Foundations Of Cognitive Science

Differential Analyzer

The differential analyzer was an analog computer developed by Vannevar Bush (1931), who was interested in developing machines that expressed information in terms of physical measures, such as the turning of a shaft (Zachary, 1997).  Work on the differential analyzer was begun in 1928, and it was completed in 1931 at a cost of $25,000.  It was MIT’s first computer.  The purpose of the differential analyzer was to solve differential equations.  The differential analyzer was a set of electric motors that drove a series of gears and shafts; the moving components represented the values of different values in a differential equation of interest, and physical connections amongst the components were physical implementations of relationships amongst mathematical variables.  “Calculations were carried out by brute force.  Metal clanked against metal until a solution arrived” (Zachary, 1997, p. 51).

One key idea underlying the device was the use of analog integrators: devices that integrated variables with respect to others by rotating discs.  “If [the integrator’s] disc be turned at constant speed, having at any time an angle x, and if its displacement be varied in accordance with a variable y, its output will yield the value of ò y dx. (Bush, 1936, p. 663).  Such an integrator could then be “back-coupled” to other components that depended on y, so that they were constrained by the integrator to always be dealing with the current value of the integrated y.  Complicated equations involved setting up such back-coupling amongst a number of integrators, each representing different variables, and with physical relations between shafts representing relationships or dependencies between variables.  These relationships had to be set up by hand; such a setup required physically manipulating machine components, which could take a number of days for each equation; the machine could only solve one equation at a time because its workings were set-up dependent (Zachary, 1997).

Once the machine was set up, a shaft representing values of the independent variable was rotated, and its effects on other variables was simply observed.  “When the independent variable shaft is now turned, every other shaft is driven, and the machine is constrained to move in accordance with the equation” (Bush, 1936, p. 664).


  1. Bush, V. (1931). The differential analyzer. A new machine for solving differential equations. Journal of the Franklin Institute, 212, 447-488
  2. Bush, V. (1936). Instrumental analysis. Bulletin of the American Mathematical Society, 42(10), 649-669.
  3. Zachary, G. P. (1997). Endless Frontier: Vannevar Bush, engineer of the American Century. New York: Free Press.

(Added November, 2010)