Overview
Summary: A pleasant hike around the charming city of Leiden to see all eight of the city's wall formula!
Distance: 8 kilometres (5 miles) – scroll to the bottom of the post to see the map!
Start point: Leliestraat bus stop
End point: Leiden Central train station
This post has been a long time coming... Back in January 2022, Brett and I hiked a route to see the eight Physics “muurformules” or “wall formulas" dotted around the nearby city of Leiden. We'd seen many of the murals before on random trips to the city, but this was our first time actively seeking them all out. A few months later, in June, we saw most of them again with our friend Paul while we spent a few days in the Netherlands on our Interrailing trip. And now, over a year after we first hiked the route, I'm finally getting around to finishing off this post – my apologies for the *slight* delay...
Background
Instead of traditional street art, the walls of Leiden are home to over 100 hand-painted poems in different languages, scattered across the city. Inspired by the poems, physicists Sense Jan van der Molen and Ivo van Vulpen came up with the idea to create a series of physics murals around the city to celebrate famous physicists that have spent time in Leiden. They realised that, like a poem in a foreign language, "you can sense the beauty of a formula even without fully understanding it."
Designed and painted by the TEGEN-BEELD foundation, the first equation appeared on the walls of Leiden in 2015, with the rest appearing in the years since. In recognition of the wall formula project, Van der Molen and Van Vulpen were awarded the first ENW Communication Award, which is awarded annually to "scientists who have dedicated themselves to disseminating science."
This 8 kilometre (5 mile) hike took us around three hours to walk, which included a couple of detours and a long break for a hot drink. If the instructions included below are confusing, don't worry – the map at the bottom of this post should definitely be of help! The route takes you through some of the iconic areas of Leiden, but does miss other important places that shouldn't be missed on your trip to this beautiful city. You could make this hike part of a longer day trip to Leiden!
This blog post was a collaborative effort. Brett – our resident physicist – has provided us some notes on each of the eight equations, so we can better understand what we're looking at! More details on each equation can be found on the muurformules website.
Getting to Leiden Centraal
Leiden is a historic city located between Amsterdam and The Hague. Its beautiful canals and lack of tourists give it a charm sometimes hard to find along the crowded streets of Amsterdam. Leiden is easily accessible by public transport from other major Dutch cities – the intercity train will get you to Leiden Centraal in 35 minutes from Amsterdam or just 11 minutes from Den Haag Centraal. You can use the NS website to plan your journey.
Getting to the start of the hike
The start is easily accessible by bus or on foot.
By bus from Leiden: buses 2, 3, 4 and 45 all will take you to the start in under 15 minutes from Leiden Centraal. Get off at Leliestraat.
On foot: the start is a 2-kilometre walk from Leiden Centraal or a 650-metre walk from Leiden Lammenschans (another local train station)
The hike
When you arrive at the Leliestraat bus stop, walk back towards the main canal circling the city centre. Before reaching the bridge, turn right onto Zoeterwoudsesingel. Follow this for awhile before turning right at Fruinlaan.
1. Van der Waals equation of state
The first equation can be found on the side of a white house across the street from the Stedelijk Gymnasium Leiden – you don't have to cross the major road to see it. The physicist behind this equation, Johannes Diderik van der Waals, was born in Leiden in 1837 and defended his PhD thesis at Leiden University in 1873.
Notes from a physicist: Perhaps you remember the formula PV=nRT from your high school chemistry class. It relates the pressure, volume, and temperature of a gas. It’s only an approximation, however, and a slightly more accurate (but more complicated) equation, the Van der Waals equation of state, is featured here.
Once you've finished admiring the mural, walk back to the canal and turn right back onto Zoeterwoudsesingel. Cross the bridge and then walk back along the canal through the Plantsoen park. When you get to the main road, turn right and follow the road to Oranjeboomstraat.
2. Snell’s Law
As you continue straight along this road, you will pass two of the equations, the first of which is visible above a friets shop, at the intersection with Hogewoerd. This equation was named after Willebrord Snellius, who was born in Leiden in 1580 and became a Professor of Mathematics at the University of Leiden in 1615.
Notes from a physicist: You might have noticed how a straw in a glass of water appears discontinuous as it transitions from the air into the water. The mathematical description of this phenomenon, of how light changes angle as it passes through different media, is Snell’s Law.
3. Lorentz Force
Another hundred metres further down the street, you'll pass a cute restaurant with the mural painted on one side. This equation was first described by Hendrik Lorentz, a Nobel Prize winning Dutch physicist who studied at the University of Leiden before becoming a professor in theoretical physics at the age of just 24!
Notes from a physicist: An electrically charged particle is always sensitive to an electric field, but only responds to magnetic fields when it’s moving. This is known a Lorentz Force. Does a moving electrically charged object create a magnetic field? Yes, it does! Earth’s electrically charged molten core moves, creating the magnetic field that helps us navigate.
From there, continue straight, then turn left onto Kaasmarkt right before you reach the bridge. Follow this road and cross at the pedestrian bridge. Stay straight until you reach the main shopping street – Haarlemmerstraat – and then turn left and follow the road until you reach the Hartebrugkerk, a large church. Here, hang a right and then take your first left.
4. Einstein field equation
After walking a few hundred metres, you should find yourself outside of the Boerhaave Museum, a museum all about the history of science and medicine – definitely worth a visit if you have time! Just past the museum entrance, you'll be able to see the Einstein field equation painted beautifully on the wall above you.
Noes from a physicist: In 1915, Einstein completed his General Theory of Relativity, which describes how gravity, matter, space, and time interact. One consequence of his theory is that massive objects – like stars – bend the fabric of space and time. This prediction was verified dramatically in 1919, when, during a solar eclipse, stars that should have been hidden behind our sun were in fact visible, because their light rays bent around our sun. This result, and the equations that predicted it, are shown here.
Albert Einstein first visited Leiden in 1911, when he stayed with Lorentz (who we just discussed above!). Throughout his career, Einstein visited Leiden frequently and was a professor at the university. Apparently Einstein was quite fond of Leiden, calling it "that delightful piece of land on this barren planet." You can learn more about Einstein's time in Leiden in this article.
Now, head back to the high street, across the river and then turn left onto Breestraat. Follow the road until you reach Diefsteeg, where you turn right.
5. Electron Spin equations
The narrow alley emerges into an open square, where the Electron Spin equations can be seen on the wall of an old house.
Notes from a physicist: Electrons have angular momentum, much like – but not exactly like – a spinning ball has angular momentum. Two PhD students at University of Leiden (George Uhlenbeck and Samuel Godsmit) derived this property of electron angular momentum and spin in their PhD theses in the 1920s.
Next, walk past the Pieterskerk, turn left down another narrow alley and then walk along Langebrug until you reach a huge university building on your right.
6. Huygens' Pendulum Formula
Take a left down Plaatsteeg and the tower should be visible. The Huygens' Pendulum Formula is best seen from in the small garden at the bottom of the tower. This formula is named for Christiaan Huygens, who studied law and mathematics at the University of Leiden from 1645 to 1647.
Notes from a physicist: The regular oscillating motion of pendulums have long been used to measure time and serve as clocks. However, it wasn't until 1656 when Christian Huygens found a way to relate the length of a pendulum to how long it takes to swing back and forth. This simple formula, which predicts that a longer pendulum takes longer to swing back and forth, is shown here.
From the tower, enjoy walking along the Rapenburg canal, arguably one of the most beautiful canals in the city. Turn left and cross the canal when you reach the Leiden Botanical Garden (well worth a visit if you have time!). Enter the outer walls of the garden and follow the path around until you cross the bridge over to the Leiden University campus. From here, turn left and follow the Witte Singel until you reach a small park.
7. Oort constant
On the wall of a residential building, you will see the equation for the Oort constant, named for Jan Hendrik Oort, a Professor of Astronomy at the University of Leiden. The mural is located just across the river from the Leiden Observatory, where Oort worked for many years.
Notes from a physicist: The Oort Cloud is a region of our outer solar system where most of our comets come from.
Walk through the park, cross the bridge and then head right down the canal towards the final stop on this *wild* tour of Leiden.
8. Lorentz contraction equation
When you reach the main road, turn left and follow the road until you reach the train tracks. The Lorentz contraction equation is visible on the wall of a white building, best seen from the other side of the train tracks.
Notes from a physicist: Early in his life, Einstein spent a lot of time thinking about trains. What would happen if you rode in an extremely high-speed train to try and follow a light beam? After years of pondering this question, he came to the conclusion that light always seems to move at the same speed, no matter how fast we move. The only way for the speed of light to remain constant no matter how fast we ourselves move, is if space and time itself expanded and contracted; sped up and slowed down. The equation that describes this space and time dilation is shown here. The faster an object moves, the more flattened out it appears. It’s impossible to observe this with our naked eyes for everyday objects, but relativity is nonetheless very important for things like radioactive decay and GPS satellites.
From this point, it's a short walk back to Leiden Centraal, or you can head back into the centre to continue exploring this enchanting old city.
We thoroughly enjoyed our walk around Leiden to see the beautiful muurformules, discovering parts of the city we had never visited before. The murals highlight one of the many different ways that science can be communicated, as well as the importance of combining science and art. Maybe one day in the future, one of Brett's equations will be included on the walls of this historic city!
Resources:
Route map: https://www.alltrails.com/explore/map/map-february-2-2022-4-19-pm-5460b9e?u=m
Muurformules website: https://www.muurformules.nl/
Dutch train planner: https://www.ns.nl/en
Atlas Obscura: https://www.atlasobscura.com/places/leidens-wall-formulae