The second MIT differential analyzer is probably the best machine ever built for solving most differential equations. It regularly has an accuracy of 1 part in 10,000. This is enough for most engineering problems. If greater accuracy is needed, the second differential analyzer cannot provide it. Once in a while the machine can reach an accuracy of 1 part in 50,000; but, to balance this, it is sometimes less accurate than 1 part in 10,000.
The MIT differential analyzer No. 2 can find answers to problems very quickly. The time for setting up a problem to be run on the machine ranges from 5 to 15 minutes. The time for preparing the tapes that set up the problem is, of course, longer; but the punch for preparing the tape is a separate machine and does not delay the differential analyzer. The time for the machine to produce a single solution to a problem ranges usually from 3 minutes to a half-hour. It is easy to put on a problem, run a few solutions, take the problem off, study the results, change a few numbers, and then put the problem back on again. This virtue is a great help in a search in a new field. While the study is going on, time is not wasted, for the machine can be busy with a different problem.
Running a problem a second time is a good check on the reliability of an answer. For, when the problem is run the second time, we can arrange that the machine will route the problem to other mechanisms.
The machine has a control panel. Here the operator watching the machine can tell what units are doing what parts of what problems. If a unit gives trouble or needs to be inspected, the clerk can throw a “busy” switch. Then the machine cannot choose that unit for work to be done. The machine contains many protecting signals and alarms. It is idle for repairs less than 5 per cent of the time.
It is not easy to determine the total cost of the machine, for it was partially financed by several large gifts. Also, much of the labor was done by graduate students in return for the instruction that they gained. The actual out-of-pocket cost was about $125,000. If the machine were to be built by industry, the cost would likely be more than 4 times as much. A simple differential analyzer, however, can be cheap. Small scale differential analyzers have been built for less than $1000; their accuracy has been about 1 part in 100.
There are many things that this machine cannot do; it was not built to do them. (1) It cannot choose methods of solution. (2) It cannot perform steps in solving a problem that depend on results as they are found. (3) It cannot solve differential equations containing two or more independent variables. Such equations are called partial differential equations; they appear in connection with the flow of heat or air or electricity in 2 or 3 dimensions, and elsewhere. (4) It cannot solve problems requiring 6 or more digits of accuracy. (5) The machine, while running, can store numbers only for an instant, since it operates on the principle of smoothly changing quantities; however, when the machine stops, the number last held by each device is permanently stored.
None of these comments, however, are criticisms of the machine. Instead they show avenues of development for future machines. As was said before, for solving most differential equations, this machine has no equal to date. The range of problems which any differential analyzer can do depends mostly on the number of its integrators. The second differential analyzer has 18 and provides for expansion to 30. The machine is constructed, also, so that it can be operated in 3 independent sections, each working to solve a different problem. The differential analyzer can operate unattended. After it has been set up and the first few results examined, it can be left alone to grind out large blocks of answers.
An interesting example of the experimental use of a differential analyzer in a commercial business is the following: In Great Britain, R. E. Beard of the Pearl Assurance Company built a differential analyzer with 6 integrators. He applied this machine to compute to 3 figures certain insurance values known as continuous annuities and continuous contingent insurances. He has described the machine and the application he made in a paper published in the Journal of the Institute of Actuaries, Vol. 71, 1942, pp. 193-227.
Chapter 6
ACCURACY TO 23 DIGITS:
HARVARD’S IBM AUTOMATIC
SEQUENCE-CONTROLLED CALCULATOR
One of the first giant brains to be finished was the machine in the Computation Laboratory at Harvard University called the IBM Automatic Sequence-Controlled Calculator. This great mechanical brain started work in April 1944 and has been running 24 hours a day almost all the time ever since. It has produced quantities of information for the United States Navy. Although many problems that have been placed on it have been classified by the Navy as confidential, the machine itself is fully public. The way it was working on Sept. 1, 1945, has been thoroughly described in a 540-page book published in 1946, Volume I of the Annals of the Harvard Computation Laboratory, entitled Manual of Operation of the Automatic Sequence-Controlled Calculator. Since then the machine has been improved in many ways.