TL;DR: Many models of the future exist. Several are relevant. Hyperbolic model is strongest, but too strange.
Our need: correct model of the future
Different people: different models = no communication.
Assumptions:
Model of the future = main driving force of historical process + graphic of changes
Model of the future determines global risks
The map: lists all main future models.
Structure: from fast growth – to slow growth models.
Pfd: http://immortality-roadmap.com/futuremodelseng.pdf
If I remember my philosophy lessons in high-school, Hegel was the proponent of the idea that history faces moments where it develops a thesis, which eventually makes the opposite thesis grows, until finally the two are reunited in a synthesis. That is, a progression, circular in nature, but still expanding.
It's curious that the spiral in the picture grows inwards, not outwards. Weird.
I think your memory of Hegel is correct.
By the way he also thought that Prussia of the beginning of 19 century is ultimate end of history. He also thought that the history is a story of "establishment of the Spirit", and so the God is in the future - so he was near prediction of future superhuman AI, but idea of Prussia as ultimate state prevented him from following his own logic to its end. This of cause is just my interpretation.
The picture is result of internet search of an image by keywords "spiral development". But the fact that it is inward could make sense if we think of it in the context of exponential acceleration. If it will be 3D, it will be a conus.