Anachronistic Hearts

The Antikythera mechanism is an ancient Greek analogue computer which has also been described as the first example of such device used to predict astronomical positions and eclipses for calendar and astrological purposes decades in advance. It could also be used to track the four-year cycle of athletic games which was similar to an Olympiad, the cycle of the ancient Olympic Games.

This artefact was retrieved from the sea and identified as containing a gear by archaeologist Valerios Stais, among wreckage retrieved from a shipwreck off the coast of the Greek island Antikythera. The instrument is believed to have been designed and constructed by Greek scientists and has been variously dated to somewhere between 205 B.C. to 60 B.C., but the consensus is about 87 B.C.
The device, housed in the remains of a 34cm × 18cm × 9cm (13.4” × 7.1” × 3.5”) wooden box, found as one lump, later separated into three main fragments which are now divided into 82 separate fragments after conservation works. Four of these fragments contain gears, while inscriptions are found on many others. The largest gear is approximately 14 cm (5.5”) in diameter and originally had 223 teeth.

It is a complex clockwork mechanism composed of at least 37 meshing gear wheels enabling it to follow the movements of the Moon and the Sun through the zodiac, to predict eclipses and even to model the irregular orbit of the Moon, where the Moon's velocity is higher in its perigee than in its apogee. This motion was studied in the 2nd century B.C., by astronomer Hipparchus of Rhodes, and it is speculated that he may have been consulted in the machine's construction.
The knowledge of this technology was lost at some point in antiquity. Similar technological works later appeared in the medieval Byzantine and Islamic worlds, but works with similar complexity did not appear again until the development of mechanical astronomical clocks in Europe in the 14th century. All known fragments of the Antikythera mechanism are kept at the National Archaeological Museum in Athens, along with a number of artistic reconstructions and replicas of the mechanism to demonstrate how it may have looked and worked.

The notion of a mechanical calculator for mathematical functions can be traced back to the Antikythera mechanism of the 2nd century BC, while early modern examples are attributed to Pascal and Leibniz in the 17th century. In 1784 J. H. Müller, an engineer in the Hessian army, devised and built an adding machine and described the basic principles of a difference machine in a book published in 1786 (the first written reference to a difference machine is dated to 1784), but he was unable to obtain funding to progress with the idea.

Charles Babbage began to construct a small difference engine in c. 1819 and had completed it by 1822. He announced his invention on 14 June 1822, in a paper to the Royal Astronomical Society, entitled "Note on the application of machinery to the computation of astronomical and mathematical tables". This machine used the decimal number system and was powered by cranking a handle. The British government was interested, since producing tables was time-consuming and expensive and they hoped the difference engine would make the task more economical.

In 1823, the British government gave Babbage £1700 to start work on the project. Although Babbage's design was feasible, the metalworking techniques of the era could not economically make parts in the precision and quantity required. Thus, the implementation proved to be much more expensive and doubtful of success than the government's initial estimate. In 1832, Babbage and Edward Robertson produced a small working model (one-seventh of the calculating section of Difference Engine No. 1, which was intended to operate on 20-digit numbers and sixth-order differences) which operated on 6-digit numbers and second-order differences.

By the time the government abandoned the project in 1842, Babbage had received and spent over £17,000 on development, which still fell short of achieving a working engine. The government valued only the machine's output (economically produced tables), not the development (at unknown and unpredictable cost to complete) of the machine itself. Babbage did not, or was unwilling to, recognize that predicament. Meanwhile, Babbage's attention had moved on to developing an analytical engine, further undermining the government's confidence in the eventual success of the difference engine. By improving the concept as an analytical engine, Babbage had made the difference engine concept obsolete, and the project to implement it an utter failure in the view of the government.

Babbage went on to design his much more general analytical engine, but later produced an improved "Difference Engine No. 2" design (31-digit numbers and seventh-order differences), between 1846 and 1849. Babbage was able to take advantage of ideas developed for the analytical engine to make the new difference engine calculate more quickly while using fewer parts.

The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage. It was first described in 1837 as the successor to Babbage's difference engine a design for a simpler mechanical computer.

The Analytical Engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer.

Babbage's first attempt at a mechanical computing device, the Difference Engine, was a special-purpose machine designed to tabulate logarithms and trigonometric functions by evaluating finite differences to create approximating polynomials. Construction of this machine was never completed; Babbage had conflicts with his chief engineer, Edward Robertson, and ultimately the British government withdrew its funding for the project.

During this project, he realized that a much more general design, the Analytical Engine, was possible. The work on the design of the Analytical Engine started in c. 1833.

The input, consisting of programs ("formulae") and data was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary base-10 fixed-point arithmetic.

There was to be a store (that is, a memory) capable of holding 1,000 numbers of 40 decimal digitseach (ca. 16.2 kB). An arithmetic unit (the "mill") would be able to perform all four arithmetic operations, plus comparisons and optionally square roots.[16] Initially (1838) it was conceived as a difference engine curved back upon itself, in a generally circular layout, with the long store exiting off to one side. Later drawings (1858) depict a regularized grid layout. The mill would rely upon its own internal procedures, to be stored in the form of pegs inserted into rotating drums called "barrels", to carry out some of the more complex instructions the user's program might specify.

The programming language employed by users was three different types of punch cards used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back. There were three separate readers for the three types of cards. Babbage developed some two dozen programs for the Analytical Engine between 1837 and 1840, and one program later. These programs treat polynomials, iterative formulas, Gaussian elimination, and Bernoulli numbers.

In 1842, the Italian mathematician Luigi Federico Menabrea published a description of the engine based on a lecture by Babbage in French. In 1843, the description was translated into English and extensively annotated by Ada Lovelace, who had become interested in the engine eight years earlier. In recognition of her additions to Menabrea's paper, which included a way to calculate Bernoulli numbers using the machine (widely considered to be the first complete computer program), she has been described as the first computer programmer.