The Arithmeum

Darrell had two back-to-back meetings in Germany, so we traveled to Bonn a day early to explore. Our first stop was one of the more unique museums we've been to - the Arithmeum.

A colorful blending of math, science, technology and art at the Arithmeum

The Arithmeum has four floors of mathematical devices - beginning on the top floor with calculi - counting stones showing an approximately 6,000 year old number system in Mesopotamia. They also have early abacuses from a number of regions, and counting coins from the Middle Ages. Below is an interesting combination of an abacus with a mid-80's calculator!

Calculator paired with a traditional Japanese Soroban (abacus) - 1985

The displays form a historic timeline of advancement in calculating devices - most of which I did not know even existed. Going down one floor you move into the world of Napier's Rods and other calculating devices built by engineers, watchmakers, and even barons!

A version of Napier's Rods that was invented by Henri Genaille, a French railroad engineer, in 1885

Paris watchmaker Rene Grillet combined a simple adding/subtracting unit with Napier's Rods in cylindrical form to create this pocket-size calculator in 1678!

The Arithmeum had some displays you couldn't touch, and others where you were encouraged to use them to see how they worked. These displays included a handout or even a 3-ring binder with detailed instructions on how to use the device.

Hands-on simplified Napier's Rods with information about the Scotsman John Napier (1550-1617) and directions for how to use the rods for multiplication and division, and even squaring and finding square roots for the more talented visitor!

Going down to ground level you enter the world of more recent mechanical calculating machines, many of which were industrially produced and have instructions for their use. One of my favorites is "Consul", The Educated Monkey.

First patented in 1889 in Munich, and then modified and patented as a child's toy in the USA in 1916, you can still buy both antique (expensive) and modern calculating monkeys! Just move the monkeys feet to the numbers you want to multiply (up to 12 x 12) and the answer is between the monkeys hands.

Of course most of the calculating devices were more serious and could multiply past 12 x 12!

This Webb Ribbon Adder from 1891 was operated by pulling chains down

This Dalton adding machine form 1902 was designed by H. Hopkins and was the first with a sliding carriage, but the novel 10-keyboard did not gain acceptance

We then went to the basement where there is an entire wall of adding machines, plus early voting and punch card machines, and the earliest computers.

An entire wall of adding machines - engineering art!

This Pantograph as used during the 1890 US Census to transfer information from the census to punched cards. One person could punch 700 cards per day. On the right, Darrell is casting his vote on an early voting machine.

One last word from the Arithmeum: "The symbiosis of science, art and technology in the Arithmeum was not haphazard but intended. 'We have Art to save us from perishing through Truth'. This saying of Nietzsche is today more to the point than ever before. Aesthetics and beauty help us to live and experience more fully in our homogeneous and rushing world."

“When a certain degree of technological ability has been achieved, science and art tend to merge into aesthetics. All great scientists are at the same time also artists.“ Albert Einstein, 1923

Thank you to the Arithmeum and their excellent website for the information for this post.

Note: If you have gotten more curious about the history of mathematics, and you can't make it to the Arithmeum in Bonn, here is a website by the prolific Luke Mastin that covers the Story of Mathematics in terrific detail!

Rambling in Greece

Darrell and I decided to get a last gasp of summer warmth in Greece before returning to Switzerland for the next two months. We flew into Athens on October 18^th and used the metro and our feet to get us to our Airbnb near Syntagma (Constitution) Square. It was warm but hazy, perhaps because Athens has high levels of air pollution from the traffic and functions of a very crowded city.

View from Likovittos Hill towards the Acropolis

We had a 6^th floor Airbnb with a good, though long-distance, view of the Parthenon lit up at night. We shared a nice bottle of wine left by our hosts as we enjoyed the city from the balcony.

The Parthenon, lit up in the background, from our 6th floor view

The next morning we took a 3-hour city tour by bike through the well-recommended “Athens by Bike” company. We met our "superguide" Sapfo and the three other couples on our tour. Sapfo is an energetic and knowledgeable tour guide with a bit of sauciness that draws you in and reveals some personal insights into the city she loves. Sapfo first took us up a quiet hill in a park that sees few people and provided a good overview of the areas we would tour.

Superguide Sapfo Tavouti of Athens by Bike

She showed us numerous sites, both ancient and modern, and also gave us a short lesson in Greek. Using an ancient tablet she taught us some basic Greek so we wouldn't be able to say “That’s Greek to me” anymore.

Sapfo helping us read Greek from an ancient marble message

With perfect timing, we were able to watch the changing of the guards in front of the Presidential mansion. The young Greek soldiers selected for this honor make only 8.6 euros (less than 10 dollars) a month for this service to their country. Thank goodness they get food and housing for the 9 months of mandatory service. If you are curious what this ceremony looks like, there are numerous videos online.

The changing of the guards involves ritualized movements

After our great tour, we wandered the impressive museum by the Acropolis, and returned to some other sites Sapfo had pointed out that we wanted to see more closely. We hiked up a side trail to get this view of the Panathenaic Stadium that was built entirely in marble around 344 AD and had a 50,000 seat capacity. It has hosted numerous games including the opening and closing ceremonies of the first modern Olympics in 1896.

The all-marble Panathenaic Stadium in Athens

On the way back to our apartment, Darrell took a photo of two ubiquitous aspects of life in Athens - motorcycles and cats. There are many, many cats - presumably mostly feral - all over the areas of Greece we saw...

Motorcycles and cats are common sights - not always together!

From Athens, we used our feet, the metro, a bus, and a taxi to get us to the start of our planned 6-day bicycle ride on the Peloponnese Peninsula. While many travelers may just spring for a taxi, we like the challenge of finding our way new places using public transportation. Plus we are more imbedded in the local experience and save some euros.

We met Dimitris, the representative from Arcas Travel, in Vytina, a traditional village in the mountains outside of Tripoli. He brought our bicycles, panniers, first aid kit, repair kit and GPS for our trip. We got “sorted” quickly and then went out to eat to load up on the wonderful local food before beginning our trip the next morning.

Darrell on our first day of biking in the mountains north of Tripoli

I won’t detail every day, but suffice to say we saw a lot of archaeological sites, many museums, orange groves, olive trees, a cave, some woods, small villages, larger towns, the Argolic coast, and some serious hills! We started off with gray skies and rain for the first three days, but had nice sun for the last three. This self-guided tour was well-organized and we would recommend it to others who like a little exercise in their excursions.

Harvesting walnuts for a snack by the ancient wall of Mantinea (460 BC) Photo by DK

Lonely beach in Paralion Astros after the summer season has ended (Photo by DK)

Our guide reading to us in English (phew!) on our tour of the Kapsia Cave

Water from the Kapsia cave/sinkholes and Argolic plains emerges in an underwater spring off this semi-circular enclosure

Mosaic in the wonderful museum in Argo

Marble block "storage" outside of Argo

Water running down the Argolic plain leaves high water mark trash on the banks

Stone Circle A in Mycenae used for royal burials in the 16th Century BC

Water supply at Mycenae accessed from inside the walls to deep underground outside the walls

Testing the acoustics in the theater at Epidaurus

Bench seats in the 3rd C BC theater

For those of you interested in more "environmentally friendly" travel we found Arcas Travel through a consortium company called Responsible Travel. Both companies provided good communication and excellent service.

After our bike tour ended, we took a 2-hour morning boat ride to the island of Hydra, which has almost no motorized vehicles on it. We stayed in another Airbnb with an amazing view looking down on the main town and the harbor.

View of the main village on the island

Hydra cats waiting for a fish handout

Loading olive oil on the four-legged transport available on Hydra

The steep, narrow, stone streets of Hydra are easy to get lost in!

Darrell and Mindy at the top of Mount Eros on Hydra

You can see we had a grand time in the small bit of Greece we were able to see in two weeks.  The history and culture and scenery and food are all amazing - and the Greek people are some of the most authentically friendly people we've ever met. Thank you all for sharing your country with us.