Exhibition Processing Unit

Who used to calculate in the past?

> Careers > Collage:   

Mining Officer

© SLUB / Deutsche Fotothek


© Adam-Ries-Bund e. V. /Adam-Ries-Museum Annaberg-Buchholz


© Adam-Ries-Bund e. V. /Adam-Ries-Museum Annaberg-Buchholz


© Adam-Ries-Bund e. V. /Adam-Ries-Museum Annaberg-Buchholz


© Adam-Ries-Bund e. V. /Adam-Ries-Museum Annaberg-Buchholz


© https://commons.wikimedia.org


Multiplying with your fingers

© ZCOM-Stiftung

Our 10 fingers are the oldest calculating tool we have. They formed the basis for the development of the decimal system. Our fingers can be used not only to add and subtract, but also to multiply.

Facts & figures:

The word digital originally comes from the Latin term digitus, one of the ten fingers for counting, which is why it also came to mean a single number symbol in Latin. The word eventually entered English as “digit” – with the same two meanings as in Latin.


Calculation aids – yesterday´s means?

About the abacus:


Instructions for using a Chinese abacus, published in Hong Kong, year unknown

© Prof. Jörn Lütjens

Using an abacus at the fish market in St. Petersburg

© http://www.sliderulemuseum.com


Russian Large Schoty abacus, circa 1965

Price: 3 roubles, 40 kopeks

Japanese Soroban abacus, first half of 20th century

Lender: Mathematisch-Physikalischer Salon, Staatliche Kunstsammlungen Dresden

The abacus has been used as an aid to computation for over 5,000 years – and still is today. There are also different variants: suanpan = Chinese abacus, soroban = Japanese abacus, schoty = Russian abacus.

Facts & figures:

A calculating contest was held in 1946 in which Kiyoshu Matzukai from Japan used an abacus to compete against a computer. The winner was the Japanese calculator with his abacus.

In the Middle Ages the most widely used computation method involved calculating on lines. Traders and merchants used reckoning tables, marked cloths or counting boards for this purpose. The written form of calculation invented in India was not customary in Europe at that time.

Facts & figures:

Real coins were not used for performing calculations on counting boards, but so-called jetons. These were just reckoning counters and had no actual value.


About Adam Ries:

“May that everyone understand the art of reckoning* with pleasure and merriment

Motto of the mathematician and reckoning master Adam Ries (1492–1559)

Adam Ries spread the art of reckoning through his German-language arithmetic books. He built on the traditional system of calculating on lines, advancing to “modern” calculations with Indian-Arabic numbers, quill and paper.


The world’s only copy of the third edition of the first arithmetic book

© Adam-Ries-Bund e. V. / Adam-Ries-Museum Annaberg-Buchholz

The only known portrait of Adam Ries appears in his third arithmetic book, Practica, dating from 1550

© Adam-Ries-Bund e. V. / Adam-Ries-Museum Annaberg-Buchholz


About John Napier:

“Seeing there is nothing that is so troublesome to mathematical practice … than the multiplications, divisions, square and cubical extractions of great numbers … I began therefore to consider in my mind by what certain and ready art I might remove those hindrances*.”

John Napier (1550–1617), Scottish mathematician and natural philosopher

Almost at the same time as the Swiss clockmaker Jost Bürgi (1558–1632), Napier developed further the concept of logarithms, which had already been known since early times in India. Napier’s bones, the computational aid he invented to make multiplying and dividing large numbers easier, were based on them.


John Napier (1550–1617), Scottish mathematician and natural philosopher

© Wellcome Library, London

In 1614, Napier described logarithms in his book Mirifici Logarithmorum Canonis Descriptio.

© https://commons.wikimedia.org


Napier’s bones, England circa 1700

Lender: Mathematisch-Physikalischer Salon, Staatliche Kunstsammlungen Dresden

Facts & figures:

The underlying principle of Napier’s bones was also used in the first mechanical calculator, Wilhelm Schickard’s calculating clock.

( See Interface section in the main room of the exhibition)

Using logarithms makes it possible, for example, to replace a multiplication with an addition that involves much less calculation. Furthermore, logarithms describe phenomena like the spirals of a snail shell in a mathematically elegant way.

Log tables were an important calculating tool for centuries. In German schools the tables were only replaced by slide rules in the 1960s.


About Oughtred portrait:

William Oughtred (1574–1660), English mathematician* and clergyman

William Oughtred became known for the invention of the circular slide rule, an idea which he published in writing for the first time in 1632. The slide rule with movable inner rule was introduced by Robert Bissaker in 1654 and Seth Patridge in 1657. Oughtred was also the first mathematician to use the Greek letter π (pi) to denote the ratio of a circle’s circumference to its diameter.

Cover of ARISTO – “Announcements for the Friends of the House of Dennert & Pape – Hamburg” (1954)

In 1624, ten years after Napier published his description of logarithms, the English theologian and mathematician Edmund Gunter (1581–1626) developed the first calculating rule with a logarithmic scale. Ground-breaking, however, was Oughtred’s invention of the slide rule, which was only replaced by the electronic pocket calculator at the end of the 1960s.


Exhibits: (Manufacturer, year)

Meissner Multi slide rule (VEB Mantissa Dresden, circa 1970)

REISS Darmstadt slide rule (VEB Mess- und Zeichengerätebau Bad Liebenwerda, 1970s)

ARISTO BISCHOLAR slide rule (Firma Aristo-Werke Dennert & Pappe, 1974)

CONCISE NO. 300 circular slide rule (Firma Concise Co., LTD Tokyo, circa 2008)

CONTROLLER circular slide rule (Nestler company, circa 1965)

On loan: Dr. Zülke, Hoyerswerda

Facts & figures:

James Watt used a slide rule to design his steam engine. Slides rules were also used to calculate the Golden Gate Bridge in San Francisco. Astronauts even took slide rules into space on the Apollo missions.

About slide rules:

Produx Record M mechanical calculator made by Record, GDR circa 1968

Price: 17.40 GDR marks

Addiator Duplex mechanical calculator made by Addiator Rechenmaschinenfabrik, C. Kübler, Berlin, circa 1955

Lender: Dr. Zülke, Hoyerswerda

Because they were inexpensive and easy to use, the Addiator was one of the most popular calculating devices of the 20th century. It goes back to the invention of the French polymath Claude Perrault (1613–1688). This mechanical instrument for addition and subtraction was first marketed in Russia around 1850.


Mechanical calculators

Leibniz quotation:

“It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines* were used.”

The polymath Gottfried Wilhelm Leibniz (1646–1716)

There were mechanical calculators before Leibniz. Known examples include Schickard’s calculating clock of 1623 and the Pascaline, which Blaise Pascal produced from 1645 onwards. Nevertheless, it was Leibniz who developed the operating mechanisms that mechanical calculators were to use to perform calculations until the invention of the computer and beyond: the pinwheel calculator and the Leibniz wheel or stepped drum.

“I believe I have finally found a reliable and simple procedure that also takes less space…”

Leibniz’s note on the stepped drum* in a manuscript dated 8 May 1682

Leibniz presented his first calculating machine in London in 1673. Three of Leibniz’s four mechanical calculators worked with stepped drums. The 1675 Paris machine used the pinwheel as a memory system. Leibniz and the Italian mathematician Giovanni Poleni (1683–1761) developed this technology independently of one another.


Notes by Leibniz on the stepped drum dated 8 May 1682

© Gottfried Wilhelm Leibniz Bibliothek – Niedersächsische Landesbibliothek Hannover. Signatur der Manuskriptseite: LH XLII, 4, 1, Bl. 40r                              

“Living calculating bench”, Leibniz’s calculator based on the stepped drum (replica 1988)

© Historisches Museum Hannover

Pinwheel calculator sketch by Leibniz, before 1676

© Gottfried Wilhelm Leibniz Bibliothek – Niedersächsische Landesbibliothek Hannover. Signatur der Manuskriptseite:  LH XLII, 5, Bl. 29r

Giovanni Poleni (1683–1761), Italian mathematician*

Poleni is considered the inventor of the pinwheel calculator alongside Leibniz.

© http://history-computer.com/

Pinwheel sketch by Poleni (1709)

© https://commons.wikimedia

Patent for the pinwheel calculator by Willgodt Theophil Odhner, 1891

The industrial manufacturing of mechanical calculators began in the second half of the 19th century, when the pinwheel design competed with the stepped drum. The Swede Willgodt Theophil Odhner (1845–1905) patented his pinwheel calculator in the USA in 1878 and in Switzerland in 1891. Machines based on the Odhner design were regarded as very robust and continued to be used until the 1980s.

Description of the Brunsviga 13RK calculator – with the Odhner pinwheel mechanism, 1950s

The Braunschweig-based German company of Grimme, Natalis & Co. acquired an Odhner licence. Their Brunsviga 13RK calculator therefore also worked with a pinwheel system.


Brunsviga 13 RK by Braunschweig-based company Grimme, Natalis & Co., 1950s

The Brunsviga was the most popular mechanical calculator in Germany and continued to be produced until the 1960s.


About the portrait of Charles Xavier Thomas de Colmar (Main figure in audio guide)

Charles Xavier Thomas de Colmar (1785–1870), French inventor*

After completing his military service Thomas became the main partner in an insurance company. The calculation of insurance claims induced him to start constructing a mechanical calculator. He patented the first model in 1820 and called it the arithmometer or arithmomètre in French.

Thomas arithmometer / patent drawing

The patent drawing of 18 November 1820 describes how the Thomas arithmometer works.

Working on the stepped drum principle, the arithmometer could master all four basic arithmetic operations. In around 1850 it became the first industrially manufactured mechanical calculator. Thomas’s factory produced roughly 1,500 machines by 1878.

Facts & figures:

In November 2013 a Thomas arithmometer – reputedly manufactured around 1835 – was sold at auction in Cologne for 233,000 euros.


About the Burkhardt Arithmometer exhibit

The Burkhardt arithmometer was manufactured in Glashütte (Saxony) between 1876 and 1878. It has a 6-digit input register, a 16-digit output register and a turn counter. The inside of the machine is made out of steel and brass and the housing of wood.

Lender: Mathematisch-Physikalischer Salon, Staatliche Kunstsammlungen Dresden

Arthur Burkhardt’s patent document and drawing

Arthur Burkhardt (1857–1918) founded the first German mechanical calculator factory in Glashütte, Saxony, in 1858. The Burkhardt arithmometer is based on the Thomas arithmometer and also worked on the principle of the stepped drum.


About Curta

Curta Type I mechanical calculator in presentation case – partially disassembled (circa 1950)

Lender: Technische Sammlungen Dresden – Museum of Science and Technology

Curta Type II mechanical calculator (end of the 1950s)

Lender: Stiftung Deutsches Technikmuseum Berlin

The world’s smallest mechanical calculator was invented by the Austrian Curt Herzstark (1902–1988). As a half Jew he was sent to Buchenwald Concentration Camp in 1943. There he was forced to design the small calculating machine. Liliput, as the machine was originally called, was meant to be bestowed upon Adolf Hitler as a gift for the “final victory”.

Facts & figures:

The Curta was also taken on two Mount Everest expeditions – thereby helping to ascend the mountain mathematically.

Display case/models:

The stepped drum is a cylinder with nine raised teeth of different lengths. These teeth can mesh with a slideable sprocket with ten teeth. Digits are entered with a full turn of the stepped drum. Depending on the position of the sprocket, a specific number of teeth on the drum mesh with it, which turns a counting wheel.

Therefore, if you want to enter the digit 9, you move the sprocket to the position where all 9 teeth on the drum mesh with the sprocket during a full turn of the drum. The counting wheel then displays 9.

Presentation model with stepped drum (from a mechanical calculator)

Lender: Stiftung Deutsches Technikmuseum Berlin

A number of projections (pins) can be extended from the pinwheel using a lever. These pins then mesh with a cog that has ten teeth and is connected to a counting wheel. After completing a full turn of the pinwheel the counting wheel shows the appropriate digit.

You therefore have to extend 9 pins using the lever to enter the number 9. When you turn the pinwheel through a complete revolution, the 9 pins mesh with the cog and turn the counting wheel to the number 9.

Working model with pinwheel

Don’t be afraid to touch. Give it a try!

Functioning model of a pinwheel calculator

Addition with the pinwheel calculator

Before making a calculation, make sure the model is reset to its initial state:

  • The result display must be reset to zero by turning the star (1).
  • The lever (2) of the turning wheel (3) must be engaged.

Input the first addend (number to be added) using the adjustment bar (4). This pushes the respective number of teeth (5) outward.

Release the turning wheel from its anchoring by pulling lightly on the lever. Then turn the wheel clockwise through exactly one revolution. This transfers the number to the storage register (6).

Then the second addend is entered by turning the adjustment bar (4).

Turning the wheel (3) through another revolution transfers the second number via the teeth to the storage register (6). That is where you can read the result without carryover.


Calculating machines in series

Mechanical calculators

Initially, machines with a stepped drum mechanism were easier to manufacture. In the 20th century, however, economical, compact and low-maintenance pinwheel calculators became serious market competitors. Compared to the first electronic calculators, on the other hand, the stepped drum had the advantage that it could be turned at high speed using a motor. In the case of the pinwheel, a substantially greater mass had to be moved.

At the beginning of the 20th century, inexpensive adding machines only capable of carrying out additions and subtractions became commonplace. More expensive three-operation machines could also multiply and four-operation machines also divide.

Exhibits: (Manufacturer, year)

Brunsviga 10 mechanical calculator (Grimme, Natalis & Co. Braunschweig, circa 1940)

Triumphator CN mechanical calculator (VEB Triumphator-Werk Rechenmaschinenfabrik Leipzig-Mölkau, circa 1953)

DARO Ascota 314 mechanical calculator (VEB Secura-Werke Berlin, 1970s)

Olympia192-060 mechanical calculator (Olympia-Werke AG Wilhelmshaven, 1950s)

Wanderer Continental 700 accounting machine (Wanderer-Werke Chemnitz, 1930s)

NISA AK5 mechanical calculator (Národní podnik Nisa in Proseč near Liberec/Czechoslovakia, circa 1970)

Cellatron R43 SM mechanical calculator (Mercedes-Büromaschinen-Werke AG/Zella-Mehlis/Thuringia, 1960s)


Digital art

Digital art moves at the interface between the digital and the analogue, between the virtual and the real and between human and machine.

It encompasses all forms of artistic expression that are created or are only possible with the aid of a computer.

Its beginnings were strongly influenced by scientists who attempted to represent mathematical problems in visual form.

School student project: computers were people

The word “computer” only came to be generally used to describe electronic calculating devices from the mid-1950s onwards. Before that in the English-speaking world computers were people who were employed to perform calculations. German Rechenknechte (literally, calculating servants) also worked for companies or private individuals that had a lot of calculating work – and usually used contemporary calculating tools for that purpose. Today computer technology is becoming integrated into almost all areas of life and is thus turning people back into computers again.


People did the calculations in the past – and today?


Electromagnetic switch. A relay consists of a coil with an iron core. When electricity flows, a magnetic field is created and the switch/armature closes.


Small and large relay

>>> More information at our cycle crank in the Mainboard section


On, off and selector switch; power amplifier


> low-cost component

> unsusceptible to power and voltage peaks

> potential-free isolation (voltage- and current-free)

> simple structure


> slow

> large mass

> noise during switching


For example:

> Z3


> Mark I

Facts & figures:

The name comes from the French word relayer meaning “take over from someone at work” (once: change of horses at post houses).

If a computer (program) is not working properly, it is often because of a “bug”. Grace Hopper is said to be responsible for using the word in connection with computers for the first time. She reported that on 9 September 1945 (actually 1947) a moth in a relay of the Mark II computer caused it to break down. She wrote the following note in the logbook: “First actual case of bug being found.”


Joseph Henry (1797–1878), US physicist

“Electrical energy and magnetism* will change the world.”

In 1835 Henry invented the electromagnetic relay without which neither simple switching of electrical circuits nor telegraphy over longer distances would have been possible – let alone many early computers.


Z3, 1961 – replica 1961

© ZCOM-Stiftung  

 OPREMA computer, 1955

© Zeiss Archiv



Active electrical component. In its simplest form, a diode, an electron tube contains a heated cathode (hot cathode) and an anode. The cathode emits negatively charged electrons that are attracted by the positive anode. This stream of electrons can be influenced by a control grid between the cathode and anode.

>>> More information at our cycle crank in the Mainboard section


Switch, signal amplifier


> fast and controllable

> far lower “switching” mass and

> far higher “switching” frequencies than a relay


> limited working life > high wear

> heating required > energy consumption/heat build-up

> sensitive to vibration, fragile glass tube

> large space requirement

> high price


For example:

> Atanasoff-Berry-Computer

> ZRA1

> Z22

> Colossus


Facts & figures:

The name diode for the simplest tubes is made up of the Greek dyo (two) and electrode. Triode comes from the Greek tria (three) plus electrode.

Tubes are still used in many fields even today. For example, they are used in high-end tube amplifiers. Many electric guitarists and bass players also appreciate the characteristic sound of a tube amp.



Electronic semiconductor device. A transistor consists of three layers: an emitter made of a semiconducting material (silicon) into which atoms with a surplus of electrons are implanted and an equally “doped” collector on the opposite side. In between lies the so-called base furnished with atoms that have a shortage of electrons. Because of the charge distribution this is known as an NPN transistor (negative-positive-negative). The opposite order also exists in the shape of the PNP transistor.

>>> More information at our cycle crank in the Mainboard section


Switch, amplifier


> smaller > enables miniaturization

> more effective > precise definition of switching times and high switching frequencies

> more robust

> cheaper


> sensitive to voltage spikes between collector and emitter

> cannot infinitely be reduced in size > See Moore’s Law, Interface section in the main room of the exhibition


For example:


> Mailüfterl

> Siemens 2002

> present-day computers

Facts & figures:

Transistor is a portmanteau of the English words “transfer resistor”, whose function corresponds to an electrical resistance controlled by an applied electrical voltage or electrical current.

Transistors are regarded as the most widely manufactured device in human history.

US physicists John Bardeen, Walter Brattain and William Shockley developed the first functioning bipolar transistor at the Bell Laboratories in 1947. They were awarded the Nobel Prize in Physics for their invention. It is largely unknown that two German physicists also invented the transistor independently of them: Herbert Mataré and Heinrich Welker managed to build a functioning transistor in France at almost the same time.


How does a computer calculate?


The decisive breakthrough towards the present-day computer was the development of the integrated circuit. The underlying idea was to accommodate all the elements of a computer on one chip*: including the arithmetic unit, the control unit and different types of memory…

Extremely thin wafers are cut from mono-crystal silicon. Masks are used to form structures on them: for transistor structures, for example, they define where boron or phosphorus ions are implanted into the wafer for negatively and positively conducting areas. Wiring masks, on the other hand, determine where troughs have to be etched into the isolator and filled with copper. As a result, over 1,000 process steps lie between the raw wafer and the completed end product, which is separated into individual chips or dies.


Jack Kilby (1923–2005), US engineer (centre) with colleagues from Texas Instruments in Dallas (early 1960s)

“It’s true that the original idea* was mine, but what you see today is the work of probably tens of thousands of the world’s best engineers, all concentrating on improving the product…”

* Together with Robert Noyce, Kilby is regarded as the inventor of the integrated circuit – for which he received the Nobel Prize for Physics in 2000 – and is described as “father of the microchip”.


Robert Noyce (1927–1990), US physicist* with integrated circuit (1959)

Noyce developed the first monolithic integrated circuit – an electrical switch the size of a fingernail on a silicon wafer.

Facts & figures:

Jack Kilby’s first integrated circuit in 1958 consisted of 4 transistors and 4 capacitors. Before the end of 1958 Robert Noyce managed to place several transistors, diodes and resistors on a single chip. By 1970 it was already possible to install 2,000 transistors, by 1981 450,000 transistors and by 2018 up to 50,000,000,000 tiny transistors on one chip.

As dimensions became smaller and smaller, switching times and computers also became faster and faster. It was eventually possible to mass produce logic modules on an assembly line, which in turn considerably reduced the cost.

In 2017 the smallest structures on a chip were 7 nanometers “large”. A human hair has a diameter of 60,000 nanometers.


From garage to world power – This is how we calculate today!

Micro” became the buzzword for a new era: microprocessor, microchip, microcomputer…

The miniaturization of computing opened up completely new possibilities – for users at work and in their free time… And for enterprises that grew into global giants from humble garage beginnings.

Collage:professional applications    




Car mechanic

School student





And tomorrow?

“Zero or one? Both!*”

Gero von Randow, Zeit Online, 2014

Today’s computers are based on electronic components that switch back and forth between two electrical states. Quantum computers also work on the basis of the behaviour of elements that change their state – but not instantaneously. They can be said to be in two overlapping states at once. These computers would be able to search through huge amounts of data in a flash.

Illustration(s) for quantum computers etc.

D-Wave 2000Q

© D-Wave Systems Inc.

D-Wave microchip with 2,000 qubits – this processor is called a quantum processing unit or QPU for short

© D-Wave Systems Inc.

Cryogenic refrigerator – cryogenic cooling of the quantum computer with helium or nitrogen. The microchip is regularly cooled down in the refrigerator.

© D-Wave Systems Inc.

Discover Supercomputer 3 – field of application: climate simulation at NASA

© NASA /https: //images.nasa.gov


Attention: Something is being calculated here!

VEB Robotron / today Robotron Datenbank-Software GmbH

Founded in 1969 (GDR) / Refounded in 1990

Today the company is active in the field of software development.

Annual turnover: 43.8 million euros (2017)

Company quote: “Achieving more with data”



© Robotron Datenbank-Software GmbH



The RoboGate is used to monitor industrial machinery. Irregularities in a manufacturing process or product faults can be detected in real time with the aid of smart sensors and algorithms and then evaluated using cloud-based analytical methods.


Microsoft Corporation

Founded by Bill Gates and Paul Allen in 1975

International software and hardware manufacturer – one of the most famous firms and largest software developers in the world

Annual turnover: 89.95 billion US dollars (2017)

Quote from Bill Gates, cofounder of Microsoft, 2020

“The thing that I feel best about, it’s being involved in this whole software revolution and what comes out of that, because you can go all over the world and go into schools and see these computers being used and go into hospitals and see them being used, and see how they’re tools for sharing information that hopefully leads to more peaceful conditions, and just the great research advances that come out of that.”


Microsoft Windows 98 handbook (English title: Getting Started)


Apple Inc.

Founded by Steve Jobs, Steve Wozniak and Ron Wayne in 1976

It is one of the world’s best known firms, a manufacturer and developer of computers, application software and consumer electronics.

Annual turnover: 229 billion US dollars (2017)

Quote from Steve Jobs: “It’s really hard to design products by focus groups. A lot of times, people don’t know what they want until you show it to them.”


Apple TV, third generation, 2012

This is a set-top box for connection to a television set or computer. Unlike the first generation of Apple TV, this model was much smaller. Thanks to the Apple A5 processor it could play videos in Full HD quality.

Mac mini, second generation, 2006

The portable small computer has a Core Solo T1200 processor clocked at 1.5 GHz and a storage capacity of 60 GB. It features quiet operation and balanced energy management.

Apple Magic Mouse, 2009

The optical mouse has a Multi-Touch surface. Its wireless connection is made via Bluetooth. The design of the Apple mouse is also interesting. It is very light and easy to operate.


ATARI Inc. / today: Atari SA

Founded by Nolan Bushnell and Ted Dabney in 1972

The company develops and manufactures consumer electronics and computer games.

Annual turnover: ‎15.4 million euros (2016/2017 business year)

Quote from Nolan Bushnell, cofounder of Atari:

“The ultimate inspiration is the deadline.”


Atari Portfolio, 1989

This portable and universally deployable 16-bit computer enabled users to carry out calculations, write texts and manage data. The computer also had a memory card with a capacity of 64 KB. Its weight made it very handy: it only weighs roughly 500 grams. In Germany the computer was sold for 999 deutschmarks.

Captain Blood game

The French video game made by the ERE Informatique company was written for the Atari ST computer. Later the game was also ported to other computers. The music was created by French composer Jean-Michel Jarre. He is regarded as a pioneer of electronic music.


Nintendo Switch console

Lender: Nintendo®


­­­­­­Google, LLC / parent company: Alphabet Inc.

Founded by Larry Page and Sergey Brin in 1998

The Google search engine is the world’s most visited web page. Google LLC offers various services, including: Google Books, Gmail, Google Translate and Google Maps.

Annual turnover of Alphabet Inc.: 110.8 billion US dollars (2017)

Quote from Sergey Brin, cofounder of Google (2004)

“Solving big problems is easier than solving little problems.”

Quote from Larry Page, cofounder of Google (2006)

“People always make the assumption that we’re done with search. That’s very far from the case. We’re probably only 5% of the way there. We want to create the ultimate search engine that can understand anything. Some people could call that artificial intelligence.”


Google search engine

Screenshot, 5 September 2018


Tesla Inc.

Founded in 2003 – the logo is also a tribute to the physicist and inventor Nikola Tesla.

The company is active in the automotive and solar sectors as well as in energy storage. It is regarded as a trailblazer in the field of autonomous driving and electromobility.

Annual turnover: 11.76 billion US dollars (2017)

Quote from Elon Musk, Tesla founder

“I don’t create companies for the sake of founding companies, but to get things done.”


Robert Bosch GmbH

Founded by Robert Bosch in 1886

Manufacturer of household appliances and pioneer of the development of autonomous driving

Annual turnover: 78.1 billion euros (2017)

Quote from Robert Bosch: “It’s better to lose money than trust.”


The world is run by a search algorithm

The Internet? It’s the information world of the future! Search engines? They’re the gateways to that world. The only thing is that the search for a specific piece of information often ends in a huge number of search results.

This is where the search algorithm comes into play, the core program of different search engines like Google, Yahoo! or Bing. It delivers the appropriate results for keywords in search engine result pages (SERPs) and orders them according to the respective ranking factors.


Diagram on the search algorithm – step by step to a result

© Sándor P. Fekete, Sebastian Morr

Facts & figures:

The best known search algorithm is probably Google’s PageRank. It examines web page results according to their competence, link structure and relevance – in a nutshell, it measures the number of pages linked with them and weights them accordingly. Following the Hummingbird update of 2013 the search engine is also said to recognize the context of terms.

The designation algorithm for precisely defined computational processes or general procedures goes back to a work written by the scholar Abu Dscha’far Muhammad ibn Musa al-Chwarizmi (circa 780–between 835 and 850).

Facts & figures:

For each number of discs there is only one most efficient sequence of moves – in other words, an algorithm as a clear set of instructions for solving the problem. Because it can be calculated by a computer program consisting of a few lines of code, the Tower of Hanoi is a classic example of a problem that requires a “machine-based” solution.


The Tower of Hanoi

According to an old legend, a tower stands in a temple. It consists of 64 golden discs stacked in order of size with the largest at the bottom. The temple monks are given the task of moving the stack of discs to another place.

In doing so, however, they must follow three rules:

First: Only one disc may be moved at a time.

Second: There is only one auxiliary stack for temporarily storing the discs.

Third: A larger disc cannot be placed on top of a smaller disc.

It is said that the end of time will come when the new tower is completed.

Try it out!


Calculate laboratory

Calculate with Triumphator 

Imagine you work in a large accountancy office in 1924. By chance, you are handed a surveyor’s calculation dating from 1620 and you need to check it quickly with a Triumphator mechanical calculator.

9427 x 4578


Step 1 Reset the calculator to its starting position by pressing the clear levers (1 and 2) and the carriage lever (3).

Step 2 Enter the large number (9427) into the input register (4).

Step 3 Next you need to multiply the individual digits of the second number. Begin with the ones digit (8). To do this you must pull lightly on the handle (5) and turn it eight times in a clockwise direction.

Step 4 Then you must push the carriage lever (3) back once. As a result, the carriage moves to the tens position. Now turn the handle (5) seven times for the tens digit. The turn counting register (6) shows how many times you have already turned the handle.

Step 5 Push the carriage lever (3) back once. The carriage moves to the hundreds position. Now turn the handle (5) five times.

Step 6 Push the carriage lever (3) back once. The carriage moves to the thousands position. Now turn the handle (5) four times.

Step 7 If you have done everything correctly, you can now read the second number in the turn counting register (6) and the result appears in the result register (7).


Calculate with KC85 

Imagine you are a student at a vocational school in the GDR during the 1980s and have a computer science lesson on a KC85/4.


Immediately after BASIC loads it is possible to execute BASIC commands in direct mode. The command CLS (Clear Screen), for example, deletes the complete contents of the screen. Try it out!

If a coherent BASIC program has to be produced, the commands of the program have to be written one after another in lines numbered in ascending order. It makes sense not to number these lines in steps that increase in units of one, but to use a sequence of tens, because this makes it easy to insert extra lines in between if necessary.

  1. BASIC program: ZUSE

A first simple program could read:

10 PRINT „Konrad Zuse 1910-1995“;SPC(3);

20 GOTO 10


The program is started with the command RUN. The command GOTO 10 in line 20 results in an infinite loop that continuously outputs the message “Konrad Zuse 1910-1995” followed by three spaces to the monitor screen.

The operation of the program can be interrupted with the BRK (Break) key.

You can display (list) the program stored in memory with the LIST command. The NEW command deletes the program from memory.

The KC85/4 does not have an internal hard disk drive or similar device that makes it possible to permanently store programs. The program is only held in working memory (RAM) while the computer is switched on.

  1. BASIC program: CIRCLES

This program draws circles on the screen using random positions, diameters and colours. The user of the program determines the minimum and maximum diameter of the circles and their number by making appropriate inputs:

10 WINDOW 0,31,0,39 : PAPER 0 : CLS

20 INPUT „Min. radius: “ ;R1

30 INPUT „Max. radius: “ ;R2

40 INPUT „Number of circles: “ ;N : CLS

50 FOR I=1 TO N

60 X=320*RND(1) : Y=255*RND(1) : R=R1+(R2-R1)*RND(1)

70 CIRCLE X,Y,R,15*RND(1)



In line 10, a viewport is defined with the WINDOW command and the background colour is set to black with PAPER 0. The lines 20, 30 and 40 request user inputs. Inside the FOR NEXT loop (lines 50 to 80) random values for the positions and diameters of the circles are created using the RND (random) command on line 60. The CIRCLE command on line 70 draws randomly distributed circles in the WINDOW viewport using randomly selected colours.


Calculate with the abacus

Imagine you are at a Greek market in the 5th century BC and buy the following: 5 litres of olive oil for 134 drachmas and 100 grams of sheep cheese for 7 drachmas. > Calculate how many drachmas you have to pay for your purchases with the help of the ABACUS.

The traditional school abacus consists of 10 rows with 10 beads each for the numbers from 1 to 10 billion. All the beads start off on the left-hand side.


Numbers can be represented using beads in the different rows. > Let’s start with 134, for example. This number consists of one bead in the hundreds row, three beads in the tens row, and four beads in the ones row.

If you want to add seven to this number, this is what you have to do:

Step 1 On the ones row you push the remaining six beads to the right-hand side.

Step 2 Since the row is now full, you have to perform a carryover to the tens row. You therefore push a bead to the right in the tens row.

Step 3 Don’t forget afterwards to move all ten beads in the ones row back to the left-hand side. Now you still have to push the last bead for the number seven to the right-hand side of the ones row.

Step 4 Now the abacus displays the result: 141.


Example: 6 x 4 means nothing other than 6 + 6 + 6 + 6

Step 1 You have to represent the six four times on the abacus. Use the top row as a counting row and push four beads to the right-hand side.

Step 2 Represent the number six on the abacus by pushing six beads to the right on the ones row. Take one bead away on the counting row by pushing it back to the left.

Step 3 For the next six, push the remaining four beads on the ones row to the right, perform a carryover to the tens, then push all ten ones back to the right and the two missing ones to make up the six back to the right again – then reduce the beads in the counting row by one.

Proceed in the same way for Step 4 and 5.

Step 6 Now you have entered the six on the abacus four times and the result should be in front of you.

Now imagine you are in ancient Egypt and are helping to build the pyramids. Roughly 450,000 blocks are required for one side of the Great Pyramid of Giza. > Use the ABACUS and calculate now many bricks you will need in total.



Imagine you are learning arithmetic from the famous reckoning master Adam Ries over 400 years ago. You have to complete the exercise 9 + 11 using the LINES ON A COUNTING BOARD.

The following rules apply: each field (to the left and right of the vertical line) can only hold a maximum of four counting tokens on each horizontal line and a maximum of one token in the space between the lines. Each individual counting token has the value of the number next to which it lies –for example, 1 or 5 or 10.

Step 1

If you want to lay the number nine, you have to place four tokens in the left-hand field on the ones line and one token in the space between the lines next to the five (4 x 1 + 1 x 5 = 4 + 5 = 9).

Step 2

For the number eleven you place one counting token in the right-hand field on the ones line and one token on the tens line (10 + 1 = 11).

Step 3

If you want to add the two numbers, you push the counting tokens from the right-hand field onto the same lines and the same space in the left-hand field.

Step 4

Then you begin from bottom to top: five counting tokens are carried over and become an additional counting token in the space between the lines above. The two counting tokens in this space are now carried over and become one counting token on the line above it. Finally, the result is very easy to read:

According to Adam Ries, two counting tokens on the 10s line make…


Calculating with the slide rule

Imagine you are a school student in the 1960s. The pocket calculator has not yet been invented and you have to calculate the sum of 2 x 2 using a SLIDE RULE…

Step 1 > Hold the slide rule in your hand. Move the slide in the middle of the rule to the right and the left. You can also pull it right out to get a better feel for how it works. Move the cursor, the part with the vertical line, backwards and forwards.

Step 2 > Look for the basic scales C and D. These are the most important scales, which enable you to carry out the operations multiplication and division.

Note: Addition and subtraction are not possible with a slide rule!


Step 3 > You can complete the multiplication of 2 x 2 by first finding the 2 on scale D and then moving the slide to position the 1 on scale C over the 2 on D (Step 1).

Then you have to look along scale C for the 2 – in other words, the second factor – and read the result from scale D (Step 2).

You certainly would not have required a slide rule for this calculation, but this method does not only work with whole numbers!

Step 4 > If you want to find the sum of 2 x 1.6, leave the settings as they were for Step 1 of 2 x 2 and you can read the result from scale D opposite 1.6 on scale C. There you will find the answer 3.2.





Calculating with Napier’s Bones

Imagine you are a surveyor in 1620. Your master expects you to find out how large his forest is. Fortunately, you have heard about NAPIER’S BONES and can thus very quickly calculate the forest area. The forest is 9,427 metres long and 4,578 metres wide. These numbers have to be multiplied to determine the area.

Step 1

Note down the numbers:


x 4578

Step 2

Lay the bones for the first factor (9427).

Step 3

Form the product of the individual digits (4,5,7,8) with 9427. Begin with the last digit

(8) and work your way to the front. To get the product for the digit 8, you have to add the numbers in the 8 row. Single numbers are written down as they are, while numbers in the diamond-shaped boxes belong together and have to be added together before being written down.

Step 4

The subtotals have to be added together to get the final result.