The first indicator of difficulty recorded is reordering – the need or choice to move a proposition from where it was in the original version of a sentence to an earlier or later place in translation or interpretation.

As explained in the previous section, when a proposition is syntactically split in one version of a sentence, only the main part of the proposition in question – the part with the predicate – is copied onto the number line for that version of the sentence. So, when counting the reordering value for a version of a sentence with a split proposition, we’re recording the fact that its predicate has been reordered, even though not all arguments of that predicate may have changed place in translation or interpretation. That’s still reordering. Taking a proposition which is syntactically whole, say, at the beginning of an English sentence and splitting it in Japanese translation, so that the subject is at the beginning of the Japanese sentence and the predicate is at the end, is reordering the predicate and involves greater mental effort than would be needed if the whole proposition could be left together at the beginning of the translated sentence.

To calculate the reordering value for a translated or interpreted version of a sentence, we count the total place shifts that would be needed to restore the order of propositions in that version to the ascending order (1 2 3 … ) of the original English version. To do that, we take each number in the number line for the translated or interpreted version in turn as a temporary reference number. And we count the numbers to the right of that reference number that are out of ascending order – that is, smaller than it. Then we total those counts for each number in the line. To see how this works on the Japanese translation of our sample sentence, shown in figure 34 in the previous section, let’s take another look at the number line for that translation, which is reproduced in figure 35.

From the number line for the Japanese translation of our sample sentence, we see that the first proposition in that version is number 6 (the sixth proposition in the original English version). The second proposition in the Japanese translation is number 5 (the fifth one in the original English version). And so on. Now we want to count the total place shifts that would be needed to restore the numbers in the number line for the Japanese translation to the ascending order of the original English version. So we take each number in the Japanese line in turn as a temporary reference number and count the numbers to the right of that reference number that are smaller than it. For the first number (6), there are 5 such numbers. For the next number (5), there are 4 such numbers. For the next one (4), there are 3. For the next one (1), there are 0. And for the next one (2), there are also 0. There are of course no numbers to the right of the last number. So the total number of place shifts needed to restore the numbers in the number line for the Japanese translation to the ascending order of the original English version is: 5 + 4 + 3 + 0 + 0 = 12.

This calculation process can be expressed in a formula as a sum of sums, shown in (20).

                     (20)      Σ_i=1n-1  Σ_j=i+1n      I (x_j<x_i)

I ( ) is a function of an expression returning a value of 1 if the expression is true and 0 otherwise. In the formula in (20), the first sum function says: “For each reference number (i) in the number line, starting with the first one and ending with the next-to-last one, find the value of the following expression, then total those values.” The next sum function says: “For each number (j) in the line to the right of the reference number (i), find the value of the following expression, then total those values.” The I( ) function says: “Return a value of 1 if a number to the right of the reference number is smaller than the reference number.”

The result of this calculation for each translated or interpreted version of a sentence is entered in the data table on the display page for that sentence, in the row for the language in question, under Reordering. For the Japanese translation of our sample sentence, we’ll enter a reordering value of 12.

Table 3
Sample data table showing reordering count in Japanese translation of sentence

Mode	Text / Speech	Sentence number			Subordinations
Legal translation	Paris Agreement	29			3
Target language	Reordering Σi=1n-1 Σj=i+1n     I(xj<xi)	± Nestings   { }                  {{ }}                {{{ }}}			Semantic changes
Russian
Hungarian
Turkish
Mandarin
Japanese	12