I don't know how to help you with trace mode, but I
can describe what happens with the phrase you are
working at understanding:

/:1{|:ds

The synonym for this that would normally be written
is:

/:1{"1 ds

This may be read so:

Sort by column one of ds.

The transposition in your phrase (|:) makes your
phrasing so:

Sort by row one from the array that results from
transposition of axes of ds.

Written in an interlinear style:

Sort (by row) one from (the array that results from)
/:             1    {          

the transposition of axes of ds.
            |:               ds

The (transposed) array referred to is:

   |:ds
+---------+--------+---------+
|Harry    |Jane    |Peter    |
+---------+--------+---------+
|Potter   |Eyre    |Rabbit   |
+---------+--------+---------+
|1998     |1847    |1904     |
+---------+--------+---------+
|childrens|classics|childrens|
+---------+--------+---------+

Note: "By row" is implied by the natural ordering of
axes in J.

Hope this helps,

Tracy

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