Hossein Jorjani
First publication: 2026 – 07 – 31
Human beings have a natural tendency to arrange ideas along a single axis. Political doctrines, philosophical systems, and even scientific theories are commonly represented as occupying positions on a line, with one doctrine at one end and its supposed opposite at the other. Such representations are intuitively appealing because they simplify comparison. Yet they also conceal an important assumption: that conceptual distance is linear.
Even when a second dimension is introduced—as in the familiar political maps contrasting economic and social liberties—the underlying geometry usually remains Euclidean. Ideas are imagined to inhabit a flat plane in which distance is measured along straight lines. This convention is so deeply ingrained that alternative geometries are seldom considered.
Yet there is no philosophical necessity that conceptual spaces should be linear or even flat. Just as the geometry of physical space may be curved, so too may the geometry of conceptual space. The apparent distance between two theories depends not only on their positions but also on the geometry and metric of the space in which they are compared. Two theories that appear maximally separated in one representation may become immediate neighbours when examined along another conceptual dimension.
An instructive biological analogy is provided by the phenomenon of ring species. There, neighbouring populations remain sufficiently similar to interbreed, while the terminal populations—although connected through a continuous chain—have diverged so far that they no longer do so. The paradox lies in the fact that continuity produces apparent opposition.
Conceptual space may display an inverse phenomenon. Two doctrines that are conventionally presented as opposites may, when projected onto a different dimension, prove to share the same underlying structure. Their apparent opposition results not from fundamental conceptual distance but from the choice of projection.
Political thought offers numerous illustrations. Liberal individualism and classical Marxism are traditionally regarded as ideological opposites. Yet, when compared according to their underlying conception of the human person, both may be interpreted as forms of anthropological reductionism: the former primarily understands the individual as an autonomous bearer of rights, the latter as a member of a socio-economic class. The disagreement concerns which single characteristic is privileged, not the assumption that one characteristic should be privileged.
A similar observation may be made in economics. Capitalist competition and socialist central planning are ordinarily distinguished by ownership and allocation mechanisms. Yet if the comparison is made along another dimension—the effective number of autonomous decision-making centres—their trajectories may converge. One process proceeds through market consolidation toward increasingly concentrated economic control; the other begins from political centralization. Their historical mechanisms remain different, but under this metric the limiting structures may exhibit unexpected proximity.
The lesson is therefore methodological rather than political. The apparent distance between ideas is never an intrinsic property of the ideas themselves, but a consequence of the geometry in which they are represented. Once the possibility of conceptual curvature is admitted, doctrines conventionally placed at opposite ends of a spectrum may become neighbouring points on a different surface. In this respect, conceptual space exhibits an inverse analogue of ring species: where biological continuity culminates in apparent opposition, philosophical analysis may reveal that apparent opposites are joined by an underlying structural continuity. The geometry of ideas, no less than the geometry of physical space, determines what we perceive as near and far.
Hossein Jorjani 