Numbers are a human invention. As intelligent and rational creatures, we have learned to operate effectively in a world of abstract thought, where the concept of numbers goes beyond what we can count. But as humans, we cannot discount the evolutionary basis for how our apparatus works.
It turns out that numbers that are really large or really small are well-nigh impossible for us to comprehend. Upon careful inspection, this is not surprising, as comprehension is simply a form of analogy-making. We understand things when we can compare and contrast them with other things we are already familiar with. When we are presented with numbers that are very different from what we encounter in everyday experience, we have no way to make sense of them. Here are some examples:
Despite the beautiful pictures of galaxies you might have seen, the scale of the Universe is so vast that a galaxy is mostly empty space. For instance, the average density of our Milky Way galaxy — together with all its brilliant stars and planets — is conservatively estimated to be of the order of 1 kilogram over every billion cubic kilometers. If you imagine a box that spans a kilometer across on every side, magnify it a thousand million (1,000,000,000) times, and add a bag of potatoes into this box — that’s how empty our galaxy is. The space between galaxies is far emptier.
We estimate that there are 2 trillion galaxies in the observable universe. A trillion is a million million. To put that in context, a trillion is a number that is so large that removing a few millions doesn’t make much of a difference — you’re still left with about a trillion. Astronomers conservatively estimate that there are about a 100 million stars in the average galaxy, and about 1,000,000,000,000,000,000,000,000 stars in all in the observable universe. That’s one followed by 24 zeros.
Okay, now here’s a fun fact: there are more molecules of water in a few regular-sized drops than the total number of stars in the observable universe. All it takes is about a hundredth of a liter of water.
Molecules are pretty average-sized in the bigger scheme of things. The Planck length is the theoretical minimum limit to distance you can meaningfully speak of. Nothing smaller than the Planck length exists, according to present-day theory. The Planck length is so small that if you were to magnify a particle that spans the width of a human hair (~0.1 mm) to the size of the observable universe, the Planck length would itself be as big as the original size of the particle (~0.1 mm).
And finally, humans have evolved on our planet for millions of years, right? It turns out that if you overlay the Earth’s entire history until today over a 24 hour clock (midnight to midnight), single cell life forms appeared at around 4 am, multicellular organisms appeared at around 5:30 pm, and all of human history spans the last two minutes until midnight.
Life is all about perspective.