Coffee: The mathematical and the beautiful

Last week, a new study was published that explored the mathematics behind brewing the perfect filter coffee.  The research, summarised here, modelled the brewing process as being composed of a quick, surface extraction from the coffee grounds, coupled with a slower brew, where the water was able to get into the interior of the coffee grind. It was an interesting study and the authors are now looking at grind shape and the effect of how you wet the grounds. However, what struck me was that the authors mentioned scanning electron microscopy (SEM) images of ground coffee. A lovely idea, what does coffee look like when magnified hundreds (or thousands) of times?

So here are a few images that I found shared under Creative Commons Licenses. I hope you find them as fascinating as I do.

1) A green coffee bean:

Green coffee bean under the microscope

A green coffee bean. Sadly no details as to magnification. Image shared under CC license from Nestle, Flickr

2) Instant Coffee

Instant coffee from Nestle

Spray dried instant coffee from the Nestle, Flickr account. Image shared under CC license.

3) Roast and ground coffee (fluorescence microscopy image)

ground coffee, fluorescence image

Ever wondered what your coffee looked like when magnified many times? This image using fluorescence microscopy is of roasted coffee. Note the similarities between this image and the following one (which has a scale bar).  Image shared under CC license from Nestle, Flickr

3b) More ground, roasted coffee, this time from Zeiss

Zeiss roast coffee

Scanning electron microscope image of roast (and ground) coffee magnified 750x. Image from Zeiss, Flickr, Todd Simpson, UWO Nanofabrication Facility. Shared under CC license. (To put the scale bar in perspective, it is the size of the smallest particles in an espresso grind. Clearly, the grind here is quite coarse).

4) Finally, an image of tea, just to keep this article tea-coffee balanced:

Green tea under the microscope

Green tea as seen under the microscope by the scientists at Nestle. Shared under CC license Nestle, Flickr.

If you come across any great images of coffee (or tea) under the microscope, please do share them. In the meanwhile, enjoy your coffee however you brew it.

Beautiful coffee

beauty in a coffee, coffee beauty

Interference patterns on bubbles in a coffee cup.

In the UK Science Museum’s library there is a book, written in 1910, by Jean Perrin called “Brownian Movement and Molecular reality”. To some extent, there is nothing surprising about the book. It describes a phenomenon that occurs in your coffee cup and the author’s own attempts to understand it. Nonetheless, this little book is quite remarkable. It is perhaps hard, from our perspective in 2016, to imagine that at the time of Perrin’s work, the idea of the existence of molecules in water was still controversial. It was even debated whether it was legitimate to hypothesise the existence of molecules (which were, almost by definition, un-detectable). However, none of that is really relevant to the question confronting today’s Daily Grind. Today, the question is how can this book help us to find beauty in a coffee cup?

What does a one hundred year old book have to do with finding beauty in a coffee cup? Perrin received the Nobel Prize in 1926 for his work establishing the molecular origins of Brownian motion and, associated with it, his determination of the value of Avogadro’s constant. It is perhaps why he wrote the book. (The experiment that he used to do this is described in a previous Daily Grind article that can be found here.) It is in his description though, both of the theory and the experiments involving Brownian motion that this little book is relevant for today. One word repeatedly crops up in Perrin’s description of Brownian motion. It comes up when he describes the theory. It comes up when he describes other people’s experiments. It comes up when he describes bits of the maths of the theory. The word? Beautiful*.

Michael Polanyi

Michael Polanyi,
by Elliott & Fry, vintage print, (1930s),
Thanks to National Portrait Gallery for use of this image.

Throughout history, many scientists have recognised, and worked for, the beauty that they see in the science around them. In a 2007 TED talk, Murray Gell-Mann said

“What is striking and remarkable is in fundamental physics a beautiful or elegant theory is more likely to be right than a theory that is inelegant.”

So it is interesting that, although we may agree that scientific theories can be “beautiful” or “elegant”, we do not seem to have a way of quantifying what precisely beauty is. It is similar for those things that are beautiful that we find in every day life. The beauty of a sunset, or the way the light catches the ripples on the surface of a lake, these are things that we recognise as beautiful without being able to articulate what it is about them that makes them so. Instead we recognise beauty as something that strikes us when we encounter it. Elaine Scarry has talked about this as a “de-centering” that we experience when we come across beauty. Scarry writes that, when we encounter the beautiful:

“It is not that we cease to stand at the center of the world, for we never stood there. It is that we cease to stand even at the center of our own world”.¹

It is therefore quite concerning that she goes on to suggest that conversations about beauty (of paintings, poems etc) have been banished from study in the humanities “…we speak about their beauty only in whispers.”¹ This does not seem to have happened yet in science where it is still common to hear about a beautiful equation or an elegant experiment. But is there a creeping ‘ideological utilitarianism” in the scientific community? According to Michael Polanyi ²

“Ideological utilitarianism censures Archimedes today for speaking lightly of his own practical inventions and his passion for intellectual beauty, which he expressed by desiring his grave to be marked by his most beautiful geometrical theorem, is dismissed as an aberration.”²

While we may recoil from this sentiment, what do we write (or expect to read) in grant applications, scientific papers, popular science or even scientific outreach? How often is the utility of a piece of research emphasised rather than its elegance?

Earth from space, South America, coffee

Does an appreciation of beauty help with a wider understanding of justice and environmental concerns?
The Blue Marble, Credit, NASA: Image created by Reto Stockli with the help of Alan Nelson, under the leadership of Fritz Hasler

Another interesting question to ponder is whether our ability to appreciate (and discuss) beauty has wider ramifications. As many others have argued before her, Scarry suggests that the appreciation of the beauty in the world connects with our sense of justice¹. Recently the Pope too, in his great environmental encyclical, Laudato Si’ wrote³:

“If someone has not learned to stop and admire something beautiful, we should not be surprised if he or she treats everything as an object to be used and abused without scruple.”

Could it be true that part of the motivation that we need to change our ecological habits or stimulate our search for wider social justice is enhanced by our ability to slow down and appreciate the beautiful, wherever and whenever we find it?

So to return to our coffee. Is there something, anything, about our coffee or our tea that gives us such a radical de-centering experience? Can we, like Jean Perrin, appreciate the subtle beauty of the molecular interactions in our cup? Do we appreciate the moment as we prepare our brew? Or are we ideological utilitarians, seeing in our cup just another caffeine fix?


* Technically, the book in the Science Museum Library is a translation of Perrin’s work by Frederick Soddy. It is possible that it is Soddy’s translation rather than Perrin’s work itself that uses the word ‘beautiful’ repeatedly. It would be interesting to read Perrin’s book in its original French.

I would like to take this opportunity to say thank you to the Science Museum Library for being such a valuable resource and to the staff at the library for being so helpful.


“Brownian movement and molecular reality”, Jean Perrin, translated by F. Soddy, Taylor and Francis Publishers (1910)

1 Elaine Scarry, “On Beauty and Being Just”, Duckworth Publishers, 2006

2 Michael Polanyi, “Personal Knowledge, towards a post-critical philosophy” University of Chicago Press, 1958

3 §215 Laudato Si’, Pope Francis, 2015

Tea Gazing

Milky Way, stars, astrophotography

The Milky Way as viewed from Nebraska. Image © Howard Edin (

A recent opinion piece about last week’s announcement of the detection of gravitational waves at LIGO drew my attention to a quote from Einstein:

The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed.

Einstein was not the only scientist to have expressed such sentiments. Many scientists have considered a sense of wonder to be integral to their practice of science. For many this has involved gazing at the heavens on a clear night and contemplating the vastness, and the beauty, of the universe. Contemplating the twinkling stars suggests the universe outside our Solar System. Watching as the stars twinkle gives us clues as to our own planet’s atmosphere. Of course, it is not just scientists who have expressed such thoughts. Immanuel Kant wrote:

“Two things fill the mind with ever-increasing wonder and awe, the more often and the more intensely the mind of thought is drawn to them: the starry heavens above me and the moral law within me.“*

light patterns on the bottom of a tea cup

Dancing threads of light at the bottom of the tea cup.

The other evening I prepared a lovely, delicate, loose leaf jasmine tea in a teapot. I then, perhaps carelessly, perhaps fortuitously, poured the hot tea into a cold tea cup. Immediately threads of light danced across the bottom of the cup. The kitchen lights above the tea cup were refracted through hot and not-quite-so-hot regions of the tea before being reflected from the bottom of the cup. The refractive index of water changes as a function of the water’s temperature and so the light gets bent by varying amounts depending on the temperature of the tea that it travels through. Effectively the hotter and cooler regions of the tea act as a collection of many different lenses to the light travelling through the tea. These lenses produce the dancing threads of light at the bottom of the cup. The contact between the hot tea and the cold cup amplified the convection currents in the tea cup and so made these threads of light particularly visible, and particularly active, that evening. It is a very similar effect that causes the twinkling of the stars. Rather than hot tea, the light from the distant stars is refracted by the turbulent atmosphere, travelling through moving pockets of relatively warm air and relative cool air. The star light dances just a little, with the turbulence of the atmosphere, this way and that on its way to our eyes.

Marcus Aurelius wrote:

Dwell on the beauty of life. Watch the stars, and see yourself running with them.Ҡ

Marcus Aurelius of course didn’t have tea. Watch the dancing lights in the tea cup and see yourself sitting with it, resting a while and then watching while dwelling on the beauty in your cup.

*Immanuel Kant, Critique of Practical Reason

†Marcus Aurelius, Meditations