We’ve all come across compression at some time or the other. Maybe it’s been physical compression – a magical sponge that springs back to its normal size when released and watered. The suitcase you have to sit on to squeeze the airspace from. The propane in that heavy cylinder you lugged back to plug into your barbeque grill. Or perhaps it’s been software compression; the compacting of data, a thousand holiday snaps chewed and regurgitated by a JPEG or GIF compression algorithm.

The idea of removing extraneous space is very familiar. 

On both a cosmic scale and an atomic scale the observation that everything is ‘mostly empty space’ has been made many times. But it can still be surprising to see just how true that statement is. 

When I was writing my new book, The Zoomable Universe (and naturally this post is in no way, whatsoever a sneaky hint that you, dear reader, might be interested in this book) I decided to use this for some dramatic effect.

What if we could somehow gather up all the stars in the Milky Way galaxy and arrange them right next to each other – like a great box of tightly packed apples? Nature would never allow this of course, gravitational forces would take over and the stars would likely merge into one colossal black hole, with some complaining along the way. But as a thought experiment this is a great way to illustrate the amount of space in a galaxy.

The answer is pretty shocking. If we assume that there may be some 200 billion stars in the Milky Way, and we generously assume that they’re all about the physical diameter of the Sun (which is an overestimate, since the vast majority of stars are less massive, and smaller), we could still get them all into a cube that would fit within the orbital diameter of Neptune in our solar system.

In other words, if our Milky Way spans roughly 1021 meters across its disk, we’ve now gathered up every single star and plopped them all into a cube that spans less than 1013 meters. That’s a healthy compression factor of a 100 million in linear scale.

For a little more perspective, imagine that you compressed your car lengthwise by 100 million times, it would end up being about 50 nanometers across. That’s roughly the width of a virus.

There is an enormous amount of empty space in space. Although it would be a bit massive to haul around, you could pack up a whole galaxy and have it to go. 

And that leads me to the next level of craziness. Within the observable universe, defined by our cosmic horizon of light travel since the Big Bang, current estimates suggest that there are anywhere between 200 billion galaxies and possibly as many as 2 trillion galaxies. (although that high number incorporates all the little 'proto-galaxies' that end up merging to make bigger galaxies).

Let’s be bold and take that larger number anyway. Now let’s pack up all the stars in all of those galaxies – again we’ll be spectacularly generous and assume that they’re all the size of the Milky Way (most will actually be a lot smaller). This will leave us with 2 trillion cubes, each spanning 1013 meters. Put these cubes together into a bigger cube and we’re left with a mega-cube with sides of lengths that are approximately 1017 meters.

Pretty big right? Well, no, not on a cosmic scale. Remember that our Milky Way’s diameter is of the order of 1021 meters, so a 1017 meter size cube is still only 1/10,000th of the size of the galaxy. In fact, 1017 meters is only about 10 light years!

Naturally this is all a bit of a parlor trick. But it does drive home just how little of the volume of the universe is actually occupied by denser matter. To quote the marvelous Douglas Adams: “Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.” (The Hitchhikers Guide to the Galaxy). 

I’d like to think that Adams would’ve enjoyed The Zoomable Universe too.