PHYSICAL QUANTITIES
Suppose that we wish to make an analogue machine. We need to represent information by a measurement of something. What should we select? What physical thing to be measured should we choose to put into the machine? Different amounts of this physical quantity will match with different amounts of the measurement being expressed. In the case of the doorpost, the string, and the slide rule, the physical quantity is distance. In many fire-control instruments, the physical quantity is the amount of turning of a shaft ([Fig. 5]). Many other physical quantities have from time to time been used in analogue machines, such as electrical measurements. The speedometer of an automobile tells distance traveled and speed. It is an analogue machine. It uses the amount of turning of a wheel, and some electrical properties. It handles information by means of measurements. The basic physical quantity that it measures is the amount of turning of a shaft.
Fig. 5. Measurement by amount of turning of a shaft.
DIFFERENTIAL ANALYZER
The biggest and cleverest mechanical brain of the analogue type which has yet been built is the differential analyzer finished in 1942 at Massachusetts Institute of Technology in Cambridge, Mass. The fundamental physical quantity used in this machine is the amount of turning of a shaft. The name analyzer means an apparatus or machine for analyzing or solving problems. It happens that the word “analyzer” has been used rather more often in connection with analogue machines, and so in many cases the word “analyzer” carries the meaning “analogue” as well. The word “differential” in the phrase “differential analyzer” refers to the main purpose of the machine: it is specially adapted for solving problems involving differential equations. Now what is a differential equation?
DIFFERENTIAL EQUATIONS
In order to explain what a differential equation is, we need to use certain ideas. These ideas are: equation; formula; function; rate of change; interval; derivative; and integral. In the next few paragraphs, we shall introduce these ideas briefly, with some explanation and examples. It is entirely possible for anyone to understand these ideas rather easily, by collecting true statements about them; no one should feel that because these ideas may be new they cannot be understood readily.
PHYSICAL PROBLEMS
In physics, chemistry, mechanics, and other sciences there are many problems in which the behavior of distance, of time, of speed, heat, volume, electrical current, weight, acceleration, pressure, and many other physical quantities are related to each other. Examples of such problems are: