Wren

Hanging out at J+A Cafe, Clerkenwell

Exterior of J and A cafe (the bar is on the other side of the passageway)

Exterior of J and A cafe (the bar is on the other side of the passageway)

Tucked down a little alley, in the back streets of Clerkenwell is the J+A Cafe. Not just a cafe, but also a bar, J+A is a satisfying place to find, particularly if you happen to find it serendipitously. As you head down the alley, the café is on your right whereas the bar opens up on your left. The café is simply furnished, with bare brick walls adorned with a few impressionist paintings. There are plenty of seats at which to enjoy good coffee and home-made cake. Their website suggests that J+A specialise in Irish baking and so we dutifully had a slice of Guinness and chocolate cake with our coffees. Importantly, the dreaded “does it contain nuts?” question was met with a knowledgable answer and without the ‘frightened bunny face’ that I often encounter when I ask this question. J+A definitely gets a tick in the ‘cafe’s with good nut knowledge’ box on my website.

Lights were suspended from the ceiling, connected by wiring that was allowed to hang down, a section of electrical wire held at both ends and freely hanging. While I’m sure that this was done for aesthetic reasons (and certainly it works on that level), such hanging wires are in fact far more than merely pleasing to the eye. Such hanging wires were a mathematical puzzle just four centuries ago. Indeed, these simple hanging wires form curves that are so important they get their own name; they are catenary curves, from catena, the Latin for chain.

lights at J and A coffee Clerkenwell

Between each lamp, the electrical cord formed a catenary curve.

Galileo had thought that a wire hanging under its own weight and suspended at its two end points formed a parabola. A fairly simple curve that is easy to describe mathematically. It was natural for Galileo to assume that these catenary curves were really parabolic. He had earlier shown that objects that fell with gravity followed parabolic paths, and after all, the hanging wires did look almost parabolic. It fell to Joachim Jungius to show that the curve was not parabolic and then to Huygens, Bernoulli and Leibniz to derive the equations determining the form of the curve. Although the differences between the parabola and the catenary curves are subtle, they have profound consequences.

When a chain, or a wire, is suspended and allowed to hang under its own weight, it forms a catenary. Flipping this around, quite literally, a catenary arch will be self-supporting. This means that a vault made of a series of catenaries or a dome that is made into the shape of a catenary will be self-supporting with no need for buttresses. This property of the catenary curve was used by Antonio Gaudi in his designs of the Casa Mila in Barcelona and also by Christopher Wren. The famous dome of St Pauls is not a catenary, but it is not one dome either. It is in fact 3 domes stacked together. The outer dome is spherical (which is weak from a structural point of view) while the inner dome is a catenary. The dome between these two was designed, using the mathematics of the day, to support the impressive outer dome (more info here and here). Wren, was not just an architect, he was also a keen mathematician, there is maths, physics and beauty throughout many architectural designs.

Mathematics in the city reflected in the lights of J+A.

J+A is at 1+4 Sutton Lane, London EC1M 5PU

 

Gravity and Grace at the Wren cafe

Wren cafe, St Nicholas Cole Abbey

Inside the Wren cafe

There is a lot to like about the Wren cafe. Firstly, there is the space that it occupies (inside St Nicholas Cole Abbey). I went at lunchtime when the way that the light came through the stained glass windows made the cafe a very relaxing and open space. The coffee is from Workshop, complementary water came in 3 flavours (mint, cucumber or lemon) while the food is cooked on site. This is important because it means that they have a great nut policy and could tell me which dishes were likely to contain nuts etc. A further nice feature of the lunch menu at the Wren was that you could select your portion size. Food waste is a major issue for our society and is not helped by the ‘one size’ portions served at many food outlets and cafes. Lunch was offered in two sizes (technically as a side or a main) but the ‘side’ was more than adequate for a mid-week lunch. Sofas in the corner of the room meant that you could relax and take in your surroundings in a comfy environment or, if you were just there for lunch, ordinary chairs and tables were dotted around the room.

Of course, a place such as this will have plenty of things to notice about it. Whether your interest is in architecture or science, there is plenty to observe around you. What I would like to focus on though is a bit of science history that connects the name of this cafe with Isaac Newton, John Theophilus Desaguliers and the dome of St Paul’s Cathedral (which you can see from the front of St. Nicholas Cole Abbey).

View of the Dome from the cafe

The Dome of St Paul’s, visible from the side of the Wren cafe.

Perhaps we all remember the story told to us at school about how Galileo dropped two balls of different mass from the top of the leaning tower of Pisa. According to the story, the balls fell to the earth at the same time, thereby showing that the acceleration due to gravity was independent of the mass of the object and paving the way for Newton’s theory of gravity. Sadly, it seems that Galileo may never have actually performed the experiment (even if it was “re-created” in 2009). However there is evidence that Isaac Newton did perform exactly this experiment in 1710 from the dome of the soon-to-be-completed St Paul’s Cathedral.

“From the top of St Paul’s church in London in June 1710 there were let fall together two glass globes, one full of quick silver [mercury], the other of air”¹. The globes fell 67m before shattering onto the cathedral floor (I’d hate to have written the risk assessment for that experiment). To avoid the possibility of human error, a trap-door mechanism had been designed to ensure that both globes dropped simultaneously. According to the story of Galileo told to us at school, we can calculate how long it would have taken those globes to drop to the floor: 3.7 seconds, independent of mass. So is this what Newton observed? No! The heavy glass globes took 4 seconds to fall, but lighter ones took 8-8.5 seconds! A few years later and Desaguliers repeated the experiment from slightly higher in the dome (but this time with hog’s bladders rather than glass) and obtained the same result.

View of St Paul's Cathedral London

Another view of St Paul’s. Hard to believe that Newton actually dropped liquid mercury from the dome.

This surprising result can be explained when we realise that Newton was investigating not gravity, but air resistance. While the gravitational acceleration is independent of mass, the upwards force due to the air resistance depends primarily on the object’s size (and velocity). This means that the deceleration caused by the air resistance will be different for two globes of the same size but different mass (Force = mass x acceleration). Heavy objects will fall faster in air (until the objects reach their terminal velocity).

There is a certain irony in the fact that this result is opposite to what we feel should happen based on what we learned at school of Galileo’s experiments challenging the scientific orthodoxy of the time. However the result of Newton and Desaguliers’ experiments do not contradict the theory of Newton or Galileo, they just add an extra layer to the problem. We do not exist in a vacuum, we need to think about the air around us too.

Both Newton and Desaguliers were regular coffee drinkers albeit at different coffee houses. Desaguliers frequented the Bedford Coffee House in the north east corner of Covent Garden while Newton regularly retired to the Grecian in Devereux Court (just off Fleet Street). Coffee houses were places that the latest science, politics or philosophy were discussed and debated. The Wren describes itself on its website as existing to “serve the ministry of St Nick’s talks“. Sadly I experienced no discussion or debate on my visit (just a very nice, but solitary, lunch and good coffee) but it is interesting to see the tradition of the 17-18th century coffee houses continued in this Wren designed church and cafe.

The Wren cafe can be found inside St Nicholas Cole Abbey, 114 Queen Victoria St. EC4V 7BJ

[1] The Dawn of Fluid Dynamics, Michael Eckert, Wiley-VCH (2006)

Coffee house info: London Coffee Houses by Bryant Lillywhite (pub. 1963)