Promising the Moon

[Campbell Ritchie]

I opned a new tab on FF and it showed me what is new in“Pocket,” as usually happens. I clicked on this link which is Big Think asking how you can fold paper thick enough to reach the moon. They said you need to fold it 42× to get a stack tall enough to reach the Moon. They must have been reading Douglas Adams. But I challenge readers: if you have an A4 sheet, 297×210×0.1mm, how wide would the stack of paper be after its 42nd fold ?

[Paul Clapham]

Well, of course it would be microscopically small. That's why the current record holder for paper-folding chose a piece of paper which was nothing like A4.

[Campbell Ritchie]

Even her piece of paper ¾ mile long wouldn't be large enough.

Paul Clapham wrote:Well, of course it would be microscopically small.

Smaller than that. I made it about 1.4e-12m starting with A4. 1.4pm, while the size of a hydrogen atom is more like 0.1nm (1 Angstrom if you like old measurements). Long before this time, you would have to slice the cellulose molecules in the paper in pieces :wink:

[Liutauras Vilda]

It is quite interesting when you think about it. Indeed.

public class Test {

    public static void main(String[] args) {
        double paperThickness = 0.1 / 10 / 100 / 1000; // 0.1mm to km
        double distanceToMoon = 380000;                // in km

        int folds = 0;

        while (paperThickness < distanceToMoon) {
            paperThickness *= 2;
            folds++;
        }

        System.out.println(folds);
    }
}

[Tim Holloway]

You should check out a proper authority such as Randall Monroe.

The problem with doubling anything is that the more you fold it, the harder it gets to fold it next time.

However, there's no need to write fancy algorithms to compute. Since you're doing a binary fold, to reach the moon, you just need to compute t*2^n, where "t" is the thickness of one sheet of paper, solving for n and assuming absolutely no space between layers.

Conversely, the horizontal dimensions would be the original paper size proportional to division by 2^n assuming you fold in an aspect-preserving way and assuming that the fold point has no dimension of its own (though in actuality, the fold point would be as wide as the folded paper is thick).

[Paul Clapham]

Campbell Ritchie wrote:I made it about 1.4e-12m starting with A4. 1.4pm, while the size of a hydrogen atom is more like 0.1nm (1 Angstrom if you like old measurements). Long before this time, you would have to slice the cellulose molecules in the paper in pieces :wink:

When you fold the paper with width W in half, you don't end up with a width of W/2. Some of the width contributes to the new (doubled) thickness, so the new width is more like (W-T)/2. Starting from an A4, the width is then less than the thickness after 8 folds. And it's mechanically difficult to fold a flat object with a non-trivial thickness in half -- try folding your phone's charging cable in half and you'll see that making the result be flat requires breaking things -- so you'd be hard pressed to achieve even 7 folds.

I'm sure I'm redoing the calculations done by all those other people on the web who have come up with 7 or 8 folds as the maximum.

[Campbell Ritchie]

You would have to cut the creases on the paper once the thickness of each fold is greater than its width. If not earlier.