The progress is a linear scale represented as a converging logarithmic spiral, where you move centripetally, till the singularity point where "physics" (the empiric reality) and "mathematics" (the abstract model of reality) get totally merged, and a "mathematical catastrophe" happens, making the current reality undefined and starting the process from scratch.
The model of "cycles" is ancested from the moonly and yearly recurring events (natural and astronomic), like the moon phases, summer/winter, living beings life cycle, etc.
The biological and technical progress has little to do with cycles, at it is running as a sequence of linearly increasing quantity growth with periodic quality leaps, when the biosphere opens a new ability to manage the electromagnetic bonds. The system complexity is rising with no reverse since the Solar System had appeared.
The time interval between the leaps is permanently decreasing from leap to leap, but every time the previous interval is much greater than the next one, to call them "cycles" except on a very logarithmic scale.