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Computers, Statistics, and Mathematics
A R T H U R ROSE AND J O A N A. S C H I L K The Pennsylvania State College, State College, Pa.
R. C U R T I S J O H N S O N Washington University, St. Louis, Mo.
This review gathers together the more important recent literature references and indicates the status of development of the general technology of computers, statistics, and mathematics. Most attention is given to the publications of the last 2 or 3 years, but earlier references are included to provide basic information. This review is divided into sections on automatic computer applications, statistical methods, and miscellaneous special mathematical techniques. The division is somewhat arbitrary, since there are close interrelations between the use of computers and new mathematical techniques, and both of these may be involved i n the more complex applications of statistical methods.
deal with the use, construction, operation, etc., of digital computers (9A, I I A , WOA, %A, 4IA, 65A), while others are concerned solely with analogdevices(IOA, IQA,46A, 47A, 5WA, 54A, 57A, 6WA, 66A). Digital Computers. Large scale digital computers have been well publicized. A list of such machines built or being built in 1951 is available. Information on large scale equipment may also be obtained (IWA) from surveys of this type of machine ( 6 A , W6A, 36A). These large computers are extremely expensive to build and operate, and hence are used for problems of great complexity. No references were found to the use of these very large calculators for solution of chemical or chemical engineering problems. Of much greater interest to the average chemist or engineer are the moderate size digital computers. These are suitable for solution of many research and development problems and are not hopelessly expensive for industrial or college research organizations to purchase or operate. A variety of general and specialized digital devices are available, becoming-available, or have been proposed or described (WIA, 24A, %A, 38A, SQA, QWA--44A,48A, bOA, 6 I A , 6QA, 63A). The possible applications of these moderate scale digital computers includes recording, storage and handling of original and derived data, conversion of original to modified data, analysis and correlation of data, and design and theoretical calculations. The largest and most expensive of the moderate size automatic computers have a capacity approaching that of the very large devices. Thus, one device that is now becoming available can deal with both numerical and alphabetical data without special coding. This has practically unlimited programing capacity and has a readily available memory of 12,000 digits or characters, and a tape memory of about 1,500,000 digits per tape. At the other extreme stands a readily available machine very frequently used for payroll and billing calculations in accounting departments. This has a memory of only a few dozen digits and a very limited program capacity. However, i t can and has served admirably for small scale calculations, and such equipment has in many cases been the starting point for a computing program involving the larger computers for larger problems. It is false economy to try to use an inadequate computer, especially since the larger of the moderate size machines are available on a rental basis. Some help from an expert applied mathematician should be considered as almost an integral part of the larger automatic computers. Applications of Digital Computers. The applications of digital computers in industrial chemistry range from calculation of tables of values of elementary thermodynamic or physical
D M I C A L engineering and chemistry have always made
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extensive practical use of applied mathematics. Many chemical engineers and chemists have been better practical mathematicians than many mathematicians, but this situation is now changing rapidly. The advent of automatic computers has stimulated the interest of mathematicians in engineering and scientific computation. The existence of automatic computers is also increasing still further the use of mathematics in correlating and predicting chemical and engineering phenomena. A parallel development is occurring in the use of mathematical statistics and other specialized mathematical techniques. A brief section of this paper is given over to the problems of filing and finding literature references, since computers are already serving as tools in this area, and increasing use of such devices seems inevitable.
Automatic Computers
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Most of the development of automatic computers of both digital and analog types has occurred within the last 10 years. The use of these devices in research and development problems has accelerated markedly within the past few years. This paper reviews the information available in the literature under the following topics: Reviews of computers, for those interested in general background Brief discussion of the moderate size digital computers now available Specific ap lications of digital computers to chemical engineering and cgemical problems Brief discussion of available analog computers Specific applications of analog computers Special devices accessory to automatic computers Reviews. The use of high-speed computing equipment for the solution of many chemical and chemical engineering research, design, and development problems is a comparatively new field, and the average chemical engineer or chemist, unfamiliar with the specific details of computers, may obtain a general picture of the principal types of computers available, their prices, principles of operation, etc., by reference to the articles which review these subjects in a broad and comprehensive manner ( I A , 4A, IWA, M A , 34A, 35A, 37A, 6 4 A ) . Several reviews of more specialized aspects of computers are available. Some of these
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Table I. Specific Applications of Digital Computers Reference Atanasoff J V and Brandt A. E J . OptiEal kol.'Amer 26, 88 (1936j Brinkley, S. R.. Jr., 1x2, EBG.CHEM., 4 3 2471 (1951) Brinkley S. R . , Jr., and Smith, R. W., Jr., Pgoc. Sei. Computation Forum (IBM), 1948, pp. 77-82: 1949, pp. 58-83 Brough, H. W., Schlinger, W. G., and Sage, B. H., IND.ENG.Cxmr., 43, 2442 (1951) Chem. Eng., 5 9 , 2 2 4 (November 1952) Connolly T. J., Frankel S. P.,and Sage B. H. Am. Inst. Elec. Engrs., M i d . Papeks 50-259 (1950) Cox, E. G., Gross, L.,, and Jeffrey, G. A., Proc. Leeds Phal. Lit. Sac., 5 , Pt. I, 1 (1947) Daigle, E. C., and Young, H. A . , Anal. Chem., 24, 1190 (1952) Donnell, J. W., Proc. Ind. Computation Seminar ( I B M ) . 1950, pp. 91-3 Donnell, J. W., and Draper, R. W., ISD.ENG.CKEM.,43, 2449 (1931) Donnell J W., and Turbin I
