The Power of the Cube: Grasping the Unfathomable

(First published in 2011)

We live in the Milky Way Galaxy, a large spiral galaxy, and our closest big galaxy neighbour is the Andromeda Galaxy. To find it, you can look for Cassiopeia, which is a W-shaped constellation of stars, and the second “V” points to the Andromeda Galaxy. We can easily see its center with binoculars on a very dark night, but fully lit, the whole galaxy would be 8 times wider than the moon from edge to edge.

The Andromeda Galaxy is 2.5 million light-years away from us. A light-year is a measure of the distance you can travel in one year at the speed of light, which is 300,000 kilometers per second. If you multiply this out, the distance traveled in 2.5 million years multiplies out to 23 quintillion, or 23,000,000,000,000,000 kilometers (see table below).

I order to visualize this more easily, imagine there is a one-millimeter cube (about the size of a large grain of sand) placed at every kilometer from here to the Andromeda Galaxy. If  you could travel there in your space ship at the speed of light and put a coffee cup out the window to capture these, it would fill up once per second, which you quickly transfer to a large roasting pan, filled once per minute. Each hour you have filled up a cubic meter with the roasting pan. Since there are one thousand millimeters in a meter, you now have a cube with one billion cubic millimeters, and you have traveled a billion kilometers. Continuing on your journey at the speed of light gathering cubic millimeters, you manage to fill up a five-story apartment building after a year, and by the end of your 2.5 million years, you have piled these into a cube-shaped stack, three kilometers high, deep, and wide.

You now decide to take a 12 kilometer walk around your big 27 cubic kilometer stack to get a better comprehension of just how far that Andromeda Galaxy is away. You stretch each step out to one meter (those are big steps), and at 100 steps per minute, about what your heart rate is, you have gone one kilometer in ten minutes. At the base of your stack, you pass by a cubic meter every step, one hour of coffee-cup collecting, representing one billion kilometers of travel. After half an hour you reach the edge of your cube and look back at the bottom edge row of 3,000 cubic meters. That row took 4 months of coffee-cup-catching.

You turn 90 degrees, and continue around the base, and after two hours you have walked around your giant stack. It is too high to see the top, so you get in your car and drive one hundred kilometers away,  park, and look back. So 27 cubic kilometers would be 3x3x3, like a Rubik’s cube sitting there in the distance. This would now look about the size of your thumbnail which is about two centimeters long at arm’s length.

Using the power of the cube as a visualization tool, you have collapsed an unfathomably large distance from a straight line of one-dimension into a three-dimensional pile that you can walk around in two hours.

Distance to Andromeda Galaxy
light years to Andromeda	2,500,000	2.5 million light years
speed of light in kilometres per second	300,000	three hundred thousand
seconds in a year	31,557,600	thirty two million
Kilometers to Andromeda	23,668,200,000,000,000,000	twenty three quintillion kilometers (difficult to visualize!)
Cube root of 23 quintillion	2,870,718	two point nine million (more fathomable)
millimeters in a kilometer	1,000,000	one million
2.9 million millimeters	2.9 kilometres	kilometres

Age of the Earth and age of me: 

Here is one more visualization example using cubic millimeters, or one billion of them in a cubic meter.

The age of Earth, 4.5 billion years. Taking the cube root, this gives us 1,650. So a cube in your living room 1.65 meters on each side or 5′ 5″ would contain 4.5 billion cubic millimeters.

In 2020, I am 64 years old, which is a perfect cube, 4 on each side.  What is amazing is that in the same room, at one moment you can be looking at something that represents the age of the Earth, and yet sitting on top of that, I can still see my age as a little cube 4 millimeters or on each side, about the size of a match head.