In the movie Arrival, Ian decoded the final diagrams on a computer. The computer shows these diagrams.
They contain only numbers and no units at all.
What are the units for these numbers?
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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.
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.