zlacker

> endure the multiple weeks of effort required to learn the basics

J for C programmers is a good book - https://www.jsoftware.com/docs/help807/jforc/contents.htm - and it could take significantly less than many weeks to "get" some important ideas. Specifically, make sure you understand ranks at chapters 5 and 6.

After you understand how +/ with different ranks can sum along different axis, you're well on the way.

I mean, here is a cube of numbers:

       i. 2 3 4
     0  1  2  3
     4  5  6  7
     8  9 10 11

    12 13 14 15
    16 17 18 19
    20 21 22 23

Plain +/ sums along the leading axis -

       +/ i. 2 3 4
    12 14 16 18
    20 22 24 26
    28 30 32 34

That's because rank of +/ is infinity, so / inserts pluses between highest-ranked items, of which there are two - a square

     0  1  2  3
     4  5  6  7
     8  9 10 11

and square

    12 13 14 15
    16 17 18 19
    20 21 22 23

(rank is a sort of dimension). So +/ just adds, element by element, these two squares together, giving the resulting square.

If you specify +/"0 - this sets the rank of the verb (function) to 0 - then +/ will be applied to each number separately and results will be combined. Adding a single number (not with itself - just as it is, without the other argument for summation) makes the same number, so +/"0 doesn't change the result - it's the same cube as in i. 2 3 4

Trying with +/"1 gives

       +/"1 i. 2 3 4
     6 22 38
    54 70 86

That's because +/"1 now is a verb of rank 1, so it works with items (subarrays) of rank 1. In cube i. 2 3 4 there are 6 subarrays of rank 1, 3 of them are in the first "plane" and 3 of them are in the second "plane". +/"1 takes each such subarray of rank 1 separately and sums elements in it (inserts + between elements of such array), and J then aggregates results into the array.

Finally,

       +/"2 i. 2 3 4
    12 15 18 21
    48 51 54 57

sums within 2-dimensional arrays. Elements of such arrays are 1-dimensional arrays, so those arrays are summed, element by element. There are two planes, so the result has two element (two arrays of rank 1), and each element is array of rank 1, obtained from summing 3 arrays of rank 1.

The book tells it better, of course.