The skill builds on the concept of carving, or paddling an arcing path. Picture the canoe in motion with the bow cradled by bow waves. By using the 2 X 4 technique you can control how these bow waves direct the canoe’s path (much like the reins on a horse). The 2 X 4 makes paddling a solo canoe easier by maximizing forward speed, providing directional control and reducing the reliance on steering with momentum robbing friction strokes.
Over on CBoats, Kelvin Horner provided an authoritative take on the notion:
The 2x4 concept of paddling has it's uses as a drill to deepen the paddlers understanding of how the 4 elements of power, shaft angle, stroke position and edge can be used to control the direction on the boat. It needs to be combined with an understanding of a lot of other concepts to give 'complete control of the solo canoe' [...]
Corrections are often executed at the stern of the boat, cross forward sweeps do not always do the trick. In other words your offside stern quarter isn't very efficient, that's one of the reasons why we pry [...] A well executed power/pry combination works a treat [...] The power of your forward strokes also needs to be varied [...] Bow and stern trim has just as much effect on a turn as edge [...] There are lots of other things!
I know the 2x4 concept isn't meant to be used alone but it doesn't give any context. Many paddlers take these kind of articles as absolutes, they are not. Add it to your paddling and use it to deepen your understanding of how things work [...] Remember that paddling isn't a mathematical equation!
"Gord" adds further perspective:
The 2x4 method is a system of teaching beginners to paddle. It has been adopted by ORCKA and Paddle Canada for teaching whitewater canoeing [...] In a teaching progression it is taught first to prevent the students from using stern strokes that kill momentum during ferries, eddy turns, etc. Later on, students are introduced to stern corrections. The 2x4 becomes the foundation upon which other strokes are added to develop skilled paddlers [...]