The knots display is on your left as you enter the Culture Center. If you click on it, Soren asks you to put the cards in order to show how the different knots are tied. This is an optional puzzle, but read to the end of the hint for a picture showing the arrangement you need.
The cards in place show what kind of knot is being displayed in that row. For each knot, there are five stages.
Pick up a card and see if you can figure out which knot it pertains to and what stage in the knot tying it might represent. You can move cards around, so you can put them anywhere you want and move them to their final positions later.
You can also scroll down the available cards (using your mouse's scroll button) until you find cards you recognize.
Most of the steps are pretty obvious, especially since only one of the three knots uses two separate pieces of string. Any card with a blue string will be part of the middle knot.
If you've put all the cards in place and nothing happens, here's the arrangement you need.
When you're done, what you get is ... a festival flyer that says "GUNPOWDER" on the back. Huh.
As far as I can tell, this is a total red herring. No one in this game ever does anything with gunpowder in any way. Well, who knows; maybe it's part of someone else's mystery that just happens to overlap.