pendulum – Bean Thinking

Feeling the Earth move at Pritchard and Ure, Camden

Egg no pales, coffee, garden centre — Fried egg on cactus leaves. Cactus festival at Pritchard and Ure, Camden

Good coffee in a garden centre, in (nearly) central London, with some physics thrown in? Today’s cafe-physics review seems unlikely on several levels. And then it becomes even more unlikely as you realise that this garden centre and café are also a social enterprise where people “disadvantaged in the labour market” are helped back to employment through working here. All in all, Pritchard and Ure represent a great café to have come by.

Pritchard and Ure can be found in the gallery space of a warehouse type shop that houses the Camden Garden Centre. They serve Workshop coffee together with an extensive selection of alternative drinks and food. As it was lunchtime we enjoyed a spot to eat which gave me an opportunity to try cactus (it was cactus festival at the garden centre). Cactus leaves with re-fried beans and a cactus-water mocktail which came together with a reusable metal straw. The straws were being sold (together with brush straw cleaners) at the counter. After lunch there was a very well made long black (interestingly I was given the choice to have it either as a 6oz or an 8oz, ie. more or less water depending on whether I wanted more or less coffee taste) and resisted (somehow) one of the tempting cakes before having a wander in the garden centre.

equations art work coffee Camden — But are they real?
The equations are the writing on the wall at this cafe.

There are of course many things that you can notice and connect with/to in a garden centre. Plants, biosphere, windows and greenhouse effect, the carbon cycle, the nature of colour, the list could go on. In addition to all of these, to the left of the counter was an art piece on the wall with a list of various equations and comments. Were all these equations real? One thing in particular though in this café/garden centre was particularly mesmeric: the disco ball suspended as a pendulum from a beam across the ceiling. Initially we watched as the ball just glinted reflected light as it slowly swayed to and fro in its oscillation. It took 22 seconds to cover 5 oscillations while I estimated it was 7m in length. Knowing that there is a formula for calculating the period of oscillation I wondered, was my estimation any good?*

During the hour it took us to enjoy lunch, the position of the Sun moved in the sky so that the disco ball started to reflect an array of polka dots of light onto the walls surrounding us (you can see these in the photo). Owing to the combined rotation and oscillation of the ball it wasn’t too easy to measure the time period from these oscillations but about 4 seconds per swing (as I had obtained by merely watching the ball) seemed comfortingly correct. The sun slowly moved round and these dots danced until at some point the sun had moved far enough that the glitter ball was no longer in direct light. But had the Sun moved or the Earth rotated underneath it? We all know the answer (or at least we think we do), but we could use the pendulum to prove it (and to calculate our latitude).

discoball cafe — Disco ball pendulum together with polka dot reflected sunlight. The view from the gallery at Pritchard and Ure.

In various science museums around the world, different Foucault pendulums swing to and fro all day above circular patterns on the floor. The pendulums appear to rotate clockwise in the northern hemisphere and anti-clockwise in the southern hemisphere thereby illustrating the rotating earth underneath the pendulum. The idea is of course that the pendulum continues to swing in the same plane as it was when it was started off but as it is swinging the earth is rotating underneath it giving an apparent rotation of the pendulum swing over the course of a day. If we were at the north (or south) pole, the period of one complete rotation of the pendulum through a circle on the floor would take 24h. As most of us are not at the pole (and Pritchard and Ure certainly is not), the period of complete rotation is lengthened by a corrective factor proportional to the sine of the latitude. Consequently, it is perfectly feasible for us to calculate our latitude by observing a pendulum swinging for long enough in the absence of any breeze.

It is a great piece of evidence for the rotation of the earth (and by implication the fact that the earth is not flat and that the sun is not going round the earth each day). It’s also a very simple (hiding some complicated maths) demonstration that anyone could set up if they wished to carefully do so. So next time you see a disco ball suspended as a pendulum in a café, you would have another reason to start singing “I feel the Earth, move, under my feet…”

Pritchard and Ure is in the gallery of Camden Garden Centre at 2 Barker Drive, St Pancras Way, NW1 0JW

*7 m is an over estimate of the length of the pendulum based on the period of the oscillation. A length of 7m would give a time period of 5.3 seconds, whereas 22 seconds for 5 oscillations is about 4.4 seconds for one giving a calculated length of just under 5m. More details about how to calculate this are here.

Time to enjoy a Beethoven coffee

Portrait bust of Beethoven, Anna EG Hoffman, in the British Museum collection © Trustees of the British Museum

It is said that Beethoven prepared his coffee by counting, precisely, 60 beans per cup. Biographies of Beethoven certainly suggest that he had a significant coffee habit. Banned by his doctor from drinking coffee towards the end of his life, there are many references to him frequenting coffee houses in earlier years. Sadly, I have not found the source for the 60 beans story and so would not like to comment on its veracity. Nonetheless, it is a good story and it does link with coffee so, as today (17th December) is the 244th anniversary of his baptism (it is assumed that he was born the day before on 16th December 1770), it is “Beethoven day” on the Daily Grind.

To me, what lends some credibility to the 60 beans story is the fact that, as coffee lovers, we can be very particular about the way we prepare our brew. Some people, for example, weigh the amount of the coffee and the quantity of water and brew their coffee according to instructions from one of the various online brewing tutorials (see here for a good one from Hasbean). Personally, in the morning, I am far too bleary eyed to consider getting the kitchen scales out, nor would I count a certain number of beans. I do however count the number of seconds that I take to grind my coffee with my trusty burr grinder (always set to the same level of grind of course). Can counting the number of seconds for a quantity of grind possibly be a good way of measuring a specific quantity of coffee?

Did Galileo drop balls from the top of the tower?

Galileo Galilei (1564-1642) died before coffee was properly introduced to Europe. He is relevant to this story though owing to his work on clocks and timing devices. One way that Galileo measured time was to collect water in a jug over the measurement period. It seems that this is almost the reverse of my morning coffee ritual. To check that he was measuring time correctly however, he needed a second, independent method. Of course, Galileo couldn’t use a watch or pendulum because watches hadn’t been developed at the time and Galileo himself was doing the work needed to understand pendulums and make them useful for clocks. So what else could he use to measure time? There is a clue to another method that Galileo used in his experiments on falling balls. Although there are questions as to whether Galileo really did drop balls from the top of the Tower of Pisa, we do know that he did experiments which involved rolling bronze balls down a groove. Along the groove were marks where strings made from gut had been pulled across the groove such that they made a sound as the ball passed, perhaps like the sound of a harp being plucked. By adjusting the position of these strings, the interval between the sounds from different gut strings could be made to match a known rhythm. The time it took for a ball to fall down the groove was being measured by matching its descent to a known tune. This suggests that Galileo sang while he was making his key measurements and that it was this that allowed him to start to understand how bodies fell under gravity. Singing was Galileo’s (surprisingly accurate) method of measuring time.

Which brings me full circle back to Beethoven. Beethoven certainly knew the “mechanician” Mälzel who invented the metronome as we now know it. There are also indications that Beethoven was aware of early versions of Mälzel’s invention. In 1813, the Wiener Vaterländische Blätter wrote “…Herr Beethoven looks upon this invention as a welcome means with which to secure the performance of his brilliant compositions in all places in the tempos conceived by him, which to his regret have so often been misunderstood“. It seems that in the two hundred years between Galileo and Beethoven, there had been so many improvements to clocks and timing devices that singing, which had started off as a way to measure time, was now itself being regulated by the clocks that singing may have helped to develop.

How many beans go to make your morning coffee?

So how is a Beethoven coffee, assuming that there is any veracity to the legend? Sixty beans works out as 8-10g which, depending on the amount of water in the cup could be weaker (or stronger) than modern brews. In my cup, it was slightly weaker than I am used to. I enjoyed my “Beethoven coffee” while listening to his String Quartet Op 74, “Harp”. As I sipped the coffee while listening to the first movement, I could almost hear the gut strings of Galileo’s experiment being plucked as the balls rolled by. The coffee itself (Costa Rica, Finca Arbar El Manatial, Yellow Honey, Caturra/Catual) was very smooth and rich, as you would expect from a coffee from Has Bean. Described in the tasting notes as “….An amazing caramel and milk chocolate sweetness partnered with delicate peach and apricot acidity…” It was the perfect coffee to enjoy with the Harp quartet piece. Sometimes it is important to take time to go slow and enjoy the coffee.

So why not raise a mug today to Beethoven and savour a Beethoven coffee? Please leave any comments using the form below, especially if you know a reliable reference to Beethoven’s coffee habit or have suggestions as to how to improve my morning brew.