Grapefruit, York Minster and the Grand Canyon

The most pressing question of this turbulent age is surely this: can you fit more grapefruit into York Minster, or York Minsters into the Grand Canyon? This blog is about questions which have answers, how we can think about estimating things, and whether any of this makes sense.

The pink grapefruit

On the evening of October 26th I was sat with my friend and respected historian of 20C Britain, Sam Wetherell, in a Glasgow restaurant. Jist Misto is probably best described as a fusion restaurant. It features America themed burgers. One of them is the Grand Canyon burger, which we both ate. For reasons which are now totally lost to the imperfections of memory, Sam wondered aloud how many grapefruit would fit in York Minster. This certainly seems to be a question which has an answer. And then, following this, perhaps somewhat obviously – how many Minsters can we fit in the Grand Canyon. Which number is bigger?

In order to unpack, or perhaps pack, all this, I’ll take us through some estimates, refine them, and then reflect on what the point of this absurdist exercise is. There is definitely a point.

First, grapefruit. What is a grapefruit? In lieu of expert knowledge on the subject, Wikipedia usually suffices. This is a good time to extol the virtues of Wikipedia. For a while after its launch in 2001 it was probably a little unreliable, but things have changed. Moderators have been hard at work for the last 17 years and it’s now a valuable resource, especially for information that people would have no good reason to fake. I trust the grapefruit numbers. They are between 10 and 15 cm in diameter, which is a radius of 5 to 7.5 cm. Assuming they’re spherical, we can use V=4/3 π r³ to get the volume. The upper and lower radius values mean volumes differ by factor of 3.4 different, so we’re already operating in quite a wide margin and we haven’t even begun to think about York Minster. Let’s opt for the middle of the range and go with 6cm radius for a grapefruit. This gives us a volume of roughly 900cm³ – which is about a litre, so far so good.

It turns out there is a great deal more information available about grapefruit, for the avid reader. A grapefruit has an approximate mass of 200g (a weight of 2 Newtons). This will be important shortly.

Converting between cubic centimetres and cubic metres requires dividing by 1,000,000 (which is 100 x 100 x 100). The task now should be simple (although it isn’t): calculate the available volume of York Minster and divide by the average volume of a grapefruit. Using the value we calculated above, we have the average volume of a grapefruit as 0.0009m³.

York Minster seen from the side - a long building with a pair of towers at one end and a massive central tower with two perpendicular windows. The round rose window can be seen on the south transcept.
York Minster, picture by MatzeTrier

I got in touch with York Minster. It doesn’t know its own volume.

I suppose this is not surprising, I don’t know my internal volume either. Happily enough people have measured its dimensions approximately. York Minster is Northern Europe’s biggest gothic cathedral. Roughly, it’s 160m long, 76m wide and 26m high to the vault. There are towers, and the fact that the building is a cross shape, and the horribly complex internal structure, but let’s just see what number we get using those dimensions first. The product of these dimensions is 316,160m³. So, dividing this by the grapefruit volume, we get a grand total of 350 million!

But, we should also consider packing fraction. All those stacked grapefruit don’t fully occupy the space they sit in. And, which is worse, the packing fraction depends on how well you arrange them. The best we can possibly do is around 74% of the volume. So we could reduce the maximum number by a factor of ¾. This doesn’t really compete with the uncertainty in the size of the grapefruit. If you studied the link above you’ll have seen that grapefruit are really oblate spheroids – and these pack slightly differently to spheres, as discussed here. But if we opted for grapefruit which were pre-selected to be 12cm in diameter, we’d get 74% of 350 million in the cathedral – around ¼ of a billion -That’s about 3 grapefruit each for everyone in the UK. Breakfast is sorted.

Incidentally, around 5 million tonnes of grapefruit are produced annually – around 25 billion of them! We have enough for 100 minsters full, but this wasn’t the question.

File:Grand Canyon view from Pima Point 2010.jpg
The Grand Canyon, picture by Chensiyuan

So, on to Minsters in the Grand Canyon. This calculation is almost impossible a priori, but luckily the Grand Canyon considers itself important enough to have an estimate of its volume. The national parks service website suggests “The volume of the Grand Canyon is estimated to be 5.45 trillion cubic yards” . I don’t know who made this estimate, but we’ll go with it.  This is 4.2 trillion cubic metres. Dividing this by the approximate volume of the minster gives a mere 13 million! This is obviously a massive overestimate of the packing fraction, since minsters are complex structures, and I’d guess do not stack well. Even so, this is dramatically fewer than even our most conservative grapefruit-in-minster packing estimate, which would be around 100 million if we randomly packed the cathedral with large grapefruit. So there it is. If we took into account the towers, that would make things worse for the minsters. The grapefruit have it, the grapefruit have it.

Or do they? Let’s move away from abstract forms and consider practicalities. How do we actually get grapefruit into the Minster. Imagine the scene. Here’s the Archbishop of York, atop a step ladder, carefully piling grapefruit in neat pyramids in the North Transept. They tessellate nicely, and up to about 6 feet he has no problems. But the further he goes the harder it gets. The roof of the Minster is still way off. Outside truckloads of grapefruit are souring in the mid-day sun.

The compressive force needed to burst an orange is about 400 Newtons. I know grapefruit are not oranges, but they’re not far off. Under the weight of 200 grapefruit the bottom one would burst.  All stacked up they would reach a height around 24 metres. So, now, we’re 2 metres shy of the top and the bottom layer has exploded. Grapefruit juice is flooding the cobbles. We can now squeeze more in, but at what point are we no longer dealing with grapefruit, if they’re all mushed and festering? The Archbishop is knee deep in grapefruit juice. This will not do.

And this is all to say nothing of packing Minsters into the Grand Canyon. The totally facetious answer to how many Minsters would fit in the Grand Canyon is 1 – because there is only one Minster. But is the Minster even still the Minster if we move it to Arizona? Does moving it there mean it’s not York Minster any more? Is the answer 0? If we could replicate them, one by one, building them in York and shipping them over land and sea to America, how many could we do? Once there, they would stack very poorly – Minsters are far more compressible than grapefruit. After several hundred thousand years of hurling cathedrals into the world’s biggest canyon, the miles deep layer of rubble on the canyon floor is surely indistinguishable from a pile of limestone. Is anyone still counting?

This slightly mad gallop through the world of 3D object packing has, hopefully, demonstrated exactly why physical units are idealised and abstracted and do not rely, for example, on actually filling a space to understand its volume. The last remaining physical quantity that is governed by a reference unit, the kilogram of mass, is due to be replaced by an idealised quantity. Equivalent assumptions are implicit in all forms of social science too. Take elections for example. Polls are now so heavily over analysed that it’s easy to lose sight of the fact that model building, idealisation and the practice of prediction are built on a great many assumptions. People are wildly more complex than fruit. This is often characterised, incorrectly in my view, as uncertainty in election forecast models. One of the key implicit assumptions in election prediction is that there exists some meaningful measurable quantity – just like a grapefruit’s mass – that can be elicited from voters prior to the election. It’s not just that the polls are often wrong, or uncertain, it’s that people are not static measurable objects. Despite recent attempts to characterise humanity as a mechanistic ensemble of preference adopting programmable automatons, we cannot be packed liked grapefruit. Even grapefruit can’t be packed like grapefruit, as the Archbishop surely knows.

(all the pictures are from Wikipedia, thank you to MatzeTrier – Own work, CC BY-SA 3.0, and Chensiyuan –

The energy of hurricane Irma

Hurricane Irma is currently tearing through the Caribbean, with its sights set on Florida, causing catastrophic damage and loss of life. Numerous news reports have attempted to capture the magnitude of Irma’s power. One particularly potent comparison, used in many places, relates Irma to all the bombs dropped during World War 2 (here, here ,here)

“Irma holds about 7 trillion watts – twice the energy of all the bombs used in World War II. ”

— Independent

Of those three, only the Express gets the units right, since a Watt is a Joule per second, so talking about a Watt as an amount of energy doesn’t really make sense. By comparison, total global energy consumption in 2014 was 109,613 TWh, which equates to a power of 12.5 TW on average. So even if the units aren’t quite reported correctly, this storm is certainly very big.

The source of the number is MIT Professor of Atmospheric Science Kerry Emanuel. None of the articles describe how this estimate is arrived at, but a little googling reveals a great discussion of estimating a hurricanes power by the NOAA. This page quotes a 1999 paper by Emanuel himself, entitled ‘The power of a hurricane: An example of reckless driving on the information superhighway’. In the article, Emanuel estimates that hurricanes have power ratings of between 3TW and 30TW, placing Irma towards the lower end of these estimates, which does’t quite make sense to me – if anyone has thoughts on this, please leave something in the comments. In Emanuel’s estimate, the power of the hurricane scales with the cube of the wind velocity and the square of the radius.

Of some amount of irony is the article’s discussion of the unreliability of relating hurricane power to things like bombs. It concludes:

“While the World Wide Web can serve as a valuable source of information, it is clearly susceptible to the rapid propagation of misinformation…While a realistic estimate of power dissipation in an average hurricane is two orders of magnitude less than most values found on the Web, it is still an impressive quantity, equivalent to the world-wide electrical generation capacity as of 1 January 1996, as reported by the US Department of Energy.”

— K. Emanuel

Estimating a hurricane’s power is clearly not an easy task – and making sure these estimates are accurately reported on the web even harder – even when an author has warned of these difficulties in the past.

Refs: Emanuel, K. A., (1999): “The power of a hurricane: An example of reckless driving on the information superhighway” Weather, 54, 107-108

Breaking the mould

Britain is a damp place. Like much of north western Europe, New Zealand, and isolated sections of other countries it has an ‘oceanic’ climate. This means we enjoy a mild and soggy environment, with relative humidity averaging somewhere around 75% in summer, with higher values in winter.

The incredible mould-as-art of Daniele Del Nero. The UK housing stock is in desperate need of renewal.  The incredible mould-as-art of Daniele Del Nero. The UK housing stock is in desperate need of renewal.

While this means we avoid very harsh winters, mould is an ever present concern. Like fire, mould needs three things to grow: food, warmth and moisture. There are thousands of different types of domestic mould. Domestic moulds feed on dust and other organic matter and grow most optimally in warm (15°C – 30°C) conditions above 65% relative humidity. Good ventilation inhibits mould growth,

The presence of mould in a home can have severe direct impacts on respiratory health, as well as potentially negative impacts on mental health. And while I can’t really comment on this case in particular, Brittany Murphy’s mother is convinced, apparently, that her daughter and partner were killed by toxic mould.

My wife and I live in a small basement flat, converted in the late 90’s from a larger Victorian house. While the flat is relatively well insulated it suffers from poor ventilation and almost no natural light. Until a couple of weeks ago the extractor fan in the bathroom was ineffective, and we had to rely on a dehumidifier to remove excess moisture. Fortunately, the landlord has recently replaced the extractor fan, but drying clothes is still difficult without a tumble dryer or external space to do so.

A survey of renters found that 61% suffered from mould, damp or leaking roofs and windows. The advent of the housing crisis means that renting out spaces which were not designed for habitation is now extremely profitable. The UK housing stock is in desperate need of renewal – a warm, dry, healthy home should not be a luxury.


James Baldwin’s birthday

Yesterday, 2nd August, would have been James Baldwin’s 93rd birthday. Every bit of his writing that I’ve come across is magnificent. His work made, and continues to make, one of the most profound contribution’s to America’s understanding of itself. Earlier this year I saw, I am not your negro, which was one of the most moving documentaries I’ve ever seen. Many other people have explained how excellent he is in much better words than I ever could, so I recommend looking it up.

Through the course of idle browsing I came across the following often shared quote, attributed to Baldwin. It took over an hour to determine and locate its original source. This New York Times obituary does not give its source. Several pieces attribute it to ‘The Fire Next Time’, but it was published much earlier, when Baldwin was 31 years old, in Harper’s Magazine in 1955.

“I imagine one of the reasons people cling to their hates so stubbornly is because they sense, once hate is gone, they will be forced to deal with pain.”

— James Baldwin. “Me and My House” Harper’s Magazine; New York, N.Y.211.1266 (Nov 1, 1955): 54.

The essay is about his fraught relationship with his father, and like everything he wrote is deeply insightful. The context of that quote is important, as is the essay as a whole. I reproduce it here and fully recommend you read the whole thing. Inspirational quotes are too often torn from the context that give them meaning.

P.S. Another google revealed that the reference for this quote was, somewhat embarrassingly, very readily available at Wikiquote. This was perhaps lesson that some things at least aren’t as difficult as first they seem.

Sources and streams

Marx remarks somewhere that the tradition of all dead generations weighs like a nightmare on the brains of the living. And so it goes with one of academia’s most arduous traditions, the literature review.

I’ve decided to do something a little unorthodox for a piece I’m writing for my upgrade (the equivalent of orals in the US) and trace the sources of all the claims that a central review paper makes, so as to understand how we know what we know.

The topic and review paper I’ve chosen aren’t really worth remarking on here. Rather I want to describe the way that doing this exhaustive and exhausting process maps, metaphorically at least, onto finding the source of a river.

Each reference which is made in the paper forms a stream which connects it to other papers and references. Some are easy to trace back to their source, whether it be an empirical study or survey. Other claims are made without reference and rely on our trust of the person making it.

There are moments when the stream disappears underground and reappears somewhere unexpected. This happened explicitly in a case where the reference pointed to the wrong paper, only for it to become clear that the origin of this incorrect reference was itself a third paper referenced later in the text.

Other times when papers don’t explicitly cite their source, especially in papers written by  non-academic bodies like government agencies, the stream gets lost and mixed up with all the other citations form the paper, forming something like a lake.

Perhaps this is all obvious to post-structuralists, but this process has been a lesson about how knowledge doesn’t fall into discrete individual quanta that can unproblematically followed back to their origin. There’s much more mud and confusion in the water. But the water definitely exists, even if the course it takes isn’t always obvious.

This is a map of the Nile and its drainage basin ( This is a map of the Nile and its drainage basin (

P.S. In the spirit of good citation practice, here’s where that quote at the start comes from here:

Grenfell Tower

One of the central reasons I became interested in energy in the built environment was because of the significant number of people in the UK who live in buildings which are not fit for habitation. Despite the vast wealth of this country, the provision of safe and healthy housing for everyone, especially the poorest, still alludes us. This is fundamentally a political problem – the technical expertise to build adequate housing has existed for decades – efforts to provide it are persistently undermined by those who seek to cut corners and maximise profits.

The tragedy at Grenfell Tower in Kensington is likely to be the single greatest loss of life in a domestic building in the UK since the Blitz. Yet it is not an isolated incident. In 2009, six people lost their lives in a fire at Lakanal House in Camberwell. The loss of life was entirely avoidable. Early signs from Grenfell point to a catastrophic combination of cost cutting, aesthetic pressure from rich neighbours, and a total disregard by the local and national authorities of the warning signs which the residents persistently raised.

I won’t be able to adequately address the grief, the loss and the anger of the residents and their loved ones in this blog, but neither could I pass over them in silence. It will require the persistent focus of those working in subjects related to the health and safety of buildings to ensure the voices of those effected are not silenced. We won’t have finished our task until events like those at Grenfell are impossible.