What distinguishes the analytical "knot system" from prehistory knot tying?

Answer

Codification of crossing rules and abstract mathematical properties

The fundamental difference between ancient knot tying and the modern knot system lies in the shift from function/aesthetics to abstraction. While ancient cultures utilized knots for practical necessities like securing items or for decorative purposes like Celtic artwork, these traditions focused on utility or visual appeal, relying on experiential knowledge. The 'knot system,' conversely, emerged as a branch of topology where the focus became the formal, analytical study of how a loop closes upon itself, isolating the mathematical structure from the material used (like rope or fiber). This required codifying the fundamental rules governing crossings and deformations, which became the basis for abstract mathematical classification rather than simple utility.

What distinguishes the analytical "knot system" from prehistory knot tying?

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