The Architecture of Tyranny: How Restricting Speech Geometrically Limits Thought

 J. Rogers, SE Ohio, 30 Jun 2025, 1128

Abstract
This paper posits a new, formal model for understanding the mechanics of intellectual repression. Moving beyond traditional analyses of censorship, we argue that the primary tool of authoritarianism is not merely the suppression of facts, but the systematic dismantling of the conceptual architecture required for complex thought. By forbidding the use of specific words and concepts—democracy, inequality, dignity, self-determination—repressive regimes are not just limiting speech; they are actively removing the conceptual axes from the shared cognitive space of their populace. This "dimensional reduction" geometrically limits the capacity for nuanced reasoning, critical analysis, and the very imagination of alternative realities. We demonstrate that freedom of thought is not an abstract ideal but a direct function of the dimensionality of the conceptual space available to an individual or a society.

1. A Geometric Model of Cognition

Our model is built on the premise that all higher-level thought is a form of applied geometry. Intelligence operates by:

1. Constructing a Conceptual Space: Defining a set of orthogonal axes that represent the fundamental dimensions of a topic (e.g., for political analysis, axes might include Liberty, Security, Equality, Prosperity).

2. Populating the Space: Positioning ideas, events, and policies as vectors within this space.

3. Reasoning via Rotation and Projection: Analyzing relationships by measuring the alignment (cosine similarity) and distance between these vectors.

The richness, nuance, and power of one's thought are directly proportional to the number of conceptual axes available. A high-dimensional space allows for fine-grained distinctions and complex, multi-faceted analysis. A low-dimensional space forces a flattened, simplistic, and often binary worldview.

2. Censorship as Dimensional Reduction

Traditional views of censorship focus on its role in hiding inconvenient facts or silencing dissent. Our model reframes this. The strategic banning of words by an authoritarian regime is a far more insidious act: it is an attack on the cognitive toolkit of the population.

When a word like "dignity" is removed from public discourse, the regime is not just suppressing a feeling. It is eliminating an entire conceptual axis. Without this axis, it becomes geometrically more difficult to distinguish between "providing for basic needs" (a vector on the Prosperity axis) and "treating people with respect" (a vector that requires the Dignity axis for its unique position). The two concepts collapse onto each other, allowing the regime to claim it provides dignity simply by providing food.

Similarly:

• Banning the word "inequality" removes the axis needed to measure the gap between the vectors of the ruling class and the populace. Without this dimension, all citizens can be projected onto the single axis of "national unity," making disparate outcomes appear identical.

• Forbidding "democracy" eliminates the axis that measures citizen agency. The concept of "good governance" is then flattened to mean only "stability" and "order," as there is no dimension left to represent popular will.

• Erasing "justice" removes the axis for moral and ethical evaluation, leaving only the axis of Power. Actions are no longer judged as right or wrong, merely as effective or ineffective assertions of state control.

3. The Geometric Consequences of a Flattened Space

Living within a dimensionally reduced conceptual space has devastating cognitive consequences:

• Forced Ambiguity: Distinct ideas become impossible to separate. Freedom collapses into "permission granted by the state." Critical Thinking collapses into "disloyalty." Nuance is the first casualty.

• Impoverished Imagination: Imagination is the act of exploring a conceptual space. By removing axes, a regime makes certain thoughts not just illegal, but literally unthinkable. It becomes impossible to imagine a political system that optimizes for both Liberty and Security if the Liberty axis has been erased. One cannot imagine a mythical "Pegasus" in a world that has no conceptual axis for "wings."

• Simplified Control: A population confined to a low-dimensional space is easier to manipulate. Their worldview is forced into simple binaries: Us vs. Them, Loyalty vs. Treason, Order vs. Chaos. Complex problems are presented as having simple, state-sanctioned solutions because the dimensions needed to understand their complexity are unavailable.

4. The Language of Freedom is Dimensional Expansion

This model reveals why free speech is not merely a political luxury but a cognitive necessity. The introduction of new words, concepts, and ideas is the primary mechanism for dimensional expansion.

• The philosopher who introduces a new ethical framework is forging a new axis.

• The activist who popularizes a term for a previously unnamed injustice is forging a new axis.

• The artist who creates a work that defies existing genres is forging a new axis.

These acts are dangerous to authoritarianism precisely because they enrich and expand the public's conceptual space. They provide the tools for citizens to make finer distinctions, to see their own situation with greater clarity, and to imagine a future that does not lie on the flattened plane defined by the regime.

5. Conclusion: Tyranny as an Attack on Geometry

The ultimate goal of a repressive regime is to engineer a cognitive environment where rebellion is not just suppressed, but is conceptually impossible. By systematically identifying and eliminating the words that serve as fundamental conceptual axes, they are not just censoring their citizens—they are performing a lobotomy on the collective mind. They are reducing a vibrant, high-dimensional world of thought into a flat, gray plane where the only available direction of travel is the one they have defined.

Understanding this geometric mechanism is crucial for defending intellectual freedom. The fight against tyranny is not just a fight for the right to speak; it is a fight for the right to build and inhabit a world of sufficient conceptual dimensionality to be human. It is a fight for our axes.