# Landmark Numbers and Bad Number Analogies

Did you know between London and New York
you could fit over 556,000 orcas
nose to tail all the way across?
Which means London and New York
are roughly 556 Kilo Killer Whales apart.
Now that is a bad number analogy,
but what is a good number analogy?
who you may know from BBC Radio 4's "More or Less"
and they discuss good ways to use statistics to understand the world around us.
But I didn't want to interview Tim in a way that would be dangerous.
I thought "wouldn't it be great if I could have a chat with Tim",
but I want to do it safely.
If only there was some kind of standardised unit
that could make sure we stand a safe distance apart.
[bell dings]
And so I'm joined by Tim, exactly...
one double-decker bus away
and we're going to talk about
But before that can we just agree when it comes to an intuitive sense of distance...
the double-decker bus is good.
-It's great. I mean this is not only a beautiful bus... -Amazing bus.
but it's just a beautiful way of understanding certain kinds of quantities.
So when I was a child, I would read all of these books about dinosaurs,
and they would always compare the size of dinosaurs
to the size of buses and it works so well because...
-every child knows how big a bus is. -Yeah.
Yeah, I've never seen a dinosaur, I've seen buses and they're about the same size.
So it's really helpful. It's really helping me think more clearly about something that I've never seen.
I saw a news story a couple years ago
where they looked at an asteroid which was going to be very close to Earth.
Maybe a meteor, and they said it was about the size of a double-decker bus.
I was like "oh, perfect, I instantly have a sense of how big that bus is."
And I should make it very clear for people around the world:
in the UK, the preferred systems of units go
metric, imperial, double-decker buses.
-Yeah. -There's a long tradition of using buses and I'm all for it.
and in your line of work you come across some horrific ones.
Yeah, well I'm an economist so I'm often confronted with...
examples of people measuring dollar amounts or amounts in pounds. Financial amounts.
So the, you know, the budget deficit of such and such a country, for example.
People get very very excited about budget deficits for some reason,
especially when they're thought to be too big.
And so you say okay, the budget deficit: if you turn that into dollar bills
and if you had a stack of dollar bills, that stack of dollar bills would be...
whatever, it would stretch to the sun or stretch to the moon or-- and it's not helping.
It's not helping. I mean, there are so many reasons why it's not helping.
One reason is-- well Matt, let me just ask...
How many dollar bills is that many dollar bills? Any idea?
Umm, two... 200.
-It's about 10,000. -10,000! I'm way off.
Well, yeah, so it's not-- this is why it doesn't help.
Um, I mean, of course I had to check so 8,000 dollar bills to the yard.
So about 9,000 dollar bills or 8,500 to the meter.
But you know the fact that even to start making sense of the analogy
you immediately had to go and google 'how many dollar bills in a metre?'
-Not helping. -And who has a big stack of dollar bills?
-I certainly don't. -Like if it was tens, it's an order of magnitude less.
-Hundreds, another order of magnitude less. -Yep.
To say nothing of the fact that you...
probably don't intuitively know how far away the moon is.
Exactly and I get really annoyed at any kind of..
solar system analogy to try and make sense--
Like I haven't got an intuitive sense of a debt of billions or trillions of dollars.
But I haven't got an intuitive sense of how far away the moon is. It's not helping me at all.
Yeah, it's... it's up there
you've got some fantastic examples of something I realise I've been doing,
but I didn't know the name of
-which is landmark numbers. -Landmark numbers.
It's a great idea. So, the paternity of this idea--
So on my radio show "More or Less"
we often ask 'well, is that a big number?'
You know, how do you compare this number? Is it big? Is it small?
And one of our loyal listeners, a gentleman called Andrew Elliott
liked the idea so much he wrote a book called "Is That a Big Number?"
And in his book, he introduced this idea of...
-landmark numbers which I like so much... I stole it back. -You stole it back.
So it's now in my book "How to Make the World Add Up" as one of many many tools to make sense of the world.
And the basic idea of the landmark number is...
You won't you know, if you're confronted with some kind of claim, some sort of quantity,
you need to make sense of it and you can make sense of it by comparing it with an intuitive quantity.
So landmark number is using a landmark to be able to orientate yourself.
-So you're in a new situation, you've got a new number, -Yeah. Yeah.
How big is that asteroid? How big is that dinosaur?
and you know how big a double-decker bus is.
So it's that principle
and I advocate that everybody should basically memorise a few simple landmark numbers.
You don't need many.
And then, it's actually not very complicated when you see a claim to go 'well, how does that compare with...
you know, something else that I'm carrying around in my head.'
So what we thought we would do is, Tim and I are going to compare our favourite landmark numbers
that we already have in use.
There may be some overlap. If we miss any, put them in the comments below.
We'll try and assemble...
like the minimal toolkit of landmark numbers everyone should keep on the inside of their head.
-Absolutely -And I...
The first one I realised I just intuitively always keep in mind
is that the population of the US is about a third of a billion
which I find very useful.
And the UK is a bit shy of a tenth of a billion.
It's about what, 60... 70 million.
Yeah it's about-- it's actually two-thirds of a hundred million right now.
-It's about 66... 67 million. -That's handy.
Uh, yeah, it's handy if you're that kind of person
but the point is-- so you say it's really handy to...
to know that the population of the US is a third of a billion.
I think everybody should know roughly the population of the country they live in.
But we should explain why that's handy.
Because then, you can then start doing some very very simple sums.
So somebody says 'oh this is going to cost a billion dollars.'
You can immediately go 'well, that's three dollars per person.' Immediately.
Exactly. Whenever I hear any kind of government spending or cost or investment in the US
I multiply it by three and go 'well, there's that much per person'
-because I have an intuitive sense-- -Multiply it by three and then take a billion off.
-Oh yeah, that's implied. -And divide by a billion.
-And so... who would ever make that mistake? -"That's implied."
Who would make that mistake? Um, so, but then I have an intuitive sense of one human
-and one human having some money. -Yeah.
And that makes way more sense for me as soon as I put it in terms of per person.
A great recent example: so Matt Hancock, who is in charge of the healthcare system of the UK...
He recently said, if everyone in the country who's overweight
lost five pounds
then the National Health Service of the UK would save a hundred million over five years.
And people were emailing me and saying 'well how does he know that,' 'that sounds like nonsense to me.'
But you can, with landmark numbers you don't need to ask 'how does he know that.'
You don't need to ask whether it's nonsense. You can just ask 'well how big is that sum of money?'
So we can do it knowing the population of the UK, so 100 million...
-[Tim] We know that's £1.50 per person. -[Matt] Yeah, easy.
[Tim] It's over five years because that's how politicians always make numbers look bigger.
[Tim] So £1.50 over five years. This is not hard maths, right?
You don't need to break out the calculator. It's 30p per person per year.
So what he actually said was,
if basically everybody lost some weight, it would save the National Health Service, 30p per person per year.
So to which, my response is, 'huh, yeah okay, I'm surprised it's not a bit bigger.'
I do it the other way around I went-- whenever I hear 'so much over n years'
-to make it sound bigger -Yeah.
I just divide by n to get my annual amount, in which case was 20 million.
And then my rule of thumb is, 'is it bigger or smaller than the population?'
I'm like, well 20 million's less than 67 million
that we've got at the moment. So it's a sub-pound amount per person.
And once you're less than a pound, you're like, we don't need to worry about the decimal points here.
I mean, the point here is... this is not hard sums.
Okay. These are not difficult numbers to remember.
They're not difficult sums to do.
But you can always google it.
And you can always get out a calculator or get out a spreadsheet if you're not confident.
But usually you don't even need to do that.
And that's what I love about, when people came to you with the Matt Hancock stat,
before you bother looking into it, you can just check...
-should I even bother. -Yeah.
And so you know if it's even worth the effort to check Matt's stat.
Yes, and Matt just to be clear: Matt Hancock. He's not my favourite Matt.
I love the fact you phrased that to not imply I AM your favourite Matt.
Just that Hancock is not.
-Well... -I'll take it. That's fine. It's fine.
I also keep in my head...
human days per year.
So in the US,
it's 120 billion human days per year
-if you multiply the population by 365 and a bit. -That's good. That's a new one on me.
In the UK, 25 billion human days per year.
So whenever I hear 'this is going to cost £50 billion'
I'm like, in my head, I'm like 'oh, okay, that's like £2 per person per day.'
And so then I can get that as a, kind of, like a budget...
-regular spend. -Yeah, it gives gives you a sense. So...
another one that I really like, because I like skyscrapers,
is the height of the Empire State Building. So this is just totally changing it up
but height of the Empire State Building is, if I remember rightly, 381 metres.
So like 200 metres is already a pretty tall building,
a kilometre is-- well, that's really big, that's bigger than any skyscraper.
And I've immediately got a sense because I've been there. I've seen it.
Even if you haven't seen it, you might have been there in the-- seen it in the movies.
You just get a sense of how big this thing is,
and that gives you a sense of, well, how big 400 metres is.
Another number I keep in my head, I don't know how useful this is,
is I remember a human lifetime is roughly 30,000 days.
and I know that because I celebrated my 10,000-day birthday...
-pretty much within a couple years of before I turned 30. -[Tim] Right.
And so whenever I am given a thing of an amount of time or whatever I go:
'Okay, but your life is 30,000 days.'
And you can then, that's what you've got.
I can then use that to contextualise other lengths of time.
Yeah, that's... I like that one even if I'm now having an existential crisis.
Actually, it reminds me. Another simple way of getting your units right,
-It's just how many seconds is that? -Oh, yeah.
So this is...
in nerd land, this is a very popular trick
-[Tim] but a million seconds is I think about 11, 12 days. -[Matt] Yeah.
[Tim] And a billion seconds, which sounds very similar, doesn't it? That "million" "billion".
A billion seconds: 32 years-ish and then a trillion seconds, obviously 32,000 years.
So really-- I was actually talking to my son just yesterday. He had the Guinness Book of Records.
And he asked me who the richest man in the world was. He had the answer in front of him.
It's Jeff Bezos of Amazon. And so we just were talking about...
-His wealth. -Yep.
He's over \$100 billion, and I said well, let's think about that in a dollar a second.
How much is a million dollars a dollar a second? How much is a billion dollars a dollar a second?
How much is Jeff Bezos worth a dollar a second?
And really just-- really got hold of just how much money it is and the answer is because we...
So a billion dollars a second, it would be 32 years. So he's got-- he's got more than \$100 billion.
So then you're about 3,500 years a dollar a second
to get everything that Jeff Bezos has got, and at that point my son, who's only nine years old,
he's like 'all right. Yeah, I got it. It's a lot of money.'
And like a human lifetime is about a third of a hundred thousand...
and if they've got a hundred billion, that's a million more.
So he's making across his life. That's...
what, \$3 million a day?
-That's insane! -Yeah, so that's-- yeah, that's another way of doing it.
I mean obviously at this point we're starting to,
you know, we starting to get deeper into the weeds
but the point is, once you start realising that there are these comparisons out there,
that it's not very hard to compare one thing to another.
And once you have a centre-- I know how long a second is. I know how long a day is.
I know how big a bus is. I know how tall the Empire State Building is.
You know, I know what £1 in my pocket feels like.
You've got these numbers, they're our friends.
And you start comparing them to numbers that you don't know so well.
And everything just makes more sense and it's nothing technical about it. It's nothing hard about it
The maths that my son who's nine years old...
has already learned at school is enough.
Easily enough to do these operations.
I love the way you describe these numbers as being our friends.
Apart from the fact that's how I view all numbers
but it's like you meet a new stranger number and you can:
oh it's okay, I can get a friend of mine to give me an introduction.
To get to know them and understand if they're worth...
-Worth getting to know better. -Yeah. Yeah, you're looking for that common ground.
-They're-- we've gone super nerdy. haven't we Matt? -It's fine.
The moral of the story is you've got to take it in intuitive steps.
Otherwise, it just takes one unintuitive step in the chain...
-and the whole analogy is broken. -Yeah, and--
Yeah, and the question is: what are you trying to do
because very often the people who are saying
'oh this stack of dollar bills would reach all the way to the sun'
They're trying to make you upset about something or they're trying to make you impressed by something.
They're trying to engage an emotional reaction.
And one of the key principles in the book is:
Don't engage your emotional reaction. Try to calm down.
There's so much anger out there or-- not always anger
but just people trying to get you excited in one way or another.
And that doesn't help you understand anything. By all means get angry. By all means get excited.
But first understand what is actually happening
and the way I like to use landmark numbers
is to keep that intuitive sense so I get what's going on.
The reason that so many of the comparisons that we see are unhelpful
They want you to hurry up and feel something.
Tim's fantastic book is out on the 17th of September in most of the world
and next year in the US.
Of course, if you'd like to pre-order it on Maths Gear we would hugely appreciate that.
Tim is going to sign loads of copies.
And on the back there is a quote from me
So if you want, optionally, you can get a copy that I have also signed the back of.
The link is in the description below.
And finally, if you do have a landmark number [Matt rings bell]
you would like to share, please do put it in the comments below.
I will go through and pin whichever one is my favourite.
[Stand-Up Maths theme]
Thanks for watching! If you would like more Tim Harford,
Numberphile have simultaneously released a video where Tim tells a story about,
well, I think it might be the greatest statistical story of all time.
It involves storks. It's out now and you should definitely go watch it.
[Stand-Up Maths theme continues]
Also pre-order the book.