The Uses of Numbers in Research

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.

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