Does Size Matter?

For all of our strengths, there is one concept that we as humans are unable to grasp – scale. We perceive the world around us relative to ourselves, but how can we gauge where we stand in the grand scheme of things? If grains of sand are small and mountains are big, what lies on either side of that scale?

Let’s start by building up the ladder from the bottom rung.

Singularity

A singularity is a point with no dimensions. No length, no width, no height.

We think that singularities might exist in places like the centre of black holes, where all the matter is compressed into one infinitesimal point. However, this is little more than science fiction, since the laws of physics don’t apply to such a scale.

Planck Length: 1.6 x 10-35 Metres

The ‘Planck Length’ is a theoretical length where the laws of physics become relevant.

For reference, the notation:

1.6 x 10-35 metres

Means that the decimal point is moved to the left 35 places.

= 0.(35 zeros)16

If there was no minus sign, the decimal point would be pushed to the right the same number of places, resulting in a really big number instead.

Unfortunately, our theories of gravity and quantum mechanics break down entirely at distances less than the Planck Length, so let’s jump ahead to some more familiar examples.

Atomic Size: 10-10 Metres

Clocking in at around ten million billion billion Planck Lengths, we arrive at the average size of an atom. Atoms themselves are compound particles – they consist of electrons, which as we understand them are fundamental particles, as well as protons and neutrons, which are made up of smaller particles known as quarks.

Interestingly, most of the atom is empty space. If we scaled up an atomic nucleus to be the size of a basketball, the electron would orbit at a radius of a few kilometres!

Minimum Size of Human Comprehension: 10-4 Metres

The smallest thing visible to the naked eye is approximately the width of a human hair, or 0.1 millimetres across.

Interestingly, this actually isn’t the smallest thing humans can perceive. Our sense of touch is far more refined, and studies have found we can detect nano-scale wrinkles (10-9 metres) on a seemingly smooth surface with our fingertips.

Blue Eyes‘, by Michael Dawes on Flickr, Licensed under Creative Commons

Size of a human: 2 Metres

Humans clock in on the scale at around a trillion trillion trillion Planck Lengths. For some perspective, the virus organism which causes the common cold is 3 x 10-8 metres across, so we are bigger relative to them than the planet earth is to us.

Maximum Size of Human Comprehension 102 Metres

The largest objects we can properly comprehend are things like buildings or trees. However, even the tallest building ever erected – the Burj Khalifa – is almost a kilometre tall, which is so big that we can only understand it intuitively through another measure: time.

For example, if you were to drop a coin off the top of the Burj Khalifa, it would take almost exactly 13 seconds to hit the ground.

We’ve reached the limit of human comprehension, but we’re still only thinking locally!

California Redwood Trees are some of the largest flora on earth,
note the size of your humble author for scale.

Diameter of the Earth: 107 Metres.

Our humble little earth is around 12 thousand kilometres across. Pretty substantial compared to us humans, but in the grand scheme of things we’ve still barely begun.

Jupiter is so large that you could fit up to 1,300 Earths inside it, and the sun can fit around 1000 Jupiters!

Scope of Human Influence: 1013 Metres ≃ 0.001 Light Years (Ly)

Launched in 1977, Voyager 1 left the confines of our solar system in August 2012, and has been venturing out into interstellar space for the last 7 years.

It is the furthest any human construction has ever been from Earth. Even still, while it has already been travelling for 40 years, it would take another 74,000 years to reach our nearest neighbouring star, Alpha Centauri.

Size of the Galaxy: 1021 Metres ≃ 100,000 Ly

Our star is but one of many in the Milky way galaxy, which is so large that it takes light over a hundred thousand years to travel from one side to the other (since light travels at 1 Ly per year).

But just as our sun is one of many stars in the galaxy, our galaxy is one of an estimated 2 trillion galaxies in the observable universe.

The Hubble Ultra-Deep field looks into the distant expanse of our universe.
Every prick of light in this photograph is another galaxy, far far away.

Hubble Ultra-Deep Field. Photo Credit: NASA, STScl, ESA

Size of the Observable Universe: 1027 Metres 93 Billion Ly

We can only see far-off stars and galaxies in the universe if the light has had time to travel and reach us.

Since the universe is only 13.7 billion years old, and light travels at a finite speed, we can only see things up to a finite distance away.

However, this 93 Billion Ly is just the part of the universe we can see. There’s nothing to say the universe isn’t much, much bigger than this – just that we will never be able to see it.

Existential Thoughts

The length scale of the universe spans from the tiny Planck Length to the vastness of the observable universe, but we can only perceive a small fraction of this scale.

It’s incomplete to consider our place in the universe without taking into account both the micro, and the macroscopic world. However, the sheer incomprehensibility of the numbers involved makes any discussion of scale big or small essentially meaningless to humans.

If anything, all we’ve managed to prove is that size doesn’t matter, it’s what you can do with it that counts.