A short (lived) black

coffee at Story
A black coffee with bubbles on top. The colours on a bubble are the result of light interference. But sometimes the top of the bubble could appear black. What is happening there?

The long black can be distinguished from the Americano by the order in which the espresso and the water are added to the cup. This in turn will affect the type of bubbles on the surface of the coffee. As a guess, the long black (espresso last) will have many more but smaller bubbles than the Americano (water last) which will probably have larger, but fewer bubbles. Perhaps this guess is wrong, this could be an excuse to get out and drink more coffee.

We are used to the coffee being black and the bubbles on the surface reflecting a rainbow of shimmering colours that change with the light and with time before they finally burst. We know the physics of the colours on the bubbles: they are the result of the interference of reflections from the outer and inner surface of the bubble cancelling out certain colours and adding to others dependent on the bubble skin’s thickness. But what about black bubbles? Or, if not entirely black, perhaps the cap of the bubble can, for a short while, appear black just before the bubble bursts?

It is easier to take a short break from coffee and look for this effect in soap films. Like the bubbles on coffee, soap bubbles are caused by the surfactant in the soap solution having a hydrophilic (water loving) and hydrophobic (water hating) end. The hydrophilic end of the surfactant can point into the water (coffee) leaving the hydrophobic end to form a surface. When this is agitated with air, the hydrophilic ends remain contacted with water resulting in bubbles which are thin layers of water surrounded by these surfactant molecules. In coffee the surfactant is not soap but is formed by the lipids and fatty acids. These bubbles are therefore slightly weaker than the soap based bubbles and so while they will form on a coffee, it is not easy to make a film of a coffee bubble in the same way as you can dip a wire loop into a soap solution and come out with a soap film.

However, we can use the stability of the soap film to investigate the colours in the coffee bubbles and watch the colours evolve with time. At this point, I would strongly encourage anyone reading to grab a solution of soap and a wire loop and start playing with soap films.

Soap film in a wire loop held by a crocodile clip.
A soap film in a wire loop showing reflected horizontal coloured bands that are the result of light interference.

Holding the wire loop so that the soap film is vertical with a light source shining at it, we can watch as the film changes from being uniformly transparent to having bands of colour form and move down the film. We watch as there is a red/green band and another red/green band and then on top of the bands there appears a white, or at least pale blue, almost white, band and above that a layer that doesn’t reflect the light at all. If we view the soap film against a dark background looking only at the reflected light, this top portion of the film appears black. Rotating the loop we can see that the bands effectively stay in the same position because it is gravity pulling on this soap film that is causing the film to be thicker at the bottom than at the top. And we recognise that the coloured bands are revealing that thickness change to us by the fact that they are changing throughout the film. If we are careful as we rotate the wire, we could even see vortex like motions as the layers settle into their new position relative to the frame including at the very top where there are swirls and patches of fluid that mix the black layer with the coloured bands. What is going on there?

In fact, this black layer is one of the thinnest things that they human eye can see, and it occurs because of a subtle piece of physics. All waves have a number of properties defined by the position of the peaks and troughs on the wave. The wavelength is the distance between two equivalent points on the wave. The amplitude is the height of the peak (or trough). And the phase is the position of the wave relative to the peak (or trough). When light is reflected at a surface of a material that has a refractive index greater than that which the light is travelling through (eg. air into water, soap, or glass), the reflected wave has a 180 degree phase shift relative to the incident wave. Each peak becomes a trough, each trough becomes a peak. When light is already travelling through water, soap or glass and gets reflected at the surface of the material that is effectively air, there is no phase shift and the light is reflected back with the same phase as the incident wave (a peak remains a peak and a trough a trough).

At the top of the soap film, the layer is so thin that the light reflected from the first surface (180 degree shift) overlays that reflected from the back surface (no phase shift) so that peak and trough cancel each other out and we see no light reflected whatsoever for any visible wavelength; the surface looks black.

As bubbles ‘ripen’ or age, they will become thinner at the top of the bubble. It is at this point that you may be lucky enough to see a region of the bubble from which no light is reflected, this is the black film.

Which leads to some immediate questions. When we look carefully at the soap film, the boundary between the upper white band and the black film is quite sharp, it is not gradual as we may expect if the soap film were completely wedge shaped with gravity. It suggests that the top of the film is very thin and then suddenly gets thicker at the point where we start to see the colour bands. Moreover, the black film does not appear to mix with the thicker film just beneath it. As we watch, just before the soap film bursts, we get turbulence between the black layer and the thicker film, but the turbulent patterns appear like two fluids next to each other, not the same fluid in a continuum. And then, one final question. If we can’t measure the thickness of the black film with light (because it is all reflected as black) how can we know how thick this film is? If we rely on the light interference method, all we can say is how much thinner it is than the wavelength of light.

In fact, careful experiments have revealed two types of black film, which to us experimenting at the kitchen table would be indistinguishable. There is the common black film and the Newton black film. The Newton black film is effectively two layers of surfactant molecules only and is about 5nm thick (which is 5 millionths of a millimetre). The common black film is thicker, but is still much less than 100 nm thick. Investigating how these films behave is still an active area of research.

One last observation may prompt us to play for a bit longer with the soap films. Johann Gottlob Leidenfrost (1715-94) noted that if you put a sharp object such as a needle through the region of the soap film that showed the coloured bands, the film could self-heal and wouldn’t necessarily burst. If however you pierced the black region of the film, the film always burst entirely.

It seems that we could play endlessly with soap films, perhaps while watching the bubbles in our coffee. However you enjoy your coffee, have fun experimenting.

A couple more soap films showing reflected coloured interference bands. At the top, the film has become so thin that no light is reflected (clearly seen in the image on the right, where the lamp in the top left should be a circular reflection but is not reflected in the region above the coloured bands). In the image on the left, you can see what looks like turbulence or mixing just above the uppermost band.

To err is human…

Press Room coffee Twickenham
A smaller V60. For one cup you would use less coffee, but the errors on the measurement will always be there.

Preparing a good V60 requires 30g of coffee (for 500 ml of water)*. This can be measured using a set of kitchen scales, but a first estimate can also be obtained, if you are using whole coffee beans, by timing the passage of the grind through the grinder. Using an Ascaso burr grinder, my coffee used to come through at an approximate rate of 1g/s, so that, after 30 seconds, I’d have the perfect amount of coffee. Recently however this has changed, depending on the bean, sometimes 30g is 40 seconds, sometimes just less than 30 seconds.

Clearly there is an error on my estimate of the rate of coffee grinds going through the grinder. This may be influenced by factors such as the hardness of the bean (itself influenced by the degree of roast), the temperature of the kitchen, the cleanliness of the grinder and, the small detail that the ‘seconds’ measured here refers to my counting to 30 in my head. Nonetheless, the error is significant enough that I need to confirm the measurement with the kitchen scales. But are the scales free of error?

Clearly in asking the question, we know the answer will be ‘no’. Errors could be introduced by improper zero-ing of the scales (which is correct-able), or differences in the day to day temperature of the kitchen (not so correct-able). The scales will also have a tolerance on them meaning that the measured mass is, for example, only correct to +/- 5 % Depending on your scales, they may also only display the mass to the nearest gramme. This means that 29.6g of coffee would be the same, according to the scales, as 30.4g of coffee. Which in turn means that we should be using 493 – 507 ml of water rather than our expected 500 ml (the measurement of which also contains an intrinsic error of course).

Turkish coffee
A Turkish coffee provides a brilliant illustration of the type of particle distribution with depth that Jean Perrin used to measure Avogadro’s constant. For more information see here.

The point of all of this is that errors are an inescapable aspect of experimental science. They can also be an incredibly helpful part. Back in 1910, Jean Perrin used a phenomenon that you can see in your coffee cup in order to measure Avogadro’s constant (the number of molecules in a mole of material). Although he used varnish suspended in water rather than coffee, he was able to experimentally verify a theory that liquids were made up of molecules, by the fact that his value for Avogadro’s constant was, within error, the same as that found by other, independent, techniques. Errors also give us an indication of how confident we can be in our determination of a value. For example, if the mass of my coffee is 30 +/- 0.4 g, I am more confident that the value is approximately 30 g than if the error was +/- 10 g. In the latter case, I would get new scales.

But errors can also help us in more subtle ways. Experimental results can be fairly easily faked, but it turns out that the random error on that data is far harder to invent. A simple example of this was seen in the case of Jan Hendrik Schön and the scientific fraud that was discovered in 2002. Schön had shown fantastic experimental results in the field of organic electronics (electronic devices made of carbon based materials). The problem came when it was shown that some these results, despite being on different materials, were the same right down to the “random” noise on the data. Two data sets were identical even to the point of the errors on them, despite their being measurements of two different things.

A more recent case is a little more subtle but crucial for our understanding of how to treat Covid-19. A large study of Covid-19 patients apparently showed that the drug “Ivermectin” reduced mortality rates enormously and improved patient outcomes. Recently it has been shown that there are serious problems with some of the data in the paper, including the fact that some of the patient records have been duplicated and the paper has now been withdrawn due to “ethical considerations”. A good summary of the problems can be found in this Guardian article. However, some of the more worrying problems were a little deeper in the maths behind the data. There were sets of data where supposedly random variables were identical across several patients which suggested “that ranges of cells or even entire rows of data have been copied and pasted“. There were also cases where 82% of a supposedly random variable ended in the digits 2-5. The likelihood of this occurring for random variables can be calculated (it is not very high). Indeed, analysis of the paper showed that it was likely that these values too were either copy and pasted or “invented” because humans are not terribly good at generating properly random numbers.

A gratuitous image of some interesting physics in a V60. If anyone would like to hire a physicist for a cafe, in a 21st century (physics) recreation of de Moivre’s antics at Old Slaughters, you know how to contact me…

Interestingly, a further problem both for the Ivermectin study and for the Schön data comes when you look at the standard deviation of the data. Standard deviation is a measure of how variable is the measured outcome (e.g. duration of time a patient spent in hospital). For the ivermectin study, analysis of the standard deviations quoted on the patient data indicated a peculiar distribution of the length of hospital stay, which, in itself would probably just be a puzzle but in combination with the other problems in the paper becomes a suggestion of scientific fraud. In Schön’s data on the other hand, it was calculated that the precision given in the papers would have required thousands of measurements. In the field in which Schön worked this would have been a physical impossibility and so again, suggestive of fraud. In both cases, it is by looking at the smaller errors that we find a bigger error.

This last detail would have been appreciated by Abraham de Moivre, (1667-1754). As a mathematician, de Moivre was known for his work with probability distribution, which is the mathematics behind the standard deviation of a data set. He was also a well known regular (the ‘resident’ mathematician) at Old Slaughters Coffee House on St Martin’s Lane in London[1]. It is recorded that between 1750 and 1754, de Moivre earned “a pittance” at Old Slaughters providing solutions to games of chance to people who came along for the coffee. I wonder if there are any opportunities in contemporary London cafes for a resident physicist? I may be able to recommend one.

*You can find recipes suggesting this dosage here or here. Some recipes recommend a slightly stronger coffee amount, personally, I prefer a slightly weaker dosage. You will need to experiment to find your preferred value.

[1] “London Coffee Houses”, Bryant Lillywhite, 1963

Up in the air with a Pure Over Brewer

The diffuser sitting on top of the Pure Over coffee brewer. The holes are to ensure that the water falls evenly and slowly onto the grounds below.

The Pure Over is a new type of coffee brewer that is designed to brew filter coffee without the need for disposable paper filters. The brewer, which is completely made of glass, is a perfect size for brewing one cup of coffee and, as promised, makes a lovely cup without the need for wasteful paper filters. Generally, for 1-cup filter coffees, the Pure Over has become my go-to brewing method, although it does have a few idiosyncrasies to it that are helpful to be aware of while brewing.

An advantage of this brewing device is that it provides a large number of opportunities for physics-watching, including a peculiar effect that connects brewing coffee to an air balloon crash into the garden of a London Coffee House. It concerns a feature of the Pure Over that is specific to this particular brewing device: the ‘diffuser’ that sits on top of it.

The glass diffuser has five small holes at the bottom of it which are designed to reduce the flow of the water onto the coffee bed so that it is slower and more gentle. In order to avoid the paper filters, the Pure Over features a filter made of holes in the glass at its base. This filter does surprisingly well at keeping the coffee grounds out of the final brew, but it works best if the coffee bed just above it is not continuously agitated. The idea of the diffuser is that the coffee grounds are more evenly exposed to the water, with the grounds closest to the filter being least disturbed and so the coffee is extracted properly.

As water is poured from a kettle through the diffuser, the water builds up in the diffuser forming a pool that slowly trickles through the holes. Initially this process proceeds steadily, the water is poured from the kettle into the diffuser and then gently flows through and lands on the coffee. At one point however, the pressure of the steam within the main body of the brewer builds until it is enough to push the glass diffuser up a bit, the steam escapes and the diffuser ‘clunks’ back onto its base on top of the pure over. Then, this happens again, and again, until there is a continuous rattle as the steam pressure builds, escapes and builds once more.

The ideal gas laws, such as that found by Jacques Charles, relate the volume and pressure of a gas to its temperature. The application of the laws helped to improve the design of steam engines such as this Aveling and Porter Steam Roller that has been preserved in central Kuala Lumpur, Malaysia.

The pressure of the steam builds until the force exerted upwards by the rising steam is greater than the weight of gravity pulling the diffuser down. Once enough gas escapes, the pressure is reduced and so the steam no longer keeps the diffuser aloft which consequently drops with a clunk. The motion could take our thoughts to pistons, steam engines and the way that this steam movement was once exploited to drive our industrial revolution. Or you could go one stage earlier, and think about the gas laws that were being developed shortly before. There’s Boyle’s Law which relates the pressure of a gas to its volume (at constant temperature). That would perhaps partially explain the behaviour of the pure over. But then there’s also Jacques Charles and his observation that the volume of a gas is proportional to its temperature (at constant pressure). This too has relevance for the pure over because as we pour more water in from the kettle, we warm the entire pure-over body and so the temperature of the gas inside will increase. Consequently, as the amount of hot water in the pure over increases, the temperature goes up, the volume of that gas would increase but is stopped by the diffuser acting as a lid. This leads to the pressure of the gas increasing (Boyle) until the force upwards is high enough, the diffuser lid rises upwards on the steam which escapes leading the pressure to once again drop and the diffuser top to go clunk and the whole cycle begins again.

Of course, we know that Boyle’s law is appropriate for constant temperature and Charles’s law is appropriate for constant pressure and so the laws are combined together with the Gay-Lussac/Amonton law into the ideal gas laws which explain all manner of things from cooling aerosols to steam engine pistons. And yet, they have another connection, which also links back to our pure over, which is the history of hot air balloons.

Charles discovered his law in around 1787, a few years after the first non-tethered hot air balloon ascent, in Paris, in June of 1783. The hot air balloon is a good example of the physics that we can see in the pure over. Although Charles must have suspected some of the physics of the hot air balloon in June, he initially decided to invent his own, hydrogen filled balloon which he used to ascend 500 m in December of 1783. Hydrogen achieves its lift because hydrogen is less dense than air at the same temperature. However, it is the hydrogen balloon that links back to coffee and coffee in London.

hot air balloon
The ideal gas laws also contribute to our understanding of the operation of hot air balloons. We are familiar with them now, but how would such an object have been perceived by observers at the time of the first flights?

The first balloon flight in England took place using a hydrogen, not a hot-air, balloon in 1785. The balloon was piloted by Vincenzo Lunardi who was accompanied by a cat, a dog and, for a short while, a pigeon (before it decided to fly away). But it was not this successful flight that connects back to coffee, it was his maiden flight on 13 May 1785. On that day, Lunardi took off from the Honourable Artillery Company grounds in Moorgate, flew for about 20 minutes and then crashed, or as they said at the time “fell with his burst balloon, and was but slightly injured”(1) into the gardens of the Adam and Eve Coffee House on the junction of Hampstead Road and, what is now, Euston Road. In the 1780s the Adam and Eve coffee house had a large garden that was the starting point for walks in the country (in the area now known as Somers Town)(2). Imagine the scene as, quietly appreciating your tea or coffee, a large flying balloon crashes into the garden behind you.

The Adam and Eve is no longer there, in fact, its original location now seems to be the underpass at that busy junction, and the closest coffee house is a branch of Beany Green. However there is one, last coffee connection and it brings us back to the pure over. The pressure of the steam under the diffuser needs to build until the upwards force of the steam can overcome the gravitational force down of the weight of the glass diffuser. In the same way Lunardi had to have enough lift from the hydrogen balloon to compensate for the weight of the balloon and its passengers. Lunardi had wanted to be accompanied by another human on the day of his successful flight. Unfortunately, the mass of two humans in a balloon was too much for the balloon to accommodate which is why, the human was replaced by the dog, the cat and the pigeon.

Which may go some way to illustrate how far the mind can travel while brewing a cup of coffee, particularly with a brew device as full of physics as the Pure Over.

1 London Coffee Houses, Bryant Lillywhite, George Allen and Unwin publishers, 1963

2 The London Encyclopaedia (3rd edition), Weinreb, Hibbert, Keay and Keay, MacMillan, 2008

Viewing an eclipse, the coffee way

NASA image of annular eclipse from space
A different perspective? This is the view looking towards Earth of the 2017 Annular solar eclipse over South America. Taken by the EPIC DSCOVR project of NASA.

This week, on Thursday, June 10th, 2021, there will be a solar eclipse. If you are at high latitudes in the Northern Hemisphere including parts of Canada, Greenland and Siberia, you will see a so-called ring of fire as the moon moves in front of the Sun. At lower latitudes the eclipse will be much more partial and in London we are expecting to see 20% of the Sun obscured by the Moon.

You can read more about solar eclipses on other websites such as here or here, on Bean Thinking, we are going to focus on the coffee links to the eclipse.

The first coffee link comes in how to view it. This website suggested a number of ways of viewing the eclipse, one of which was to use a colander. This suggests a perfect adaptation to a view via coffee: the Aeropress filter cap. The idea behind the method is that each of the holes provides a type of pin-hole camera to image the Sun. Knowing roughly where the Sun will be at 10.06am (BST = UTC+1), we can construct a device to hold the aeropress filter cap so that we can see 97 images of the Sun projected onto a piece of paper: 97 images of the Sun to be eclipsed over the following 2hours 18 minutes. The maximum eclipse is around 20% of the solar disc and occurs at approximately 11.15 (although the exact fraction obscured and timing depends on your location). The Aeropress Eclipse viewing device shown in the photo here has an added (smaller) pin hole which should provide a more focussed image of the Sun and so will provide a second way of imaging the eclipse.

A second coffee link comes with thinking about why this particular solar eclipse is not ‘total’ anywhere on earth but is instead described as annular. And to do this, we’ll think about a coffee bean. The amazing visual spectacle of a total solar eclipse occurs because the moon is 400 times smaller than the Sun but is (on average) about 400 times closer to the Earth. So when we think about looking at a coffee bean, held at arms length from our eye (about 60cm), it would totally obscure (eclipse) an object 3.2 m tall, 233.5 m away*.

Eclipse viewer
An aeropress based device for viewing the eclipse. The strings attached to the cardboard flap at the top allow the angle of the aeropress filter cap to be fixed at different points. The camera is at the approximate point where the images will be projected onto paper.

The word “average” though hides an important detail that neither the Moon’s orbit around the Earth, nor the Earth’s orbit around the Sun are completely circular. On the 10th June 2021, the Moon will be two days past its maximum distance (apogee) from the Earth, and while the Sun is also nearly at its maximum distance, the distance ratio will mean that the Moon does not entirely obscure the Sun. Instead, if we return to our coffee bean analogy, it is the equivalent of stretching our arm 2 more centimetres and noticing that the object that was obscured is no longer completely obscured.

This will still make for a fantastic view if you are in Greenland, Siberia or happen to be at the North Pole where you will see a dark disc surrounded by a ring of Sun. For those of us further south, we will only see the Sun partially obscured by the Moon. Nonetheless, such an opportunity in any one particular location doesn’t come super-often (although worldwide there are often several eclipses per year, in London there will only be 42 partial eclipses in this current century). And in London, we have to worry about the weather too. So, if the weather is good for you, why not have a go viewing it, particularly if you adapt a piece of coffee brewing equipment to do so, and post your pictures of the effect here, or to Bean Thinking on Twitter or Facebook.

Finally, the timing of the eclipse is perfect for a mid-morning coffee, though maybe you’ll have to brew with something other than the Aeropress. Have fun.

*These figures have been calculated using a ratio of the size of the Moon to the Sun as 1:400.8 and an average distance of 1:389.2 (calculated from the average values). The distances on June 10 2021 mean that the distance ratio is closer to 1:377

Update to post, the day before (9 June 2021): This is the Aeropress viewing device in action, but 24h before the eclipse. Will the clouds stay away tomorrow?

The Aeropress Eclipse viewer in action. The images of the Sun are projected onto the cardboard behind the filter cap.

Update 10 June 2021: It was cloudy in London and I couldn’t get the Aeropress filter cap method to work in the brief periods of sunshine during the eclipse. Suspect it was a problem with focus-distance/angle/remaining cloud cover at points. However, the smaller pinhole did work (see the blurry image below) and the clouds did mean that there was a natural filter that made a direct photograph possible (see below). Do share your images here if you managed to view it.

Although there were brief periods without cloud, focussing issues etc. meant that I couldn’t get the Aeropress filter cap viewing method to work. Maybe for the next one!
A smaller pinhole did give an image of the Sun being eclipsed (lower blurry bright image)
The fact that it was cloudy did mean however that I could take a photograph of the eclipsed Sun directly. This was at about 11.10am (5 minutes or so before the maximum point of eclipse)

Pure Percolation

Pure over boxed
The Pure Over in its box. The glass base is designed with an inbuilt filter, avoiding the need for disposable paper filters but making the physics of percolation unavoidable.

It was entirely appropriate that the first coffee I tried in the Pure Over coffee brewer was the directly traded La Lomita Colombian from Ricardo Canal via Amoret Coffee. Ricardo was a special guest at one of the Coffee and Science evenings we held at Amoret Coffee in Notting Hill (pre-pandemic) where, among other things, he spoke about how he is using Biochar on his coffee farm. Biochar is a porous, charcoal based material that can help to provide the coffee plants with nutrients as well as water, thereby reducing the amount of fertiliser the plants need. To understand how it works, we need to understand a bit about percolation, which of course we also need to understand in order to brew better coffee in the Pure Over. Indeed, there are enough similarities, and an extension to a quirk of how espressos are brewed, that it is worth spending a little more time thinking about this process and the connections revealed as we brew our coffee.

Percolation recurs in many of the brew methods we use for making coffee. The V60, Chemex, Kalita wave, percolators and the espresso itself, all rely at some point on water flowing through a bed of ground coffee. The flavour of the resultant cup is dependent on the amount of coffee surface that the flowing water is exposed to together with the time that it is in contact with the coffee. What this means is that grain size, or the degree to which you grind your coffee, is critical.

Playing with brewing coffee, we know some things by experience. Firstly, frequently, the flow through a coarse grind of coffee will be quite fast (probably too fast to make a good cup). Secondly, we know that for any particular brew method, the more water we pour into the brewer, the faster the water initially comes through. We also know that we can affect the flow rate of water through the coffee if we increase the area of the coffee bed, or decrease its thickness. These observations were quantified into an equation by Henri Darcy in 1856. Darcy’s work had been as an engineer, designing and building public works such as the aqueduct that brought drinking water into the city of Dijon in the 1840s. Darcy received significant recognition at the time for his work including the Légion d’honneur, but it is more for a later set of experiments and particularly for his equation that we remember him today. In the 1850s Darcy was working on the problem of water purification. Passing water through a bed of sand is still used as a method of purifying the water today. Darcy used a series of cylinders filled with sand to investigate how quickly water trickled through the sand bed in order to come up with a proper quantification of those things that we too know by experience with our coffee filters. You can read about the mathematics of Darcy’s equation here.

espresso puck
An espresso puck. The compact structure nonetheless allows water to percolate through it at high pressure.

Darcy found that the flow rate of water through the sand bed increased when the porosity of the bed was higher (fine, dense sand would delay the flow of the water more than coarse, loosely packed sand). If there was a greater pressure on the water at the top of the bed (ie. more water is on top of the sand), the flow rate through the bed would increase too. Conversely the flow would get slower as the water was made more viscous. This is something we too know from experience: try to pour honey through the coffee grounds and it just won’t work.

For us to apply Darcy’s insights into making better coffee, it means that we need to think about the grind size. Too coarse and there will be lots of empty space through the bed of grounds: the porosity is high, and the water will flow straight through. Too fine and the flow rate will decrease so much that rather than just the sweet and slightly acidic solubles that first come out of any coffee extraction*, there could be too much of the bitter organic compounds that come out later, changing the character of the cup. With coffee we have an additional concern. Unlike sand, coffee grinds will swell, and splinter, as water is added to them, closing up any narrower paths and lengthening the brew time. This also means that, unless we properly wet the grounds prior to filtering our coffee, the extraction will be non-uniform and not reproducible. Another reason to bloom coffee thoroughly before brewing.

There is one more factor in brewing our coffee however that Darcy’s equation, which is valid for more stable systems, overlooks. Darcy assumed a constant flow rate of water through the sand bed, but coffee is different. In his book about espresso*, Illy showed that the flow of the water through an espresso puck was not constant over time. Something really interesting was happening when you looked carefully at an espresso puck. Ground coffee can come in a large distribution of sizes. In addition to the grind that we are aiming for, we also get a whole load of smaller particles called ‘fines’. Sometimes this is desirable, but with espresso, and by extension with our filter coffees, these fines add a twist to the physics of the percolation. As the espresso water is pushed through the coffee puck, the fines get pushed down through the puck between the ‘grains’ of the coffee grinds. This reduces the flow rate of the water until the point at which they get stuck. This will have the effect of increasing the contact time between the coffee and the water and so allowing more flavour solubles to be extracted. But crucially, these fines remain somewhat mobile. If you were to turn the whole espresso puck upside down (and Illy had a machine that allowed him to do this in-situ), the fines would again go on the move. Migrating from the new top of the puck to the new bottom. Filling the voids between the slightly too coarse grains. Complicating the simplifications in Darcy’s equation, but adding flavour to our brew.

Watch House coffee Bermondsey
There is a fountain on the wall (right hand side) of the Watch House cafe in Bermondsey. Many public fountains in London date from the 1850s emphasising just what a problem access to drinkable water once was.

Which leaves the connection between the farming method and the coffee. Biochar is formed by burning carbon containing waste (such as plant matter) in a low oxygen environment. Burying the resultant charcoal is therefore a way of storing carbon, and preventing its release into the atmosphere, for many years. But it is not just good for carbon storage. The buried charcoal is highly porous and traps nutrients within its structure so that the plants growing near it can be fertilised more efficiently. Moreover, the fact that it is porous, just like the coffee or sand beds, means that it traps water for a long time. Consider how long it takes a used filter full of coffee grounds to completely dry out! The water gets trapped within the porous structure and does not evaporate easily. This aspect of the biochar means that, as well as nutrients, the plants that grow nearby get a good source of reliable water. The ancient civilisations of the Amazon region used something similar to biochar in their farming techniques resulting in soil now known as “Terra Preta”, an extremely rich form of soil that improves plant growth. On his farm, Ricardo is going fully circular and making his biochar out of old coffee trees. The old trees thereby giving new opportunities to the fresh growth. It is a carbon capture scheme that reduces the need for fertilisers and that relies on percolation physics to work to best effect for the plants.

It seemed a moment of perfect coffee-physics poetry to use coffee grown on a farm using these techniques while initially experimenting with my own, percolation sensitive, Pure Over brewer. Percolation physics and interconnectedness all in one cup.

*Illy and Viani (Eds), “Espresso Coffee”, 2nd Edition, (2005)

In search of origins

Amaje coffee
Buriso Amaje Coffee from Ethiopia via Amoret Coffee in Notting Hill. The Jimma 74158 and 74160 varietals are selections from coffee grown in the wild.

It was a goat herder named Kaldi, so the story goes, who first noticed the effect of coffee beans on the the energy levels of his goats. After telling the local abbot of his observations, the monks at the nearby monastery realised that this drink could help them stay awake during prayer and so the reputation, and consumption, of coffee spread from Ethiopia and then throughout the world.

While the details may be questionable, there is evidence that the coffee plant originated in Ethiopia. Coffee still grows wild in parts of Ethiopia and the oldest varietals are also to be found there. And so, when I realised that my latest coffee was an Ethiopian Natural of varietal Jimma 74158 and 74160, roasted by Amoret coffee in Notting Hill, I thought, why not do a coffee-physics review rather than a cafe-physics review? For there are always surprising links to physics when you stop to think about them, whether you are in a cafe or sampling a new bag of beans.

This particular coffee was grown by Buriso Amaje in the Bensa District of the Sidama region of Ethiopia. The varietals were selections from the Jimma Research Centre from wild plants that showed resistance to coffee berry disease and were also high yielding. Grown at an altitude of 2050m, the naturally processed coffee came with tasting notes of “Blueberry muffin, white chocolate” and “rose petal” among others. Brewed through a V60, it is immediately clear it is a naturally processed coffee, the complex aroma of a rich natural released with the bloom. Indeed, the bloom was fantastically lively with the grounds rising up with the gas escaping beneath them in a manner reminiscent of bubbling porridge (but much more aromatic). And while I lack the evocative vocabulary of Amoret’s tasting notes, the fruity and sweet notes were obvious, with blueberry a clear descriptive term while I would also go for jasmine and a slight molasses taste. A lovely coffee.

Brewing it again with an Aeropress, the tasting notes were different. We could start to ponder how the brew method affects the flavour profile. But then we could go further, how would this coffee taste if brewed using the Ethiopian coffee ceremony? Which leads to further questions about altogether different origins. Where did this come from and how do our methods of experiencing something emphasise some aspects while reducing others? Ethiopia offers a rich thought current if we consider how things originated because it is not just known for its coffee, Ethiopia is also home to some of the world’s oldest gold mines. Today, one of the larger gold mines in Ethiopia lies just to the North West of where this coffee came from, while a similar distance to the south east is a region rich in tantalum and niobium. We need tantalum for the capacitors used in our electronic devices. In fact, there is most likely tantalum in the device you are using to read this. While niobium is used to strengthen steel and other materials as well as in the superconductors within MRI machines. Where do these materials come from?

The Crab Nebula is what remains of a supernova observed in 1054AD. Explosions like these are the source of elements such as iron. Image courtesy of Bill Schoening/NOAO/AURA/NSF

Within the coffee industry there has been a lot of work done to demonstrate the traceability of the coffee we drink. But we know much less about the elements that form the components of many of the electronic devices that we use every day. And while this leads us into many ethical issues (for example here, here and here), it can also prompt us to consider the question even more fundamentally: where does gold come from? Indeed, where do the elements such as carbon and oxygen that make coffee, ultimately, come from?

The lighter elements, (hydrogen, helium, lithium and some beryllium) are thought to have been made during the Big Bang at the start of our Universe. While elements up to iron, including the carbon that would be found in coffee, have been formed during nuclear fusion reactions within stars (with the more massive stars generating the heavier elements). Elements heavier than iron though cannot be generated through the nuclear fusion reactions within stars and so will have been formed during some form of catastrophic event such as a stellar explosion, a supernova. But there has recently been some discussion about exactly how the elements heavier than iron formed, elements such as the gold, tantalum and niobium mined in Ethiopia.

One theory is that these elements formed in the energies generated when two neutron stars (a type of super-dense and massive star) collide. So when the LIGO detector, detected gravitational waves that were the signature of a neutron star collision, many telescopes were immediately turned to the region of space from which the collision had been detected. What elements were being generated in the aftermath of the collision? Developing a model for the way that the elements formed in such collisions, a group of astronomers concluded that, neutron star collisions could account for practically all of these heavier elements in certain regions of space. But then, a second group of astronomers calculated how long it would take for neutron stars to collide which led to a problem: massive neutron stars take ages to form and don’t collide very often, could they really have happened often enough that we have the elements we see around us now? There is a third possibility, could it be that some of these elements have been formed in a type of supernova explosion that has been postulated but never yet observed? The discussion goes on.

coffee cup Populus
Where did it all come from? Plenty to ponder in the physics of coffee.

The upshot of this is that while we have an idea about the origin of the elements in that they are the result of the violent death of stars, we are a bit unclear about the exact details. Similarly to the story of Kaldi the goat herder and the origins of coffee, we have a good idea but have to fill in the bits that are missing (a slightly bigger problem for the coffee legend). None of this should stop us enjoying our brew though. What could be better than to sip and savour the coffee slowly while pondering the meaning, or origin, of life, the universe and everything? That is surely something that people have done throughout the ages, irrespective of the brew method that we use.

As cafes remain closed, this represents the beginning of a series of coffee-physics reviews. If you find a coffee with a particular physics connection, or are intrigued about what a connection could be, please do share it, either here in the comments section, on Twitter or on Facebook.

Coffee quakes

ripples on coffee at Rosslyn, the City
From ripples on the surface, to listening to the sound your coffee makes. What links a coffee to an earthquake?

What do you hear when you listen to your coffee? Or a related question, what links your coffee to earthquakes and seismology?

In recent weeks I have been making coffee with milk, not often, but enough to notice something slightly strange. While heating the milk in a small saucepan, I have accidentally tapped the side of the pan while the milk was in it. The tap, perhaps unsurprisingly, produced a ripple on the surface of the milk propagating away from the point of tapping. But what was surprising was that a very short time later, a second ripple was generated, this time from the other side of the pan propagating back towards the original wave.

The first ripple had not yet travelled across the milk surface before the second ripple had been generated and travelled back towards it. Something was causing a vibration on the other side of the pan before the first ripple had had a chance to get there. Was the pan acting like a type of bell which, as I tapped it, started to resonate all around its circumference?

Assuming that the vibration of the tap travels at the speed of sound through the metal of the pan, it would take about 50 μs for the vibration to travel half way around the circumference of the pan (diameter 14cm, with a speed of sound in steel ~ 4500 m/s). But then, if the pan were resonating, the resonance frequency would depend on the speed of sound in the milk filling the pan, which would increase as the milk was warmed. Would we see evidence for this if we video’d tapping the pan as we heated the milk?

coronal hole, Sun
Observing periodic changes to the luminosity of stars can indicate the elements within them. Image credit and copyright NASA/AIA

Rather than watching the liquid within, we could also learn about the interior of a cup of coffee by listening to it. The “hot chocolate effect” is the classic example of this. The effect occurs when hot chocolate powder is added to warm water or milk and stirred. Think about the pitch of a sound made by tapping gently on the base of your mug while you make a cup of hot chocolate. Initially, adding the powder and stirring it will introduce air bubbles into the liquid. As you stop stirring the hot chocolate but continue to tap the base of the cup the air bubbles leave the drink. The cup is acting as a resonator, so the sound that you hear (the resonance of the cup) is proportional to the speed of sound in the liquid in the cup. As the speed of sound in hot water containing lots of air bubbles is lower than the speed of sound in hot water without the air bubbles, the note that you hear increases in pitch as the bubbles leave the drink. You can read more about the hot chocolate effect in an (instant) coffee here.

It is here that we find the first connection between coffee and earthquakes. Seismologists have been listening to the vibrations of the Earth for years in order to learn more about its interior. By observing how, and how fast, waves travel through the earth, we can start to understand not only whether the inside is solid or liquid, but also what the earth is made from. This is similar to learning about the air bubbles in our hot chocolate by listening to the sound of the mug. More recently, the seismologists have shown the effect of the Covid-19 related “lockdowns” on reducing seismic noise. Something that does not have an obvious coffee cup analogy.

But seismology is not just confined to the Earth. Vibrations of a different kind have also been used recently to learn more about the interior of stars, although here it is a mix of seeing and ‘listening’. Generally, when the surface of an object vibrates, it leads to compressions and expansions of the medium within the object. This is the essence of what sound is. But in a star, these compressions and expansions also result in changes to the luminosity of the star. So, by looking carefully at the frequency of the variation in brightness of different stars, it should be possible to work out what is going on inside them. It is a branch of physics now known as “Astroseismology”. Recent astroseismology results from NASA’s Kepler satellite have been used to challenge theories about how stars form and evolve. It had been thought that as a star develops, the outer layers expand while the core gets smaller. The theories proposed that this would result in a certain change to the rotation speed of the core of the star. The astroseismology observations have revealed that, while the gist of the theory seems right, the core rotates between 10 and 100 times slower than the theories would predict. As one astroseismologist said “We hadn’t anticipated that our theory could be so wrong…. For me, finding that problem was the biggest achievement of the field in the last ten years.”.

We now use strain gauges in electronic measuring scales. They were originally invented for an entirely different purpose.

Seismology and astroseismology offer clear links between listening to your coffee cup and earthquakes (or star quakes). But there is one more earthquake related connection to the coffee cup and it could be noticed by any of us who want to improve our home brewing technique.

To brew better coffee, we need to measure the mass of the coffee beans that we are using. Typically we will use a set of electric scales for this. Inside the scales is a device, called a strain gauge, that shows a change in its electrical resistance as a result of the pressure on it (from a mass of coffee for example). The scales translate this change in the electrical resistance to a mass that is shown on the display. One of the inventors of the strain gauge however was not thinking about measuring the mass of coffee at all. His interest was in earthquakes and specifically, how to measure the effect of the stresses induced by earthquakes on elevated water tanks. In order to do that he needed a strain gauge which led to the devices that you can now find in your measuring scales.

Two links between your coffee cup and earthquakes or seismology. Are there more? Do let me know of the connections that you find, either in the comments below or on Twitter or Facebook.

Smelling collectively

You can see the steam rising above the cup in this coffee at Carbon Kopi. But you will have to imagine the aroma.

It is hard to choose the best thing about coffee, so many aspects combine to make a good cup. But one of the key things about drinking coffee, particularly if you have had a difficult meeting or have just come in from the cold, is the aroma that wafts up as you grind the beans, add water to bloom the coffee and then brew. In happier times, we may be walking down the street preoccupied about something that is going on and then suddenly get hit by a fantastic aroma that signals our proximity to a good cafe. We perhaps ‘follow our noses’ to the source of the smell and then breathe in the scents as we enter the cafe. Which brings us, in a round about way, to moths and a recent paper that appeared in Physical Review E.

It is not that moths have been shown to have a particular liking for the smell of coffee. That may be an area of future research for somebody. But they do need a very good sense of smell because they need to be able to ‘follow their noses’ in order to find the source of a smell that they are interested in (typically a pheromone released by a female moth). This female moth may be located 100s of metres away from the male and probably does not emit that much odour, so how do the male moths find her?

In a similar manner to our approach to the aromatic coffee shop, the moths first travel against the wind, aware in some sense that the smell is carried downstream. If they lose the scent, they then fly perpendicular to the wind flow in an attempt to sniff the aroma once more. This pattern of zig-zagging flight allows them to approach the source of the smell fairly quickly*.

Eggs of a large cabbage white butterfly. No real links with coffee and few with moths, but the adult pair may well have had to find each other using the sense of smell.

It’s a clever method that is perfect if the wind flows in one direction without any turbulence. But how many times have you watched as leaves have been swept up in the wind flow and danced a swirling vortex pattern before falling back to the ground? Or, as you approach the side of a tall building, you get hit by a gust of wind that seems to come in a number of directions all at once because of the way that it is being affected by the presence of the building wall? We can see a similar thing in babbling streams and in our coffee as the convection currents swirl in vortices. The real world is not so simple as a linear wind flow, in the real world the wind is turbulent.

And yet still the moths find their way to the source of the smell that they are seeking. How do they do it, and could we design a robot (or robots) to emulate the moths in order to find, for example, chemical leaks? It was these questions that were addressed by the recent paper in Physical Review E. In the study they used mathematical calculations to look, not at the behaviour of an individual moth, but at the behaviour of a swarm of moths, a group of moths all searching for a mate.

In the computer model, each individual moth could discern the wind speed and direction and also detect odour molecules. So, left to their own devices, the individuals in the model would follow the zig-zag pattern of individual moths observed in nature (this was a deliberate element of the model). But the model-moths were given another ‘sense’: the ability to see the behaviour of their fellow model-moths. Which direction were the others going in? How fast were they moving?

The model-moths were then provided with one final behaviour indicator, a parameter, β, which was called a ‘trust’ parameter. If β = 0, the model-moths did not trust what the others were doing at all and relied purely on their own senses to reach the prize. Conversely, if β = 1, the model-moths completely lacked confidence in their own ability to discern where the smell was coming from and followed the behaviour of their peers.

We find our way to a cafe via visual cues or perhaps the sounds of espresso being made. But can we also follow the aroma?

Running the model several times for different wind conditions including a turbulent flow, the authors of the study found that the moths reached the destination smell best if they balanced the information from their own senses with the behaviour of their peers. In fact, the best results were for a trust factor, β ~ 0.8-0.85 meaning that they trusted their peers 80-85% of the time and relied on their own decisions 10-15% of the time. If they did that, they reached the smell source in only just slightly longer than it would take a moth to fly directly to the source of the smell in a straight line. An astonishingly quick result. As the authors phrased it, the study indicated that you (or the moths) should “follow the advice of your neighbours but once every five to seven times ignore them and act based on your own sensations”.

Now it would be tempting to suggest that this study has no relevance for us individuals finding a coffee shop and minimal relevance to coffee. But that I think would be premature. For a start, a similar result was found when the question was not about moths but about the best way for a crowd of people to leave a smoke filled room. If everyone behaved individualistically, or conversely, if everyone behaved in a purely herd like manner, the crowd took longer to escape the room than if people balanced their individualistic needs with a collective behaviour. It is a push to suggest that the same thing may be relevant for us finding cafes, but who knows what may happen post-lockdown(s) as we collectively attempt to find a well made flat white to enjoy outside our homes. Maybe we too need to trust our own senses some of the time but be open to taking the advice of those around us too.

*You can read more details in the paper Durve et al., Phys Rev E, 102, 012402 (2020)

Missing matter

soya latte at the coffee jar camden
Not one made by me! But instead a soya-latte at the Coffee Jar a couple of years ago.

During these strange times of working from home, perhaps you, like me, have been preparing a lot more coffee. For me this has included, not just my regular V60s, but a type of cafe-au-lait for someone who used to regularly drink lattes outside. My previous-latte-drinker turns out to be a little bit discerning (the polite way of phrasing it) and so prefers the coffee made in a similar way each day. Which is why I’ve been weighing the (oat) milk I’ve been using.

So, each morning to prepare a coffee, I’ve been using a V60 recipe from The Barn and then, separately, weighing out 220g of refrigerated oat milk into a pan that I then heat on the stove. Generally I heat the milk for just over 5 minutes until it is almost simmering whereupon I pour it into a mug (with 110 – 130g of coffee inside – depending on the coffee). Being naturally lazy, I keep the cup on the scales so that it is easier to pour the milk in and then, completely emptying the pan into the coffee, the scales register an increase of mass (of milk) in the cup of 205-210g. Which means about 10-15g of milk goes missing each morning.

Now clearly it is not missing as such, it has just evaporated, but it does prompt a question: can this tell us anything about the physics of our world? And to pre-empt the answer, it actually tells us a great deal. But to see how, we need to go on an historical diversion to just over three hundred years ago, when Edmond Halley was presenting an experiment to the Royal Society in London. The experiment shares a number of similarities with my heated oat milk pan. It was later written into a paper which you can read online: “An estimate of the quantity of vapour raised out of the sea by the warmth of the Sun; derived from an experiment shown before the Royal Society at one of their late meetings: by E Halley“.

lilies on water, rain on a pond, droplets
Coffee, evaporation, clouds, rain, rivers, seas, evaporation. Imagining the water cycle by making coffee.

Halley heated a pan of water to the temperature of “the Air in our hottest summers” and then, keeping the temperature constant, placed the pan on a set of scales to see how much water was lost over 2 hours. The temperature of the air in “our hottest summers” cannot have been very high, perhaps 25-30C and there was no evaporation actually seen in the form of steam coming from the pan (unlike with my milk pan). Nonetheless, Halley’s pan lost a total of 13.4g (in today’s units) of water over those two hours.

Halley used this amount to estimate, by extrapolation, how much water evaporated from the Mediterranean Sea each day. Arguing that the temperature of the water heated that evening at the Royal Society was similar to that of the Mediterranean Sea and that you could just treat the sea as one huge pan of water, Halley calculated that enough water evaporated to explain the rains that fell. This is a key part of the water cycle that drives the weather patterns in our world. But Halley took one further step. If the sea could produce the water for the rain, and the rain fed the rivers, was the flow of the rivers enough to account for the water in the Mediterranean Sea and, specifically, how much water was supplied to the sea compared to that lost through the evaporation? Halley estimated this by calculating the flow of water underneath Kingston Bridge over the Thames. As he knew how many (large) rivers flowed into the Mediterranean, Halley could calculate a very rough estimate of the total flow from the rivers into the Mediterranean.

Grecian, Devereux, Coffee house London
A plaque outside the (old) Devereux pub, since refurbished. The Devereux pub is on the site of the Grecian Coffee House which was one of the places that Halley and co used to ‘retire’ to after meetings at the Royal Society.

The estimates may seem very rough, but they were necessary in order to know if it was feasible that there could be a great water cycle of rain, rivers, evaporation, rain. And although Halley was not the first to discuss this idea (it had been considered by Bernard Palissy and Pierre Perrault before him), this idea of a quantitative “back of the envelope” calculation to prompt more thorough research into an idea, is one that is still used in science today: we have an idea, can we work out, very roughly, on the back of an envelope (or more often on a serviette over a coffee) if the idea is plausible before we write the research grant proposal to study it properly.

So, to return to my pan of oat milk simmering on the stove. 15g over 5 minutes at approaching 100C is a reasonable amount to expect to lose. Only, we can go further than this now because we can take the extra data (from the thermostats we have in our house and the Met Office observations for the weather) of the temperature of your kitchen and the relative humidity that day and use this to discover how these factors affect the evaporative loss. Just as for Halley, it may be an extremely rough estimate. However, just as for Halley, these estimates may help to give us an understanding that is “one of the most necessary ingredients of a real and Philosophical Meteorology” as Halley may have said before he enjoyed a coffee at one of the Coffee Houses that he, Newton and others would retire to after a busy evening watching water evaporate at the Royal Society.

Rosie and Joe, St Giles churchyard

Coffee in a Wake Cup at Rosie & Joe in St Giles. The space rewards those who notice.

There is a long history of hospitality on the site of St Giles in the Fields stretching back far earlier than the Notes coffee barrow. But Rosie & Joe is a lovely iteration to that tradition. There’s a definite focus on tea at Rosie & Joe but the coffee is roasted by Square Mile and prepared on a La Marzocco machine. There is also a good selection of food to nibble on (as well as more food stalls nearby on weekday lunchtimes). And although it is a cart, there are a few seats and tables dotted around so it is easy to sit back and enjoy your coffee while the world races by.

St Giles High St is a very busy road and yet, sitting in the churchyard of St Giles is strangely peaceful. Despite the traffic and the occasional siren, it is one of those rare places in London that you can find the stillness to listen. A beautiful place to enjoy a coffee from an independent stall in fact! And if you have your own cup with you, there is even 10p off your coffee. The coffee was smooth and sweet, fruity but definitely a sweet and full bodied type of fruity cup. But why was it so peaceful? Was it merely that it was a lovely (but breezy) spring morning when I tried Rosie & Joe? Or was it that it is a small bit of nature in a built up environment? Both of these helped but I think it is also the way that the place rewards those who notice by offering more each time you look.
The ghost sign hidden behind the tree just outside the churchyard.

There’s the, perhaps slightly grim, history suggested by the fact that the ‘garden’ is significantly raised above the level of the pavement in parts. There’s the brickwork and stone walls of the church itself of course. The ‘ghost sign’ on a nearby building that is revealed to the coffee drinker by the fact that the tree between us and it has not yet got its summer leaves. And then the nod to the history of the site hinted at by the coffee cart itself: Since Matilda, wife of Henry I founded St Giles’ leprosy hospital on the site, a “cup of charity” was given to condemned prisoners as they made their way past St Giles on their way to their execution at Tyburn*. Very different now, but the tradition of refreshment for the traveller is continued.

But then a fire engine’s siren reminds you that you are in a cosmos, a universe filled with beautiful physics. You know whether the fire engine is approaching or has passed away from you from how the pitch of the sound changes as it goes past. The Doppler shift meaning that sound waves travelling towards you have a shorter wavelength (higher frequency, higher pitch) than those travelling away (longer wavelength, lower frequency, lower pitch). And part of the beauty of physics is that it is so universal; what works for sound also works for light. If an object emitting light is moving away from us, the light appears to have a longer wavelength (lower frequency, it is red-shifted) than if the same object were stationary or moving towards us where it would appear as if it emitted light with a shorter wavelength (higher frequency, blue shifted).

signboard at Rosie and Joe
Doesn’t a right imply a duty? There’s a lot that could be said about #supportindependent
So, similarly, if we were to look at the surface of a rotating planet and saw how the light reflected off that planet’s surface, the side of the planet that was rotating towards us would look ever so slightly bluer than the side rotating away from us which would look slightly redder. And if the planet’s surface was like Venus and obscured by clouds (rather like the ghost sign at Rosie & Joe will be obscured by leaves in a couple of months time) we could use the reflection of radio waves from the surface rather than visible light to see the same red-shift/blue-shift in the radio waves as the planet rotates**. In this way we could determine the direction of rotation of the planet and how fast it was rotating just as we get an indication of the speed of the fire engine from listening to the sound of the siren.

The siren takes us from a consideration of inner stillness to a recognition of the scale of the universe. Which is rather apt for a cafe in a churchyard, where the architecture of a church is often designed to be read symbolically, from the person to their place in the grand scheme of things***. One great thing about this particular cafe though was how much there was to see that cannot be included in this cafe-physics review for reasons of space. The location truly rewards those who pay attention to what they notice here. I can only recommend that you take some time out, take your re-usable cup and go to find some time to enjoy your coffee (or tea) in this quiet space in central London.

*The London Encyclopaedia, 3rd Edition, Weinreb et al., 2008

**Astronomy, the evolving universe, 6th Edition, Zeilik, 1991

***How to read a church, Taylor, 2003

Rosie and Joe can be found in St Giles in the Fields churchyard, Monday-Friday.