities, then if A and B are counted against each other, they will be found to have the same number. We may formalize this relation (mathematically) as

If A = C and B = C, then A = B.

2. Starting with a single entity and adding continu­ally to it another entity, one can build up a series (or set) of entities that will have the same number as any other collection whatsoever.
3. If A and X are two collections that have the same number, and B and Y are two other collections that have the same number, then a collection obtained by adding A to B will have the same number as the number obtained by adding X to Y.

In terms of mathematics, we may state this as

If A = X and B = Y then A + B = X + Y

These apparently simple, to most of us obvious, rules charac­terize the cardinal use of numbers, which form the basis of count­ing; particularly familiar is rule 3. Let us say, for some purpose, that the total population of Chicago and New York City together needs to be measured. To do it, we do not require that all men, women, and children of both these cities be huddled together in a place where we do the counting from start to finish. We do the following:

1. The population of Chicago is found; it is noted as a number, say Nc.
2. The population of New York City is found; it is noted as a number, say
3. The population of Chicago + the population of New York City is found as Nc +Nn.

This very simple procedure, obvious to most of us, is an appli­cation of rule 3 of counting above. Though the other two rules are even more fundamental, this one, by virtue of being “mathe­matical,” presents explicitly the fundamental principle of the use of cardinal numbers, namely, counting.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

After admitting that counting is the basis of measurement, we may ask the question, Can any quality whatsoever of a thing or things (external to us) be measured? If we supply the answer no to open the issue, then a more specific question is, What are the qualities that can be measured? Let us say that a man has a bunch of red roses in his hand. We can readily think of two qualities: (1) all the many subqualities like the color, smell, shape, and struc­ture that characterize the familiar red rose, and (2) the fact that there are twelve of them, each of which is interchangeable with any other in the bunch. The “twelve” in this is as much a quality of the bunch as the first and is symbolized by the numeral “12.” Now, let us say that the person holding the red roses decides to buy another bunch of red roses. When he then holds the bunches together, there occurs no change in the quality “red roses,” but a change does occur in the quality “twelve.” If the person now holding the red roses wants to “measure” this new quality, he counts the total number of roses. Needless to say, he may do it in several different ways.

One-by-one, arithmetically symbolized as

1+ 1 + 1 + . . . until he counts the last one

Two-by-two, arithmetically symbolized as

2 + 2 + 2 + . . . until he counts the last two

Three-by-three, arithmetically symbolized as

3 + 3 + 3 + . . . until he counts the last three

Or (this is important), he may do it by any of several other combinations, which can be arithmetically symbolized, for instance as 6 + 3 + 4 + 2 + 5 + 4. Whatever the particular method he may use, he will count twenty-four as the new number, and this quality, which has been “quantified,” is symbolized by the new numeral “24.” This last operation is that of addition, one of the four basic arithmetic processes. We may now ask, Within those twenty-four red roses obtained from two bundles, can he perform the operation of subtraction? The answer is obviously yes. Similarly, we may be assured that, limited to those twenty- four red roses, he may perform the operations of multiplication and division as well.

It is now worthwhile to remind ourselves that the “twenty- four” the person counted as a total number is a quality, with this difference: it is a quality that is measurable. We may now sum­marize that the measurable qualities are those that are amenable to counting and can be subjected to the arithmetic operations. Such ones are quantifiable qualities, commonly expressed as quantities. Those that cannot be so quantified are numerous and all around us. There are several qualities, which though tracked by human perception, cannot be subject to measurement. The stink of a rotten fish and the sweetness of a lily are distinguished by the same perception. When there are more lilies gathered together, there may even result a higher intensity of the sweet smell, but it is not measurable, at least not yet. The jarring noises of a pneumatic hammer in action as well as the song of a cuckoo are both distinguished by the same perception. But there is no scale of gradation for the “sweetness” of the sound between these extremes. Similar extremes can be found in perceptions of taste and touch, wherein, despite the ability to distinguish and even give a qualitative description that “this is sweeter than that” or “this is gentler to the touch than that,” there are yet no gradations or graduations conforming to unified scales of measurement. When we go beyond our perceptions, measurement of qualities becomes even impossible. How can beauty, kindness, honesty, courage, and the like be measured? Such lapses are often quoted by those bent upon pointing out the limitations of science.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

We have noted that in the process of answering the question, How many? (when relevant), we need counting, and that count­ing, besides being a measurement by itself, is the basis of all other measurements. When we measure the height of a person who is, let us say, 5’10”, we are in effect counting the number of one- inch-long pieces, placed end to end, that cover the entire length of the person while he is standing erect, from the bottom of his foot to the top of his head, which comes to be seventy in number. The height scale against which he was made to stand, and on which his height was “read,” simply served the purpose of a refer­ence, conforming to the first rule of counting, namely,

If A = C and B = C, then A = B

where A is the height of the person in inches, B is the number of one-inch-long pieces required for the purpose, and C is the height read on the scale. (Instead of having individual one-inch pieces separately in a bunch, we have such lengths imprinted on the height scale for convenience).

Now, let us say that a person’s weight needs to be found and that we have a conventional weighing balance for the purpose. Placing the person on one pan, the required number of one- pound weights are placed on the other pan until neither of the two pans sinks. Then, the weight of the person is obtained by counting the number of one-pound weights required for the purpose. If instead of all one-pound weights, we used one hun­dred-pound weight, one fifty-pound weight, two ten-pound weights, and three one-pound weights, we do the simple addi- tion—(1 x 100) + (1 x 50) + (2 x 10) + (3 x 1)—and obtain the weight of the person as the sum: 173 pounds.

Another “property” of the person can be so measured: the per­son’s age, which is the number of years elapsed since the person was born. Here the counting is even more direct. Suppose on the first birthday of a person a marble were placed in a pouch, and at the end of another year, another marble were placed into the same pouch, and another marble after another year, and so on, until now. If we now want to know the age of the person, we need only open the pouch and count the number of marbles in it. The same result is obtained if we do the arithmetic of subtract­ing the year of birth from the current year (which indeed is the way age is most often found). Age, counted in years, is the mea­sure of elapsed time. If the time elapsed for an event requires less time, say the timing of a 100-meter sprinter, we count in seconds and decimals of seconds with an appropriate stopwatch. The above three properties of the person, height (in terms of length), weight (mass, to be more precise), and age (in terms of time), being measurable, are “quantified.” These also happen to be three of the most fundamental qualities directly measurable in the physical world. It is necessary to note that the inch, pound, and year (or second) are arbitrarily defined units. We may count the length, the weight, and the time equally well in any other unit. When so done, the numbers arrived at will be different, but with no change in the rule (or principle) of measurement.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

Using only the three quantities mentioned above, we can make a lot of measurements in the physical world. For instance, confin­ing ourselves to length alone, we can measure the area of a given (flat) surface. Consider an area whose length is 3 inches and the width is 2 inches. If we draw the lines at the markings of inch lengths, we get six area “pieces,” each piece having 1-inch length and 1-inch width.

If there is another area whose length is 5 inches and the width is 6 inches, drawing the lines as mentioned above, we get thirty area pieces, each 1 inch long and 1 inch wide. Similar “tri­als” with areas of different lengths and different widths should have led the first observer(s) long ago to the conclusion that area can be obtained by multiplying length by width, when both are measured in the same units. The logical process that led to that conclusion we now call induction, and we expect the elementary school student to be capable of it. It is interesting to note that the observation above is the basis of such induction, and in that sense, this “knowledge” is “experimental” in nature. Further, we should note that the width is measured and counted in inches, in the same way that the length is measured. Also, the resulting pieces of area are measured in inches, both the length and width of which are just 1, and designated as “1 square inch” or “1 inch square.” A similar construction, counting, and induction has led to the observation that volume, counted as the number of “1 cubic inch,” is given by multiplying length x width x height, all in inches. The fact that using any other unit of length instead of inches results in the corresponding square and cube is a rela­tively minor detail. Area and volume are quantities derived from one basic quantity: length.

Even more obvious are quantities that are derived from more than one basic quantity. For example, we can distinguish between an automobile moving fast and another moving slow. But when we want to specify what is “fast” and what is “slow,” that is, when we want to quantify the quality of “fastness,” we need to measure speed. Unlike length or weight, speed involves two basic quanti­ties that need to be separately measured: (1) the distance moved, and (2) the corresponding time elapsed. Then, by dividing the number of units of distance by the number of units of time, we obtain the defined quantity known as speed. Speed is thus a quantity, easily obtainable by a simple derivation, but not mea­surable independently; it is expressed as distance moved in unit time. Similarly, we distinguish that steel is heavier than alumi­num. But when we want to specify how much heavier, we need to know the density of each, which is obtained by measuring the weight and volume of each, then dividing the weight of each by the corresponding volume.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

A unit is a quantity used as a standard, in terms of which other quantities of the same kind can be measured or expressed. We discussed earlier measuring the height of a person and used the inch as the unit of length. The inch itself is an arbitrarily defined quantity, meaning there is nothing in nature to recommend this particular length over any other length. If we want to measure the length of a tennis court, we may use the foot as a better unit, and if we want to express the distance between Boston and New York, we may use the mile as a convenient unit. The relations among the inch, foot, and mile, meaning for instance, how many inches make up a foot, are again arbitrary decisions. These are neither nature dictated nor made inevitable by reason; they are purely manmade. But all those who use these units are bound by a com­mon agreement, referred to as a standard. A standard inch is the same length whoever uses it, whenever, wherever. Similar consid­erations apply to units of weight: the pound, ounce, ton, and so forth. The units of time—the year, day, hour, minute, and sec­ond—are no different in this regard, except that a day is about the same duration as the earth takes to make a rotation on its own axis.

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.

We have mentioned three quantities—length, mass, and time— with some familiar units to express these. We may at this point note that the inch, the pound, and the second used in this discus­sion are simply circumstantial, in that, being located in the United States, I have used the units familiar to the general public in this country, almost all other countries have switched to the metric system, which is also the basis for the International System of Units (SI) more commonly followed by the scientific commu­nity. These three quantities are so fundamental that all quantita­tive relations in the physical world dealing with motion and the tendencies of objects to motion—the aspect of physics known as “mechanics”—can be adequately analyzed in terms of these. To deal with all other quantitative aspects of the physical world, only four additional quantities are required: (1) temperature difference (in degrees centigrade or Fahrenheit), (2) intensity of light source (in candles), (3) electric charge (in coulombs), and (4) amount of substance (in moles). As mentioned earlier, some of the other quantities that are thus far nonmeasurable may, in the future, be made measurable, hence quantified. Besides these seven funda­mental quantities, a considerable number of derived quantities are in use; we have cited speed and density.

The statement of the magnitude of a physical quantity con­sists of two parts: a number and a unit. The height of a person can be 6 foot, not just 6. Further, it is “foot,” not “feet,” because the height is six times 1 foot, or 6 x 1 ft. If we so choose, we can also state the height in inches: 6 ft. = 6 x (1 ft.) = 6 x (1 ft x 12 in.) = 72 in. Now let us consider a derived quantity: speed. An automobile requiring 4 hours to cover a distance of 240 miles obtains an average speed: length/time = 240 mi./4 hr. = 60 mph. Here we divided one number by another to obtain sixty. Further, we performed division between the two units to obtain the newly derived unit: mph. As in the case of fundamental units dealt with before, here again, a number combined with a unit expresses the magnitude of the physical quantity, speed. The magnitude, 60 mph, if we so choose, can be expressed in other units by using the required simple computation. While dealing with physical quan­tities, whether fundamental or derived, the units should be included throughout the computation. One may cancel, multi­ply, or divide units, as if they were numbers. Suppose we want to express the speed in feet per second. Knowing that 1 mi. = 5,280 ft. and 1 hr. = 3,600 sec., we proceed as follows:

1 mph = 1 mi. + 1 hr. = [1 mi. x (5,280 ft./1 mi.)] + [1 hr. x (3,600 sec./1 hr.)]

= 5280 ft./3,600 sec.

= 1.47 ft./s

Using this new unit, the average speed, 60 mph, may now be written as

Average speed = 60 x (1 mph)

= 60 x (1.47 ft./s)

= 88.2 ft./s

Source: Srinagesh K (2005), The Principles of Experimental Research, Butterworth-Heinemann; 1st edition.