286 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1960 



the instructions, will have to refer to some other specified drawer for 

 the data he needs to follow out the instruction. He also has a pad of 

 paper on which to store temporarily the results of each operation he 

 performs in obeying these instructions. Except for the first drawer, 

 the clerk will not know in advance which drawers contain numbers 

 and which contain instructions. 



Yet by following the above procedure, which involves performing 

 very simple operations at each step, it is possible for the clerk to solve 

 a large number of problems including some of the most abstruse 

 mathematical problems. The clerk will not need to know what he is 

 doing or why. 



As an example let us consider in detail how this technique can be 

 used to calculate the value of a sum of money subject to compound 

 interest. Assume that we wish to do this for just 20 periods of inter- 

 est accumulation. Further assume that the file drawers (storage 

 locations) are numbered 000, 001, 002, and so on. The clerk goes 

 first to the first drawer (number 000) and finds there an instruction 

 which says, "Take the number in drawer 020 and write it on the pad." 

 The clerk then goes to drawer marked 020 and in it finds a number 

 representing the initial value of principal. Having written this on 

 the pad, he next goes to drawer 001 and reads the instruction there. 

 It says, "Multiply the number on the pad by the number in drawer 

 021 ; leave only the answer on the pad." Since the number in 021 will 

 represent the interest rate, the result of this multiplication would be 

 the amount of interest earned. The clerk now goes to drawer 002, 

 where he is instructed to "Add the number in 020 to the number on the 

 pad." In so doing the new value of principal is computed. He then 

 goes to 003, where the next instruction is, "Store the number on the 

 pad in drawer 020, leaving the pad blank." (This storing of a number 

 in a drawer always means that the number that was previously in that 

 location is erased. However, the process of reading a number in a 

 drawer does not affect that number.) 



Now the clerk, upon going to drawer 004 for his next instruction, 

 might find, "Go to storage location 000 for your next instruction." If 

 so, he will again repeat the instructions in 000, 001, 002, 003, and 004 

 in turn, but this time using the new value of principal. This sequence 

 of operations will be repeated over and over again. Each time this 

 "loop" is repeated the number in 020 will increase, representing the 

 value of principal with the accumulated interest for that number of 

 interest periods. Thus if the initial number in 020 represented $10,000 

 and the number in 021 represented 5 percent, then the values in 020 

 would represent $10,500 after the first loop, $11,025 after the second, 

 $11,556.25 after the third, and so on. 



However, this process would not solve the problem as originally 

 stated, which specified that the process must stop after 20 calculations. 



