weird
did you know 42 imaginary paper folds could reach the Moon?
doubling starts quietly, then gets completely out of hand.
42 doublings
about 439,805 km in the ideal model
starting at 0.1 mm; actual paper cannot keep folding like this.
- 10: 10.2 cm
- 20: 104.9 m
- 42: past the Moon
the idea
start with paper 0.1 millimetres thick and imagine doubling its thickness 42 times. the result is about 439,805 kilometres, greater than the Moon's average distance. this is a mathematical thought experiment, not a practical folding challenge.
how it works
after ten folds, the model gives about ten centimetres. after twenty, about 105 metres. after thirty, about 107 kilometres. another twelve doublings take it past the average Earth–Moon distance.
go deeper
why does doubling feel so sneaky?
start with paper 0.1 millimetres thick and imagine doubling its thickness 42 times. the result is about 439,805 kilometres, greater than the Moon's average distance. this is a mathematical thought experiment, not a practical folding challenge.
the first fold gives 0.2 mm, the next 0.4 mm. those increments feel small. but every new doubling adds as much thickness as all the existing layers put together.
look at every ten doublings
after ten folds, the model gives about ten centimetres. after twenty, about 105 metres. after thirty, about 107 kilometres. another twelve doublings take it past the average Earth–Moon distance.
the model tracks only thickness. actual paper runs out of usable area, resists bending, compresses, and cannot form the ideal stack indefinitely.
where does forty-two come from?
multiply the starting thickness by two raised to the number of folds. using 0.0001 metres gives about 439.8 million metres after 42 doublings.
thickness = 0.0001 × 2⁴² metres ≈ 439,805 km
why not call this a real-world prediction?
- a mathematical model can isolate one striking relationship while deliberately leaving out physical constraints. its assumptions determine what its answer means.
- changing the initial thickness changes the fold count. the headline uses exactly 0.1 mm and the Moon's average distance.
sources & further reading
concepts: exponential growth · powers of two · modelling
2 minute read