Plato

In their Elements at Bean Reserve, Bangsar, KL

coffee in Bangsar at Bean Reserve

Bean Reserve, Bangsar, Kuala Lumpur. Note the logo on the window.

The first thing that struck me as I entered Bean Reserve in KL was the geometry. Somewhat hidden along a street behind Jalan Maarof, Bean Reserve offers a quiet space amidst the bustle of Bangsar. The 2D representation of a 3D object that is Bean Reserve’s logo is somehow mirrored in the choice of the tables and chairs that are contained in the cuboid space of this café. Triangular tables are arranged to form larger, quadrilateral tables. Circular stools nestle underneath square tables. Light streams into the café from a large window on one side of the room. The other side features a sliding door that was occasionally opened, revealing the desks of The Co, a co-working space that shares the building of Bean Reserve.

Although we only tried the drinks (an exceptionally fruity long black and a very cocoa-y iced chocolate), there looked to be an interesting selection of edibles on offer, with a bottle of chilli sauce stored behind the counter. Soy milk was available if you prefer non-dairy lattes and there were a good range of drinks on offer from nitro-cold brew to iced chocolate, just what can be needed in the heat of KL! Coffee is roasted by Bean Reserve themselves (who are both a café and a roastery), thereby providing the residents of (and visitors to) Bangsar with a seasonally varying range of great, freshly roasted coffee.

geometry at Bean Reserve

Triangular tables and circular stools.

The different geometrical features in the café immediately suggested Euclid to my thoughts. Written over 2300 years ago, Euclid’s The Elements was, for many years, the text book on geometry and mathematics. It is said that Abraham Lincoln taught himself the first 6 books of The Elements (there are 13 in total) at the age of 40 as training for his mind¹. Working from 5 postulates and a further 5 common notions, Euclid describes a series of elegant mathematical proofs, such as his proof of the Pythagoras theorem. And so, it may be appropriate that there is one more geometrical connection between the ancient Greeks and Bean Reserve: That sliding door that connects the café to the working space of The Co.

The space, occupied by The Co, behind the sliding door seems to be much larger than the café. But how much larger is it? Double the length? Double the volume? This is similar to the problem that perplexed the Delians. The idea is simple: Find the length of the side of a cube that has a volume exactly double that of a given cube. It is thought that the problem may have been formulated by the Pythagoreans, who, having succeeded in finding a method of doubling the square (see schematic), extended that idea to 3D. Could a simple geometrical method be used to double the cube? (There is of course the alternative legend about the problem having been given to the Delians by the Oracle)

A geometrical method for finding the length of a square with twice the area of a given square… now for 3D

It turns out that this is a tough problem, but one that may again have relevance for our world today. While researching this café-physics review, I came across a book by TL Heath² that had been published in 1921. In his introduction he wrote:

The work was begun in 1913, but the bulk of it was written, as a distraction, during the first three years of the war, the hideous course of which seemed day by day to enforce the profound truth conveyed in the answer of Plato to the Delians. When they consulted him on the problem set them by the Oracle, namely that of duplicating the cube, he replied, ‘It must be supposed, not that the god specially wished this problem solved, but that he would have the Greeks desist from war and wickedness and cultivate the Muses, so that, their passions being assuaged by philosophy and mathematics, they might live in innocent and mutually helpful intercourse with one another’.

 

 

Bean Reserve can be found at 8 Lengkok Abdullah, Bangsar, 59000 Kuala Lumpur, Malaysia

¹History of Mathematics, An Introduction, 3rd Ed. DM Burton, McGraw-Hill, 1997

²A History of Greek Mathematics, Thomas Heath, Oxford at the Clarendon Press, 1921

 

The coffee cave

Americano, Caravan coffee, Skylark, Wandsworth

Gazing into a coffee you can see the reflection of your face looming back at you.

Have you ever gazed into your coffee as you take a mouthful only to get disturbed to see a distorted view of your face looming back at you from the coffee? Has it struck you that while you often see such reflections, you rarely see shadows? Try it first with water and then coffee. Can you, perhaps, see a shadow on the coffee where you cannot see shadows on the water? Why would this be?

For a shadow to be visible on a surface, the surface must scatter enough light so that the contrast between shadow (where there is no light to scatter) and non-shadow (where the surface is illuminated) can be seen. Although a shadow (or at least the relative lack of light) is always going to be present behind any obstacle, it is whether or not it can be seen on the surface of the water/coffee that is at issue here. Pure water is of course quite transparent. Without anything in the water to scatter the light (such as mud for example), the light passes straight through the water to the other side. Overall, not enough light is scattered back from the surface of the water to generate the contrast required for seeing shadows. Seeing shadows on pure water is going to be hard.

Chemex, 30g, coffee

The concentration of suspended particles will depend on how you make your brew

By contrast, coffee contains suspended particles, in fact they are part of the very essence of the drink. These particles offer a surface to scatter the light back towards the observer and so highlight the shadows formed by the object between the coffee and the light. It strikes me that different brew methods will result in different amounts of sediment and suspended particles in the coffee and therefore a greater or lesser tendency of the coffee to reveal shadows. Perhaps if anyone does notice that it is harder to form shadows on coffee prepared by a Chemex  than a French Press (for example) they could let me know using the comments section below.

Shadows have been used by philosophers to illustrate by allegory how we perceive the world around us. In the tale of Plato’s cave a group of prisoners are held in a cave such that they can only ever see the shadows playing on the cave’s wall. The shadows are formed by a fire behind the prisoners that the prisoners cannot see. As they can only see the shadows, they start to think that it is the shadows themselves that are ‘real’. It is a tale questioning the reality of what we currently see and also our inability to adjust to the differences between looking directly at the Sun or discerning shadows in the dark. In the story of the cave, it is the fire, or the Sun that causes the shadows that deceive the prisoners. No consideration was given to the role played by the wall on which the shadows dance. Yet we can see from our coffee that to understand the world of shadows we do not merely need a light source. To understand shadows, we need a surface from which to reflect the shadows. Perhaps we need to spend some time contemplating our coffee, the shadows and what they can tell us about the world and how we see it.

For details about this and other phenomena involving light and its interaction with the world around us, see: “Color and Light in Nature”, David K. Lynch and William Livingston