There are plenty of things that are hard to understand.
Quantum mechanics.
Tax returns.
Anyone who doesn’t love 80s movies.
But occasionally, we come up against something, not just difficult,
but literally beyond our understanding.
Something our brains simply aren’t wired for.
And my favourite example of this is scale.
Our brains have evolved to make sense of things we experience -
so some sizes we can understand pretty easily.
Beyond that, our imaginations can get us a bit further,
but pretty soon we hit the limits of what our brains are capable of comprehending.
I can tell you that a quark, one of the smallest things in the universe,
measures one attometer in length
- a billionth of a billionth of a meter -
but that doesn’t really mean anything to us,
it just sounds impressively tiny.
So when it comes to understanding
the extremely small or the absurdly big
we don’t really stand a chance -
our hardware simply isn’t up to the task.
So now that that’s understood...
Let’s try anyway.
Imagine that you’re standing directly outside the Empire State Building.
In your hand is a smartphone, about 10cm long,
and on the ground in front of you is a 2mm grain of sand,
made up of around fifty quintillion 0.2 nanometre wide atoms,
one of which contains a quark that we want to get a closer look at.
We’re going to do that by scaling everything up.
Without warning, the phone in your hand expands
to the height of the Empire State Building.
The top of the building itself disappears into the clouds,
and the International Space Station drifts past the windows of the 29th floor.
Back on the ground,
our grain of sand is now a towering boulder the size of a house.
This is a pretty dramatic shift of scale,
so it’s a little frustrating to find that
the atom containing our quark is still less than 0.0008mm across.
So, let’s go bigger.
The ground shakes as our
two storey grain of sand becomes a 102 storey grain of sand.
The smartphone now towers nineteen kilometres above Manhattan.
The Empire State Building reaches almost a fifth of the way to the moon.
The atoms...
are still less than 0.04mm long.
Our quark isn’t even visible under a microscope.
Ok then, let’s really dial it up.
This time, our atom expands to the size of the Earth.
The grain of sand is now about half the width of our solar system.
Your phone is over 6 trillion kilometres long,
and the Empire State Building is now easier to measure in light years.
2566 of them, to be precise.
Back on Earth we can finally get a good look at the quark, which is...
about six and a half centimetres across.
Clearly there’s a fundamental problem here.
To get a grip on the tiniest parts of an atom
- itself smaller than we can conceive -
we have to think about that atom on the scale of a planet,
which is bigger than we can conceive.
But in doing so
every other part of our frame of reference disappears off the top of the scale,
and we’re back to... nothing meaning anything.
A grain of sand reaching to the edge of the solar system is meaningless
if we don’t understand how big the solar system is.
So, let’s take things in the other direction, and scale down.
The Earth shrinks from almost 13,000 kilometres across
to the original size of the grain of sand.
The moon is a 0.5 millimetre speck of dust 6 centimetre away,
and the sun, originally a 1.4 million kilometre wide
ball of burning plasma 150 million kilometres away,
is roughly the size and distance
of a bowling ball at the other end of a bowling lane.
At this scale, Pluto is about a 10 minute walk away.
But to trek halfway across our solar system,
which was how big the grain of sand got,
we’d need to walk for another 9 and a half hours.
After that, if you fancied popping over to check our nearest star Alpha Centauri,
it would be a quick stroll from New York to Las Vegas...
and then most of the way back.
But even that counts as nearby.
at this absurdly reduced scale,
the edge of the Milky Way would still be over 37 million kilometres away.
And just like that, we’re back into the realm of the inconceivable.
The universe is unfathomably large, made of unimaginably tiny parts.
And trying, however hopelessly, to get our heads around that can be really fun,
but there’s also a serious and important side to this topic:
Every day we are bombarded with large numbers.
Millions of jobs, billions of people,
trillions of dollars.
Numbers so large that
just like the size of a quark or the width of our solar system,
we have no intuitive sense of what they really mean.
What’s more,
we hear these figures so often that they can start to sound a bit interchangeable,
which is crazy.
A million seconds is about 11 and a half days.
A billion seconds is just over 31 and a half years,
and a trillion seconds is a mind-bending 31 and a half thousand years.
When you think about it like that, it’s hard to imagine anyone mixing them up,
but it happens surprisingly often,
because we become accustomed to using these numbers
without a frame of reference.
Designer and writer Eames Demetrios said that
“not understanding scale in this day and age is a form of illiteracy”.
And while a true, intuitive understanding of gigantic numbers and galactic distances
might be beyond us,
it’s important we at least try.
Because while the size of an atom or the length of a light year
might not have any immediate bearing on our lives,
the millions, billions and trillions that we’re confronted with every day, do.
And not understanding those,
means not understanding the world we live in.