11 June 2014

Arithmeum, part 1

I am planning to add a few posts about data in the real world, yes life and data also exist outside the internet. I have no idea how I will achieve this as I do not go out so often. Keep your fingers crossed :) 

If you are into a data analysis, you have argued with your data more than once. Pieces of data software have made you crazy. Be honest, you have insulted Excel or any other application. After reading this magical blog post you will appreciate modern data programs. You will purr like a kitty thinking of calculating on your computer.

I have visited Arithmeum, a museum devoted to calculating methods and machines. It is placed in Bonn, Germany

It is not a typical museum where you cannot touch anything, there are many replicas of old calculating machines with the description how to use them in German and English so you can get wild and calculate. 

Let's start this long journey.

4000 BC
Calculi (we can call them directly “small pebbles”, sounds less fancy but it's the same).
Calculi are the first simple reckoning aids, used in Uruk in the southern Mesopotamia (nowadays: the south part of Iraq) 6000 years ago. They were used by accountants. Calculi have different shapes, which probably represents different numbers.


3000 BC
They look like cookies but these clay tablets were used to depict calculations concerning the allocation of grain and brewing ingredients (barley and malt) so they were used in a good cause. The partial sums are placed on the front and the final sums on the back of the clay tablets. Next to each number there is an image showing a product that was an object of the calculation.


from 13th to 16th century
Quipu – Incas' databases.
The Incas sent messages by couriers, so weight of data carriers had meaning. They recorded numbers by knots. Their form, number and sequence, the placement of the main and secondary ropes, and even colours of ropes were used to encode the data.
Census data needed for tax reasons were collected in this way too.


From 13th century

Reckoning coins were used in France and later in the other parts of Europe. Hope that you did not think that in so elegant place somebody could have used pebbles to calculate :)

A reckoning table, a replica of the table from 15th century, the original table-top was for some time used as a door, so you see how useful it was. Can you do this with Excel? I can imagine the owner of the table, the body shaped by carrying the piece of furniture and the brain developed by calculating, perfect combination :)



This Russian abacus is from 20th century, it's twelve rows of beads, the short row containing only four beads is for quarter roubles.

Traditional Japanese abacus joined with an electronic pocket calculator. Nothing can stop the owner of this treasure from calculating, running out of battery is no problem.

Calculating in the 17th century

The first calculating machine was invented by Wilhelm Schickard in the first part of the 17th century.

Napier's rods (Napier's bones) looks like a gaming machine but it was an important invention and became the inspiration for many constructors.


John Napier was an interesting person, google to learn more lol
Just to encourage you to investigate this gentleman: he occasionally requested that the water mill adjacent to Merchiston Castle be stopped so he could think undisturbed. He knew that science needs sacrifices but the people of his times had strong connection with food so there was no such option.

A pocket version of Napier's rods.

Blaise Pascal's father was a tax officer, he asked Blaise to help him with calculations. The young Pascal was annoyed by the length of the process and invented a calculating aid. Now you know what to do if you want to become a parent of genius lol

The replica of Blaise Pascal's calculating machine.

Leibniz's notes contained a sketch of a pinwheel with pins representing numbers. 

Calculating in the 18th century

The four-species pinwheel machine of Giovanni Poleni works with weights, six-digit results can be obtained and it looks like a clock :)

Braun's bling-bling  machine was more appreciated for the design than the calculating skills. Name of the ruling king placed on the machine is an evidence that Braun had also business skills.


Jacob Leupold constructed a calculating drum, based on Napier's rods. Ascetic wooden design of this machine shows that Leupold didn't match to his times.


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