Raju Varghese (via Sploid) claims that if you fold a piece of paper 103 times, the thickness of your paper will be larger than the diameter of the observable universe: 93 billion light years. The explanation is simple enough – every time you fold a piece of paper you double its thickness and when you start doubling things they get very large very quickly – but I couldn’t leave this without checking the numbers for myself.
Of course, I couldn’t resist checking this for myself and pulled out a calculator. I soon found that the mental juggling needed to get from fractions of millimetres to kilometres was too much for my little brain and converting between millimetres and light years was going to be impossible.
So I wrote a script. The code is pretty simple, as you can see below, although I did have a four fold discrepancy when I first ran it (I came up with 107 folds needed, rather than 103). It turned out that my initial thickness of the paper was out by a factor of 10. Once I fixed this, everything matched.
#!/usr/bin/env python """ Foldpaper Calculates the thickness of a piece of paper after n folds """ thickness = 0.1 folds = 0 meter = 1000 kilometer = 1000000 lightyear = 1000000 * 9000000000000 size_of_universe_in_mm = 93000000000 * lightyear while thickness < size_of_universe_in_mm: thickness *= 2 folds += 1 if int(thickness / lightyear) > 1: print(folds, int(thickness/lightyear), 'light years') elif int(thickness / kilometer) > 1: print(folds, int(thickness/kilometer), 'kilometers') elif int(thickness / meter) > 1: print(folds, int(thickness/meter), 'meters') else: print(folds, thickness, 'mm')
And then, with a slight edit, I dumped the results into a table so that I could add a few comparative distances.
|15||3 metres||Taller than the average human|
|22||419 metres||Taller than The Shard in London|
|27||13 kilometres||We’re now standing higher than Mount Everest|
|42||439804 kilometres||Now we’ve just passed the Moon|
|51||225179981 kilometres||And the Sun|
|56||7205759403 kilometres||And finally we reach Pluto|
|69||6 light years||With a single fold, we have shot past Alpha Centuri|
|83||107460 light years||And now the thickness of our piece of paper is larger than the Milky Way|
|88||3438722 light years||And in a few short folds, we pass Andromeda|
|103||112680053353 light years||And with that final fold, we have exceeded the size of the Universe|
Exponentiation is awesome.