Orders of huge

When it comes to really big numbers, we often lose perspective of what we are actually talking about because we have no easy way to compare these magnitudes with any everyday concept. To try to convey some scale to the concept of one googol (the namesake of Google and a number composed of 1 followed by 100 zeros or 10¹⁰⁰), Dutch youtuber Daniel de Bruin manufactured a gearbox composed of 100 gears with 10:1 reduction on each step. The device is propelled by an electrical motor that causes the first gear to rotate 1000 times in an hour, so the second one turns 100, the third one 10 times and so forth, so that after 1 googol turns of the first wheel, the last one would have turned once. Of course, as the author points out, one would only see movement in the first ten wheels over the course of a usual human lifetime, while the other 90 would simply stay put. That is the scale of googol.

However, it is not necessary to go so high to reach dizzying numbers. The estimated total number of atoms in the universe is between 10⁷⁸ and 10⁸². The higher figure seems to be already quite close to one googol and yet we would need one billion billion universes to have one googol of atoms. There goes nothing.

Photo: piqsels.com

Now let us take another step down: stars are huge, and therefore must contain a very large number of atoms. A star like the Sun (which is not among the biggest ones) contains approximately 10⁵⁷ atoms, which still leaves us with somewhere between 10²¹ and 10²³ stars in the universe. This is already a much smaller number, but it is still a lot more than the number of grains of sand on Earth. In fact, we would somewhere between a hundred and ten thousand Earths to have as many grains of sand as there are stars in the observable universe.

The stars are grouped in galaxies, and galaxies are known to be huge, so we could go down in number a lot by counting galaxies instead. The Milky Way contains approximately 700 billion stars (that is approximately 10¹²), so we land with a number between one and one hundred billion galaxies in the universe (between 10⁹ and 10¹¹). This means that, if we were to put just one person in every galaxy, the chances are that we will run out of people in the world before we are done. And there would certainly not be enough people to put one person in every star of our galaxy (even if it would be very uncomfortable to be even in the surface of the star, let alone in its nucleus).

And how about space and time? The universe is said to be huge in terms of volume, but is it big enough to reach one googol of something? The volume of the observable universe is estimated to be 10⁸⁰ cubic meters, so we still fall short. Even going to cubic millimeters would only give us 10⁸⁶. With respect to time, it is obviously much smaller than space: universe is estimated to be approximately 13.8 billion years old or 400 quadrillion seconds (4 * 10¹⁷ seconds). The smallest amount of time that "makes sense" from the physical point of view is the Planck time, approximately 10^-43 seconds, so measuring the age of the universe in Planck time units it would up to roughly 10⁶¹ Planck times of age, so time is definitely smaller than space.

If you are feeling dizzy with all the numbers, perhaps it would be good to sit back an enjoy this video demonstrating the relative size of the Moon, the planets of our solar system and some of the best and biggest known stars. Enjoy!