by Rob Eastaway
One of the unsung luxuries of modern living is that we have apparently limitless drinkable water available to us at all times. Yet a huge amount of that drinkable water, which is treated at some expense, is never consumed but is literally flushed away. But how much?
London has a daytime population of around 10 million, including those who travel to the city to work. We can be confident that all of them will use a toilet at least once, and more likely it’ll be five or more times during the day. So we’re looking at 50 million toilet visits in London per day.
Pondering for a moment (but not for too long) on practicalities, all ‘female’ visits are going to involve an individual flush, but perhaps only 25% of ‘male’ visits will do so (the majority of them being at urinals). So we’re looking at, say:
25 million female flushes
25 × 0.25 male flushes
~ 30 million flushes per day.
How much water is sent down the drain during a single flush? It is going to vary from WC to WC,9 but picture filling the tank using one-litre jugs, and even the most eco-friendly flush is going to use up three or four litres. So a very conservative estimate would say that London alone flushes away 100 million litres each day, and it’s probably going to be a lot more.
A hundred million litres is 0.1 billion litres. To put that in perspective, an Olympic swimming pool holds about 2.5 million litres, so every day, toilet flushing in London could empty the equivalent of up to 100 swimming pools – the size of a small lake.
Of course water in itself is environmentally neutral. But the creation of reservoirs inevitably interferes with natural surroundings, because it means diverting rivers, building damns and pumping water. And in times of drought, water being used by humans is water that is being diverted from other fauna and flora.
COWS VERSUS HUMANS – WHICH EMITS THE MOST METHANE?
On the subject of effluent, let’s turn our minds to cows. Why? Because of methane.
Methane is one of the worst greenhouse gases: in fact scientists estimate that, over a 20-year period, methane can trap 100 times more heat in the atmosphere than the same amount of carbon dioxide.
The alarming increase of methane in the atmosphere has largely been blamed on cows, especially beef cattle, whose methane emissions when digesting grass produce monumental quantities of the gas. (Contrary to popular belief, this is mainly through burping rather than flatulence.) That’s why there’s an urgent push to reduce the world’s consumption of beef.
The average cow produces somewhere between 200 and 500 litres of methane per day (that’s a huge figure, not one I felt qualified to estimate at all, so I looked it up – and even official sources vary hugely in the figure they quote).
Cows aren’t the only creatures responsible for methane. Every living creature contributes methane as a natural part of its digestion or decomposition. That includes humans. In the seminal paper ‘Investigation of Normal Flatus Production in Healthy Volunteers’ by J. Tomlin, C. Lowis and N.W. Read (what do you mean, you haven’t read it?), the authors concluded that the average human on a diet that includes 200 g of baked beans, produces about 15 ml of methane per day. To put that in context, remember that the figure for cows is of the order of hundreds of litres per day. So the average cow produces over one thousand times as much as the average human.
There are, of course, a lot more humans than cows (in the UK, seven times as many), but that still means that the total methane output of cows is hundreds of times higher than that of humans. And while the ratios will differ in other countries, it’s reasonable to suppose that the global picture is similar: methane is mainly a cow problem.
Still, there are billions of humans, so how much is the world’s human flatulence contributing to global methane levels?
15 mL × 8 billion h 100 million litres per day.
That’s roughly enough to fill London’s Albert Hall, or the main concert hall of the Sydney Opera House, or – appropriately – one of the old Victorian gasometers that can still be seen dotted around the landscape of Britain.
HOW MANY PLANES ARE IN THE SKY AT THE MOMENT?
In 2016, the BBC ran an excellent three-part documentary called City in the Sky (hosted by Hannah Fry and Dallas Campbell) in which it was revealed that at any time, one million people are flying in a plane. It seems a staggering figure. Many thousands of planes in the air at any time, each spraying carbon dioxide high into the atmosphere. But can this figure be true?
Most of us probably notice at least a couple of planes flying overhead every day, but it is a stretch (for my imagination at least) to picture those few hundred people overhead representing one million constantly in the air across the world.
To start this estimation, you might think first about an extremely busy airport. The one I’m most familiar with is London’s Gatwick Airport. Watching from the terminal I never have to wait long for a plane to take off: I’d guess one plane departs every minute. Those planes might spend anything between 30 minutes and 15 hours in the air, but what’s the average duration of a flight? Maybe two hours?
So if each Gatwick plane is in the air for 120 minutes, and each minute one Gatwick plane is taking off, while one of the earlier flights is landing, that suggests there are about 120 Gatwick planes in the air at any moment. However, planes don’t take off at this rate for all 24 hours of a day. Noise restrictions mean that airport activity is very limited during the small hours. So let’s halve that figure to, say, 50 planes from airports like Gatwick are in the air at any time.
London Heathrow is busier than Gatwick, but the volume of flights tails off when you think about other airports in the UK. Is it reasonable to guess that there’s the equivalent of five Gatwick airports sending out planes in the UK? That would mean that 250 planes that set off from the UK are in the air at any time.
The number of planes leaving a country is likely to be linked to the size of its economy. Rich countries, and those with large populations, will no doubt fly more planes than small, poor ones. The USA is five times as populous as the UK, and richer. It’s also spread over a bigger area, which will increase the need for planes. So if the UK has 250 planes in the air, then the USA surely has 3,000. Of the nearly 200 other countries in the world, we can probably ignore all but a handful – but combine the biggest economies, perhaps they are the equivalent of another 10 USAs? That would suggest something like 30,000 planes in the air at any time. If there are, on average, 50 people on a plane, we get:
50 passengers × 30,000 planes
= 1.5 million passengers in the sky,
which is consistent with that description of a ‘city in the sky’.
The ‘official’ figures for air traffic published online suggest 30,000 planes in the sky is an over-estimate, with a variety of sources suggesting the real figure is somewhere between 5,000 and 10,000 (though this doesn’t account for private and military planes). But even at the low end of the estimate we’re talking about hundreds of thousands of people and millions of tons of metal in the sky above us. And a lot of fresh carbon dioxide being sprayed into the atmosphere, too.
CAN WE PLANT A TRILLION TREES?
According to the National Oceanic and Atmospheric Administration, the level of carbon dioxide in the atmosphere has increased by more than 25% in the last 70 years. It’s been known for over a century that carbon dioxide in the atmosphere magnifies the greenhouse effect, and therefore contributes to global warming.
One way we might reduce the amount of carbon in the atmosphere is to plant trees, as they absorb the gas. By the time a tree has matured, it will have locked away anything up to a ton of carbon dioxide. But how many trees would it take to offset the carbon dioxide that is produced each year?
In 2017, a group of conservation organisations, including the World Wide Fund for Nature, launched a campaign called ‘Trillion Trees’. The idea is to increase the number of trees across the globe by one trillion by the year 2050. This, they reckon, would be enough to compensate for the world’s curren
t CO2 emissions. It is an ambitious and noble aim, though not everyone agrees that even this mass planting would be enough on its own.
But a trillion trees? How can we get our heads around that number?
One way to start is by thinking of some familiar woodland, or a planted forest. I grew up near Delamere Forest in Cheshire. Most of the forest was made up of young conifers. Even in sections where trees were densely packed, I reckon that trees were at least a couple of metres apart. Set out in a rectangular grid, that would mean a hectare of land (that’s 100 metres square) might contain:
50 × 50 = 2,500 trees.
A square kilometre would have 250,000 trees, so four square kilometres – i.e. a square plot of just 2 km × 2 km – would give us about a million trees. That sounds a lot, but remember that a trillion is a million times bigger than one million.
Based on my crude estimate, to reach the target of one trillion trees we’d therefore need:
4 × 1,000,000 = 4,000,000 square km
of densely packed trees to meet the trillion target.
Let’s compare that to somewhere we know.
The area of Wales is roughly 20,000km2. France is a bit more than 500,000km2. India is about three million km2. So we might be talking about new forestry that would cover 20 Waleses, eight Frances or India-plus-a-bit. I’ll leave you to judge whether that sounds like a lot.
There’s another way of looking at one trillion. There are seven billion people on the planet, so that means we need:
1 trillion ÷ 7 billion h 100 more trees
per person on the planet.
Next question: where are we going to plant them? And who will do the planting?
FERMI FOR THE FUN OF IT
We’ve seen plenty of examples where back-of-envelope calculations can have a practical benefit – whether it’s checking out the viability of a business plan, understanding our impact on the environment, or challenging a politician’s statistical claims.
But there’s no need to stop there. There are many Fermi-style questions that are no more than flights of fancy, a serendipitous exploration for those with a curious mind. Some people enjoy Fermi questions as a form of mental exercise – or as a way of passing the time when waiting in a queue. I was drawn into this form of thinking from an early age – whenever we were sat waiting for an event to start (a play, a cricket match, it didn’t matter), my dad would invariably ask the open question: ‘I wonder how many people there are here today’ or ‘I wonder what they make in ticket revenue.’
So, in the spirit of idle curiosity and wanting to exercise skills in estimation, here are some final Fermi questions that have little practical benefit, and their own peculiar fascination.
HOW LONG TO COUNT TO A MILLION?
If you have children, you’ve probably had that joyful moment when they start to count and realise that they could, in theory, keep on counting for ever. How high could they get?
Try counting aloud at a ‘normal’ speed … one, two, three, four … you are probably counting at about two numbers per second. That suggests you’ll get to 100 in about a minute, 1,000 in ten minutes, and one million in 10,000 minutes, which is about seven days if you manage to stay awake. Well, except … it takes longer to say big numbers. Start counting from (say) 243,100: how far do you get in a minute? Instead of two numbers per second, you’re now probably taking over two seconds per number – that’s only a quarter of the speed.
In the count to a million, the vast majority of numbers will be long, multi-syllabled ones. So two seconds per number is a reasonable estimate, which makes two million seconds. Even without sleep, that’s about 25 days (pretty much one month) to count every number up to a million.
If you’re American, you might shave a little bit off that time, because you don’t use the word ‘and’ in your spoken numbers. What a Brit calls ‘One thousand two hundred and four’, an American calls ‘one thousand two hundred four’. I estimate that’s a saving of about 5% of spoken time.10
This time-shaving helped Jeremy Harper of Birmingham, Alabama, who currently holds the world record for counting to the largest number. In the summer of 2007, Harper counted from one to one million. It took him just under three months. Given that he needed to sleep, eat and take mental breathers, it’s impressive that this is only three times as long as our theoretical non-sleep minimum of one month.
Will anyone ever count higher than this? Well, there’s one guy who’s trying.
Count von Count, the Transylvanian Muppet who loves to count, has a Twitter account. Every day, the Count counts another number in words. Sometimes he counts two, or even three numbers in a day. Last time I looked, he was still in the low 2,000s. How long will it take him to get to one million? At this rate, roughly 500,000 days should do it, which is over a thousand years (500,000 ÷ 365 h 1,000). But he doesn’t have to stop there.
He could keep going until … well, until he exceeds his Twitter limit of 280 characters. But how long will that be?
Since the Count counts US-style, he doesn’t have ‘ands’ to worry about. And let’s assume that every time he adds another three zeroes, he moves up the standard scale, from billion to trillion to quadrillion.
The limit on how far the Count can go isn’t the magnitude of the number. After all, the number
90,000,000,000,000,000,000,000,000,000 can be written in just 17 characters: Ninety Octillion! (The Count always puts an exclamation mark at the end of his tweets.)
Before he gets to 90 octillion, however, he is going to encounter numbers that exceed his Twitter limit. For example, let’s pick a random number that’s over 20,000 times smaller than 90 octillion – 3,865,497,871,750,829,425,934,673. That requires 285 characters when written in full, Count-style. (In full, it’s: Three septillion eight hundred sixty-five sextillion four hundred ninety-seven quintillion eight hundred seventy-one quadrillion seven hundred fifty trillion eight hundred twenty-nine billion four hundred twenty-five million nine hundred thirty-four thousand six hundred seventy-three!)
What’s the smallest number that breaks the Twitter limit? To find it, we need to pack our number with the numbers that use up the most letters: seven and seventy. You might even want to see if you can work out exactly which number it will be before you look it up (hint – it’s in the sextillions). Don’t forget there are no commas, and the Count always ends with an exclamation mark. The answer is here at end of the book.
How long will it take the Count to get to this massive number? At an average of two numbers per day, it will take over 50 sextillion days, around 100 quintillion years. As I mentioned earlier, the universe will most likely end in the next few billion years, so I think we can be confident that running out of Twitter characters is one problem that the Count is not going to encounter.
HOW OFTEN DOES A TEENAGER SAY ‘LIKE’ IN ONE YEAR?
Do you ever listen to what people say? I mean, what they actually say, a transcript of the exact words that they use. It’s intriguing to do so, because a conversation that seems fluent is often packed with pauses, corrections and so-called filler words. It’s the filler words that interest me most, because they are used so often: words like ‘um’, ‘you know’, ‘er’, ‘basically’ and – the bête noire of many people – ‘like’.11
Like has been prevalent in English-speaking cultures for over 20 years, particularly among teenagers in the UK and the USA. In fact I would go so far as to claim that there are some individuals who say the word like more often than they say any other word in the English language, ahead of the supposed top 10 : the, of, and, to, a, in, is, you, are and for.
So how often might a ‘typical’ chatty American teenager say the word like in a year?
To make an estimate we need some data – which means capturing some real conversation. One way to do this is to eavesdrop in a bus queue, where there is no shortage of material. Or you could do as I did, and look for a chatty vlog channel on YouTube. Here’s one snippet of a conversation between two individuals:
&
nbsp; Person A: ‘Have you noticed that [name] has three voices, she has her normal talking voice like ‘hi guys how’s it going?’ and then she has her like pissed-off voice where she’s like ‘yo! – like – don’t ever do that again’ and then she has her cutie voice where it’s like [puts on silly voice] a wittle wabbit.’
Person B: ‘I like her cutie voice.’
That snippet of a high-energy conversation lasted 15 seconds. Between them they spoke 63 words, and the word like appeared seven times. They didn’t always use ‘like’ as a filler. Sometimes it was as a preposition (‘like a wittle wabbit’) and sometimes as a verb (‘I like her cutie voice’). But when it comes to ‘like’ counting, they all count.
In the conversation snippet, the word ‘like’ represented more than 10% of the words spoken. I call this figure the ‘like quotient’. A like quotient of 10% is not unusual – if you know somebody who says ‘like’ a lot, they probably use it at this rate. From my informal research, peak use of ‘like’ is around one in five words, or 20% – but even peak-likers don’t usually keep up that rate in all their conversation. Meanwhile, there are many teenagers who barely use the like word at all.
So let’s do the calculation for a chatty teenager with a 10% like quotient.
Let’s assume:
The average conversation rate is around 100 words per minute.
The chattiest teenager in a group (whether that’s two, three or more people) talks for about half the time. So the chatty teenager speaks 50 words per minute, which at a 10% like quotient (L.Q.) is 5 ‘likes’ per minute.
How long does a chatty teenager spend in conversation in a day? Travelling to and from school each day, they may be engaged in conversation for, say, one hour in total. Let’s add in another couple of hours in the day to cover lunch breaks and other social times. That’s three hours – let’s call it:
