What do you make of the spiral radius? I think she means that the spiral is not infinite, but that one arm goes out to a straight-line distance of 4 from the source, while the other goes out to 5. There is a straight line 9 lengths long which connects the two ends and goes through the centre, so it looks like a wave (passage of time). This would be some kind of complex quadratic function. Relations of light dark, conscious unconscious etc.

The point is that there is an 'artificial' asymmetry built-in, creating 'natural' dynamics. You could equalise the crests and troughs by having alternative waves of 5 and 4, or have the crests always 4 and the troughs always 5. Once the reader has glommed (been educated into) the dynamic, it can be modified at will by the speaker to demonstrate dynamic eruptions, while providing the comfort of an underlying structure.

Thanks @Apocryphal for the listing... I'd assumed that ACH was quite a late book, and I think this supports that conjecture. It made me realise that much of what I like is her early phase work up to mid 70s. Though I do like Tehanu, and love the follow-on The Other Wind (2001). Lavinia is extraordinarily beautiful. I gave up on Word for World is Forest as it just seemed far too stereotypically obvious and heavy handed - Avatar is quite faithful to its vision in that sense. I have similar thoughts about the Stoneteller parts of ACH but they are only small parts of the whole.

Spirals... I cannot resist going mathematically geeky here... there are two major families of spirals, the Archimedian and logarithmic. The simplest firm of Archimedian ones expand at a constant distance per cycle (there are more elaborate members of the family) whereas logarithmic tend to "open out" so that the successive arms get further apart from each other. In nature, logarithmic ones appear in slow, essentially static situations such as the shape of certain shells, or the arms of a galaxy. Archimedian ones are more found in dynamic situations such as a Catherine Wheel firework.

In polar coordinates, which are far more natural for describing spirals than Cartesian ones, there is a scale parameter for both families of spiral. One could credibly call this a radius, as it defines how rapidly the spiral unwinds. Or, equivalently, how broad an arc is being made per unit angle traversed.

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Edit: moved from other thread.

What do you make of the spiral radius? I think she means that the spiral is not infinite, but that one arm goes out to a straight-line distance of 4 from the source, while the other goes out to 5. There is a straight line 9 lengths long which connects the two ends and goes through the centre, so it looks like a wave (passage of time). This would be some kind of complex quadratic function. Relations of light dark, conscious unconscious etc.

The point is that there is an 'artificial' asymmetry built-in, creating 'natural' dynamics. You could equalise the crests and troughs by having alternative waves of 5 and 4, or have the crests always 4 and the troughs always 5. Once the reader has glommed (been educated into) the dynamic, it can be modified at will by the speaker to demonstrate dynamic eruptions, while providing the comfort of an underlying structure.

Spirals... I cannot resist going mathematically geeky here... there are two major families of spirals, the Archimedian and logarithmic. The simplest firm of Archimedian ones expand at a constant distance per cycle (there are more elaborate members of the family) whereas logarithmic tend to "open out" so that the successive arms get further apart from each other. In nature, logarithmic ones appear in slow, essentially static situations such as the shape of certain shells, or the arms of a galaxy. Archimedian ones are more found in dynamic situations such as a Catherine Wheel firework.

In polar coordinates, which are far more natural for describing spirals than Cartesian ones, there is a scale parameter for both families of spiral. One could credibly call this a radius, as it defines how rapidly the spiral unwinds. Or, equivalently, how broad an arc is being made per unit angle traversed.