Perrin

To err is human…

Press Room coffee Twickenham
A smaller V60. For one cup you would use less coffee, but the errors on the measurement will always be there.

Preparing a good V60 requires 30g of coffee (for 500 ml of water)*. This can be measured using a set of kitchen scales, but a first estimate can also be obtained, if you are using whole coffee beans, by timing the passage of the grind through the grinder. Using an Ascaso burr grinder, my coffee used to come through at an approximate rate of 1g/s, so that, after 30 seconds, I’d have the perfect amount of coffee. Recently however this has changed, depending on the bean, sometimes 30g is 40 seconds, sometimes just less than 30 seconds.

Clearly there is an error on my estimate of the rate of coffee grinds going through the grinder. This may be influenced by factors such as the hardness of the bean (itself influenced by the degree of roast), the temperature of the kitchen, the cleanliness of the grinder and, the small detail that the ‘seconds’ measured here refers to my counting to 30 in my head. Nonetheless, the error is significant enough that I need to confirm the measurement with the kitchen scales. But are the scales free of error?

Clearly in asking the question, we know the answer will be ‘no’. Errors could be introduced by improper zero-ing of the scales (which is correct-able), or differences in the day to day temperature of the kitchen (not so correct-able). The scales will also have a tolerance on them meaning that the measured mass is, for example, only correct to +/- 5 % Depending on your scales, they may also only display the mass to the nearest gramme. This means that 29.6g of coffee would be the same, according to the scales, as 30.4g of coffee. Which in turn means that we should be using 493 – 507 ml of water rather than our expected 500 ml (the measurement of which also contains an intrinsic error of course).

Turkish coffee
A Turkish coffee provides a brilliant illustration of the type of particle distribution with depth that Jean Perrin used to measure Avogadro’s constant. For more information see here.

The point of all of this is that errors are an inescapable aspect of experimental science. They can also be an incredibly helpful part. Back in 1910, Jean Perrin used a phenomenon that you can see in your coffee cup in order to measure Avogadro’s constant (the number of molecules in a mole of material). Although he used varnish suspended in water rather than coffee, he was able to experimentally verify a theory that liquids were made up of molecules, by the fact that his value for Avogadro’s constant was, within error, the same as that found by other, independent, techniques. Errors also give us an indication of how confident we can be in our determination of a value. For example, if the mass of my coffee is 30 +/- 0.4 g, I am more confident that the value is approximately 30 g than if the error was +/- 10 g. In the latter case, I would get new scales.

But errors can also help us in more subtle ways. Experimental results can be fairly easily faked, but it turns out that the random error on that data is far harder to invent. A simple example of this was seen in the case of Jan Hendrik Schön and the scientific fraud that was discovered in 2002. Schön had shown fantastic experimental results in the field of organic electronics (electronic devices made of carbon based materials). The problem came when it was shown that some these results, despite being on different materials, were the same right down to the “random” noise on the data. Two data sets were identical even to the point of the errors on them, despite their being measurements of two different things.

A more recent case is a little more subtle but crucial for our understanding of how to treat Covid-19. A large study of Covid-19 patients apparently showed that the drug “Ivermectin” reduced mortality rates enormously and improved patient outcomes. Recently it has been shown that there are serious problems with some of the data in the paper, including the fact that some of the patient records have been duplicated and the paper has now been withdrawn due to “ethical considerations”. A good summary of the problems can be found in this Guardian article. However, some of the more worrying problems were a little deeper in the maths behind the data. There were sets of data where supposedly random variables were identical across several patients which suggested “that ranges of cells or even entire rows of data have been copied and pasted“. There were also cases where 82% of a supposedly random variable ended in the digits 2-5. The likelihood of this occurring for random variables can be calculated (it is not very high). Indeed, analysis of the paper showed that it was likely that these values too were either copy and pasted or “invented” because humans are not terribly good at generating properly random numbers.

A gratuitous image of some interesting physics in a V60. If anyone would like to hire a physicist for a cafe, in a 21st century (physics) recreation of de Moivre’s antics at Old Slaughters, you know how to contact me…

Interestingly, a further problem both for the Ivermectin study and for the Schön data comes when you look at the standard deviation of the data. Standard deviation is a measure of how variable is the measured outcome (e.g. duration of time a patient spent in hospital). For the ivermectin study, analysis of the standard deviations quoted on the patient data indicated a peculiar distribution of the length of hospital stay, which, in itself would probably just be a puzzle but in combination with the other problems in the paper becomes a suggestion of scientific fraud. In Schön’s data on the other hand, it was calculated that the precision given in the papers would have required thousands of measurements. In the field in which Schön worked this would have been a physical impossibility and so again, suggestive of fraud. In both cases, it is by looking at the smaller errors that we find a bigger error.

This last detail would have been appreciated by Abraham de Moivre, (1667-1754). As a mathematician, de Moivre was known for his work with probability distribution, which is the mathematics behind the standard deviation of a data set. He was also a well known regular (the ‘resident’ mathematician) at Old Slaughters Coffee House on St Martin’s Lane in London[1]. It is recorded that between 1750 and 1754, de Moivre earned “a pittance” at Old Slaughters providing solutions to games of chance to people who came along for the coffee. I wonder if there are any opportunities in contemporary London cafes for a resident physicist? I may be able to recommend one.

*You can find recipes suggesting this dosage here or here. Some recipes recommend a slightly stronger coffee amount, personally, I prefer a slightly weaker dosage. You will need to experiment to find your preferred value.

[1] “London Coffee Houses”, Bryant Lillywhite, 1963

Coffee innovations at MacIntyre, Angel

MacIntyre Coffee AngelOne motivation behind Bean Thinking is to explore those connections that can be found when we stop to really look around us. Whether your interest is in history, philosophy or science, something in a café will prompt a train of reflections that can lead to interesting and surprising thought journeys. This is surely true for anybody in any café, if we just take the time to slow down. But, I admit a prejudice: while I had heard great things about the coffee in MacIntyre, when I had glanced in from the bus window, I saw the scaffolding seating arrangements and wooden surfaces that can be a type of design found in many new cafés. So I worried. Was it going to be hard to ‘see the connections’ in MacIntyre? Would I end up with a great coffee but a challenge to my assumptions about the ubiquity of connectivity?

Fortunately, I needn’t have worried. The two lovely coffees that I have enjoyed at MacIntyre gave me plenty of time to really savour both the coffee and my surroundings and I was wrong in my assumptions from the bus window, connections really are everywhere. The café itself was a delightful find. Watching other customers while drinking my long black, it seemed that everyone was greeted by a cheery “hello”. Many people were clearly regulars, which is perhaps unsurprising for a friendly café with good coffee in a busy area. The scaffolding and wooden seating also works in the space at MacIntyre, giving a strangely relaxing feel to the café. The café itself is rather narrow, with the seating on one side and pastries/ordering queue on the other. Tap water was delivered with the coffee, without my needing to have asked for it.

Plant, light, scaffolding at McIntyre's Angel

Good scaffolding also has good connections.
Plant and light at MacIntyre.

MacIntyre may also be a great spot if you are into people watching. Amidst the general busy-ness, I could eavesdrop on conversations about the latest coffee news and the rise of artificial intelligence (these were two separate conversations!). Perhaps the conversations were particularly noticeable owing to the acoustics of the wooden walls and the narrow, small space of the café. At various points around the café, plants hung from the scaffolding. Some of the plants were spot-lit, which caused me to wonder whether the light that the plants were receiving was optimal for photosynthesis. The menu was projected onto the rear wall of the café, which was also decorated with hexagons, an immediate connection to graphene.

But then, in my coffee cup, the significant crema on the coffee showed evidence of amazing thermal convective motion together with turbulence. The coffee itself was very sweet with nutty overtones but the movements of the crema reminded me of cloud formation in thunderstorms. Although thunderstorms didn’t make it to the thought train of MacIntyre, another form of surface motion suggested a connection to another, unusual, feature of this café. You see, MacIntyre is a cashless business, no cash is accepted even if you’re only buying a long black. Most customers on my visit paid with their contactless cards.

The idea of a cashless society is one that has obvious advantages for both the business and the government/economy (whether it has such obvious advantages for the consumer I will leave as a point to be debated). While some countries are attempting to move to a more cashless economy, for a business to be entirely cashless is somewhat innovative. Even though MacIntyre is not the only café to go cashless (Browns of Brockley is similarly cash free), it has to be one of the first cafés to do so.

Coffee at MacIntyre Angel

Coffee and water on wood at MacIntyre Coffee. Could you increase the returns on your investments by understanding the movements on the surface of a cup of coffee?

What is the connection between this and the surface movement on my coffee? Well, it is not just at MacIntyre that a café has supported an innovation that has (or may) change our economy. Just over three hundred years ago, Jonathan’s Coffee House in Exchange Alley was a place of similar innovation, though there it was a customer rather than the coffee house itself that gave the change.

It was at Jonathan’s in 1698 that John Castaing published a paper twice a week detailing the latest stock prices titled “The course of the exchange and other things”. Recognised now as the origin of the London Stock Exchange, how stocks are priced and how their prices vary with time are subject to intense mathematical modelling. Although now, these models can be extraordinarily complex, the base of many of them share a mathematical model with the movements on the surface of your coffee cup, Brownian Motion.

Jonathan's coffee house plaque

The site of Jonathan’s in Exchange Alley. Seen while on a Coffee House tour last year.

Brownian motion is the phenomenon in which small particles of dust, or coffee grains on the surface of your coffee move in a random way as a result of collisions between the particles and the molecules in the liquid. First described in detail by a botanist, Robert Brown in 1827, the experimental evidence in favour of the molecular-collision explanation of Brownian motion came in 1910 with Jean Perrin’s careful experiments (that have featured in The Daily Grind previously). The maths behind the explanation relies on the idea of the ‘random walk‘ in which each dust particle is ‘kicked’ in a random direction by the molecules in the coffee, the consequent motion being frequently described with reference to a drunkard attempting to get home after leaving the pub. However, as this concept of the ‘random walk’ was being developed for molecules in a liquid, it was simultaneously being developed to model the movements of stock prices by the mathematician Louis Bachelier. Bachelier’s model of stock prices turned out to be the same as the model of Brownian motion, but both developed independently.

As yet, it is unclear (to me at least) whether there is a link between cashless payments and some of the maths in your coffee cup but, MacIntyre would be a great place to contemplate this as you sip your brew. Never succumb to prejudices, on which note please do let me know what you think of cashless payments, a great convenience or an invasion of privacy?

MacIntyre can be found at 428 St John St, EC1V 4NJ.

Molecular reality at the Turkish Deli, Borough

Just as the air is more dense at sea-level than on a mountain top, so the granules of an emulsion, whatever may be their initial distribution, will attain a permanent state where the concentration will go on diminishing as a function of the height from the lower layers, and the law of rarefaction will be the same as for the air” (Jean Perrin)

Turkish Deli, Turkish Coffee

The Turkish Deli, Borough Market

I have long had a fascination for the history of coffee and the different styles of brew. So it should be no surprise that I went to try The Turkish Deli in Borough Market for the Daily Grind. Very close to Monmouth, the Turkish Deli serves Turkish-style coffee and a delicious looking array of Turkish delights. Although quite far from the brew bars and single estate coffee types of some cafés now in London, Turkish coffee nonetheless offers the opportunity to slow down and appreciate the moment. Perhaps even more so than an espresso, since you are forced to wait for the coffee to be ready. The coffee is presented to you, straight from the Ibrik, in a small cup with a fantastic looking crema on top of it. At this point you are told that you will have to let it settle for at least four minutes before even thinking about starting to drink it. Indeed, the person in front of me in the queue was advised that he could “sit down, watch the world go by” while waiting for the crema on the coffee to turn a very dark (black) colour, indicating that the coffee was finally ready.

before settling, Turkish coffee

Waiting for the coffee to be ready

If you take sugar in your coffee you have to add it right at the start, before the coffee is warmed to the point of boiling (though it is not boiled). The reason is fairly obvious if you think about it. Turkish coffee has a large amount of sediment, this is the reason that you need to leave it for four minutes for the sediment to ‘settle’. Adding sugar during this settling time would mean that you would need to stir the coffee which would disturb the sediment and prevent it from quickly settling. Instead, you either take your coffee sugar-less or you add your sugar before starting this settling process.

Jean Perrin, (author of the quote at the start of this week’s Daily Grind) used the gradient of sediment in a different liquid (gamboge – a bright yellow paint pigment) to confirm the existence of molecules, just over one hundred years ago. He was exploring Brownian motion, the seemingly random motion of bits of dust, sediment etc, on the top of the coffee cup which had been explained in terms of “molecules” in the coffee (or water, or paint), hitting the bits of dust on the surface. Jean Perrin (1870-1942), realised that if Brownian motion was being caused by molecules, they would not just be causing the movement of the dust (and sediment) on the surface, it would be a three dimensional effect. Measuring the gradient of sedimentation would be a way to prove the molecular theory of Brownian motion and, simultaneously, to prove the existence of molecules.

Turkish coffee

The surface of the coffee reminded me of a coastline, itself connected (mathematically) to Brownian motion

Imagine a bit of sediment in the middle of the liquid (it could be a Turkish coffee, for Perrin it was the paint). That piece of sediment is going to be pulled down by gravity but in addition, it is going to be pushed up by molecules from below and down by molecules in layers above it. This is the bit that is related to Brownian motion. We know that even after leaving it for a long time, much of the sediment is still suspended mid-way up in the cup. It follows that the total forces acting downwards on the sediment (from gravity and the molecules above it) must be the same as the total force acting upwards (from the molecules below).

This means that the mass of sediment held at any particular level in the coffee must decrease with height. If the size of each piece of sediment is identical (which was ensured by Jean Perrin in his paint but is not the case for the Turkish coffee), then the number of pieces of sediment held aloft in the coffee/paint would decrease with height from the bottom to the top. All Perrin had to do therefore was to count (with a microscope) the number of bits of sediment as a function of height in order to test whether the molecular theory for Brownian motion was correct.

Turkish coffee, Borough market, sedimentary, sedimentation

The sediment at the bottom of the cup, don’t drink this bit!

To obtain statistics, Perrin and his assistants would count 11000 particles in one emulsion and repeat this experiment 1000s of times, but his patience paid off. By 1910, (only a few years after starting his observations), Perrin could claim that “the molecular theory of the Brownian movement can be regarded as experimentally established, and, at the same time, it becomes very difficult to deny the objective reality of molecules”. In 1926 he received the Nobel prize in recognition of this work.

Returning to the coffee, it is a very good drink with which to slow down and watch the world go by, perhaps while pondering molecular reality. When you get towards the bottom, do not drink the sediment but do take time to appreciate the mouthfeel and flavour as you drink this beverage that, in many ways represents an early chapter in the coffee story and one that continues to be made very well at the Turkish Deli.

The Turkish Deli is in Borough Market, Stoney Street, London, SE1 9AA

Quotes taken from “Brownian Movement and Molecular Reality”, Jean Perrin, 1910