One of the mathematical concepts that astonishes and confuses people the most is exponential growth. There are many ways to witness its effects, but one of the simplest requires a sheet of paper. Nothing fancy—an A4 sheet will do. You fold it once, then again, and again… until you can’t anymore. Most people can’t get past seven folds, and the record is twelve, achieved using toilet paper. So what would happen if, somehow, it were possible to fold a paper 400 times? The answer… doesn’t even make sense.
Exponential Growth and a Sheet of Paper
If you’re looking for a classic example to visualize exponential growth, chess and grains of rice is ideal. What seemed like an absurd reward for a king turned into an agricultural nightmare. Thousands of years later, we still don’t know what happened to the inventor. In fact, some doubt the story’s legitimacy, but it works perfectly as a mathematical curiosity. So, how does it sound to try it at home?
I’m not talking about massacring bags of rice, but about seeing exponential growth in person. All you need is a sheet of paper. If it’s thin, it’ll be easier to work with at first… but only at first.
The famous seven-fold limit is a myth. American Britney Gallivan broke the record with twelve folds, and to do it she needed a single 1,200-meter-long sheet of toilet paper.
One detail to keep in mind is that her folds were all in the same direction, and she implemented strict rules to consider the paper “folded.” Today I propose something different: suspend the laws of physics for a while and fold an imaginary paper 400 times.
- 0.1 millimeters thick, completely indestructible.
- At eleven folds, the paper’s thickness is already like a basketball.
- 14 folds, an average human.
- 22 folds, taller than the Empire State.
- 30 folds, and the paper is already in space.
- 37 folds exceed the Earth’s diameter.
- 42 folds reach the Moon.
- 50 take us to the Sun.
- 66 folds equal a light year.
- 68 to the distance between the Sun and Proxima Centauri.
- 83 folds cover the Milky Way from one end to the other.
- 97 folds and we’re in the Andromeda galaxy.
- The entire Virgo supercluster fits in 93 folds.
- The Observable Universe ends in “just” 103 folds.
- At 133 folds, the paper exceeds a billion times the length of the entire universe.
- When folded 346 times, the paper has a thickness identical to a googol, 10^100 meters.
- And at 400 folds, we surpass that same number… but in light years.
In short, the result is inconceivable even for our reality.
