beer

The idea of a coffee at A Wanted Man

We cannot do without a view, and we put up with an illusion, when we cannot get at a truth“.

A wanted man, Chelsea, coffee cup

A wanted man becomes visible under thin coffee.

A Wanted Man on Chelsea’s Kings Road is unusual in many respects. Firstly, never before have I been to an espresso ‘canteen’, but then, neither have I had a coffee in a café that is part coffee-shop part waxing salon. While both wax based hair removal and coffee rely on bees, this is surely not the connection between these two enterprises. Nonetheless, once your coffee-loyalty card is full, you can choose: free brow shape, bikini wax or coffee. The coffee comes from Common Man Coffee Roasters in Singapore so it would be interesting to know how it was transported to Chelsea in order to retain its freshness, surely each batch is not flown in? On our first visit, we had a rich and smooth long black, a lovely aromatic banana bread and a good hot chocolate (with soy milk). There is plenty of seating in the front of the café and some more towards the back near the bar which was all fairly empty on our first visit but far more crowded (with singly-occupied tables) on my second visit (see below).

As I drank my coffee, hidden wording became visible at the bottom of the cup. “A wanted man” appeared beneath the coffee when the coffee was sufficiently thin. By tilting the cup, this “critical” thickness could be estimated, as you can see in the photos. Ah-ha I thought, the physics bit of this cafe-physics-review will be easy! The absorption of light (which we could measure by the visibility of the writing at the bottom of the cup) is directly proportional to the thickness of the absorbing liquid, the coffee. This is the Beer-Lambert law which describes how light is absorbed through substances such as coffee in which there are molecules and bits of sediment that absorb light (which is ultimately why coffee appears brown). Could I experimentally verify this bit of the Beer-Lambert law by somehow quantifying the visibility of the wording as a function of cup-tilt angle?

a tilted coffee cup at a wanted man

Absorption is a function of thickness and concentration

Before I had thought that far, I had finished the coffee, however the second part of the Beer-Lambert law could be tested by having another coffee on a separate occasion. The other part of the Beer-Lambert law states that the absorption (that’s the (in)visibility of the wording on the cup in this case) is also directly proportional to the concentration of the absorbing molecules/sediment. This makes sense, weak coffee is far more transparent than overly extracted coffee. On my second visit, the coffee tasted slightly stronger, a bit different from my memories of the first occasion. Did the “A wanted man” become visible at a different tilt angle? I would guess – or perhaps that should read ‘hypothes-ise’ – that the angle on the second occasion would have to be lower (that the coffee would have to be thinner generally).

However, while sipping my coffee (before getting to the tilt-angle-test) and looking around the second time I noticed that all along the wall where previously there had been plenty of empty tables, each one was now singly occupied by somebody using a laptop, a phone/tablet or in one case, both of these items together. This second time, my mind started wandering into more social issues, while looking at our screens and immersed in social media, are we able to see more or less, than our less absorbed fellow citizens? Does social media clarify the detail or cloud important aspects of our understanding?

Beer-Lambert applied to twitter and Facebook

Does social media do this to you? The light absorption of a coffee is determined by the thickness of the coffee and concentration of absorption sites within it.

After considering these two points, it became clear that in some ways they are connected. Admittedly a loose connection, and not one that is strictly scientific but perhaps it’s worth ‘running with it’ for a bit and seeing if it leads anywhere. Just as with the Beer-Lambert law with coffee, the more ‘interacting sites’ (or absorption sites) we encounter on social media, the harder it is to see through to the bottom. Twitter, Facebook etc. can be enormously helpful for widening our networks and learning about new things. But, as has been frequently pointed out elsewhere, they can also become quite unhelpful when we are in an “echo chamber” or when we think that points can be made in mere soundbites. Is it possible that the more absorbing and reflecting sites that we encounter, the harder it is to see anything to any greater depth? What we need is time-out, for self-reflection and for considering points made by others, on Twitter, Facebook and elsewhere.

Perhaps the best way to end such a post is with a long quote by somebody else. In fact, the same person (and in the same book) as was quoted at the beginning of this article. Perhaps it would be something to consider while we drink our coffees and hover over the ‘retweet’ or ‘share’ button. Are we helping to probe the depths of our cup by the links we share, or are we merely adding to absorption sites in soundbites in our networks?

It requires a great deal of reading, or a wide range of information, to warrant us in putting forth our opinions on any serious subject; and without such learning the most original mind may be able indeed to dazzle, to amuse, to refute, to perplex, but not to come to any useful result or any trustworthy conclusion. There are indeed persons who profess a different view of the matter, and even act upon it. Every now and then you will find a person of vigorous or fertile mind, who relies upon his own resources, despises all former authors, and gives the world, with the utmost fearlessness, his views upon religion, or history, or any other popular subject. And his works may sell for a while; he may get a name in  his day; but this will be all. His readers are sure to find on the long run that his doctrines are mere theories, and not the expression of facts, that they are chaff instead of bread, and then his popularity drops as suddenly as it rose.

John Henry Newman, The idea of a university.

A Wanted Man can be found at 330 Kings Road, London

Reading tea leaves with Einstein and my great-grandmother

tea pot science

It’s not just tea, Einstein is famous for some other physics too

Ask anyone what Albert Einstein is famous for and you’ll probably (hopefully) hear that he came up with the theory of relativity (special and general). Perhaps you may also be told that he came up with a little theory explaining the photoelectric effect for which he won the Nobel prize in 1921. Maybe, if you have read this website before, you will know that he contributed to our understanding of Brownian motion, which is a phenomenon that is frequently found in a coffee cup. But it turns out that Einstein wrote another paper, far more important than any of these others, which was about tea. Or at least, I suspect my great-grandmother would have found it more important than any of these others as it coincided with a special hobby of hers, reading tea leaves.

It seems that my great-grandmother used to enjoy reading tea-leaves. Whether it was something she had learned as a child or merely used as an interesting trick to perform at family functions, stories of her examining the patterns formed by swirling tea leaves in a cup have come down to us in younger generations. Einstein too had noticed the patterns formed by the tea leaves in the cup and had observed a problem. The problem is this: If you drink a cup of (inadequately filtered) loose leaf tea and stir it, the tea leaves collect in a circle in the middle of the base of the cup. At first this may appear counterintuitive. When we stir things, don’t things fly outwards towards the edge of the cup rather than inwards to the centre of the circle? Why is it that the leaves collect in the middle?

Thames, NASA image

How do rivers erode? What causes a river to meander? The meandering Thames, photographed by NASA, Image courtesy NASA/GSFC/MITI/ERSDAC/JAROS, and U.S./Japan ASTER Science Team

For Einstein, this tea leaf problem was connected to another phenomenon, the erosion of rivers. But it turns out that the problem is also linked to issues found in beer brewing and blood tests, and it seems, in how to poach an egg. To see the solution and therefore the connections, we need to think a bit more about how water flows. One of the brilliant lines in Einstein’s paper starts “I begin with a little experiment which anybody can easily repeat.” This experiment is to obtain a flat bottomed cup of tea with some tea leaves at the bottom of it. Now stir the tea and watch how the leaves settle, Einstein continues “the leaves will soon collect in the centre of the bottom of the cup“.

The explanation is connected with the fact that at the walls of the cup, the liquid (tea) is being slowed down by the friction between the walls and the tea. Secondly, as the tea is stirred, the surface of the tea becomes concave with a distinct dip in the centre of the swirling tea. The result of all this is that a secondary rotation is set-up where the tea flows down the sides of the cup, along the bottom and then back up in the centre and once more to the sides (have a look at the diagram, some things are easier with pictures). As they are carried along with the water, the tea leaves move towards the centre of the cup but then, being too heavy to rise again with the tea up to the centre of the cup, they stay on the bottom forming a circular patch of tea leaves.

adaptation from Einsteins paper

The secondary circular flow set up in a tea cup when it is stirred leads to a circular deposition of tea leaves (figure adapted from Einstein’s 1926 paper).

When you think about how water flows as it goes around a bend in a river, you could perhaps imagine a similar secondary flow being set up but this time from the inner edge of the bend to the outer edge and back down (so, like half a tea cup). As the water is going to be moving fastest at the outer edge, just before it plunges down towards the bottom of the river in this secondary cycle, any river erosion is going to be most noticeable on the outer edge of the bend.

It seems the effect is also used in beer brewing in order to introduce a greater concentration of hops into the brew, and to separate different types of blood cell in blood tests. So this just leaves the poached eggs. How do you poach eggs? If you have a proper poacher perhaps you get neat eggs each time but for those of us without them, poached eggs tend to be a messy cooking project. But worry no longer! Just as tea leaves collect in the centre of a tea cup, so will the egg if you ensure that your pan of boiling water is swirling around the central axis before you put your egg in. Cooking helped by physics, perfect.

For reasons of full disclosure, I should emphasise that I have only recently found this suggestion for cooking eggs ‘theoretically’ and not yet tested it. So, if you were looking for reasons to drink loose tea, or wanted to poach an egg without a poacher, perhaps you could try Einstein’s little experiment and let me know how you got on, I’d love to hear your tea leaf readings and see your poached egg results.