Humans are linear thinkers.

That is, when we think of numbers, we tend to do so in a linear sense: 1 + 1 = 2, the difference between integers is a constant equal to 1, and so on. What’s funny about that is that the universe is decidedly nonlinear. Most of the ways humans interact with the world aren’t linear, either!

Your eyes don’t see linearly; we see luminance on a modified logarithmic scale. Our hearing sensitivity is logarithmic as well. These perceptions give us a wider range of sensitivity to experience the outside world.

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So it’s odd that our brains seem to insist on churning through numbers linearly. We have an intuitive grasp of adding 1 to a number or adding some two numbers together. But if those numbers scale exponentially, our brains often fail us.

Here’s a practical example that gets impractical pretty rapidly: When you fold a piece of paper in half, it gets thicker, right? It doubles in thickness, in fact. So how many times do you have to fold a piece of paper in half such that its thickness is equal to the distance to the moon?

The moon is, on average, 384,000 kilometers from Earth, if that helps. Okay, now guess!

Got your number? Here’s the actual answer: to get a piece of paper 384,000 km thick, you’d have to fold it in half 42 times.

Yup. Just 42 (maybe that’s what Douglas Adams was thinking when he came up with this number). How can this be?

It’s because of exponential growth. Every time you fold a piece of paper, you’re not just adding two pieces together; you’re doubling them. This piles up much faster than you’d expect.

A standard piece of 8.5-by-11-inch (20-by-28-centimeter) paper is approximately 0.1 millimeter thick (as we’ll see in a moment, the exact thickness doesn’t really matter much). Fold it once, and the paper is 0.2 mm thick. Fold it again, and it’s 0.4 mm.

The thickness increases as 2 to the power of the number of folds. So after five folds, the paper is 32 times thicker. After 10 folds it’s 1,024 times thicker (in the case of our sheet of paper, that would be about one meter thick).

Our brains balk at this. After 10 more folds, you might think it would be 2,048 times thicker than it was originally, but in fact that happens after the next fold (so 11 total)! After 20 folds the paper is actually 1,048,576 times thicker—almost 105 meters, longer than a football field. After 10 more folds, so 30 in total, it’s over 107 kilometers thick. Another 10 (40 total) takes it to almost 110,000 km, so just two more makes it 440,000 km thick, comfortably past the moon. (One fewer only gets us to 220,000 km.)

See? You’re only 42 folds away from the moon. You might argue that it’ll take more folds if the paper is thinner—or fewer if it’s thicker. And this is true—but if your paper is half as thick, this only adds one more fold! If it’s twice as thick it takes one fewer fold, so honestly there’s plenty of room for error in our thickness estimate.

Now, to be fair, folding a piece of paper this many times is physically difficult, to say the least. The crease in the middle when the paper is folded is the problem here. It’s not too hard to smash that crease flat for the first few folds, but the thickness of the paper itself quickly gets in its own way, making further folding harder and harder.

You may have heard the legend that a piece of paper can only be folded seven times before it becomes impossible to do so again. For an 8.5-by-11-inch sheet, that’s not entirely wrong; after seven folds, further progress is very difficult. I’ll note, however, that in 2001 then high schooler Britney Gallivan broke this record by folding a 1,200-meter-long piece of paper 12 times! She even derived a mathematical formula showing that the fold’s curvature is what determines the maximum number of possible iterations. TV’s MythBusters also tested this, and people on the show were able to fold a gigantic 52 -by-67-meter piece of paper in half 11 times—although they had to use a steamroller and forklift (and, amusingly, a bit of jumping up and down on the monstrously thickened sheet) to do so.

If only they had gone 31 more times. NASA could save a lot of money on rockets.

Or, on second thought, it probably wouldn’t. Every time you fold the paper, it gets thicker but simultaneously narrower. After two folds, each side has half its starting length. After 42 folds, the paper can no longer even charitably be called a sheet; it will be about 0.1 micron (0.00001 cm) on a side. That’s smaller than a bacterium! Using it to climb to the moon will prove—problematic. Clearly, we’ve stepped into the realm of impossibility.

But hey, given that we’re already here, why stop at the moon? There are more distant objects.

The sun is 150 million km from Earth. Fifty folds makes the paper about 113 million km thick, so one more gets you past the sun—51 folds is about 225 million km.

The nearest star to the sun is the red dwarf Proxima Centauri, about 4.25 light-years away (or, in somewhat more familiar units, a tad more than 40 trillion km). How many folds is that? Guess first.

If you were anywhere near 69, give yourself a star (a red dwarf star, if you have one handy). That gets the paper 59 trillion km thick, or just more than six light-years (just past another red dwarf, Barnard’s Star, for that matter).

How’s that for nonlinear thinking? But we can keep going.

Our Milky Way galaxy is very roughly 100,000 light-years across. That’s 83 folds.

The Andromeda galaxy is 2.5 million light-years away: 88 folds (with some room to spare).

Okay, just one more: the observable universe is just shy of 103 folds across—that’s some 93 billion light-years, or 880 sextillion kilometers (8.8 × 1023 km).

So we’re talking about a mere 103 folds to span the entire universe. One difficulty with that (among many) is that the paper gets so narrow that it will run into severe quantum mechanical problems; it will be about as wide as a Planck length, in some ways the theoretical limit to how small any physical thing can be. (A proton is about 100 quintillion Planck lengths across, to give you a sense of scale for this.)

It’s a little odd to think that you’re a little more than 100 folds away from everything in the entire cosmos, but then again, that’s the whole point—this is further proof that we’re not good at nonlinear thinking. And that’s something I’ll always be an exponent of.