Stranded: Cologne, Bonn and the Arithmeum

McHaggis reporting here!  I have had quite a successful week – all my prayers to the Sheep gods were answered.  Do you know Julia would have gone all the way to Holland for just a weekend and then come straight home without letting me explore the wonders of Cologne and Bonn?  I couldn’t let her do that.  So I appealed to the gods for a little bit of snow so that her flight would be delayed by a couple of days, and whaddya know, we got delayed by a whole week! SCORE.

Airport friend

My Hungarian-Yugoslavian friend Geza

Of course, Julia wasn’t very happy about this at first.  There was lots of queuing to be done at Cologne/Bonn airport in order to re-book the flights, but I just took this as an opportunity to make new friends.  The photo on the left is a man called Geza, some sort of airport manager, who turned out to be half-Hungarian and half-Yugoslavian.  This precipitated some unexpected Hungarian conversation between him and Julia.  We also made friends with another of the stranded passengers: a man who works for Vogue in London.  The value of his shoes, jacket and ‘man-bag’ alone could have allowed us to hire a private jet home!  But I was more disappointed that we didn’t manage to convince him to come and give the maths department a fashion makeover.  Or, even better, turn ‘maths geek’ into the next fashion statement.  There is opportunity yet: we have his phone number!

Haggis' New Friend

My evil genius friend: name?

Cologne and Bonn were very beautiful cities and had great atmospheres with the Christmas markets going on.  It was at the Bonn Christmas market that I made another sheepy friend (which made a change after all those humans at the airport).  I haven’t worked out what to call him yet, but his character seems to be that of an evil genius.  Can anyone out there suggest a good name?

Bonn is quite a mecca for mathematicians at the moment, with not one, but THREE places to study the subject. Topologists are in a special heaven, with one of those institutes named after a topologist (Hausdorff) and another founded by one (Hirzebruch).  What was even more exciting to me was that the town has its very own mathematics museum, called the Arithmeum, and it was to there that I made a pilgrimmage on Saturday.

Well, perhaps it is stretching the truth slightly to call it a ‘mathematics museum’.  It is a museum about arithmetic, about the art of calculation.  Actually, one of my criticisms of the museum would be that it does not do enough to explain and expand upon the mathematics needed for calculational devices, of which there are lots of interesting things to say.  They do remedy this by having a series of evening lectures and children’s programmes, and another facet of the museum is that it is a gallery for art that has been inspired by mathematics.  I definitely think that if anyone is in the area that they should pay a visit, because there is something for everyone’s taste and interests.


A selection of abacuses

So, what did I find there?  The Arithmeum starts off with the earliest calculational devices: counters and abacuses (or abaci).  Abacuses were used by all ancient civilised societies: Sumerians, Egyptians, Romans, Greeks, the Chinese and Indians, and they are still in use today in Far Eastern countries such as Korea and Japan.  You can see in the (white) middle abacus that a modern calculator and ancient abacus are used together!  People who learn the abacus are often  faster at calculating than modern computers, and not only that, but I learnt from Alex Bellos at the MathsJam that a person using an abacus uses a different part of the brain than that used for language.  This means they can be playing word games whilst adding up three-figure numbers: see this amazing video for proof.

Napier's bones

Napier's bones: a 17th century laptop?

Another device to help people do quick multiplication was invented by a Scotsman: Napier’s bones.  This is a rather ingenious set of rods which basically gives all the times tables from 1 to 9, and this in turn allows people to do long multiplication, division and even the extraction of square roots.  Read the linked Wikipedia article for the details!  My companion at the museum, Carl, remarked that the pocket set of ‘bones’ shown on the right here was like an ancient version of the laptop.

Mechanical devices to do addition and subtraction were already quite difficult to make: it was Wilhelm Schickard in 1623 who first designed a system of gears that was able to ‘carry’ digits, so that after turning a wheel from 0 through 9, the next gear along would be engaged to create the number 10.  Multiplication and division required machines to also be able to shift the digits left and right, and the world had to wait for the genius of Leibniz for such a machine to be invented.  The Stepped Reckoner, as it was known, was designed in 1672 but was so far ahead of its time that the gearwork needed could not be built to the precision that was required.

Cake calculator

Cake-shaped calculator

I particularly liked this mechanical calculator, which reminded me of a birthday cake.  My apologies: I can’t remember which European emperor it was made for or by whom!

Mechanical calculators changed little in the following 250 years except for their design and size.  It was lots of fun in the museum getting to go around and push all the buttons and levers on the various contraptions!  Modern computers are extremely boring in comparison.  Modern computers also don’t have such wonderful names; I particularly liked the ‘Mercedes-Euklid’ modelMercedes-Euklid(which sadly wasn’t doing calculations mod 29!).

Difference Engine

Babbage's Difference Engine

Despite this article already being so long, it would not be complete without a quick mention of Charles Babbage.  This was a man who was also ahead of his time: he designed the world’s first programmable computer in 1822, called the Difference Engine, which was not fully built until 2000.  His partner in crime was a lady called Ada Lovelace, the daughter of Lord Byron, who wrote the world’s first computer program, designed for the Difference Engine.  Babbage called Ada “the Enchantress of Numbers”, although there was never a romantic relationship between them (as far as we know).

That’s it from me today. Farewell my friends, until my next adventure!

[P.S. Julia wishes to thank those people who helped to entertain her in Germany and get her home: Andrew Ranicki, her mum and sister, Carl McTague, Michael Wharmby (aka Sheep Man – more on him in another post), and all the people she met at Cologne/Bonn airport.]

[P.P.S. A note from Haggis: my apologies for never having blogged about the MathsJam.  Julia always claims she is too busy with other things to help me write an article. Tsk. You just can’t get the staff around here.]


5 responses to this post.

  1. Posted by Edith on December 10, 2010 at 10:00 pm

    The abacus video is amazing! How do the kids accociate words with numbers? I saw people in a big department store in Moscow using the abacus, and I couldn’t believe my eyes! They were really fast adding up! How do they do it???


    • Posted by haggisthesheep on December 10, 2010 at 10:44 pm

      What’s even more amazing is that the pupils don’t need a physical abacus to be able to do the adding up: they can do it by simply imagining the abacus! In some videos you will see them moving their fingers as if they were moving around the abacus beads.


  2. I love your history of calculating devices. I certainly could have used that when i was writing my doctoral dissertation. That is when I came across Ada Lovelace who wrote a description in 1843 of Babbage’s Analytical Engine. Today is Ada Lovelace’s 195th birthday.

    My books have been revised as an e-book “Ada,The Enchantress of Numbers:Poetical Science” with a few puzzles and games.

    If interested check out :


    • Posted by haggisthesheep on December 10, 2010 at 10:50 pm

      Thanks for the comment, and for the link to your website. Your book sounds fascinating and I’m wondering if I can persuade Edinburgh University to buy a copy for the library… Also thanks for pointing out that it’s Ada’s birthday today – a happy coincidence!


  3. It’s always nice when you can not only be informed, but also entertained! I’m sure you had fun writing this article.Excellent entry! I’m been looking for topics as interesting as this. Looking forward to your next post.


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