Not quite sure about the type of data structure that you intend. The code below would sort on 2nd column of matrix with 3 columns.

#!/usr/bin/perl -w
use strict;
use Data::Dumper;


my @AoA = ([1,2,3],
           [1,1,3],
           [1,5,2],
           [0,-1,3]
           );
           
print Dumper(\@AoA);           

@AoA = sort{@$a[1] <=> @$b[1] }@AoA;   

print Dumper(\@AoA);
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Part of my "non-understanding" is: I have a list of indices from an array that was numerically sorted. The natural thing would be to have that array in the sorted order! I don't understand why I should mess with: thing 15 should be in the place thing 2 is in now, etc. If the array is sorted, then I don't need the indices. The array is just going to be sorted further.

Can you write a simple Perl variable declaration with the type of structure that you want to sort? Something like this would be a "3D" thing.

my @AoAoA = ( [ [1,2,3] ,[1,1,3],[1,5,2] ],
              [ [0,-1,3],[1,5,2],[3,2,1] ],
              [ [0,-1,3],[1,-1,3],[5,4,2] ],
           );
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In Perl something like that or even what I showed above for a matrix is rare. The closest Perl equivalent to a 'C' 2D array is an array of hash. The reason is that this avoids all this index 1 really means NAME sort of stuff.