“Three drops of blood in your bath”


Click play to listen to the full chapter:


So, this happened …

Imagine a 4 year old girl telling her kindergarten class, “People waste one trillion of food every year! One zero zero zero zero zero zero zero zero zero zero zero zero. That’s 1 with 12 zeros. And poor people don’t even get food.

I had taught my younger daughter to say that, because she had to prepare a speech for school. To increase her environmental awareness and compassion, I chose the topic of food waste. There had been a recent article on the topic, and I decided to use that as the basis for her minute-long speech.

As an actuary, I’ve spent a lot of time with numbers. And yet even I struggled to internalize what one trillion kilograms (two trillion pounds) of food waste looks like. Certainly there was no way a 4-year old was going to truly “get it” (although you could see from her arm-waving while presenting, that she was nevertheless trying hard to convey to her classmates that it’s a big number!)

And since we’d been practising her speech for a few days, the idea of contextualizing numbers remained forefront in my mind.

So it was no surprise that when my 9 year old started talking about the Sun for her school project, I was already thinking how best to communicate how big that ball of fire really is.

Based on a quick glance at the NASA website, I pointed out to her that the volume of the Sun is a “1” followed by 18 zeroes, and the volume of the Earth is a “1” followed by 12 zeroes. Those numbers did not stir her. And even I, an actuary, couldn’t quite get a feel for the relative size of the Sun and the Earth.

Then I highlighted to her that the Sun’s volume is about the same as one million Earths. This new number helped me start to appreciate the difference, but she remained impassive.

So I brought out my phone, spent five minutes searching and calculating, and then announced to her: “If the Sun had the same volume as our bathtub filled with water, then the Earth’s volume would be the equivalent of three drops of water in that same bathtub.”

That’s when I could see her brain engaging. It was at that point that she truly appreciated the relative size of the Sun and the Earth. Success!

Suddenly, “Daddy,” my 4 year old said from behind, pulling on my sleeve. She’d heard the discussion of three drops of water in the bath, and squeezed herself into the conversation, “Can we fit one trillion of waste food in our bathtub too?”

Hmmm, looks like I’ve got a bit more work to do, to explain 1012 to a 4 year old.

Simple Definition

Three drops of blood in your bath: This is the #hashtag we give to the approach of taking hard-to-appreciate numbers, and putting them in an easy to understand (and remember) visualization.

Summarizing what it means

Humans are well known for struggling to appreciate what very big or very small numbers really mean. It’s not difficult to say the number, but we struggle to feel the number.

And I’m not talking about where we simply don’t think about the number that we have been presented. That’s a different issue, which you can read about in #[The field with a negative length].

To fix this, we need to do the following:

  1. Appreciate that numbers don’t always convey magnitude
  2. Care enough to want to communicate better
  3. Find a numerical equivalent that is easier to “get”
  4. Create an image that is vivid
  5. Share it in an engaging and memorable way.

You can apply this when dealing with both children and adults, as age doesn’t “cure” this problem. You should use it when leading, selling, negotiating, or any form of communicating.

There are clever and dumb ways of doing this. There are memorable and forgettable analogies that you can draw. We’ll explore the “how” in more detail, to help you be a powerful and effective communicator.

You can start putting this into action from today!

Discussing what it means

Numbers are not enough

It’s useful to start off with a few examples to remind you that knowing the number doesn’t always help you understand what it actually means. Challenge yourself to answer these …

  • The British Government announced in November 2020 that they are increasing the military budget by £2 trillion – does that sound reasonable, or should it be more? (Actually, the real increase was £20 billion – but these are such big numbers, did you even realize I was giving you a fake number that was 100 times too big?!)
  • How much will it cost your own government (wherever you live) to roll-out and complete the program for vaccinating everyone twice against  Covid19? Is it millions of dollars? Billions? Trillions?
  • You’ve got $100,000 invested in a fund, and you’ve just learned that they will increase their fund management fee by 0.25%. Is that a big problem?
  • It’s claimed by one news article that the 2004 Indian Ocean earthquake ‘bumped’ earth about one foot off its N/S axis … does this seem about right? Or a complete exaggeration?

Hopefully the examples above highlight that numbers are not always enough for you to appreciate the scale or the significance of the message.

And here’s an example directly from #HashtagYourLife. Read one bullet point at a time, and keep going until you can answer the following question: The #HYL chapter called #[One push-up a day] – is that a long chapter or not?

  • It’s 11,000 characters – is that a lot, for a chapter?
  • What if I say it’s 2500 words – now do you know if it’s a long chapter?
  • Or if I tell you it’s made up of 75 paragraphs – does that help you judge more easily?
  • Actually, it’s about 6 paperback pages long, without pictures – does that sound long or short?
  • You can print it on 3.5 pages (A4/Letter) – is that long for a chapter?

Again, I’ve presented five ways of describing the length of the chapter – some are useful in deciding if it’s a long chapter, and others are meaningless. And in spite of the fact that all five descriptions are correct, probably only 2-3 are useful.

(By the way, some people will think 6 paperback pages is a long chapter, and others will think it’s short. That is a completely different issue to what we’re discussing here, and is addressed in #[My Neanderthal is better].)

So how do you go about taking something that’s hard to internalize, and make it clear and memorable?

Firstly, you need to express the number as something that can be appreciated more easily. Secondly, you need to create an image that makes that number clear and memorable.

Let’s explore some examples together …

Option 1: Break the number down

In the case of my 4-year old’s speech about food waste, it’s hard to know if one trillion kilograms a year is a lot or not. (I mean, of course it’s a lot – but is it more than you’d expect?). So we break it down to understand it better:

  • One trillion kgs (two trillion pounds) a year
  • Divide it by 7 billion (the number of people on Earth) and you get 143kg per person per year
  • OK, but assume half the world doesn’t waste any food, and the other half does. So now it’s 286kg per wasteful person, per year
  • Assume they waste equally every day, so we get 0.8kg per wasteful person, per day.

We’ve taken a number that is really hard to internalize, and turned it into just under 1 kilogram (just under 2 pounds) of food waste per person per day, every day, assuming only half the planet wastes food.

This I can contextualise better! Can you too?

Option 2: Build the number up

Earlier on we saw the example where you have $100,000 invested in a fund, and you’ve just learned that they will increase their fund management fee by 0.25%. It sounds like a small number, but the question is … what does it mean to your actual fund?

You don’t need to check the maths, just trust me when I tell you this …

  • Assume you’re going to earn 5% on this fund for the next 20 years
  • Then reduce the returns by the 0.25% increase in fees
  • This will reduce your total fund by about $12,350 after 20 years, which actually sounds like a lot
  • Overall, this is nearly a 5% reduction to the final value of your investment!

As you can see, we’ve taken something that seems small, then zoomed out, and shown that actually the impact is quite  big.

Next step: Create a vivid & memorable image

Droplets in the bath

My older daughter is 9 years old, so I was very careful to talk about ‘water’ when comparing the Earth and Sun’s volume. I ended up with “Three drops of water in the bath”.

But at the time, the visual that came to my mind was actually three drops of warm blood, dripping slowly and silently into the water, spreading color from the point of contact, slightly darkening the water.

Because of the nature of the image of red blood in clear water, months down the line you will still remember the scale implied by the image. It’s a few drops of blood in the water. Not a cupful, not half the bath. Just a few drops. That’s part of what makes blood more memorable than water. A few drops of water or a few cups of water in a bath filled with water … the visual is basically the same, and the ability to differentiate relative size later on is … diluted.

The image of blood, however, is quite morbid for a 9 year old. Which is why I spoke to her about drops of water in the bath rather than blood. And it worked well enough.

When telling stories, never forget who your audience is.

On the assumption that you, dear reader, are not 9 years old, then if we are to be consistent with the goal of this chapter (vivid images that are memorable) we really must call it “Three drops of blood in your bath”.

Not even just the bath, but those drops of blood are you in your bath. Urgh.

Food waste

We understood earlier that it’s hard to appreciate what one trillion kilograms of food waste is, so we turned it into 0.8kg (1.8 lbs) per wasteful person per day. That allows us to understand the scale, but it is not particularly memorable. So the goal now is to create an image that sticks.

As mentioned above, we begin by changing the number to a ‘scale’ that works.

This number of 0.8kg / 1.8lbs is the equivalent of 24kg (53 lbs) per wasteful person per month. Well, this is about the bodyweight of a young  child. So now we can think of this food wastage as follows:

  • Imagine that every wasteful person in the world (that’s half the global 7 billion) throws away the bodyweight of a young child every month. Every single month – the bodyweight of a young child, discarded as food waste. Month after month.

That’s a much more vivid image, with the appropriate emotions (throwing away a human life??) to match.

And it doesn’t matter whether a young child weighs a little more or less than the number I used, the point is we can suddenly “feel” how much wastage this is, and the visual is horrible. Which is exactly the point. It’s certainly much more effective than quoting a big number that carries no emotions with it.

Clogging your arteries

Sixty years ago, there was an article in Time Magazine by Ancel Keys which told the world that a diet of saturated fat will cause cholesterol to clog your arteries and you’ll die of a heart attack.

This idea has, in recent years, been repeatedly proven wrong by so many papers in world-renowned medical journals. But if the scientists are telling us it’s not true, then why won’t the idea go away? Why are people still obsessed by low-fat diets, when Ancel Keys was so horribly wrong?

Part of the reason is that, over the years, this concept has been backed up by the most amazing visuals, consistent with the principles of “Three drops of blood in your bath”.

Can you picture it now? You’re eating a bacon sandwich, a thick layer of butter is oozing out, and the fat from the bacon is dripping onto your plate? And once you’ve eaten it, it goes into your blood, then starts to clog up your arteries by sticking to the walls of your blood vessels. You can almost feel your heart contracting with each mouthful, as the heart attack becomes imminent …

Absolute nonsense, though.  But very graphic, and most certainly very memorable. And that is why the idea has stuck. We believe it because we can imagine it. It feels so real to us.

Alien spaceships

And just for fun, let’s finish with a quote from “The Hitchhiker’s Guide to the Galaxy” by Douglas Adams. It’s not vivid, in fact it’s the exact opposite of vivid! But it is very memorable:

“The ships hung in the sky in much the same way that bricks don’t.”

If there is one lesson to get out of this fun quote, it’s the same as what you learned in #[Blue cheese & Apple ice-cream]: it’s OK to make it unusual, as long as it makes sense.

Now what?

This chapter exists because:

  • We need numbers when we’re communicating
  • Numbers are often hard to picture, and usually impossible to remember
  • People are terrible at communicating numbers.

Therefore, this chapter teaches us two key steps in fixing these problems:

  1. Turn the numbers into something that can be understood
  2. Create a vivid image that adds to the appreciation, and which makes it memorable.

This is something that you can start doing today. And the more you practice, the better you will get. To get yourself off to the best start, do the simple exercises in the next section.

Quickly, begin it now, before that awesome idea that you’ve got on the tip of your tongue evaporates in a puff of smoke …

Making it personal

Pretend you’re in sales. In fact, pretend you’re selling ‘selling’! Imagine you are offering a course in selling that costs $10,000 per annum. You are sure that they will be able to generate an additional $100,000 per annum as a direct result of your course. What image can you create that will help your prospect contextualize that price, in terms of what benefit they will in turn get out of it?

Imagine you’re a parent. You want your child to remember that there are 206 bones in the human body. You care less about making your child memorize that exact number, and more about giving them a real feel for the size of the number. What image will you describe?

Imagine you’re applying for a job. The person who left their job was good, but you’re actually great. What visual can you describe to the interviewing manager, that makes them get a feel for what it means to them to finally hire someone great, and not just good?

Imagine you’re writing a book called #HashtagYourLife, which is about helping people label things in their world in order to help them reduce the overwhelm they feel in this complicated world. What image would you describe that highlights the peace & clarity that they will feel, as they start to apply #hashtagging in their own lives?

Now go get out there, and make your ideas come alive!

Related stories

#[Blue cheese and Apple ice-cream]

#[My Neanderthal is better]

#[The field that became a black hole]

Headline Picture Credit