Sec­tion 13 unfolds on the eve of a sig­nif­i­cant moment in time—the sec­ond-to-last day of the 1999th year. As the Long Vaca­tion began, I indulged in my favorite pur­suit, explor­ing geo­met­ric prob­lems well into the night. When sleep final­ly took me, my mind remained occu­pied with unsolved math­e­mat­i­cal curiosi­ties. In the midst of slum­ber, a dream pre­sent­ed itself, vivid and unusu­al. I observed count­less tiny straight lines mov­ing back and forth along a sin­gle path. They resem­bled women, or so I assumed from their slen­der forms. Among them were even tinier, shim­mer­ing points mov­ing at the same speed. The entire scene was alive with a faint, rhyth­mic twittering—a strange sound­scape punc­tu­at­ed by moments of com­plete still­ness when the motion ceased. It felt more like watch­ing a mechan­i­cal rit­u­al than a soci­ety of intel­li­gent beings.

Curi­ous, I approached what appeared to be one of the larg­er female fig­ures and attempt­ed to speak. My first greet­ing received no reply, nor did my sec­ond or third. Frus­tra­tion grew as the silence became almost rude, and I placed myself direct­ly in her path, forc­ing her to stop. It was then that the truth star­tled me—the fig­ure was not a woman at all but the Monarch of this line-bound realm. With dig­ni­ty, he iden­ti­fied him­self as ruler of the world and ques­tioned my pres­ence in his domain. Apol­o­giz­ing for my intru­sion, I explained that I was a trav­el­er from anoth­er world and asked him to describe his land. Yet our con­ver­sa­tion was not easy. The King found it dif­fi­cult to believe that any­thing he didn’t under­stand could exist and treat­ed my igno­rance as mock­ery. Still, with per­sis­tent ques­tions, I man­aged to piece togeth­er the struc­ture of his real­i­ty.

This pecu­liar king­dom was entire­ly linear—what he called his world was a sin­gle straight line. That line was not part of the world; to him, it was the whole of exis­tence. Any­thing beyond it was incon­ceiv­able, not just unknown but tru­ly nonex­is­tent. He had heard my voice ear­li­er, but because he could not see me in his nar­row visu­al range, it con­fused him. Sound seemed to come from with­in his body, not from with­out, since he inter­pret­ed the exter­nal world as part of his own inte­ri­or. When I final­ly spoke direct­ly into his realm, he respond­ed only because my voice aligned with his lim­it­ed per­cep­tion. To him, the idea of a sec­ond dimension—of some­thing out­side his line—was not sim­ply unbe­liev­able; it was impos­si­ble.

The peo­ple of this land, men as lines and women as points, were sub­ject to strict phys­i­cal con­straints. All exist­ed with­in that sin­gle line, with no abil­i­ty to step aside or change lanes. Their visu­al world was reduced to dots, regard­less of who stood before them—man, woman, or child. Per­son­al­i­ty and iden­ti­ty could only be inferred from voic­es, as the eye revealed noth­ing. Since no one could pass anoth­er, once indi­vid­u­als found them­selves beside each oth­er, their lives were per­ma­nent­ly inter­twined. A neigh­bor in Lineland was not just close; they were inevitable. This per­ma­nence mir­rored mar­riage, bind­ing lives togeth­er until death inter­vened. The con­cept of sep­a­ra­tion or indi­vid­ual space didn’t exist. Every­thing about their world was confined—motion, vision, interaction—governed by the sin­gu­lar direc­tion of the line.

For mod­ern read­ers, this dream serves as a pow­er­ful alle­go­ry. It reflects how peo­ple can live with­in nar­row per­spec­tives, unaware of real­i­ties that don’t align with their expe­ri­ences. Lineland’s cit­i­zens are not unin­tel­li­gent, but they are trapped by the shape of their under­stand­ing. They don’t resist truth maliciously—they sim­ply can­not con­ceive of alter­na­tives to their lin­ear world. The Monarch’s dis­be­lief mir­rors human behav­ior in the face of rad­i­cal new ideas. It becomes a les­son in the lim­its of per­cep­tion and the chal­lenge of teach­ing new truths. Just as the King mis­took me for an inter­nal voice, many mis­take unfa­mil­iar ideas for illu­sions or threats. It takes humil­i­ty, both in dream­ing and wak­ing, to see past the edge of our own knowl­edge.

Reflect­ing on this encounter, one sees how dimen­sion­al bound­aries rep­re­sent more than phys­i­cal limits—they are sym­bol­ic of intel­lec­tu­al ones. Lineland’s rigid­i­ty is not just spa­tial but men­tal. A society’s world­view, when left unchal­lenged, can become its prison. The dream did­n’t just offer a glimpse into anoth­er realm—it served as a mir­ror to Flat­land itself. Just as Linelanders can­not imag­ine a sec­ond dimen­sion, Flat­landers scoff at the idea of a third. This real­iza­tion pre­pared me for future rev­e­la­tions. What had first seemed absurd in anoth­er world now hint­ed at truths wait­ing to be dis­cov­ered in my own.