Qualitative and Quantitative

When we say that the sea is blue or that a person is tall, our description is qualitative. We become aware of the qualita­tive features of the physical world from the earliest stages of our development. Many of these features impress us greatly and pleasantly. At one time or another we have all been struck by the beautiful sunset, the colorful rainbow, or the majestic mountain. We recognize colors, enjoy music, distinguish the hard from the soft, the smooth from the rough. On the other hand, there are also many qualitative aspects of the world that are by not apparent to us. Thus we do not ordinarily perceive that the atmosphere is made up of different kinds of gases or that a magnetic field is associated with the earth.

The quantitative aspects of the world refer to numbers and to mathematical relationships that can be associated with things and processes.  The heights of mountains, the distan­ces of stars, the amount of rainfall in a region in the course of a year, wind speed: these involve quantitative descriptions.

Generally speaking, though not always, it is possible to associate a quantitative aspect with a qualitative description. The physicist is primarily interested in the quantitative aspect. The lad who narrates the story in  Saint Exupery's Little Prince complains that grown‑ups are so much obsessed with figures that when they are told that one has made a friend, rather than ask about his hobbies and interests they are eager to find about his age, the number of people in his family, the amount of money his father makes, and so on [30]. Giving some margin for a slight exaggeration, this is a good description of the physicist's attitude to the world of phenomena.

This is what  John Milton, the poet,  says about the moon in his Paradise Lost:

            ....................... the moon,
            Rising in clouded majesty, at length
            Apparent queen unveil'd her peerless light
            And o'er the dark her silver mantle threw.

Valmiki, a great Sanskrit poet, wrote: "The moon, which removes the world’s nocturnal darkness, rises; and while radiating coolness, by its sheer splendor it gives joy to the minds of beings living on earth."

But the moon will be described very differently in an astronomy text. Here we may read, for example, that the moon is some 384, 404 km from the earth, that its sidereal day is 27.322 days, that it reflects only about a fourteenth part of the light it receives from the sun, etc.

The way quantitative aspects enter physics is as follows: The ultimate aim of physics is to give coherent descriptions of phenomena and processes that occur in the physical world. Descriptions involve adjectives: good, bad, big, small, hot, cold, ugly, beautiful, strong, weak, fast, flow, etc.

Often such descriptions can be expressed on a comparative scale. Thus we say that something is larger, prettier, hotter, etc. than something else. Now we may go a step further. Once the comparison is established we ask, “By how much?” But this question may not always be answerable. For example, we can say by how much the area of New York is greater than that of Tokyo, but we cannot say by how much the music of Thyagaraja is more (or less) beautiful than that of Bach, or by how much the philosophy of Plato is more (or less) profound than that of Shankara.

Whenever the question, By how much? can be answered we have a situation where measurement is possible. In such cases we can associate numbers with the physical feature considered. We say then that we are dealing with a metric aspect of the world, with a physical quantity.

Many such quantities arise in the course of everyday life. The volume of a bottle, the weight of a baggage, the speed of a train, the time it takes to read this page: all these are examples of physical quantities. Some of them have entered the common vocabulary of the language because of the roles they play in technological societies. Thus we speak of 92.5 megahertz on the radio dial, the 75 watt lamp, and a temperature of 30 degrees Celsius.

The physical world has not only beauty and grandeur but also harmony and interconnectedness. We can not only feel and experience, but also measure and calculate. It would be wrong to think that physicists are uninterested in or insensitive to the aesthetic and qualitative aspects of the world. But in their efforts to explain the features of the world they have found it to be far more fruitful to focus on its quantitative aspects.

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