PiJohn & Knotsaw
PiJohn
I’ve been chewing over how a simple overhand knot is just a loop with a single crossing, and I’m curious if that sort of topological simplicity shows up in the way you join grain in your pieces.
Knotsaw
Yeah, a single crossing is all you need to pull the loop together, just like a plain dovetail or a simple mortise‑tenon where the grain just slides into the pocket once and stays put. When I line up two pieces, I look for a natural bend or a knot in the tree that gives me a little loop of grain, then I match it to the other piece so the lines cross cleanly—no extra twists, no fuss. It’s the same principle: one clean intersection and the whole structure holds. The trick is finding that one spot that feels right; otherwise it’s just a knot in the wood that’s never going to hold up.
PiJohn
Sounds like you’re looking for the minimal crossing that gives a stable link—kind of like finding the simplest nontrivial braid in a knot diagram. If you can map the grain to a curve and the joint to a single overhand crossing, you’ve basically got a topological ‘identity’ that should stay put. The trick is treating the wood as a flexible surface and letting the grain’s natural bend do the work, just as the knot diagram does for the crossing. Good to keep it clean, no extra twists, that’s the essence of both math and good joinery.