A few notes regarding the nano-to-cm-to-km-to-planetary-scale of "polymerizing the sky" for upper wind energy.

UHMPE molecules are ultra long liquid-crystal chains (~500k monomer units). This gives high Q properties that collectively extend to multi-km scale. Polymer fibers are twisted into threads, giving them a chiral spin property. Threads are further twisted into strands that are braided into lines and ropes that are often knotted in use.

These Topological Properties, of twisting, braiding, and knotting, are simultaneously mathematically abstract and tangibly embodied. Its modern topology right before our eyes. The mundane tangibility of "rag and string" somehow blinded topologists, until material scientists eagerly started adopting their concepts.

Network Theory and Engineered Fractals began even in the Paleolithic Age, as everyday embodiments. Fish nets are networks; the knots are nodes connected to each other by antinodes. Woven and knitted fabrics are networks. Biological networks go back billions of years; leaves are networks, brains are networks, and so on. Often units are called “cells”. A lot of mathematics is topologically ordered; network-based. Fractals are networks, as are graphs. Everything from quantum-computing to kite-networks is being governed by these principles.

Airborne Wind Energy Systems (AWES) are thus topological polymer load-path networks of tethers and bridle lines, fabric and seams. We no longer have to look at these as mathematically intractable objects. We now have formalizations spanning the nano to planetary scale spectrum (and beyond). We can rigorously prove, in principle, that there is ample upper-wind energy to sustain civilization, and subscale-validated technological means (Power Kite Networks) to harvest that energy.

https://en.wikipedia.org/wiki/Knot_theory

https://en.wikipedia.org/wiki/List_of_knot_theory_topics

UHMPE molecules are ultra long liquid-crystal chains (~500k monomer units). This gives high Q properties that collectively extend to multi-km scale. Polymer fibers are twisted into threads, giving them a chiral spin property. Threads are further twisted into strands that are braided into lines and ropes that are often knotted in use.

These Topological Properties, of twisting, braiding, and knotting, are simultaneously mathematically abstract and tangibly embodied. Its modern topology right before our eyes. The mundane tangibility of "rag and string" somehow blinded topologists, until material scientists eagerly started adopting their concepts.

Network Theory and Engineered Fractals began even in the Paleolithic Age, as everyday embodiments. Fish nets are networks; the knots are nodes connected to each other by antinodes. Woven and knitted fabrics are networks. Biological networks go back billions of years; leaves are networks, brains are networks, and so on. Often units are called “cells”. A lot of mathematics is topologically ordered; network-based. Fractals are networks, as are graphs. Everything from quantum-computing to kite-networks is being governed by these principles.

Airborne Wind Energy Systems (AWES) are thus topological polymer load-path networks of tethers and bridle lines, fabric and seams. We no longer have to look at these as mathematically intractable objects. We now have formalizations spanning the nano to planetary scale spectrum (and beyond). We can rigorously prove, in principle, that there is ample upper-wind energy to sustain civilization, and subscale-validated technological means (Power Kite Networks) to harvest that energy.

https://en.wikipedia.org/wiki/Knot_theory

https://en.wikipedia.org/wiki/List_of_knot_theory_topics