The modern digital computer was invented and intended as device that should facilitate speed for complicated and time -consuming computation. In the majority of applications its capability to store and access large amounts of information, it`s dominant part, its primary characteristic, and its ability to compute that is its ability to calculate, and perform arithmetic operations, has in may cases become almost irrelevant.
In all these cases, the large amount of information that is to be processed represents an abstraction of a part of the real world. The information that is available to the computer consists of a selected set of data about the real world, namely, the set which is considered relevant to the problem at hand, which is believed that the desired results can be derived. The data represent an abstraction of reality in the sense that certain properties and characteristics of the real objects are ignored because they are peripheral and irrelevant to the particular problem. An abstraction is thereby also a simplification of facts.
A personnel file of an employer can be abstracted by data structures. Every employee is represented (abstracted) on this file by a set of data relevant either to the employer or to his accounting procedures. This set may include some identification of the employee, for example, his name and salary. But it will most probably not include irrelevant data such as the color of hair, weight, and height.
In solving a problem with or without a computer it is necessary to choose an abstraction of reality, i.e. to define a set of data that is to represent the real situation. This choice must be guided by the problem to be solved which follows a choice of representation of this information. This choice is guided by the tool that is to solve the problem, i.e., by the facilities offered by the computer. In most cases these two steps are not entirely independent.
The choice of representation of data is often a fairly difficult one, and it is not uniquely determined by the facilities available. It must always be taken in the light of the operations that are to be performed on the data.
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Numbers can be represented, which are themselves abstractions of properties of objects to be characterized. If addition is the only (or at least the dominant) operation to be performed, then a good way to represent the number n is to write n strokes.
