Category: Science history

Categories
Coffee cup science General Science history

A demon in your coffee

Americano, Maxwell's demon
So innocent looking. But could an imaginary demon lurking within help us to understand more fully a major theory in physics?

Is there a way of preparing an Americano that can reveal a particularly knotty problem in physics with implications for information theory?

The question arises out of a field of physics, developed through the nineteenth century, that deals with energy and temperature: thermodynamics. It is the theory that describes how a hot coffee, left in a cold room, will eventually cool to the temperature of the (ever so slightly warmer) room. And though this may seem a trivial example, the theory is immensely powerful with applications from steam engines to superconductors. But it is back with the cooling coffee that we may find a demon, and it is worth finding out a bit more about him.

There are four laws of thermodynamics (the original three and then what is known as the ‘zeroth’ law). But it is the second that concerns us here. It can be phrased in a number of different ways but essentially says that there is no process for which the only result is the transfer of heat from a cold object to a hot one. To think about our coffee, the coffee will cool down to the same temperature as the room, but as the law describes, the room cannot get colder by giving its heat to the coffee cup (so the coffee gets hotter)!

It is in fact, one of the few places in physics where there is a ‘direction’ to time. For most of the laws of physics, time could run in the opposite direction without changing the effect, but not so for this one. The second law of thermodynamics is a definite provider for an arrow of time.

coffee clock, Rosslyn coffee
The clock at Rosslyn Coffee in the City of London. But the image alludes to a fundamental truth: the way that coffee cools is one of the few areas of physics for which it matters which way time ‘flows’.

But that is a digression. We ought to return to the demon in the coffee. The second law of thermodynamics seems to be based on our common sense (though perhaps that is because our common sense is formed within the laws of physics that determine the second law of thermodynamics). But with confidence in our common sense to understand the second law of thermodynamics, let’s do a thought experiment in which we make a strange type of Americano. Imagine a cup of coffee with an impermeable partition cutting through it. Into one half of the cup we pull a lovely, single origin, espresso. The crema rising onto the surface with some brilliant tiger striping on show. Into the other half of the cup we pour some water, initially at the same temperature as the coffee. We drill a small hole in the partition and watch what happens. Of course we know what happens. Ever so slowly, the coffee starts to get into the water and the water into the coffee until we are left with a balanced Americano on both sides with both sides at the same temperature.

Great, but now let us introduce the demon. Actually, he’s called “Maxwell’s Demon” because it was Maxwell who first proposed him (in ~1871), but we can call him anything we like. Perhaps he’s not a he at all. Our demon sits next to the small hole we have made in the partition and watches as the molecules travel towards the hole from the water’s side and the side holding the coffee. This demon is a bit of a trouble maker and so any fast moving molecules (hot) from the water he allows to get into the coffee and any slow moving molecules (cold) from the coffee he allows to get into the water. He does not allow slow molecules from the water into the coffee or fast molecules from the coffee into the water. Just to add to the mix, any coffee solubles he returns to the coffee allowing only water molecules through the hole in the partition.

If our demon exists, we would end up with a lot of very fast molecules on the coffee side (which will therefore be hotter) while the water would hold slower molecules (and be colder). We’d have a very hot espresso on one side of the partition and some luke warm water on the other. It’s not only a terrible Americano but a violation of the second law of thermodynamics! Which is worse?

Although he was proposed as a thought experiment, it is a problem with serious implications for the second law of thermodynamics (which otherwise seems to be a very good model of how things work). Because while we may not seriously consider an actual demon in the coffee, what stops some mechanical tool that we make from violating the second law, if the demon, in principle, could exist? Could the second law be wrong? Could there be a way of getting heat into our coffee from a cold room?

3D hot chocolate art on an iced chocolate, Mace, Mace KL, dogs in a chocolate
Art on a hot chocolate at Mace in KL. Well, what is your mental image of Maxwell’s demon?

The consensus has been that even were the demon to exist, ultimately he is powerless against the second law which does not get overturned by his presence. Because even if we could end up with a super hot espresso on one side of the barrier and cold water on the other side, this is not the whole system; the whole system includes the demon. And the second law applies to the whole system not the system minus the demon. So when we consider the energy (and entropy) of the demon in doing the work necessary to decide which molecules to let through and which to filter out, we find that work is done on the system (by the demon) and the entropy, the disorder if you like, of the whole system has increased (which is another way of phrasing the second law). Calm is restored, we get our Americano back, the laws of physics as we understand them are retained.

But Maxwell’s demon has not been completely exorcised yet, or at least, he is proving to be quite helpful. Because it turns out that there are methods for which the energy cost for the demon is minimal and the argument above no longer works. It seems we are back to square one. But even in that situation, it was realised that the demon has to record, make a note of, which molecules are fast and which are slow, which are coffee and which are water. It has led to an understanding that information has to be part of our consideration of thermodynamics. And as our ability to manipulate nanostructures and individual atoms improves, so experiments are able to explore how information ties into thermodynamics and why Maxwell’s demon still has not undone the second law yet. But it is here that we encounter another demon, the one that is found in the details, so if you are interested you can read more about it here.

Categories
Home experiments Observations Science history slow

Missing matter

soya latte at the coffee jar camden
Not one made by me! But instead a soya-latte at the Coffee Jar a couple of years ago.

During these strange times of working from home, perhaps you, like me, have been preparing a lot more coffee. For me this has included, not just my regular V60s, but a type of cafe-au-lait for someone who used to regularly drink lattes outside. My previous-latte-drinker turns out to be a little bit discerning (the polite way of phrasing it) and so prefers the coffee made in a similar way each day. Which is why I’ve been weighing the (oat) milk I’ve been using.

So, each morning to prepare a coffee, I’ve been using a V60 recipe from The Barn and then, separately, weighing out 220g of refrigerated oat milk into a pan that I then heat on the stove. Generally I heat the milk for just over 5 minutes until it is almost simmering whereupon I pour it into a mug (with 110 – 130g of coffee inside – depending on the coffee). Being naturally lazy, I keep the cup on the scales so that it is easier to pour the milk in and then, completely emptying the pan into the coffee, the scales register an increase of mass (of milk) in the cup of 205-210g. Which means about 10-15g of milk goes missing each morning.

Now clearly it is not missing as such, it has just evaporated, but it does prompt a question: can this tell us anything about the physics of our world? And to pre-empt the answer, it actually tells us a great deal. But to see how, we need to go on an historical diversion to just over three hundred years ago, when Edmond Halley was presenting an experiment to the Royal Society in London. The experiment shares a number of similarities with my heated oat milk pan. It was later written into a paper which you can read online: “An estimate of the quantity of vapour raised out of the sea by the warmth of the Sun; derived from an experiment shown before the Royal Society at one of their late meetings: by E Halley“.

lilies on water, rain on a pond, droplets
Coffee, evaporation, clouds, rain, rivers, seas, evaporation. Imagining the water cycle by making coffee.

Halley heated a pan of water to the temperature of “the Air in our hottest summers” and then, keeping the temperature constant, placed the pan on a set of scales to see how much water was lost over 2 hours. The temperature of the air in “our hottest summers” cannot have been very high, perhaps 25-30C and there was no evaporation actually seen in the form of steam coming from the pan (unlike with my milk pan). Nonetheless, Halley’s pan lost a total of 13.4g (in today’s units) of water over those two hours.

Halley used this amount to estimate, by extrapolation, how much water evaporated from the Mediterranean Sea each day. Arguing that the temperature of the water heated that evening at the Royal Society was similar to that of the Mediterranean Sea and that you could just treat the sea as one huge pan of water, Halley calculated that enough water evaporated to explain the rains that fell. This is a key part of the water cycle that drives the weather patterns in our world. But Halley took one further step. If the sea could produce the water for the rain, and the rain fed the rivers, was the flow of the rivers enough to account for the water in the Mediterranean Sea and, specifically, how much water was supplied to the sea compared to that lost through the evaporation? Halley estimated this by calculating the flow of water underneath Kingston Bridge over the Thames. As he knew how many (large) rivers flowed into the Mediterranean, Halley could calculate a very rough estimate of the total flow from the rivers into the Mediterranean.

Grecian, Devereux, Coffee house London
A plaque outside the (old) Devereux pub, since refurbished. The Devereux pub is on the site of the Grecian Coffee House which was one of the places that Halley and co used to ‘retire’ to after meetings at the Royal Society.

The estimates may seem very rough, but they were necessary in order to know if it was feasible that there could be a great water cycle of rain, rivers, evaporation, rain. And although Halley was not the first to discuss this idea (it had been considered by Bernard Palissy and Pierre Perrault before him), this idea of a quantitative “back of the envelope” calculation to prompt more thorough research into an idea, is one that is still used in science today: we have an idea, can we work out, very roughly, on the back of an envelope (or more often on a serviette over a coffee) if the idea is plausible before we write the research grant proposal to study it properly.

So, to return to my pan of oat milk simmering on the stove. 15g over 5 minutes at approaching 100C is a reasonable amount to expect to lose. Only, we can go further than this now because we can take the extra data (from the thermostats we have in our house and the Met Office observations for the weather) of the temperature of your kitchen and the relative humidity that day and use this to discover how these factors affect the evaporative loss. Just as for Halley, it may be an extremely rough estimate. However, just as for Halley, these estimates may help to give us an understanding that is “one of the most necessary ingredients of a real and Philosophical Meteorology” as Halley may have said before he enjoyed a coffee at one of the Coffee Houses that he, Newton and others would retire to after a busy evening watching water evaporate at the Royal Society.

Categories
Coffee cup science Coffee review Science history Tea

Schrodinger’s Katsute (100), Angel

Katsute 100, tea in Islington
It was a sunny day when we visited Katsute100 in Angel, Islington

When Bean Thinking started, it was always going to be about coffee and yet, Katsute 100 is definitely a tea place. Not only that, but the idea was to see how the physics that we use to describe our universe is mirrored by the physics of the coffee and in a cafe, the physics of the every-day. On the other hand, the whole point of Schrodinger’s cat is to demonstrate how aspects of quantum mechanics are absolutely unlike our everyday experience: a cat both (and neither) dead and alive? And yet, without giving too much away, today’s cafe-physics review is absolutely this – a review of a tea house that features the famous thought experiment. How far Bean Thinking has moved!

Katsute 100 is a welcoming, and peaceful, Japanese tea place in Angel. With a full tea menu and some really great desserts, it is definitely a good place to spend half an hour, maybe more, watching the coming and going and exploring the tea. And there is certainly a lot of tea to explore, different tasting notes revealing themselves as the tea cools, the carefully placed tea pot and tray adding to the experience.

The shop itself is fairly narrow, decorated in sympathy with the Georgian age of the shop itself and with a view into a garden at the back. Japanese tea making equipment is displayed (and for sale) on the various wooden cabinets around the shop. My tea had been buttery (exactly as it had been described in the tasting notes) and the Ichigo Daifuku I had had with it was a fascinating exploration of texture. There were some Japanese art works on the wall and it was then that I saw my first one: a cat. Not a real one of course but one of several decorative cats that are, almost hiding, around the shop. The word “Katsute” has nothing to do with cats apparently meaning “once”, but nonetheless, a few cats do pop up here and there. And even where cats don’t pop up, there are drawers in the wooden cupboards that seem much like boxes, is there a cat there in the box? Is it dead, alive, both, neither? What does this even mean? And is it connected to Katsute, “once”, after all?

note the pouring slits on the teapot
Tea pot, tea cup and ichigo daifuku at Katsute 100

Looking carefully at my teapot, three grooves were carved into the spout allowing the tea to flow out. Each stream of complex flow interferes with the neighbouring stream to present an aesthetic of flowing liquid to match the sound and flavour of the tea. And of course it is reminiscent of an experiment that is key to the unfamiliarity of quantum physics: the double slit experiment.

When light (of a single wavelength, such as from a laser) is shone at a sheet with two holes in it, the light that has travelled through shows interference fringes and patterns. Indeed, it is one of the experiments that went to establishing the theory that light was a wave (and not, as Newton among others had thought, a stream of particles). The situation is quite different if you tried to pass particles through two slits, imagine a sieve with two holes and a stream of coffee beans travelling towards it, we’d expect each bean to go through one hole or the other, not both. In classical physics that’s what we would expect too and yet, when sub-atomic particles (such as electrons) were aimed at two slits and made to travel through them they interfered with each other, as if they were not particles but waves. But other experiments had shown conclusively that they were also particles and indeed, when each individually hit the detector it did so as a single spot, as a particle. Particles and waves? What was going on?

cupboards in Katsute 100
A lot of sake and a fair number of drawers. But what is behind each drawer and why is one missing?

In fact it was a result that had been predicted: Louis de Broglie had shown, theoretically in 1923, that all particles should have wave-like properties and simultaneously, that all waves should have particle-like properties. We should expect that under certain circumstances, light, electrons, neutrons etc, even atoms, should behave as particles and under certain other circumstances (such as the double slit experiment) as waves. But there was an important catch. The electron travelling through a double slit will behave as if it is a wave, passing through both slits and interfering with itself to produce the characteristic “diffraction pattern” of a wave but only if we do not try to look at it to see which slit it really passed through. If we try to detect which slit the particle has travelled through, we can indeed find that some of the electrons travel through one slit and some through the other but when we look at the resulting interference pattern it is gone! What we are left with is the (classically expected) pattern of two particles going through two slits exactly as if they had been very small coffee beans. (You can see a video of Jim Al-Khalili explaining this peculiar result here).

What is going on? To a certain extent, this question is part of the reason that quantum mechanics can seem so strange. We can’t really ask what is going on, or rather, if we ask, we cannot expect to get an answer! We can describe what happens and we can make predictions based on the mathematics that we use to describe the processes. Our technology and our understanding of physics has developed hugely because we can describe how things will behave. But we will stumble if we try to understand what is really going on behind these processes. As Feynman said in lectures he gave to physics undergraduates:

“We cannot make the mystery go away by ‘explaining’ how it works. We will just tell you how it works. In telling you how it works we will have told you about the basic peculiarities of all quantum mechanics.”§

And so things remain enigmatic. Questions that appear to show paradoxes such as the problem of Schrodinger’s cat* continue to puzzle and intrigue us. Is the cat dead or alive? Can the cat be both? Is the cat an observer and what role does the observer have in physical measurements? What does this imply for the fabric of reality? And is there a connection back to the name of this cafe, “once”?

You perhaps should not expect to find any answers in Katsute 100, but pondering these things with a good cup of tea may help advance your understanding. It will certainly help advance your mood if you are in need of some peaceful, thoughtful, time out.

Katsute 100 is at 100 Islington High St, N1 8EG

§ Feynman Lectures on Physics Volume III, 1965

*The story of Schrodinger’s cat is that a cat is placed in a box together with a small amount of radioactive source material. The box is then closed and we cannot see inside. The amount of radioactive material is such that in one hour it has a 50:50 chance of decay. If the material decays radioactively, it triggers the release of a vial of poisonous gas which would kill the cat. Our mathematical models of quantum mechanics suggest that, until it is measured, the radioactive material is in a ‘superposition of states’: it has both decayed and not decayed; the cat is both dead and alive. Only when we open the box after an hour and thereby measure the state of the radioactive material does the cat, at that point, ‘collapse’ into a state that is either dead or alive.

Categories
Coffee cup science General Home experiments Observations Science history

Telling the time with an Aeropress?

Aeropress bloom, coffee in an Aeropress
The first stage of making coffee with an Aeropress is to immerse the coffee grind in the water. Here, the plunger is at the bottom of the coffee.

On occasion, it takes a change in our routine for us to re-see our world in a slightly different way. And so it was that when there was an opportunity to borrow an Aeropress together with a hand grinder, I jumped at it. Each morning presented a meditative time for grinding the beans before the ritual of preparing the coffee by a different brew method. Each day became an opportunity to think about something new.

Perhaps it is not as immediately eye catching as the method of a slow pour of water from a swan necked kettle of a V60, and yet making coffee using the Aeropress offers a tremendously rich set of connections that we could ponder and contemplate if we would but notice them. And it starts with the seal. For those who may not be familiar with the Aeropress, a cylindrical ‘plunger’ with a seal tightly fits into a plastic cylinder (brew guide here). The first stage of making a coffee with the Aeropress is to use the cylinder to brew an ‘immersion’ type coffee, exactly as with the French Press (but here, the plunger is on the floor of the coffee maker). Then, after screwing a filter paper and plastic colander to the top of the cylinder and leaving the coffee to brew for a certain amount of time, the whole system is ‘inverted’ onto a mug where some coffee drips through the filter before the rest is forced out using the plunger to push the liquid through the coffee grind.

clepsydra creative commons license British Museum
A 4th century BC Ptolemaic clepsydra in the British Museum collection. Image © Trustees of the British Museum

Immediately perhaps your mind could jump to water clocks where water was allowed to drip out of two holes at the bottom of a device at a rate that allowed people to time certain intervals. It is even suggested that Galileo used such a “clepsydra” to time falling bodies (though I prefer the idea that he sang in order to time his pendulums). With many holes in the bottom of the device and an uneven coffee grind through which the water (coffee) flows, the Aeropress is perhaps not the best clock available to us now. However there is another connection between the Aeropress and the clepsydra that would take us to a whole new area of physics and speculation.

When the medieval thinker Adelard of Bath was considering the issue of whether nature could sustain a vacuum, he thought about the issue of the clepsydra¹. With two holes at the bottom and holes at the top for air, the clepsydra would drip the water through the clock at an even rate. Unless of course the holes at the top were blocked, in which case the water stopped dripping, (a similar thing can be observed when sealing the top of a straw). What kept the water in the jar when the top hole was blocked? What kept it from following its natural path of flowing downwards? (gravity was not understood at that point either). Adelard argued that it was not ‘magic’ that kept the water in when no air could go through, something else was at work.

What could be the explanation? Adelard argued that the universe was full of the four elements (air, water, fire, earth) which are “so closely bound together by natural affection, that just as none of them would exist without the other, so no place is empty of them. Hence it happens, that as soon as one of them leaves its position, another immediately takes its place… When, therefore, the entrance is closed to that which is to come in, it will be all in vain that you open an exit for the water, unless you give an entrance to the air….”²

inverted Aeropress and coffee stain
The Aeropress inverted onto a coffee cup before the plunger is pushed down. Complete with coffee stain behind the cup where the inversion process went awry.

Now, we would argue that whether the water flows down and out of the Aeropress, or not, depends on the balance of forces pushing the water down and those pushing it up. The forces pushing the water down and out of the clepsydra, or Aeropress, are gravity and the air pressure above the water in the cylinder. Pushing it up, it is only the air pressure from below. Ordinarily, the air pressure above and that below the water in the Aeropress are quite similar, gravity wins the tug of war and the water flows out. In an enclosed system however (if the holes at the top are blocked), were the water to flow out of the bottom, the air pressure above the coffee space would reduce. This makes sense because, if no new air gets in, the same amount of air that we had before now occupies a larger volume as the water has left it, the pressure exerted by that air will have to be less than before. A reduced air pressure means a reduced force on the water pushing it down through the filter and so the force pushing the water down can now be perfectly balanced by the force (from the surrounding air) pushing the water up: the water remains in the Aeropress. The only way we get the coffee out is to change the balance of forces on the water which means pushing down the plunger.

But perhaps it is worth stepping back and imagining what the consequences could be of having the idea that the universe was just full of something that had to be continuous. You may find it quite reasonable for example to consider that vortices would form behind and around the planets as they travelled in their circular orbits through this ‘something’*. Such vortices could explain some of the effects of gravity that we observe and so there would perhaps be no urgency to develop a gravitational theory such as the one we have. There would be other consequences, the world of vacuum physics and consequently of electronics would be significantly set back. In his lecture for the Carl Sagan Prize for Excellence in Public Communication in Planetary Science, The Director of the Vatican Observatory, Br Guy Consolmagno SJ explored previous scientific ideas that were almost right, which “is to say wrong” (You can see his lecture “Discarded Worlds: Astronomical Worlds that were almost correct” here) If it is true that so many scientific theories lasted so long (because they were almost correct) but were in fact wrong, how many of our scientific ideas today are ‘almost correct’ too?

It makes you wonder how our preconceptions of the world affect our ability to investigate it. And for that matter, how our ability to contemplate the world is affected by our practise of doing so. They say that beauty is in the eye of the beholder. For that to be true, the beholder has to open their eyes, look, contemplate and be prepared to be shown wrong in their preconceptions.

What connections do you make to your coffee brew each morning? I’d love to know, here in the comments, on Twitter or over on Facebook.

 

* Does a connection between this and stirring your freshly brewed Aeropress coffee with a teaspoon trailing vortices stretch the connectivity a bit too far?

¹ “Much Ado about Nothing: Theories of space and vacuum from the Middle Ages to the Scientific Revolution”, Edward Grant, Cambridge University Press, (1981)

² Quoted from Adelard of Bath’s “Quaestiones Naturales” taken from Much Ado about nothing, page 67.

Categories
Coffee review General Home experiments Observations Science history slow Tea

Noticing at Artisan, Ealing

coffee Artisan Ealing
A good coffee is a solid foundation for any afternoon’s noticing.

A cafe-physics review with a difference. In that, it’s not so much a review as an invitation. What do you notice in a café?

Last week, I had the opportunity to try Artisan’s Ealing branch. Although I had found a lot to notice on my previous visit to the East Sheen branch, I had a very specific reason for visiting the Ealing location of this small chain of four cafés. The coffee (espresso) was reliably good. Smooth and drinkable in a friendly atmosphere. Just as with the café in East Sheen, there were a good selection of edibles at the counter and plenty to notice. The light shades were immediately outstanding as something to notice while a framed ‘hole in the wall’ provided a conversation point. The café was very busy and while there was plenty of seating with many tables, we were still lucky to have got a table for two near the back. Behind us there was a lesson going on in the coffee school while on the wall was the calendar for the space booking downstairs. And it was this that I had come here for.

A couple of months ago, Artisan announced that this space would be available to rent to provide a friendly space (with coffee) for the meetings of local small businesses or charities. This stayed in the back of my mind for a while as it came about at roughly the same time as an idea for Bean Thinking.

Lampshades at Artisan Ealing
First the obvious. Immediately striking, these lampshades could provide several avenues for thought.

There are a couple of us who are interested in meeting, about once a month, to discuss science. As ‘science’ is quite a big subject, we thought we would limit it to science that is associated with coffee or with the café at which we are meeting. Perhaps readers of this website may realise that this is not such a restriction, it is quite easy to connect coffee to the cosmic microwave background radiation of the Universe or to chromatography and analytical chemistry. If we were to meet in a location such as Artisan, there should be plenty more food for thoughts. The lampshades prompted me to consider what made substances opaque or transparent? Where is the link to coffee and methods for measuring the coffee extraction? The hole in the wall suggested thoughts about the algorithms behind cash machines. I’m sure that there is plenty more to notice if we take the time to see it.

And so this is an invitation. Would you like to join us in exploring what we each notice about the science of our surroundings? The plan would be to meet once a month, probably starting late January 2019 or early February (date and location to be confirmed). An afternoon on the weekend is probably better than an evening and we’d probably stay for an hour or two. You do not have to be a practising scientist to come along indeed, it would be great if we could have people from a variety of walks of life. The idea is not (necessarily) to answer scientific questions that we each may have but instead to explore the science behind the questions, to find the connections that form our ideas of the universe. To really notice our surroundings and our coffees (tea drinkers would also be welcome). As a consequence of this, mobile phones/laptops etc. will be discouraged during the afternoon. We’d like to notice things around us and not be distracted by what a search engine suggests about it; if we think a search engine could help us, we’ll use it after we’ve left and come back the following month to discuss the issues further. So, if you are curious, would like to explore what you notice and can tolerate keeping your phone on silent and in your pocket for an afternoon, please do come along, it would be great to meet some of you.

menus and lampshades in Artisan
You may like to look more closely at this photo. How are the menus supported? What does that tell us about the history of science?

In order to understand whether there would be any interest in this idea and to hear your input about the format, content, location, time etc. I have set up a mailing list for these cafe-science-spaces. Please do sign up to the mailing list to hear the latest announcements concerning these events and also to email me back to contribute your opinion. You can sign up to the mailing list using the sign up form below. Alternatively, if you don’t want to sign up to the mailing list but do want to hear more, I will be advertising the events on Twitter and Facebook so please do feel free to follow me there.

 

Please enter your email address here if you would like to hear about future Bean Thinking events.

 

Categories
Coffee review Observations Science history Sustainability/environmental Tea

A post in need of a Curator(s) Coffee, Fitzrovia

espresso Curators
A deliciously intense and fruity espresso from the ‘specials’ menu at Curators Coffee.

Curators Coffee in Margaret St in Fitzrovia has been there for years. A great location just off of Oxford St, with plenty of seating and good coffee, and so it is perfect to pop into, unless you are like me and avoid the Oxford St area as much as possible. Which perhaps explains the rarity of my visits. I first popped into Curators Coffee a couple of years back (before the laws on allergen information came in) when I remember enjoying a lovely long black but couldn’t have a cake because the people behind the counter that day couldn’t tell me which (if any) cakes contained nuts. At the time, I sat upstairs and noticed the graphene type arrangement of hexagons around the back of the space and the Bramah’s 300 years of coffee makers book in a rack at the back. I had wanted to return to properly cafe-physics review the place at a later date (and try the cake) but circumstances (and Oxford St avoidance) meant that I never got round to it. Until very recently.

This time, I noticed that there were three single origin coffees available to try as espresso. Glancing at the tasting notes it was a fairly quick decision: “chocolate”. And although this time I had just had lunch and so passed on the cake, it appears that the espresso choices regularly rotate, offering an incentive to come back again and try something new. Although the café is quite large, with plenty of seating, it seems that it is also very popular. And so there were no spaces remaining upstairs. Fortunately, there were more seats downstairs and so, taking our table number with us, we made our way down the stairs and found a table at the window, as if it was waiting for us.

UFO in Curators Coffee Fitzrovia
A UFO reflected in the window? Why? What? Why (again)? It is small details such as this that reward you as you put down your smart phone and notice your surroundings.

Perhaps it is obvious that a café called Curators should have art work adorning the walls. That, and the spotlights that highlighted the work immediately caught our interest, (although it was odd to see that one of the rows of spotlights was almost devoid of bulbs). The exhibition downstairs seemed to have a tilt towards street art and a couple of decorated aerosol cans were on the windowsill priced at £15 each. Was this the time to consider why an aerosol gets cooler as you spray the walls with it?

Outside the window, a staircase leading up to the street outside had railings in straight lines leading up towards a blue sky. Inside, a space craft was reflected in the window.

Indeed, on checking again, there was a spacecraft, like a cartoon of a stereotypical little UFO, drawn onto the wall behind my accomplice’s head and reflected in the window next to it. What could it mean? Regardless of whether some UFO incidents are associated with visitors from other planets, there are a large number of scientific thought trains we can take when considering a UFO reflected in a window. To start with, how likely is it that we are alone in the universe or that there are many other intelligent life forms in other planetary systems?

The question has been answered on the basis of probability for many years. But recently, we have been finding more planets orbiting stars and crucially, more planets that are in the ‘habitable’ zone around other stars. Assuming that life elsewhere needs similar conditions to the earth’s in order to thrive, the idea of life elsewhere is becoming increasingly real.

canali Curators Coffee
If you see straight lines such as this, it is fairly sensible to infer that they were built by an intelligent life-form. Can you see canals on Mars?

Closer to home, there were even suggestions that Mars may support flowing water, thought to be a host for bacteria based life. And although these interpretations of the flow patterns observed on the Martian surface have more recently been contested (could they instead be flowing sand?), we continue to send probes (such as the Insight probe that landed recently) to the red planet to investigate its geology. Did Mars once host life?  Mars of course has a resonance in science fiction for being the planet hosting extra-terrestrial life. HG Wells imagined the Martians landing just south of London, and eventually being killed off by exposure to bacteria on earth that they had not experienced in their Martian habitat. Could life on Mars suggest a (tenuous) further link to this café on Margaret St?

Perhaps one reason that people started to imagine (intelligent) life on Mars came about because of an interesting mistranslation of an astronomical observation. While gazing at Mars in 1877, Schiaparelli noted ‘canali’ on the Martian surface. The correct translation of this in this context into English is “channels” but what the observation came to be known as was “canals”. Canals imply an intelligent builder, and hence life on Mars. Later observers also saw these ‘canals’ and a popular myth was born. It is a useful lesson for us all, sometimes how we see something can be influenced by the language we use to describe it.

soya hot chocolate, Curators
We photograph our coffee, and share it with our online friends. But would putting down our phone in a cafe be worth something for the planet as well as for ourselves? How many batteries do we need?

And then one final thought train, prompted by photographing the cafe with my mobile phone. The whole probability argument rests on two assumptions. The first is that there are other planetary systems (which we are finding). The second is that life is fairly easy to start, or at least, that the chances of producing life are not restricted to one planet a short distance away from the Sun; we are not unique. As yet we don’t know whether this assumption is justified but discoveries such as the deep sea hydrothermal vents challenge our preconceptions about the requirements for life and suggest that life could start more than once, and so could very well start on other planets, not just ours. In these vents, bacteria are known to convert what we think of as toxic chemicals into energy in a process known as chemosynthesis without the need of sunlight or other ingredients that we had thought essential to life. Could similar hydrothermal vents on other planets host new life forms?

And in a related way, what is going on with these vents? Is new life being created even now in the deep sea? In which case, what do we think about deep sea mining? If our aim is to reduce our carbon dioxide emissions by using more re-usable objects and renewable energy sources, we will require more batteries and batteries require (among other things) cobalt. If we are all to keep using mobile phones to photograph cafés, we too need the batteries which rely on these elements. A number of companies have realised that there is a vast untapped resource under the sea if only we could dredge it up. This may be easier or ultimately cheaper than recycling the old batteries. It may destroy a few hydrothermal vents or stir up the sea bed but what concern is that to us if we can gain access to more cobalt to allow us to have more batteries to allow us to all be ‘greener’.

Indeed, of what concern is that to us?

Curators Coffee is at 51 Margaret St, W1W 8SG

Categories
Observations Science history Tea

The universe and a coffee cup

a heat sensitive coffee mug
Now you see it….

Ordinarily, this week would be the turn of a cafe-physics review but circumstances have meant that this will be postponed by one week, sorry. So instead, a question. How does your coffee cup resemble the universe?

A few years ago, I was given a heat changing mug that revealed the constellations when the coffee within it was hot (and went black as the coffee was finished/went cold). Although this is not the way that the universe resembles a coffee mug, the science behind these mugs is quite interesting and they do provide a clue to the connection. The answer (or an answer, you may think of more) is in the way that the mug emits heat.

On a cold day with a hot coffee, I can be fairly sure that by putting my hands quite close but not touching the cup, I can feel the radiated warmth. Infrared waves helping prevent my fingers from becoming numb. Although there is air around the cup (even physicists don’t drink coffee in a vacuum) and so there will be heat transferred from the cup to my hands via conduction and convection, a large amount of the heat my hands receive will be radiated. It was by watching a candle flame between himself and a stove that Carl Wilhelm Scheele (1742-1786) inferred the presence of the infrared. For a coffee temperature of 60ºC (333 Kelvin), the cup would emit a range of light with a peak in intensity at a wavelength in the infrared of around 8.5 μm, about the length of a grain of espresso grind. The way that objects radiate heat is well known. Called a “black body spectrum”, all things radiate a spectrum that can be approximated to it, whether the object is a coffee cup or the universe, the difference is over what frequency range (or wavelength) the object radiates and where in the spectrum the light intensity peaks.

cold mug
Now you don’t.
The same cup as above but photographed when it is at room temperature not when it contains hot liquid.

Coffee emits light (in the infrared) at 8.5 μm because it is about 60ºC. A ‘red hot’ iron rod, still emits light in a spectrum that peaks in the infrared but appears more red than my coffee cup because the peak in the radiated intensity has decreased closer to the red region of the visible spectrum. The universe emits radiation over the same sort of blackbody curve but the spectrum emitted by the universe peaks at a wavelength of around 2cm, much longer than the coffee cup and well beyond the infrared. In fact, the universe is emitting light in the microwave region. The longer wavelength means that the universe is a lot colder than a cup of coffee. About 330º cooler in fact because the temperature of the universe is a chilly 2.7K (or approximately -270ºC).

The presence of this microwave ‘background’ was first detected in the 1960s. Further experiments in the 1990s with the COBE satellite and more recently with the Planck satellite have confirmed the almost perfect uniformity of the blackbody spectrum. No matter which direction you turn your microwave antennae to, you pick up the same background spectrum, peaking at about 2cm, all around the universe. This means that the background temperature of the universe is the same in all directions that we look, it is uniform. Indeed, it took until the sensitivity of the Planck satellite and more recently the WMAP data to show that the universe had any variation at all. And when it was revealed, it was a difference of about one part in a million. If we compare this to our coffee we can see from the lines of light that dance on the bottom of a tea cup that there is significant temperature variation within the cup. Even a difference of one degree would lead to a shift in the blackbody spectrum of the coffee cup by a few parts in a thousand: the background temperature of the universe is far more uniform than the temperature of your cup of coffee in fact the shift seems to be of the order of 0.0002º.

But, apart from an interesting curiosity why would we want to measure the temperature of the universe or know the uniformity of a cup of coffee? One reason is that knowing the current temperature and its likely cooling mechanism, means that we can calculate how long the universe, or coffee, has been cooling. If I were to drink a cup of coffee that was cooler than about 60ºC I would know that either it has been prepared much earlier and left on the counter top or that it had been prepared using water below the optimum brewing temperature. If I note from the lines of light crossing the bottom of the cup that there is a lot of convection going on in my tea cup with cells of different temperature, I could think that it is either a very cold day or that I didn’t warm the cup before I poured the coffee or tea into it.

NASA image CMB
There is even more information in the background if we start to look at the polarisation of the microwaves. The Cosmic Microwave Background showing the minute temperature fluctuations and polarisation directions. Image credit ESA/Planck Collaboration

Knowing the temperature of the universe allows us to check theories of how the universe formed (and therefore how it cools) by calculating its age and seeing if this matches with the age deduced by other means (by looking at the oldest star clusters for example). While looking at the minute temperature variations across the universe is also a test of the theories of the universe’s formation.

There are clearly differences between the universe and a mug of coffee, even a mug that shows the constellations of the stars, not least the fact that the coffee cools into the universe but the universe’s cooling is different having nothing to cool into. Nonetheless, it is remarkable that the same physical laws and mathematics that describes your cooling coffee cup can be used to describe our entire universe. So sit back, take a deep breath, and enjoy the universe through your coffee cup.

 

Categories
Home experiments Observations Science history

21 years of the coffee stain

dried coffee stains, alcohol and coffee
Happy 21st birthday to the coffee stain. But there is still much for us to learn 21 years after the first paper on the coffee stain was published.

On the 23rd October, 1997, a paper was published in the journal Nature titled “Capillary flow as the cause of ring stains from dried liquid drops.” The title is in the dry style that scientific papers can be written. An alternative title could have been “How coffee stains form”*. Perhaps you would think, surely someone had known how coffee stains formed before 1997? And maybe you would go on to think: certainly 21 years later in 2018, we’d know all there was to know about the coffee stain? I hope that readers of Bean Thinking would not think “who cares about coffee stains?”, but I wonder whether it was the combination of disinterest and assuming that someone somewhere surely knew how they formed that meant it took until 1997 for anyone to ask the question: well how do they form?

Coffee is a very popular drink among scientists, though even this does not explain how popular this paper has become. A paper’s popularity can be measured in ‘number of citations’ which tells you how many times other authors have found this piece of work important enough to reference it in their own published paper. As of early November 2018, this paper has been cited nearly 3300 times. Why? Well, there seem to be at least two reasons. Firstly, it turns out that the coffee stain effect is of enormous technological relevance; it may even have been used in the manufacture of the device you are using to read this website. But secondly even now, 21 years later, we still don’t understand what is going on, there is still much to learn and some of it is some very subtle and very beautiful physics.

the droplets ready to dry
What happens when you form coffee stains using drops containing two liquids (alcohol and water) compared to just one (water)?

Very recently for example, a new paper was published in Physical Review Letters. This one was titled “Density-driven flows in evaporating binary liquid droplets“. Another exciting title, another time we’ll retitle it for the purposes of this post: “what happens when you mix alcohol with a coffee type suspension, dry it at different angles and film it drying.” Arguably this time the given title is more succinct. Why does it make a difference if you add alcohol to your coffee rather than just drink it straight (the coffee, not the alcohol)? And what happens to the resulting coffee stain?

Maybe of an evening you’ve been relaxing with a glass of wine, or something stronger, and noticed the “legs” rising up the glass. Their formation and appearance is due to the differing surface tensions between alcohol and water and the fact that alcohol evaporates more easily than water, you can read more about that effect here. The point is that because of the difference in surface tension between alcohol and water, you get a flow of liquid from areas of low surface tension (higher alcohol content) to high surface tension (high water content). And it was this that had been thought to drive coffee stain formation in droplets which were a mix of liquids, water and alcohol for example. But how do you isolate this effect from the other effect in which alcohol evaporates more quickly than water and so there are changes in density and buoyancy of the droplet?

pendulant droplets
Drying droplets upside down. The things we do for coffee science.

To answer this you could add n-butanol to the water (or coffee) rather than alcohol. Just like ethanol based alcohol (the sort you may get in gin), n-butanol has a much lower surface tension and lower density than water but unlike alcohol, it evaporates much less readily than water. So, in a water-butanol mix it will be the water that goes first, while exactly the opposite will happen for an alcohol-water mix. In a drying droplet, the liquid evaporates most quickly from the edge of the drop. Therefore, after an initial, chaotic stage (imaginatively called stage I), you will end up with a droplet that is water rich around its rim in the alcohol-water mix but n-butanol rich around the droplet edge in an n-butanol-water mix (stage II). This suggests a way that you can distinguish the flows in the drop due to surface tension effects from those due to the differences in density between water and alcohol/n-butanol.

How would you test it? One way would be to compare the droplets evaporating as if you had spilled them on the table top with droplets evaporating ‘upside-down’, as if you had tipped the table by 180° after spilling your coffee. You can then watch the flow by taking many photographs with a camera. In this way you would be able to test whether it was surface tension flow (which should be in the same direction within the drop whether the droplet is upright or suspended) with gravity driven flow which should be opposite (the drop is upside down after all).

schematic drops upright and upside down
A cartoon of the flow found in droplets of alcohol and water mix. When upright, the flow is up through the centre of the drop and down the sides. This is expected for both surface tension based flows and flows due to gravity. When upside down, the flow is still upwards through the centre of the drop but this time the drop is upside down. So this is what you’d expect if the dense water at the edge of the drop flowed downwards (gravity based) but not if the flow were dominated by surface tension effects which should be the same, relative to the drop-interface as if the drop were upright.

The authors of the study did this and found that the flow in upright drops of alcohol-water was opposite to that in n-butanol-water drops. This is what is expected both in surface tension dominated flow and in gravity dominated flow. But, when the drops were inverted, the flow within the droplet did not change absolute direction, instead it changed direction relative to the substrate (it may be helpful to see the cartoon), in both droplet types. Expected for a gravity driven flow (dense liquids move downwards), this is exactly the opposite to what would be expected with surface tension driven flow. It is sensible to conclude that the flow in drying droplets containing two liquid types is dominated by gravity, or as the authors phrased it “density-driven flows in evaporating binary liquid droplets”.

dried upside down drops
The resultant coffee stains of drops that had been suspended upside down. They seem fairly similar to the upright ones with the exception of the central dot in many of the stains. The arrow shows some coffee that spilled down the surface as the tray was flipped over.

While the authors did a lovely job of watching the flows within the droplet, what happened to the the actual coffee stain? It could prompt us to do an experiment at home. How does adding alcohol affect the appearance of a coffee stain if the drop is upright compared to if you turned the drops all upside down? What happens if the droplet is not held upside down but instead at an angle to the vertical? There are many ways you could play with this result, see what happens, have a glass of wine and see if that gives you any insight into what you see with your coffee. As ever, have fun and if you do get any interesting results, please do let me know here, on twitter or over on FB.

 

*The dry scientific author in me wants to point out that although catchier, the title “how coffee stains form” does not actually capture the extent of the physics nor what the paper was about (the fact that this happens more often than just in coffee) and the given title was much better. The coffee drinker in me thinks yes, but, surely we could make it all about coffee anyway…

Categories
Coffee review Coffee Roasters Observations Science history slow Sustainability/environmental

A Story with many layers, Clapham Junction

Story Coffee St John's Hill Clapham
The doorway to Story, or a story depending on how you look at it.

A “ghost sign” above the door to Story Coffee on St John’s Hill ensures that you know that you have arrived at the correct place. “Peterkin Custard, Self-Raising Flour – Corn Flour, can be obtained here”, only now it is coffee rather than custard that is sold in the shop beneath. The sign is an indicator to the many tales that could be discerned while exploring the coffee within. I had had a couple of attempts to visit Story Coffee (thwarted for a variety of reasons) before Brian’s Coffee Spot’s review appeared a couple of days after one of my attempted visits. Suitably re-motivated, another trip was attempted (address checked, closing times checked) and this time we were in luck. Although a pour over is listed on the menu, sadly this was not available on our visit and so I enjoyed a lovely long black instead (Red Brick, Square Mile) while looking at the cakes on offer. There was plenty of seating in which to shelter from the rain outside and many things to notice in this friendly café. In addition to the cakes and lunch menu, a box on the counter housed “eat grub” protein bars, protein bars made of cricket powder. Are insects the future for humans to eat protein sustainably?

glass jar at Story
Through a glass darkly?
The distortions produced by the refractive indices of air, water and glass and the shape of the glass produces interesting effects on our view through it.

The tables were well arranged for people to sit chatting while enjoying their beverages and it is always an excellent thing (from a personal point of view) to encounter a café with a no laptop (or tablet) at the tables policy. Complementary tap water was available in jugs placed on each table while it was also nice to note that Story branded re-usable cups were on sale from the counter. Many things we noted can be seen in the gallery pictures in the review on Brian’s Coffee Spot: the funky fans, the egg shaped light shades, the light introduced by the large glass window panes (though it was a much fairer day on Brian’s visit than on ours). Each had its contribution to a thought train, the way the glass water jar bent the light coming through, the concept of a Prandtl boundary layer in fluids (and its connection to both fans and coffee cups). Moreover there were hexagons, which for someone who has worked on the periphery of the graphene craze, are always thought provoking.

Apart from hexagons decorating the top of the stools, there were hexagons lining the counter made of cut logs, each showing the rings from the tree that was felled. Rather than a flat surface, these hexagons were made to be different thicknesses on the wall, rather like the hexagonal columns of the Giant’s Causeway. It is a subtle thing that may have implications for the space that is otherwise surrounded by flat, solid, walls. Such spaces can become echo-y and yet, the music and conversation in Story was not overly distracting presumably because features such as the uneven hexagonal wall reflected the sound waves such that they destructively interfered rather than echoed around the room.

every tree tells a story, but which story
A macroscopic crystal of hexagonally cut logs forms the side of the counter.

Each log in the hexagonal decoration was cut with its cross-section showing a number of tree rings. We know that we can age a tree by counting the rings (though each of these would be underestimated as they have been trimmed into hexagons post-drying), but what more do the tree rings, and the trees themselves have to tell us? The rings are caused by the rapid growth of large cells during spring followed by a slower growth of smaller cells as the year progresses. But this method of growth means that the cut logs have more to tell us than just their age. The spacing between the rings can tell of the weather the tree experienced during that year, were there many years of drought for example? Such clues, from the relative density of the tree rings, can help researchers learn about the climate in previous centuries, but conversely, reading the climate report in the rings can indicate in which year a tree was felled and so the age of a building for example.

coffee at Story
Many stories start with a coffee.

And then there is more, trees will grow at an average rate per year so that, as a rough guide, the circumference of a mature (but not old) tree increases by 2.5cm per year¹. There is therefore something in the idea that you can have a good guess at how old a tree is by hugging it. But this assumes that the tree is growing in its optimum conditions, far enough from any neighbouring trees so as not to be crowded into growing more slowly. So the absolute density of tree rings must also give a clue as to whether this tree was in a dense forest or an open clearing. Which is reminiscent of something else that living trees can tell you if you listen to them closely enough: trees will grow so that their leaves are exposed to the maximum amount of light. For us in the UK, this means that the crown of a tree will frequently tip towards the south (where the Sun is most often) and there will be more leaf growth (and consequently more branches) in a southerly direction². But again, we only see this if the tree has room to grow on its own, without the crowding, and competition, of too many neighbours. A solitary tree helps us to know which direction we are walking in.

empty coffee cup Story St John's Hill
While many coffees could also tell a story. It depends on how you read them.

Which all points to the idea that there are many stories being told all around us all of the time, the ones we hear depend on what we choose to pay attention to. So what about the story behind the ghost sign above the door? The Peterkin custard company was a venture by J. Arthur Rank in an attempt to start a milling company in the mould of his father’s (Rank Hovis McDougall, later bought by Premier Foods). The company failed and Rank went on to form the Rank Organisation that was responsible for many films made throughout the 40s and 50s as well as running a chain of cinemas around the UK. Truly a sign concealing many stories.

 

Story Coffee is at 115 St John’s Hill, SW11 1SZ

¹Collins complete guide to British Trees, Collins, 2007

²The Walker’s Guide to Outdoor Clues and Signs, Tristan Gooley, Hodder and Stoughton, 2014

 

 

 

 

Categories
General Home experiments Observations Science history Sustainability/environmental

Air raising

Small waves seen from Lindisfarne
How do clouds form? How does temperature vary with altitude, and what does coffee have to do with any of it?

You put a drop of alcohol on your hand and feel your hand get cooler as the alcohol evaporates, but what has this to do with coffee, climate and physics?

Erasmus Darwin (1731-1802) was the grandfather of Charles of “Origin of the Species” fame. As a member of the Lunar Society (so-called because the members used to meet on evenings on which there was a full moon so that they could continue their discussions into the night and still see their way home) he would conduct all sorts of scientific experiments and propose various imaginative inventions. Other members of the Lunar Society included Matthew Boulton, Josiah Wedgwood and Joseph Priestley. The society was a great example of what can happen when a group of people who are interested in how things work get together and investigate things, partly just for the sake of it.

One of the things that Darwin had noticed was that when ether* evaporates from your hand, it cools it down, just as alcohol does. Darwin considered that in order to evaporate, the ether (or alcohol or even water) needed the heat that was provided by his hand, hence his hand started to feel cooler. But then he considered the corollary, if water (ether or alcohol) were to condense, would it not give off heat? He started to form an explanation of how clouds form: As moist air rises, it cools and expands until the moisture in the air starts to condense into droplets, clouds.

hole in water alcohol
There are several cool things you can notice with evaporating alcohol. Here a hole has been created in a thin layer of coffee by evaporating some gin. You can see the video of the effect here.

As with many such ideas, we can do a ‘back of the envelope’ calculation to see if Darwin could be correct, which is where we could also bring in coffee. The arabica growing regions are in the “bean belt” between 25 °N and 30 °S. In the sub-tropical region of that belt, between about 16-24°, the arabica is best grown at an altitude between 550-1100 m (1800-3600 ft). In the more equatorial regions (< 10º), the arabica is grown between 1100-1920m (3600-6300 ft). It makes sense that in the hotter, equatorial regions, the arabica needs to be grown at higher altitude so that the air is cooler, but can we calculate how much cooler it should be and then compare to how much cooler it is?

We do this by assuming that we can define a parcel of air that we will allow to rise (in our rough calculation of what is going on)¹. We assume that the parcel stays intact as it rises but that its temperature and pressure can vary as they would for an ideal gas. Assuming that the air parcel does not encounter friction as it rises (so we have a reversible process), what we are left with is that the rate of change of temperature with height (dT/dz) is given by the ratio of the gravitational acceleration (g) to the specific heat of the air at constant pressure (Cp) or, to express it mathematically:

dT/dz = -g/Cp = Γa

Γa is known as the adiabatic lapse rate and because it only depends on the gravitational acceleration and the specific heat of the gas at constant pressure (which we know/can measure), we can calculate it exactly. For dry air, the rate of change of temperature with height for an air parcel is -9.8 Kelvin/Km.

contrail, sunset
Contrails are caused by condensing water droplets behind aeroplanes.

So, a difference in mountain height of 1000 m would lead to a temperature drop of 9.8 ºC. Does this explain why coffee grows in the hills of Mexico at around 1000 m but the mountains of Columbia at around 1900 m? Not really. If you take the mountains of Columbia as an example, the average temperature at 1000 m is about 24ºC all year, but climb to 2000 m and the temperature only drops to 17-22ºC. How can we reconcile this with our calculation?

Firstly of course we have not considered microclimate and the heating effects of the sides or plateaus of the mountains together with the local weather patterns that will form in different regions of the world. But we have also missed something slightly more fundamental in our calculation, and something that will take us back to Erasmus Darwin: the air is not dry.

Specific heat is the amount of energy that is required to increase the temperature of a substance by one degree. Dry air has a different specific heat to that of air containing water vapour and so the adiabatic lapse rate (g/Cp) will be different. Additionally however we have Erasmus Darwin’s deduction from his ether: water vapour that condenses into water droplets will release heat. Condensing water vapour out of moist air will therefore affect the adiabatic lapse rate and, because there are now droplets of water in our air parcel, there will be clouds. When we calculate the temperature variation with height for water-saturated air, it is as low as 0.5 ºC/100 m (or 5 K/Km), more in keeping with the variations that we observe in the coffee growing regions†.

We have gone from having our head in the clouds and arrived back at our observations of evaporating liquids. It is fascinating what Erasmus Darwin was able to deduce about the way the world worked from what he noticed in his every-day life. Ideas that he could then either calculate, or experiment with to test. We have very varied lives and very varied approaches to coffee brewing. What will you notice? What will you deduce? How can you test it?

 

*ether could refer to a number of chemicals but given that Erasmus Darwin was a medical doctor, is it possible that the ether he refers to was the ether that is used as an anaesthetic?

†Though actually we still haven’t accounted for microclimate/weather patterns and so it is still very much a ‘rough’ calculation. The calculation would be far better tested by using weather balloons etc. as indeed it has been.

¹The calculation can be found in “Introduction to Atmospheric Physics”, David Andrews, Cambridge University Press