# The Stroud number in engineering

John M. Stroud was a psychologist who studied the decision processes of people to determine whether such processes have measurable quantities.

John M. Stroud was a psychologist who studied the decision processes of people to determine whether such processes have measurable quantities. On the basis of his research, he identified the concept of elementary discrimination-the process through which people determine, for example, whether an item is green or blue, or whether a statement is true or false. Such decisions have their root in yes-or-no determinations (yes, a given statement is true; no, it is not false).

As engineers, we recognize this phenomenon in the concept of a 'bit' of information. We make decisions about electronic circuits in order to realize a usable electronic function. If we can express the design of an electronic circuit in terms of the amount of information I in that design, and if we have an entity that indicates the amount of bits per second that we can generate or process, then we have a measure of the minimum time it takes to create the desired circuit design.

The Stroud number S, indicating the number of elementary decisions per second, satisfies this definition. Stroud's number has values between 5 and 25 elementary discriminations/second, 25 being the upper limit of images people can discriminate within a second.

M.H. Halstead uses this principle in "Software Science" (Elements of Software Science, Vol. 1. North Holland, N.Y., 1979: Computer Science Library). He describes how to measure the complexity of a software program by looking at measurable properties of the program. One of those properties is the language's vocabulary (number of distinct characters and signs, or operators and operands).

Halstead then introduces the notion of program length by looking at the number of permutations for which the operators and operands can be configured in a program consisting of N symbols. By taking the 2 logarithm of that number, he obtains a theoretical value representing the information in a certain software program.

Halstead then measures program volume, taking into account the minimum length in which a program of certain functionality can be expressed. Next, he defines a program's intelligence content as a measure of the minimum, or essential, information content of a program.

In my book The Design of Communicating Systems" (Boston, 1991: Kluwer Academic Publishers), I use a similar principle but a different measure of the information content I of a system or circuit design. I describe a model in which a designer needs to determine which building blocks to use at a certain level of description, as well as the interconnection pattern linking those blocks.