Pickup sticks is a mapping of one coordinate system to another.
But if the sticks break and need glue it still maps BUT you need to insert subprocesses that don’t map to both systems but to an internal relative coordinate system and ALSO to ANOTHER system (however you do the gluing) that’s orthogonal to the pickup sticks mapping.
Plant repair is an interesting way to look at it. Notice the tape goes AROUND.
Is “going around” the pickup sticks needed to map one tangled up coordinate to another (to win)?
No. Not at all.
But when it’s BROKEN, it still CAN MAP but the BREAK needs a fix FIRST.
This introduces TIME into the mapping.
This introduces another dimension (orthogonal). Actually 2 dimensions. as it’s going AROUND the line and ALSO this needs TIME to apply the fix in order to REPAIR the original coordinate mapping.
Same set of sticks, mapped two different ways.