Longitude – Bean Thinking

Happy New Year!

Nicaragua, direct trade, Amoret, Java beans, — Sometime this week I’ll brew this with a V60 and adapt an ‘examen’ to help me review 2019. I was thrilled to be able to meet the farmers, Dania and Desiree, at Amoret coffee earlier this year. One of the things I’m sure will feature in my ‘gratitude’ examen.

Each New Year is an opportunity to look back at the previous year, anticipate the future year and perhaps make resolutions to improve our lives, or even of those of people around us. Maybe this is even more true this year which is not just the start of a year, but of a decade.

This year I have been lucky to meet, or to continue friendship with, many people who have taught me all sorts of things about life, physics and coffee. There have also been some great finds of some fantastic cafes, trying to make a difference to their local community while serving excellent coffee.

And yet, as the year or the decade turns and we resolve to get fitter, pay more attention to sustainability or whatever seems important to us right now, we will inevitably take our existing selves into the new day and our resolutions will meet the reality of who we are: a bell rings at certain frequencies owing to the resonances of the vibration on the surface of the bell. The resonances of the bell depend on its exact shape and size, it is not easy to change the sound of the bell unless you change its temperature or even the interior to a different gas or muffle. (You can see images of how a violin vibrates at resonance here). The surface of a coffee resonates similarly, if we put it on a vibrating surface with a frequency that matches the fundamental vibrations of the surface. Nonetheless, thinking about these resonances can take us in surprising directions. The mathematics that describes them was developed by Friedrich Bessel (1784-1846) but, Bessel was not thinking about resonances when he formulated what is now known as Bessel functions. And it is possible, his life may have taken a very different direction were it not what happened from 1799.

In the new year of January 1799, when he was just 14, Bessel was apprenticed to an imports and exports company with the hope that he would become an accountant. And maybe we would have heard no more about him had he not got interested in the problem of longitude and solving the navigational issues of the time, important for the company for which he was working. This issue got him thinking about astronomy and he caught the attention of the authorities of an observatory who gave him a job there and encouraged his observations and interest. But it was while thinking about “many body problems” or how multiple massive objects interact with each other via gravity that he came up with the mathematical description that we now know as Bessel functions. It is these Bessel functions that also describe the resonances on a bell and in a coffee cup.

Sun, heat, nuclear fusion — What links coffee to the Sun? So many things! But for the purpose of this post, we can find clues as to the interior of stars by watching the way they vibrate, analogously to a bell. What would Bessel think? Image © NSO/AURA/NSF

What does this leave us with in our thoughts for 2020? That what we are interested by may lead us to discoveries in various tangential and scarcely believable connections? That what we plan for our lives may not be how they have to end up? That it benefits us to stop for 5, 10 minutes, even half an hour and just contemplate our world in our coffee? (ok, that last one did not come from Bessel). Where-ever your paths lead and your interests lie, happy new year! May the 2020s be a decade where we can all slow down, notice, contemplate and appreciate the beauty of this strangely connected world which is our home.

Doctor Espresso Putney Bridge — There is a lot of physics in this photo alone, but there is even more to be seen if you visit this lovely little cafe.

“Isn’t it a thing of beauty?” So wrote Brian’s coffee spot review of the 1956 Gaggia Tipo Americana espresso machine found at the Putney Station branch of Doctor Espresso. And it is only possible to answer this question in the affirmative. There is something about a mechanical piece of equipment (particularly if it is shiny and has levers) that ignites a feeling of awe. Perhaps it is the awareness of the complexity of the tasks that, when traced through the machine, are revealed to be the result of a series of simple, but ingenious steps. Perhaps it is the feeling that it is possible for someone, one individual, to know inside out how the piece of equipment works and, if necessary, to build it. Perhaps it is because it is shiny. Nonetheless, I had been itching to go and try The Caffetteria, the Doctor Espresso café opposite Putney Bridge station for ages, since I chanced upon its review in Brian’s Coffee Spot. Trundling through the hot streets of London in a bus in this recent heatwave nearly made me reconsider and yet we ploughed on, finally arriving in this shaded spot in the mid-afternoon.

There is very little seating inside but the shade outside enabled us to take a seat by the window. A perfect location to watch people coming and going to and from Putney Bridge Station: who will pick up that 5p on the floor? Will anyone notice? There are a few more chairs and tables across the pavement next to the tree. Several cakes tempted us but we resisted, instead I enjoyed a (single) espresso, Italian style, very drinkable. There is something very relaxing about enjoying an Italian espresso in an independent (or at least very small chain) café. The café aims to “provide a tranquil environment for customers to relax and converse” and it would certainly appear to do so with odd pieces of decor and posters prompting different bits of conversation. The barista was very friendly and trusted us to enjoy our coffee outside before coming back in to pay. Perhaps this seems a small thing, but trust helps to build societies and small gestures of good, repeated, have a ripple effect on our world¹. A nice touch.

espresso Doctor Espresso Putney — The result.
A single espresso ready for enjoying.

Brian’s Coffee Spot describes the process of ‘pulling’ an espresso using this lever machine (the oldest working espresso machine in London apparently). The machine combines the beauty of the mechanical with the skill of the barista to produce a great coffee. This is not human vs machine but human working with machine to create something that others appreciate. A similar respect for the machine was expressed by the clock maker John Harrison about three centuries ago. Harrison had just made a clock that was able to keep time accurately over many weeks while at sea. His task was necessary because having a clock that accurately kept the time at the departure port would enable a ship’s navigators to calculate their geographical position based on a comparison of this port time to the local time experienced by the ship. He was trying to solve the problem of ‘longitude’. Harrison had taken 19 years to develop his H3 clock which could keep time accurately at sea despite changes in temperature, humidity or rough conditions but within a few more years he’d produced the H4 (which can now be seen in the National Maritime Museum). Significantly smaller than the H3, Harrison said of it:

“I think I may make bold to say, that there is neither any other Mechanical or Mathematical thing in the World that is more beautiful or curious in texture than this my watch or Time-keeper for the Longitude…”²

Enjoying coffee in the company of posters — A conversation piece? The physics of buoyancy or the deceptions of marketing. You could spend a long time at Doctor Espresso thinking about these things.

Harrison lived before espresso machines were invented. Self-taught, Harrison designed and built his own clocks. How many of us would be able to do that? Although we wear watches, how many contain batteries and other components that produce a simple action (showing the time) by complex means. The opposite of what we admire in the lever operated espresso machine. Each individual element may be elegant, but as a composite it can be ugly, however aesthetically satisfying. Harrison built his first clock before he was twenty years old and almost entirely out of wood. Working on the basis of a pendulum, he ensured that the cogs did not wear down as they may be expected to do by utilising the grain of the wood and by using only fast growing oak². Why would this make a difference? Trees that grow fast will have well separated growth rings. As the ring is an area of weakness in the wood, a fast growing tree would have a lot of solid wood compared to a relatively small number of rings, thus affecting the structural properties of the cogs. Moreover Harrison’s wooden clocks did not need oiling because those bits that needed oiling were carved from a tropical hardwood that exuded its own grease. In later clocks Harrison was to overcome the problem of the varying temperature experienced at sea by inventing the bimetallic strip. Two metals of different thermal expansion coefficients placed on top of each other, this simple piece of kit is essential for all sorts of modern machinery including, probably, the espresso machine sitting beautifully at Doctor Espresso.

A warm afternoon in a café of such elegant machinery offers plenty of opportunities to ponder the world of clockwork and levers. Do we understand how having a clock would allow us to calculate our geographical position? What about latitude? How many of us could do this for ourselves? And as we check the time while finishing our espresso, how many of us can appreciate the simplicity that leads to complexity and build our own?

¹A bit of cod-philosophy formed by combining bits from Pope Francis’ encyclical Laudato Si’ with Paddington 2.

²Quoted from “Longitude”, Dava Sobel, 1995

Doctor Espresso’s Caffetteria is at 3 Station Approach, SW6 3UH