2.0 MAIN SUBDIVISIONS OF THE SYSTEM

2.0 MAIN SUBDIVISIONS OF THE SYSTEM #

2.1 #

In analyzing the functioning of the contemplated device, certain classificatory distinctions suggest themselves immediately.

2.2 #

First: Since the device is primarily a computer, it will have to perform the elementary operations of arithmetics most frequently. These are addition, subtraction, multiplication and division: +, −, ×, ÷. It is therefore reasonable that it should contain specialized organs for just these operations.

It must be observed, however, that while this principle as such is probably sound, the specific way in which it is realized requires close scrutiny. Even the above list of operations: +, −, ×, ÷, is not beyond doubt. It may be extended to include such operation as \(\sqrt{\quad}\) , \(\sqrt[3]{\quad}\) , sgn, | |, also \(\log_{10}\) , \(\log_{2}\) , \(\ln\) , \(\sin\) and their inverses, etc. One might also consider restricting it, e.g. omitting ÷ and even ×. One might also consider more elastic arrangements. For some operations radically different procedures are conceivable, e.g. using successive approximation methods or function tables. These matters will be gone into in {10.3, 10.4}. At any rate a central arithmetical part of the device will probably have to exist, and this constitutes the first specific part: CA.

2.3 #

Second: The logical control of the device, that is the proper sequencing of its operations can be most efficiently carried out by a central control organ. If the device is to be elastic, that is as nearly as possible all purpose, then a distinction must be made between the specific instructions given for and defining a particular problem, and the general control organs which see to it that these instructions—no matter what they are—are carried out. The former must be stored in some way— in existing devices this is done as indicated in 1.2—the latter are represented by definite operating parts of the device. By the central control we mean this latter function only, and the organs which perform it form the second specific part: CC.

2.4 #

Third: Any device which is to carry out long and complicated sequences of operations (specifically of calculations) must have a considerable memory. At least the four following phases of its operation require a memory:

  • (a)Even in the process of carrying out a multiplication or a division, a series of intermediate (partial) results must be remembered. This applies to a lesser extent even to additions and subtractions (when a carry digit may have to be carried over several positions), and to a greater extent to \(\sqrt{\quad}\) , \(\sqrt[3]{\quad}\) , if these operations are wanted. (cf. {10.3, 10.4})

  • (b)The instructions which govern a complicated problem may constitute a considerable material, particularly so, if the code is circumstantial (which it is in most arrangements). This material must be remembered.

  • (c)In many problems specific functions play an essential role. They are usually given in form of a table. Indeed in some cases this is the way in which they are given by experience (e.g. the equation of state of a substance in many hydrodynamical problems), in other cases they may be given by analytical expressions, but it may nevertheless be simpler and quicker to obtain their values from a fixed tabulation, than to compute them anew (on the basis of the analytical definition) whenever a value is required. It is usually convenient to have tables of a moderate number of entries only ( 100–200) and to use interpolation. Linear and even quadratic interpolation will not be sufficient in most cases, so it is best to count on a standard of cubic or biquadratic (or even higher order) interpolation, (cf. {10.3}).

    Some of the functions mentioned in the course of 2.2 may be handled in this way: \(\log_{10}\) , \(\log_{2}\) , \(\ln\) , \(\sin\) and their inverses, possibly also \(\sqrt{\quad}\) , \(\sqrt[3]{\quad}\) . Even the reciprocal might be treated in this manner, thereby reducing ÷ to ×.

  • (d)For partial differential equations the initial conditions and the boundary conditions may constitute an extensive numerical material, which must be remembered throughout a given problem.

  • (e)For partial differential equations of the hyperbolic or parabolic type, integrated along a variable t, the ( intermediate) results belonging to the cycle t must be remembered for the calculation of the cycle t + dt. This material is much of the type (d), except that it is not put into the device by human operators, but produced (and probably subsequently again removed and replaced by the corresponding data for ) by the device itself, in the course of its automatic operation.

  • (f)For total differential equations (d), (e) apply too, but they require smaller memory capacities. Further memory requirements of the type (d) are required in problems which depend on given constants, fixed parameters, etc.

  • (g)Problems which are solved by successive approximations (e.g. partial differential equations of the elliptic type, treated by relaxation methods) require a memory of the type (e): The (intermediate) results of each approximation must be remembered, while those of the next one are being computed.

  • (h)Sorting problems and certain statistical experiments (for which a very high speed device offers an interesting opportunity) require a memory for the material which is being treated.

2.5 #

To sum up the third remark: The device requires a considerable memory. While it appeared that various parts of this memory have to perform functions which differ somewhat in their nature and considerably in their purpose, it is nevertheless tempting to treat the entire memory as one organ, and to have its parts even as interchangeable as possible for the various functions enumerated above. This point will be considered in detail, cf. {13.0}.

At any rate the total memory constitutes the third specific part of the device: M.

2.6 #

The three specific parts CA, CC (together C) and M correspond to the associative neurons in the human nervous system. It remains to discuss the equivalents of the sensory or afferent and the motor or efferent neurons. These are the input and the output organs of the device, and we shall now consider them briefly.

In other words: All transfers of numerical (or other) information between the parts C and M of the device must be effected by the mechanisms contained in these parts. There remains, however, the necessity of getting the original definitory information from outside into the device, and also of getting the final information, the results, from the device into the outside.

By the outside we mean media of the type described in 1.2: Here information can be produced more or less directly by human action (typing, punching, photographing light impulses produced by keys of the same type, magnetizing metal tape or wire in some analogous manner, etc.), it can be statically stored, and finally sensed more or less directly by human organs.

The device must be endowed with the ability to maintain the input and output (sensory and motor) contact with some specific medium of this type (cf. 1.2): That medium will be called the outside recording medium of the device: R. Now we have:

2.7 #

Fourth: The device must have organs to transfer (numerical or other) information from R into its specific parts, C and M. These organs form its input, the fourth specific part: I. It will be seen that it is best to make all transfers from R (by I) into M, and never directly into C (cf. {14.1, 15.3}).

2.8 #

Fifth: The device must have organs to transfer (presumably only numerical information) from its specific parts C and M into R. These organs form its output, the fifth specific part: O. It will be seen that it is again best to make all transfers from M (by O) into R, and never directly from C, (cf. {14.1, 15.3}).

2.9 #

The output information, which goes into R, represents, of course, the final results of the operation of the device on the problem under consideration. These must be distinguished from the intermediate results, discussed e.g. in 2.4, (e)–(g), which remain inside M. At this point an important question arises: Quite apart from its attribute of more or less direct accessibility to human action and perception R has also the properties of a memory. Indeed, it is the natural medium for long time storage of all the information obtained by the automatic device on various problems. Why is it then necessary to provide for another type of memory within the device M? Could not all, or at least some functions of M—preferably those which involve great bulks of information—be taken over by R?

Inspection of the typical functions of M, as enumerated in 2.4, (a)–(h), shows this: It would be convenient to shift (a) (the short-duration memory required while an arithmetical operation is being carried out) outside the device, i.e. from M into R. (Actually (a) will be inside the device, but in CA rather than in M. Cf. the end of 12.2). All existing devices, even the existing desk computing machines, use the equivalent of M at this point. However (b) (logical instructions) might be sensed from outside, i.e. by I from R, and the same goes for (c) (function tables) and (e), (g) (intermediate results). The latter may be conveyed by O to R when the device produces them, and sensed by I from R when it needs them. The same is true to some extent of (d) (initial conditions and parameters) and possibly even of (f) (intermediate results from a total differential equation). As to (h) (sorting and statistics), the situation is somewhat ambiguous: In many cases the possibility of using M accelerates matters decisively, but suitable blending of the use of M with a longer range use of R may be feasible without serious loss of speed and increase the amount of material that can be handled considerably.

Indeed, all existing (fully or partially automatic) computing devices use R—as a stack of punchcards or a length of teletype tape–for all these purposes (excepting (a), as pointed out above). Nevertheless it will appear that a really high speed device would be very limited in its usefulness unless it can rely on M, rather than on R, for all the purposes enumerated in 2.4, (a)–(h), with certain limitations in the case of (e), (g), (h), (cf. {12.3}).

Calendar November 17, 2022