curving the x coordinate

Before the invention of the clock, re-occurrence may have been the means of quantifying our temporal stream: the repetitive nature of sunrise and sunset, pangs of hunger, moon faces, menstrual cycles, the succession of plants and the seasons were all used to understand and measure scales of time. It is interesting to consider what time might feel like without anything cyclical at all. Had we not been regulating the soul through these external structures, would a clock have come about so easily? Clocks themselves were originally invented modeling this repetition anyway and the fact that they are still shaped as circles with hands moving around them only to come back to where they began, points towards their ancestry. In order for us to conceive of rhythm as having any value at all in measurement, we would need to have it order aspects of our lives in such a way that our memory of their recurrence served us in some way (as in foraging, agriculture, hunting, as early examples). Had we only repetition of our own making as in drumming or dancing, etc., it is difficult to imagine these creations would last long enough or consistently enough for us to come to believe that such an ordering were anything but a rare patterning in the universe. I therefore tend to think that if there was no external cycling, we would not likely have built a clock and would likely conceive of time as something that flows at different rates at different times - in the way it appears phenomenologically in immediate conscious experience.

What this might mean is that quantifying time and the Cartesian technique of representing it using equal fractions originates out of our location in the Earth. A world trapped in chaotic orbit may have given rise to a "transcendental aesthetic" quite different from anything Kant imagined as necessary for the possibility of experience. Could we imagine that a graphing system where the x axis incorporates cyclical aspects of time? There are three possible ways of doing this that quickly come to mind: using a circle, a spiral, and a cylinder. Each structure has can provide us with new eyes by which to understand the dynamics of a graph-able situation. For example, a simple circle will show the different iterations that the system takes superimposed on itself and will therefore show the overall range of behaviour the object takes. The spiral will show undulations and variations clearly and it will be easy to compare the phenomena at any two or more stages within the cycle at the same point of development, but unfortunately it requires a progressively longer stretch of graph to represent equal amounts of time. This leads to a distorted understanding (but it may be partially resolved by drawing radial lines outwards from the centre point to represent segments of time). Cylinders circumvent this problem and may be easy to interpret if transparent.