If you ever indulged in the wonderful way to irreversibly waste time and lose faith in humanity in the process that is political discussion, especially on the Internet, you have probably noticed that from some degree of extremism onwards, its different kinds appear to stop ideologically diverging from each other and instead curve around and grow more similar, coming astonishingly close at the very extremes to the point of resembling something akin to a horseshoe shape; with some "wonderful" stances such as national socialism seeming to bridge the gap between two opposite ends of extremism and creating a whole new level of awful that takes the worst parts from both.
Using the popular political compass model which presents the political spectrum as a 2-dimensional Cartesian space described by two axis, economic left-right and lib-auth, and political beliefs of an actor as a vector pointing outwards from the 0 point which represents either some status quo or an arbitrary point considered the ultimate neutral center, we can start to see hints why. As political position presented in this way is essentially a divergence from the beliefs considered neutral, at some point the variety of ways to diverge simply starts to run out, leaving more and more limited options to go further, and forcing people of wildly different approaches to take increasingly similar paths.

This then suggests that the political spectrum resembles less of a 2D map and more of a surface of a 3D sphere, with the 2D representation we call a political compass being an attempt to project it onto a plane. But, this reveals not only the spherical shape, but also an existence of a third dimension, the axis of which appears to run through the centrist (neutral) pole, through the geometrical center of the sphere and the opposite pole of beliefs exactly opposite in every possible aspect to those at the centrist pole.

By cross-referencing the political beliefs found at different "longitudes" of the sphere (different quarters of the compass) but the same "latitude" and therefore the same position relative to the aforementioned third axis we can find the common traits and attempt to characterise its meaning.

I propose to define said axis as the factor of "approximate retardation". Interestingly, its neutral point appears to be located neither at the center of the sphere nor the centrist pole, but rather lost in the noise somewhere between them.

Thank you for coming to my TED talk.