Editing History of computing (section)

==Early computation==
{{For timeline|Timeline of computing hardware before 1950}}
{{See also|History of computing hardware}}
Mathematical statements need not be abstract only; when a statement can be illustrated with actual numbers, the numbers can be communicated and a community can arise. This allows the repeatable, verifiable statements which are the hallmark of mathematics and science. These kinds of statements have existed for thousands of years, and across multiple civilizations, as shown below:

The earliest known tool for use in computation is the [[Sumer]]ian [[abacus]], and it was thought to have been invented in [[Babylon]] {{Circa|2700}}–2300 BC. Its original style of usage was by lines drawn in sand with pebbles.{{Citation needed|reason=Jagged 85 cleanup|date=March 2024}}

In {{Circa|1050}}–771 BC, the [[south-pointing chariot]] was invented in [[History of China#Ancient China|ancient China]]. It was the first known [[gear]]ed mechanism to use a [[differential gear]], which was later used in [[analog computer]]s. The [[China|Chinese]] also invented a more sophisticated abacus from around the 2nd century BC known as the [[Chinese abacus]].{{Citation needed|reason=Jagged 85 cleanup|date=March 2024}}

In the 3rd century BC, [[Archimedes]] used the mechanical principle of balance (see {{section link|Archimedes Palimpsest|The Method of Mechanical Theorems}}) to calculate mathematical problems, such as the number of grains of sand in the universe (''[[The sand reckoner]]''), which also required a recursive notation for numbers (e.g., the [[myriad]] [[myriad]]).

The [[Antikythera mechanism]] is believed to be the earliest known geared computing device. It was designed to calculate astronomical positions. It was discovered in 1901 in the [[Antikythera]] wreck off the Greek island of Antikythera, between Kythera and [[Crete]], and has been dated to ''circa'' 100 BC.<ref>{{cite web|url=https://arstechnica.com/science/2021/03/scientists-solve-another-piece-of-the-puzzling-antikythera-mechanism/|title=Scientists solve another piece of the puzzling Antikythera mechanism|publisher=Ars Technica|first=Jennifer|last=Ouellette|date=12 March 2021 }}</ref>

According to [[Simon Singh]], [[Islamic mathematics|Muslim mathematicians]] also made important advances in [[cryptography]], such as the development of [[cryptanalysis]] and [[frequency analysis]] by [[Al-Kindi|Alkindus]].<ref>[[Simon Singh]], ''[[The Code Book]]'', pp. 14-20</ref><ref>{{cite web |url=https://muslimheritage.com/al-kindi-cryptography/ |title= Al-Kindi, Cryptgraphy, Codebreaking and Ciphers |date= 9 June 2003 |access-date=2022-07-03}}</ref> [[Program (machine)|Programmable]] machines were also invented by [[Inventions in medieval Islam|Muslim engineers]], such as the automatic [[flute]] player by the [[Banū Mūsā brothers]].<ref name=Koetsier>{{Citation |last1=Koetsier |first1=Teun |year=2001 |title=On the prehistory of programmable machines: musical automata, looms, calculators |journal=Mechanism and Machine Theory |volume=36 |issue=5 |pages=589–603 |publisher=Elsevier |doi=10.1016/S0094-114X(01)00005-2 |postscript=.}}</ref>

During the Middle Ages, several European philosophers made attempts to produce analog computer devices. Influenced by the Arabs and [[Scholasticism]], Majorcan philosopher [[Ramon Llull]] (1232–1315) devoted a great part of his life to defining and designing several ''logical machines'' that, by combining simple and undeniable philosophical truths, could produce all possible knowledge. These machines were never actually built, as they were more of a [[thought experiment]] to produce new knowledge in systematic ways; although they could make simple logical operations, they still needed a human being for the interpretation of results. Moreover, they lacked a versatile architecture, each machine serving only very concrete purposes. Despite this, Llull's work had a strong influence on [[Gottfried Leibniz]] (early 18th century), who developed his ideas further and built several calculating tools using them.

The apex of this early era of mechanical computing can be seen in the [[Difference engine|Difference Engine]] and its successor the [[Analytical engine|Analytical Engine]]  both by [[Charles Babbage]]. Babbage never completed constructing either engine, but in 2002 [[Doron Swade]] and a group of other engineers at the [[Science Museum, London|Science Museum in London]] completed Babbage's Difference Engine using only materials that would have been available in the 1840s.<ref>{{Cite news |title=A 19th-Century Mathematician Finally Proves Himself |language=en |work=NPR.org |url=https://www.npr.org/templates/story/story.php?storyId=121206408 |access-date=2022-10-24}}</ref>  By following Babbage's detailed design they were able to build a functioning engine, allowing historians to say, with some confidence, that if Babbage had been able to complete his Difference Engine it would have worked.<ref>{{Cite web |title=A Modern Sequel {{!}} Babbage Engine {{!}} Computer History Museum |url=https://www.computerhistory.org/babbage/modernsequel/ |access-date=2022-10-24 |website=www.computerhistory.org}}</ref> The additionally advanced Analytical Engine combined concepts from his previous work and that of others to create a device that, if constructed as designed, would have possessed many properties of a modern electronic computer, such as an internal "scratch memory" equivalent to [[random-access memory|RAM]], multiple forms of output including a bell, a graph-plotter, and simple printer, and a programmable input-output "hard" memory of [[punch cards]] which it could modify as well as read.  The key advancement that Babbage's devices possessed beyond those created before him was that each component of the device was independent of the rest of the machine, much like the components of a modern electronic computer. This was a fundamental shift in thought; previous computational devices served only a single purpose but had to be at best disassembled and reconfigured to solve a new problem.  Babbage's devices could be reprogrammed to solve new problems by the entry of new data and act upon previous calculations within the same series of instructions. [[Ada Lovelace]] took this concept one step further, by creating a program for the Analytical Engine to calculate [[Bernoulli numbers]], a complex calculation requiring a recursive algorithm.  This is considered to be the first example of a true computer program, a series of instructions that act upon data not known in full until the program is run.

Following Babbage, although unaware of his earlier work, [[Percy Ludgate]]{{sfn|Randell|1982|pp=4–5}}<ref name=":2">{{Cite web|url=http://www.fano.co.uk/ludgate/|title=Percy Ludgate's Analytical Machine|website=fano.co.uk|access-date=29 October 2018}}</ref> in 1909 published the 2nd of the only two designs for mechanical analytical engines in history.<ref>{{Cite web |url=https://www.scss.tcd.ie/SCSSTreasuresCatalog/miscellany/TCD-SCSS-X.20121208.002/TCD-SCSS-X.20121208.002.pdf |title=Percy E. Ludgate Prize in Computer Science |work=The John Gabriel Byrne Computer Science Collection |access-date=2020-01-15}}</ref> Two other inventors, [[Leonardo Torres Quevedo]]{{Sfn|Randell|1982|pp=6, 11–13}} and [[Vannevar Bush]],{{sfn|Randell|1982|pp=13, 16-17}} also did follow-on research based on Babbage's work. In his ''Essays on Automatics'' (1914) Torres presented the design of an electromechanical calculating machine and introduced the idea of [[Floating-point arithmetic]].<ref name="LTQ1914es">{{cite journal |author=L. Torres Quevedo |title=Ensayos sobre Automática – Su definicion. Extension teórica de sus aplicaciones |journal=Revista de la Academia de Ciencias Exacta, Revista 12 |pages=391–418 |date=1914}}</ref><ref name="LTQ1915fr">{{cite journal |last=Torres Quevedo |first=L. |date=1915 |url=https://diccan.com/dicoport/Torres.htm |title=Essais sur l'Automatique - Sa définition. Etendue théorique de ses applications |journal=Revue Génerale des Sciences Pures et Appliquées |volume=2 |pages=601–611}}</ref> In 1920, to celebrate the 100th anniversary of the invention of the [[arithmometer]], Torres presented in Paris the [[Leonardo Torres y Quevedo#Analytical machines|Electromechanical Arithmometer]], an arithmetic unit connected to a remote typewriter, on which commands could be typed and the results printed automatically.<ref>{{cite web|access-date=3 February 2018|title=Computer Pioneers by J.A.N. Lee - Leonardo Torres Y Quevedo|url=http://history.computer.org/pioneers/torres.html}}<!-- auto-translated by Module:CS1 translator --></ref>{{sfn|Bromley|1990}} Bush's paper ''Instrumental Analysis'' (1936) discussed using existing IBM punch card machines to implement Babbage's design. In the same year, he started the Rapid Arithmetical Machine project to investigate the problems of constructing an electronic digital computer.

Several examples of analog computation survived into recent times.  A [[planimeter]] is a device that does integrals, using [[distance]] as the analog quantity. Until the 1980s, [[HVAC]] systems used [[air]] both as the analog quantity and the controlling element. Unlike modern digital computers, analog computers are not very flexible and need to be reconfigured (i.e., reprogrammed) manually to switch them from working on one problem to another. Analog computers had an advantage over early digital computers in that they could be used to solve complex problems using behavioral analogues while the earliest attempts at digital computers were quite limited.

[[Image:Visual Smith Chart.png|thumb|A [[Smith Chart]] is a well-known [[nomogram]].]]
Since computers were rare in this era, the solutions were often ''hard-coded'' into paper forms such as [[nomogram]]s,<ref>
{{Cite book | last = Steinhaus | first =  H. | title = Mathematical Snapshots | edition= 3rd | publisher = Dover | year= 1999 | location = New York | pages = 92–95, 301}}
</ref> which could then produce analog solutions to these problems, such as the distribution of pressures and temperatures in a heating system.