6.1 History of computing machines
The goal of early machines was to carry out some physical process with less effort than would be required by a human. These machines took physical things as inputs, performed physical actions on those things, and produced some physical output. For instance, a cotton gin takes as input raw cotton, mechanically separates the cotton seed and lint, and produces the separated products as output.
The first big leap toward computing machines was the development of machines whose purpose is abstract rather than physical. Instead of producing physical things, these machines used physical things to represent information. The output of the machine is valuable because it can be interpreted as information, not for its direct physical effect.
Our first example is not a machine, but using fingers to count. The base ten number system used by most human cultures reflects using our ten fingers for counting.^{1} Successful shepherds needed to find ways to count higher than ten. Shepherds used stones to represent numbers, making the cognitive leap of using a physical stone to represent some quantity of sheep. A shepherd would count sheep by holding stones in his hand that represent the number of sheep.
More complex societies required more counting and more advanced calculating. The Inca civilization in Peru used knots in collections of strings known as khipu to keep track of thousands of items for a hierarchical system of taxation. Many cultures developed forms of abaci, including the ancient Mesopotamians and Romans. An abacus performs calculations by moving beads on rods. The Chinese suan pan (“calculating plate”)
is an abacus with a beam subdividing the rods, typically with two beads above the bar (each representing 5), and five beads below the beam (each representing 1). An operator can perform addition, subtraction, multiplication, and division by following mechanical processes using an abacus.
All of these machines require humans to move parts to perform calculations. As machine technology improved, automatic calculating machines were built where the operator only needed to set up the inputs and then turn a crank or use some external power source to perform the calculation. The first automatic calculating machine to be widely demonstrated was the Pascaline,
built by then nineteenyear old French mathematician Blaise Pascal (also responsible for Pascal’s triangle from Exploration 5.1) to replace the tedious calculations he had to do to manage his father’s accounts. The Pascaline had five wheels, each representing one digit of a number, linked by gears to perform addition with carries. Gottfried Wilhelm von Leibniz built the first machine capable of performing all four basic arithmetic operations (addition, subtraction, multiplication, and division) fully mechanically in 1694.Leibniz, Gottfried
Over the following centuries, more sophisticated mechanical calculating machines were developed but these machines could still only perform one operation at a time. Performing a series of calculations was a tedious and errorprone process in which a human operator had to set up the machine for each arithmetic operation, record the result, and reset the machine for the next calculation.
The big breakthrough was the conceptual leap of programmability. A machine is programmable if its inputs not only control the values it operates on, but the operations it performs.
The first programmable computing machine was envisioned (but never successfully built) in the 1830s by Charles Babbage. Babbage was born in London in 1791 and studied mathematics at Cambridge. In the 1800s, calculations were done by looking up values in large books of mathematical and astronomical tables. These tables were computed by hand, and often contained errors. The calculations were especially important for astronomical navigation, and when the values were incorrect a ship would miscalculate its position at sea (sometimes with tragic consequences).
We got nothing for our $\pounds$ 17,000 but Mr. Babbage’s
grumblings. We should at least have had a clever toy for our money.
Richard Sheepshanks, Letter to the Board of Visitors of the Greenwich
Royal Observatory, 1854
Babbage sought to develop a machine to mechanize the calculations to compute these tables. Starting in 1822, he designed a steampowered machine known as the Difference Engine to compute polynomials needed for astronomical calculations using Newton’s method of successive differencesNewton, Isaac (a generalization of Heron’s method from Exploration 4.1). The Difference Engine was never fully completed. but led Babbage to envision a more general calculating machine.
This new machine, the Analytical Engine, designed between 1833 and 1844, was the first generalpurpose computer envisioned. It was designed so that it could be programmed to perform any calculation. One breakthrough in Babbage’s design was to feed the machine’s outputs back into its inputs. This meant the engine could perform calculations with an arbitrary number of steps by cycling outputs back through the machine.
The Analytical Engine was programmed using punch cards, based on the cards that were used by Jacquard looms. Each card could describe an instruction such as loading a number into a variable in the store, moving values, performing arithmetic operations on the values in the store, and, most interestingly, jumping forward and backwards in the instruction cards.
The Analytical Engine supported conditional jumps where the jump would be taken depending on the state of a lever in the machine (this is essentially a simple form of the if expression).
In 1842, Charles Babbage visited Italy and described the Analytical Engine to Luigi Menabrea, an Italian engineer, military officer, and mathematician who would later become Prime Minister of Italy. Menabrea published a description of Babbage’s lectures in French. Ada, Countess of LovelaceAda Augusta Byron King (also known as Ada, Countess of Lovelace) translated the article into English.
In addition to the translation, Ada added a series of notes to the article. The notes included a program to compute Bernoulli numbers, the first detailed program for the Analytical Engine. Ada was the first to realize the importance and interest in creating the programs themselves, and envisioned how programs could be used to do much more than just calculate mathematical functions. This was the first computer program ever described, and Ada is recognized as the first computer programmer.
Despite Babbage’s design, and Ada’s vision, the Analytical Engine was never completed. It is unclear whether the main reason for the failure to build a working Analytical Engine was due to limitations of the mechanical components available at the time, or due to Babbage’s inability to work with his engineer collaborator or to secure continued funding.
On two occasions I have been asked by members of Parliament, “Pray, Mr.
Babbage, if you put into the machine wrong figures, will the right
answers come out?” I am not able rightly to apprehend the kind of
confusion of ideas that could provoke such a question.
Charles Babbage
The first working programmable computers would not appear for nearly a hundred years. Advances in electronics enabled more reliable and faster components than the mechanical components used by Babbage, and the desperation brought on by World War II spurred the funding and efforts that led to working generalpurpose computing machines.
The remaining conceptual leap is to treat the program itself as data. In Babbage’s Analytical Engine, the program is a stack of cards and the data are numbers stored in the machine. The machine cannot alter its own program.
The idea of treating the program as just another kind of data the machine can process was developed in theory by Alan Turing in the 1930s (Section 6.3 of this chapter describes his model of computing), and first implemented by the Manchester SmallScale Experimental Machine (built by a team at Victoria University in Manchester) in 1948.
This computer (and all generalpurpose computers in use today) stores the program itself in the machine’s memory. Thus, the computer can create new programs by writing into its own memory. This power to change its own program is what makes storedprogram computers so versatile.
Exercise 6.1. Babbage’s design for the Analytical Engine called for a store holding 1000 variables, each of which is a 50digit (decimal) number. How many bits could the store of Babbage’s Analytical Engine hold?

Not all human cultures use base ten number systems. For example, many cultures including the Maya and Basque adopted base twenty systems counting both fingers and toes. This was natural in warm areas, where typical footwear left the toes uncovered. ↩