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I believe Paul is preparing stock for the table top at that point in that video, just a few minutes at the end. The edge that he tests with the string must be straight to get a good, gap free lamination, so he is using a lot of care with it. Even if he wanted a slight curve (some people do that when laminating), he’d probably want to start from perfectly straight. So, this is why he is taking such care. The wide faces don’t matter too much. After gluing the stock together, the whole assembly will be planed. He’s using a fair amount of care with those surfaces, but he really can’t get in trouble with them. You might ask, what about the other edge of the board? Do you need a string there? It depends upon the worker. Paul can probably pull a gauge using the trued edge as a reference and plane to the gauge line without checking. Others may need / choose to check.
You asked about a 2×2. The answer is, it depends and it’s the job of the worker to decide. If the wood is for legs and all of the joinery is at the top for the apron, then you just need to square two faces and work relative to them for the joinery. Everything else is just “looks good, is good.” If the stock was for something that would receive a through-tenon, then it might pay to take more care with all of the faces so that you can transfer the mortise from one side to the opposite.
As you get more experience and think about the “why” of things, you’ll get a better feeling for what is necessary. Often, once you get one face true, it can be a reference for truing / testing the others. I’ve never used the string method and rely on the action of the plane plus a straight edge, but if I were doing Paul’s table, I might use the string.
Hope this helped.
- This reply was modified 1 year, 4 months ago by Ed.