Just across the street from the Hofgarten (Court Garden) in Bonn, Germany, you can find this beautiful steel-and-glass museum that was opened in 1999 as a part of the Research Institute for Discrete Mathematics of the University of Bonn.

Here you can find out more than you ever thought you wanted to know about the history of calculating over the past six thousand years, up to and including the design of current-day microprocessors on chips. (Did you know that 250,000 transistors can be placed on the tip of a pencil? That’s even more than the number of angels that used to fit on the head of a pin in the Middle Ages.)

People trying one of the interactive exhibits

The museum’s website says there are many demonstration models which “invite the visitor to discover the historical milestones of mechanical calculating, and at interactive multimedia stations the visitor can develop small microprocessors in a playful way. Early highlights in the development of computers are also exhibited.”

Baroque calculating machine from the 17th century

OK, I’m quite familiar with baroque operas, dating from 1600 to about 1750, but I must admit that I never knew there was such a thing as a baroque calculating machine. Here in the Arithmeum I learned that there really was such a thing, despite the fact that during the baroque age “there was neither a scientific nor a commercial need for calculating machines. They were exhibited in cabinets of potentates to be admired, along with androids, because they were capable of mechanically performing genuinely human actions. The series production of mechanical calculating machines did not take place until the middle of the 19th century.”

Cog-wheel calculating machine

Behind this cog-wheel calculating machine we can catch a glimpse of the Hofgarten (Court Garden) just across the street.

Historical mechanical calculating machines

A unique aspect of the Arithmeum is its collection of over 1200 historical mechanical calculating machines from three centuries, from their beginnings in the 17^th century to their abrupt end when electronic computers started taking over in the 1970s.

Mechanical calculating machines from various epochs

As I have mentioned in another connection, we 21st century folks are so accustomed to doing everything electronically that we tend to forget about (or not even know about) the amazing mechanical devices our grandparents, great-grandparents, great-great-grandparents and great-great-great-grandparents used to use.

Wall of mechanical calculating machines

In the basement of the Arithmeum there is a whole wall full of mechanical calculating machines, mainly from the first three quarters of the 20th century.

A calculating and card-punching machine

From the 1890s until the advent of floppies and hard disks, cards with holes punched in them were the medium of choice for storing large amounts of data. As late as the 1970s, punch cards were often used to store data for use on main frame computers, which by the way were usually located in the basement of a company’s headquarters since they were too heavy for any other floor.

Replica of Charles Babbage’s Difference Engine

Among the over 1200 historical mechanical calculating machines on display at the Arithmeum there are two replicas of (parts of) machines invented by Charles Babbage (1791-1871), an English mathematician and inventor who is often described as the “Father of Computing” for his contributions to the basic design of the computer — a century or more ahead of his time! He first started developing his Difference Engine in 1822.

Part of the Analytical Engine

From 1833 onwards, Babbage worked with his colleague Ada Lovelace (1815–1852) on the concept of the Analytical Engine, which despite being purely mechanical contained essentially all the components of a modern computer. They never did get it to work properly, because one or another of the mechanical parts was always failing, but the programs they wrote for it bear an amazing resemblance to the modern computer programs that we use today.

Slide rule at the Arithmeum in Bonn, Germany

Here’s an exhibit to warm the heart of anyone who was halfway serious about high school math in the pre-electronic era: a slide rule complete with instructions on how to use it and a good explanation of the principle behind it — calculating with the aid of logarithms. I still have two or three slide rules around the house (including one on a shelf by my desk), but I haven’t used them for years since a 5-Euro pocket calculator can now achieve the same results, or better. In high school the real math freaks used to wear 36-inch slide rules in a scabbard on their belts, like a sword. I wasn’t in that league, but always had my normal 10-inch slide rule with me and would have felt lost without it.

My photos in this post are from 2006. I revised the text in 2018.

See also: Cutting edge technology (of bygone decades).