# Operational definition

An operational definition of a quantity is a specific process whereby it is measured. For example, the weight of an object can be operationally defined by using a balance and standard weights. Operational definitions are also used in defining system states by a specific preparation process. For example, 100 degrees Celsius can be crudely defined by the process of heating water until it is observed to boil.

It has been said, slightly imprecisely, that the operational definition of a cake is the recipe for baking the cake,which we can regard as a state preparation process. A similar saying, if it walks like a duck and quacks like a duck, it's a duck, can be regarded as a sort of measurement process.

Despite the controversial philosophical origins of the concept, particularly its close association with logical positivism, operational definitions have undisputed practical applications. Operational definitions are particularly important in quantum mechanics, statistical physics and relativity.

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## Relevance to philosophy

The idea originally arises in the operationalist philosophy of P. W. Bridgman and others. By 1914, Bridgman was dismayed by the abstraction and lack of clarity with which, he argued, many scientific concepts were expressed. Inspired by logical positivism and the phenomenalism of Ernst Mach, in 1914 he declared that the meaning of a physical concept, such as mass, lay in the operations, physical and mental, performed in its measurement.

Thus, mass, as measured with a spring balance, and mass, as measured using a load cell are quite distinct concepts. That they are highly correlated in general is interesting, and worth noting, but ought not lead us to abstract discussions about the mass or the true mass of a body.

He developed his philosophy in his book The Logic of Modern Physics (1927).

## Relevance to standardisation

Physical quantities, such as temperature and electric current are commonly defined in textbooks in terms of their abstract definitions (vide infra). This leads to some practical difficulties for the standardisation demanded for trade and for testing the reproducibility of scientific results. Standardisation bodies, therefore, specify physical quantities in terms of operational definitions in order to facilitate agreement and reproducibility.

## Relevance to scientific practice

Operational definitions are at their most controversial in the field of psychology where intuitive concepts, such as intelligence need to be operationally definied before they become amenable to scientific investigation, for example, through processes such as IQ tests. Such definitions are used as a follow up to a conceptual definition, in which the specific concept is defined as a measurable occurrence. John Stuart Mill pointed out the dangers of believing that anything that could be given a name must refer to a thing and Stephen Jay Gould and others have criticised psychologists for doing just that. A committed operationalist would respond that speculation about the thing in itself should be resisted and comment only made on the tables of operationally defined measurements.

## Relevance to business

On October 15 1970, the West Gate Bridge in Melbourne, Australia collapsed, killing 35 construction workers. The subsequent enquiry found that the failure arose because engineers had specified the supply of a quantity of flat steel plate. The word flat in this context lacked an operational definition, so there was no test for accepting or rejecting a particular shipment or for controlling quality.

In his managerial and statistical writings, W. Edwards Deming placed great importance on the value of using operational definitions in all agreements in business. As he said:

"An operational definition is a procedure agreed upon for translation of a concept into measurement of some kind." - W. Edwards Deming

"There is no true value of any characteristic, state, or condition that is defined in terms of measurement or observation. Change of procedure for measurement (change of operational definition) or observation produces a new number." - W. Edwards Deming

## Examples

### Temperature

The thermodynamic definition of temperature, due to Nicolas Léonard Sadi Carnot, refers to heat flowing between infinite reservoirs. This is all highly abstract and unsuited for the day-to-day world of science and trade. In order to make the idea concrete, temperature is defined in terms of operations with the gas thermometer. However, these are sophisticated and delicate instruments, only adapted to the national standardisation laboratory.

For day-to-day use, the International Practical Temperature Scale (IPTS) is used, defining temperature in terms of the electrical resistance of a thermistor, with specified construction, calibrated against operationally defined fixed points.

### Electric current

Electric current is defined in terms of the force between two infinite parallel conductors, separated by a specified distance. This definition is too abstract for practical measurement so a device known as a current balance is used to define the ampere operationally.

### Mechanical hardness

Unlike temperature and electric current, there is no abstract physical concept of the hardness of a material. It is a slightly vague, subjective idea, somewhat like the idea of intelligence. In fact, it leads to three more specific ideas:

1. Scratch hardness measured on Mohs’ scale;
2. Indentation hardness; and
3. Rebound, or dynamic, hardness measured with a Shore scleroscope.

Of these, indentation hardness itself leads to many operational definitions, the most important of which are:

1. Brinell hardness—using a 10mm steel ball;
2. Vickers hardness—using a pyramidal diamond indenter; and
3. Rockwell hardness—using a diamond cone indenter.

In all these, a process is defined for loading the indenter, measuring the resulting indentation and calculating a hardness number. Each of these three sequences of measurement operations produces numbers that are consistent with our subjective idea of hardness. The harder the material to our informal perception, the greater the number it will achieve on our respective hardness scales. Furthermore, experimental results obtained using these measurement methods has shown that the hardness number can be used to predict the stress required to permanently deform steel, a characteristic that fits in well with our idea of resistance to permanent deformation. However, there is not always a simple relationship between the various hardness scales. Vickers and Rockwell hardness numbers exhibit qualitatively different behaviour when used to describe some materials and phenomena.

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