helical projections

It appears that the graph of human development as a species resembles a helix, or a spiral, as we commonly call it.

They say that fashion goes in circles, the history repeats itself, etc. However, whenever the circle starts another round, it is never truly the same: whenever the jeans become fashionable again, they are not quite the same jeans that were fashionable before – some progress has happened, something has changed. At the same time, (almost) everything in nature is periodic: the change of night and day, (arguably) the fluctuations of the financial markets.

The argument I am putting forward is that those two trends do not “just happen” – they are interrelated. And the only graph that represents both simultaneously, is not a 2D figure, it is a 3D one – a helix. As the top projection of a rising helix is a circle and the side view is a sinusoidal graph, the helix ties together the circle and the period, arguably, adding a new way of relating/representing/mapping/forecasting the periods of growth and fall and the circular motion of culture (economy).

Therefore, our culture does not move in circles – it moves in spirals. And the markets don’t simply rise and fall, but, again, spiral.


“…When I come back from Amazonia I lose sense of time and sense of number, and perhaps sense of space,” he said. He forgets appointments. He is disoriented by simple directions. ” I have extreme difficulty adjusting to Paris again, with its angles and straight lines”… He had spent so long with people, the Munduruku [an indigenous amazonian tribe], who can barely count [and barely have any straight lines or angles in the forest they inhabit] that he lost the ability to describe the world in terms of numbers…”

quote from Alex Bellos, “Here’s looking at Euclid”, 2010, cpt.0, [with my own remarks]