Square's Trial and Life Imprisonment for Preaching the Third Dimension is the culmination of Square's attempt to carry knowledge from Spaceland into Flatland: after publicly recounting his voyage with Sphere and urging his audience to abandon prejudice, he is arrested and sentenced to perpetual imprisonment. The proceeding makes the limits of demonstration the center of the case, while its aftermath shows the human cost of a revelation that Square cannot make transmissible even to those closest to him.

Background and Public Proclamation

About eleven months after returning from Spaceland, Square was already living with the strain between what he had experienced and what he could prove. He had tried to picture a Cube with his eyes closed and failed; later he managed it, but never became certain he had exactly recovered its form. If he could not convince his Grandson, he wondered, how could he convince the highest Circles? Yet his doubts did not silence him. Even in elevated Polygonal and Circular company, he sometimes let slip forbidden references to the Third and Fourth Dimensions and to seeing the interiors of things.

The immediate occasion for his public disclosure was a meeting of the Local Speculative Society at the Prefect's palace. Someone had presented an elaborate argument for why Providence had limited reality to Two Dimensions and reserved omnividence to the Supreme alone. Square began by disguising his own account as the imaginary experience of a fictitious person, but enthusiasm overcame the pretense. He gave a full account of his journey with Sphere into Space, their visit to the Assembly Hall in Metropolis, and his return home, including what he had witnessed in fact or vision. He ended by exhorting his listeners to cast off prejudice and believe in the Third Dimension. His speech brought a claim that had remained private or half-veiled into open conflict with the accepted doctrine of Flatland.

Arrest and Examination

Square was arrested immediately and taken before the Council. The following morning, in the same place where Sphere had appeared only a few months earlier, he was permitted to begin his defense without interruption. But the arrangements around the hearing had already made the likely outcome plain to him. The President noticed that the attending policemen were of an angularity little under 55 degrees and ordered them replaced by an inferior class measuring only 2 or 3 degrees. Square understood the change as a sign that execution or imprisonment was intended, and that the officials who heard his story might also be destroyed to keep it secret; replacing the better policemen with less expensive victims would reduce the cost of that suppression.

After Square finished, the President asked two precise questions. Could Square indicate the direction meant by “Upward, not Northward”? Could he show the figure he called a Cube through diagrams or descriptions, rather than by merely enumerating imaginary sides and angles? These questions echoed the problem that had defined his earlier encounters with beings of other dimensions: an inhabitant of a restricted space cannot readily demonstrate a direction or form that the space itself cannot represent. Square had escaped the limits of Lineland by moving out of its Line, and Sphere had explained that Flatland could see him only as a Circle, a section of a solid whose dimensions exceeded the plane. Now, before the Council, Square could not give the requested proof in terms his judges would accept.

Square answered that he could say nothing more and must entrust himself to the Truth, which, he believed, would prevail in the end. The President said that he concurred with this sentiment, but made the appeal to Truth the prelude to punishment rather than release: Square was to be sentenced to perpetual imprisonment. The decision preserves a distinction between acknowledging the limits of Square's proof and accepting his account. His earnestness may have moved some of the junior Circles, but it does not alter the verdict.

Sentence and Conditions of Confinement

The President presented the sentence in terms that were at once severe and measured. Square would receive no discomfort beyond what was necessary to prevent escape. He would occasionally be allowed to see his brother, who had been imprisoned before him, provided he did not forfeit the privilege through misconduct. The stated restraint is practical rather than an attempt to extract a confession: the authorities confine Square and limit his contact, while leaving his account of the Truth unrefuted in the terms of the hearing.

Seven years later, Square remains a prisoner, deprived of companionship apart from his jailers and the occasional visits of his brother. Those visits supply his only continuing family contact, but not the solidarity he hopes for. The fact that his brother is just, sensible, cheerful, and capable of fraternal affection makes his continued disbelief more painful, not less. He had been present when Sphere manifested in the Council Chamber, saw the changing sections, and heard the Circles' explanation of them. Yet week after week, across seven years, Square has repeated his own part in that event, described the phenomena of Spaceland, and rehearsed the analogical arguments for solid things without persuading him.

Failure of Transmission and Narrative Significance

The hearing's central demand for a diagram or direction foreshadows the failure of Square's teaching in prison. His account depends on a difference that cannot be fully conveyed by listing sides and angles or by repeating the words for a direction his listeners cannot experience. What once became knowledge through Square's physical passage beyond the Line, and through his rising into a view of Flatland's interiors, becomes in the Council chamber an unaccepted claim and in prison a recurring argument. The shift from movement and sight to verbal testimony marks the distance between undergoing a revelation and making another person understand it.

The sharpest measure of that distance is Square's brother. He witnessed Sphere's appearance and heard the Council's explanation, but still frankly disbelieves that Sphere exists or grasps the Third Dimension. Square therefore has no converts, despite having addressed both a public assembly and, over years, his nearest available listener. The imprisonment does not merely remove him from public life; it leaves him with the knowledge that even shared observation and repeated explanation have not overcome the conceptual boundary.

Square's closing comparison casts him as a failed Prometheus: the figure in Spaceland suffered for bringing fire to mortals, while the Flatland Prometheus lies imprisoned for bringing his countrymen nothing they can accept. He nonetheless hopes his memoirs may reach humanity in some Dimension and awaken rebels against confinement to limited Dimensionality. That hope remains unsettled by the very uncertainty he cannot resolve: he is still unsure he ever exactly imagined the Cube, and “Upward, not Northward” haunts his nightly visions. The ending holds conviction and doubt together. Square remains committed to the Truth, but his isolation, his brother's disbelief, and his uncertainty about the image of the Cube leave the revelation both consequential and painfully incomplete.