March 13, 2025 study (Cambridge University Press)
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The authors of the study applied ‘Gauss coding’.
I am of the view that a more meaningful approach is to classify knots according to geometry and loading profile.
Example: A Sheet bend is a joining knot. A Bowline is a fixed eye knot.
Both share the same core structure and therefore have the same number of crossing points and topology. What differs is application (and loading profile).
On the one hand, a society that develops and uses a ‘Sheet bend’ is doing so because they need a way to reliably unite (join) 2 ropes (and be able to untie it after heavy loading).
A society that develops and uses a ‘Bowline’ has need to form a connective eye in a rope (so it can be used for attachment to things) but remains easy to untie even after heavy loading.
I also hold the view that societies/civilisations that developed sailing vessels had need of rigging. As the vessels grew in complexity - so did the need for more advanced rigging techniques.
Vegetable fibre ropes were the main types used. It wasn’t until relatively recently (in terms of the timeline of human existence) that steel wire rope and pressed swages were used (although synthetic fibre ropes are still used today).
My point being that more advanced civilisations had a need for more complex rigging methods using vegetable fibre rope - and this was the driver for technical innovation. And we can say that sailors/sailing is likely the principal activity that drove knotting innovation.
In more recent human history, mountaineering, vertical rescue, caving, and rope access, also drives knotting innovation. So it should be that England, Spain, France, and the Dutch, would have been driving a lot of innovation with knots and splices (since they had substantial fleets of advanced sailing ships). Technical advancements in transport (eg ships at sea) drove the need for technical innovation in knots. Dare I say it, many technical advancements were made during world wars - eg the development of the atomic bomb, jet engines, rocket engines, radar, etc.
EDIT NOTE: The transfer of technology from one nation/civilisation to another occurred when items/vessel/things were captured (including capture of scientists). For example, rocket technology was transferred to the USA with the capture/surrender of German V2 scientists. In the same way, the capture of French/Spanish ships would have enabled transfer of their rigging techniques to the English (and vice versa).
We should also see some earlier use of cordage in Egyptian and Roman sea going vessels. Military vessels relied on oars rather than sail. However merchant vessels did use some sails (but not at the same level of advancement as from the mid 16th century). Unfortunately, it is extremely difficult to find any surviving records of precisely which knots Romans used at sea.