Giant brains; or, Machines that think

by Edmund Callis Berkeley

THE DIFFERENTIAL ANALYZER

The basic scientific articles on the two differential analyzers at Massachusetts Institute of Technology are:

Bush, Vannevar, The Differential Analyzer: A New Machine for Solving Differential Equations, Journal of the Franklin Institute, vol. 212, no. 4, Oct. 1931, pp. 447-488.

Bush, Vannevar, and Samuel H. Caldwell, A New Type of Differential Analyzer, Journal of the Franklin Institute, vol. 240, no. 4, Oct. 1945, pp. 255-326.

Some of the less technical articles about the second differential analyzer at M.I.T. are:

Caldwell, Samuel H., Educated Machinery, Technology Review, vol. 48, no. 1, Nov. 1945, pp. 31-34.

Genet, N., 100-Ton Brain at M.I.T., Scholastic, vol. 48, Feb. 4, 1946, p. 36.

Anonymous, Mathematical Machine; New Electronic Differential Analyzer, Science News Letter, vol. 48, Nov. 10, 1945, p. 291.

Anonymous, Robot Einstein: Differential Analyzer at M.I.T., Newsweek, vol. 26, Nov. 12, 1945, p. 93.

Anonymous, M.I.T.’s 100-Ton Mathematical Brain is Now to Tackle Problems of Peace, Popular Science, vol. 148, Jan. 1946, p. 81.

Anonymous, The Great Electro-Mechanical Brain; M.I.T.’s Differential Analyzer, Life, vol. 20, Jan. 14, 1946, pp. 73-74 ...

Anonymous, All the Answers at Your Fingertips; in the Laboratory of M.I.T., Popular Mechanics, vol. 85, Mar. 1946, pp. 164-167 ...

A differential analyzer was built at the Moore School of Electrical Engineering:

Travis, Irven, Differential Analyzer Eliminates Brain Fag, Machine Design, July 1935, pp. 15-18.

A differential analyzer was built at the General Electric Company, Schenectady, N. Y. Instead of using a mechanical or electrical amplifier of the motion of the little turning wheel riding on the disc, this machine follows the motion using polarized light. This machine is described in:

Berry, T. M., Polarized Light Servo System, Transactions of the American Institute of Electrical Engineers, vol. 63, Apr. 1944, pp. 195-197.

Kuehni, H. P., and H. A. Peterson, A New Differential Analyzer, Transactions of the American Institute of Electrical Engineers, vol. 63, May 1944, pp. 221-227.

A differential analyzer has been put into use at the University of California:

Boelter, L. M. K., and others, The Differential Analyzer of the University of California, Los Angeles: University of California, 1947, 25 pp.

A differential analyzer was built at Manchester University, England. It was built first from “Meccano” parts, at a total cost of about 20 pounds, and later refined for more exact work. Some articles dealing with this differential analyzer are:

Hartree, D. R., The Differential Analyzer, Nature, vol. 135, June 8, 1935, p. 940.

Hartree, D. R., The Mechanical Integration of Differential Equations, The Mathematical Gazette, vol. 22, 1938, pp. 342-364.

Hartree, D. R., and A. Porter, The Construction of a Model Differential Analyser, Memoirs and Proceedings of the Manchester Literary and Philosophical Society, vol. 79, July 1935, pp. 51-72.

Other small scale differential analyzers built in England are covered in:

Beard, R. E., The Construction of a Small Scale Differential Analyser and Its Application to the Calculation of Actuarial Functions, Journal of the Institute of Actuaries, vol. 71, 1942, pp. 193-227.

Massey, H. S. W., J. Wylie, and R. A. Buckingham, A Small Scale Differential Analyser: Its Construction and Operation, Proceedings of the Royal Irish Academy, vol. 45, 1938, pp. 1-21.

A differential analyzer constructed in Germany is briefly described in the following:

Sauer, R., and H. Poesch, Integrating Machine for Solving Ordinary Differential Equations, Engineers Digest (American Edition), vol. 1, May 1944, pp. 326-328.

From the historical point of view there are some interesting papers on a machine for solving differential equations by Sir William Thomson (Lord Kelvin), including one by his brother James Thomson. They are in the Proceedings of the Royal Society, vol. 24, Feb. 1876, pp. 262-275. The method of integration by a machine is described, but the state of machine tools at the time was such that no accurate mechanism was constructed. Another interesting paper foreshadowing the differential analyzer is:

Wainwright, Lawrence L., A Ballistic Engine, Chicago: University of Chicago, thesis for Master’s Degree, 1923, 28 pp.

Some of the applications and mathematical limitations of differential analyzers are covered in:

Bush, V., and S. H. Caldwell, Thomas-Fermi Equation Solution by the Differential Analyzer, Physical Review, vol. 38, no. 10, 1931, pp. 1898-1902.

Hartree, D. R., A Great Calculating Machine: the Bush Differential Analyser and Its Applications in Science and Industry, Proceedings of the Royal Institution of Great Britain, vol. 31, 1940, pp. 151-170.

Hartree, D. R., and A. Porter, The Application of the Differential Analyser to Transients on a Distortionless Transmission Line, Journal of the Institute of Electrical Engineering, vol. 83, no. 503, Nov. 1938, pp. 648-656.

Hartree, D. R., and J. R. Womersley, A Method for the Numerical or Mechanical Solution of Certain Types of Partial Differential Equations, Proceedings of the Royal Society of London, series A, vol. 161, 1937, pp. 353-366.

Maginniss, F. J., Differential Analyzer Applications, General Electric Review, vol. 48, no. 5, May 1945, pp. 54-59.

Shannon, Claude E., Mathematical Theory of the Differential Analyzer, Journal of Mathematics and Physics, Cambridge, Mass.: Massachusetts Institute of Technology, vol. 20, no. 4, 1941, pp. 337-354.