Create a system of recording information using knots on a string, or multiple strings. If desirable, reuse any ideas from Incan quipus, though most of that knowledge is lost.
Knots are neat because information is being recorded in topology, which is different from most other methods of recording information. Consider how difficult it is to turn a knot into not-a-knot, or turning a left-handed knot into a right-handed one. Compare that to the ease of altering information in other media: it typically requires only a local change.
Modern technology can create extremely durable fibers for long term preservation of information: which fibers should be used? Knotting puts stress on a string.
Should the nature of the knot matter, e.g., size, type, or should it just be binary of whether there is a knot at a position or not? A special type of string could be amenable to X-ray CAT scans which could decode the internal structure of a knot. Specially colored fibers could allow 3D computer vision techniques to derive the type of knot just by examining its outer surface.
Modern technology can probably make knots at very precise locations on a string.
Intriguing is having the knots on loops of string as knot theory does it instead of straight segments. We need some way of fusing the ends of a string (without a knot) -- many such ways exist -- or directly creating loops of string with knots on them (e.g., 3D printing).
Knots have an attractive feature that they can be read by touch, e.g. in low light environments or with failing eyesight.