Third Millennium

The Third Millennium is the calendrical threshold at which Square’s encounter with Sphere moves from private instruction toward public crisis. As the final sands fall on the year 1999, a new millennium begins; at its first hour, the Flatland Council repeats a centuries-old resolution against people claiming revelations from another world. The contrast between a moment that opens Square’s understanding and an institution that treats it as a recurring threat gives the date its decisive significance.

Midnight and the Change of Era

On the last day of the 1999th year, with rain marking nightfall, Square sits with Square's Wife reflecting on the past and the coming year, century, and Millennium. The narration pauses to clarify that “sitting” in Flatland names a mental state of volition, not a bodily posture in the sense familiar to Spaceland. This qualification makes the scene’s temporal threshold also a threshold between systems of experience: even ordinary words for posture require translation across dimensions.

Square's Wife approaches the mysterious visitor, whom she first mistakes for a perfect Circle, and then leaves when he asks to speak privately with her husband. Square glances at the half-hour glass: its last sands have fallen, and the Third Millennium has begun. The precise, domestic sign of elapsed time places the extraordinary encounter inside an ordinary household, while the new era lends the meeting an air of historical importance.

A New Year in Higher Space

The change of millennium follows Square’s earlier lesson in Lineland. There, King of Lineland cannot understand movement beyond his Line as a direction available to him; Square demonstrates it by moving out of the King’s world. While Square remains partly visible, the King insists that he has not moved; once Square leaves the Line, the King declares him vanished and dead. The episode establishes the limits of a world whose inhabitants mistake their own restricted space for all space.

Sphere later explains that Flatland is a level surface and that a three-dimensional solid can appear there only through a section. Sphere’s changing cross-sections are circles to Flatlanders, just as Square appeared as a line in Lineland. Under Sphere’s guidance, Square rises above his native plane and sees the interiors of houses and creatures, then mines and caverns concealed beneath the surface. The experience recasts visibility: what had seemed inaccessible or hidden becomes open from a higher vantage, without becoming a supernatural privilege.

The Millennial Council

At the first hour of the first day of the year 2000, Square and Sphere descend near the Metropolis while the highest Circles are meeting in solemn conclave. Their gathering follows precedent: the Council met at the corresponding hour at the beginnings of years 1000 and 0. Square’s brother, a perfectly symmetrical Square and Chief Clerk, reads the earlier minutes, which record the same policy at both meetings.

The resolution instructs district Prefects to search for people claiming revelations from another world. Its punishments are ranked by geometric class: Isosceles figures are to be destroyed, regular Triangles scourged and imprisoned, Squares or Pentagons sent to an asylum, and figures of higher rank arrested and brought to the Capital for examination. The recurring decree turns the millennium into an instrument of state surveillance, using a scheduled anniversary to renew an old response to disruptive knowledge.

Revelation Meets Repetition

As the Council passes the resolution for a third time, Sphere tells Square that death or imprisonment awaits anyone preaching the Gospel of Three Dimensions. Square, newly convinced that the reality of space is palpable and teachable, asks permission to descend and enlighten the assembly. Sphere refuses for the moment and instead enters the gathering himself, proclaiming the existence of a land of Three Dimensions.

The younger Counsellors recoil as Sphere’s circular section widens before them. Six low-class Isosceles figures rush toward him, but the Circle they see is already disappearing from their grasp. The presiding Circle shows no surprise; the secret archives, accessible only to him, record similar events at the two earlier millennial openings. He orders that nothing be said outside the Cabinet. Thus the anniversary reveals not simply a new age but the persistence of concealed knowledge: the Council’s official posture of alarm coexists with private awareness that the phenomenon has happened before.