In the movie Arrival, Ian decoded the final diagrams on a computer. The computer shows these diagrams.

enter image description here

They contain only numbers and no units at all.

What are the units for these numbers?

  • 6
    From what I remember Jeremy Renner's character was measuring the "negative space" of the data, which ended up being 0.08333. He even says, as a fraction that is 1 of 12. - So, it's a percentage and therefore doesn't need a "unit".
    – Oliver_C
    Commented Feb 2, 2017 at 11:55
  • 1
    Aryxus is correct. However, I think you'll need some Calculus knowledge to come to the formula used to calculate empty space before you actually understand what's going on. Unfortunately, that was 30 years in my past (which is linear. ;o) ) and there's no way I'll ever be able to remember it. Commented Feb 10, 2017 at 19:08

3 Answers 3


Each number represented one instance of a symbol (the alien 'sentence'). The gaps were, presumably, space where a symbol would fit but where one was not present.

Ian (Renner) then calculated the percentage of space the symbols took up versus the empty space to come up with the 1:12 ratio.

  • 1
    Maybe as an English example to prove that this is the correct answer: "STACKEXCHANGE" = 1; "STA__EX___NG_" = 0.5 (approximately); "_____________" = 0. If you hide letters from a book (but keep the whitespace they leave), you can guess at how many letters have been removed.
    – Flater
    Commented Feb 14, 2019 at 8:04

I have not seen this movie but the numbers look like frequencies, i.e. 1 is a full bar. 0.77 means 77% of the bar is red (bottom one) and 0.07 is 7% of the bar is white. Looking at the graph, is see a network with colored node, so it's probably the frequency of those nodes that are affected by something (white and red) like an epidemic (the sick and the dead for example).


The movie made a mistake, though. Renner's character announces that he measured the ratio of postive space to negative space and it is exactly .08333 (repeating) then "explains" that's 1/12 giving the audience the magical "12" insight that suggests the American have only a portion and the other portions have been distributed to the other civilizations through the other ships: 12 in all.

But, there are not 12 OTHER ships. There are 12 TOTAL ships. So, there are 11 other ships and 11 other pieces. As such, the ratio should have been 1:11 (the part the Americans have: the 11 missing parts.)

It appears the visual artists understood this, but something got lost in the process. Notice in the picture that the data forms a 1:11 ratio.

  • 2
    There are two types of ratio... yours is one... part to part... the other kind is more like a fraction - part to whole 1:12 one in twelve... you have one out of twelve total things. mathsisfun.com/numbers/ratio.html
    – Catija
    Commented Feb 27, 2017 at 19:59
  • The ratio of positive space to negative space is 1/11. The ratio of positive space to total space is 1/12. Not sure if it was clearly conveyed in the movie. Commented Apr 30, 2017 at 19:37

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