Sec­tion 1 intro­duces a world unlike ours—Flatland—a place con­fined entire­ly to two dimen­sions. The name is not used by its inhab­i­tants, but it serves to help three-dimen­sion­al read­ers under­stand the lim­i­ta­tions of life in such a plane. Imag­ine a sheet of paper where geo­met­ric shapes—Lines, Tri­an­gles, Squares, and more—move freely along the sur­face. They can­not rise above or sink below it. These fig­ures aren’t drawn or imag­ined; they are liv­ing, think­ing beings, each defined by their sides and angles. Years ago, this world was the only real­i­ty its nar­ra­tor knew. Since then, how­ev­er, his mind has been expand­ed, lead­ing him to reflect on his for­mer igno­rance. What was once his entire uni­verse has now become mere­ly a coun­try in a much larg­er exis­tence.

To some­one from a three-dimen­sion­al world, the idea of not rec­og­niz­ing shapes visu­al­ly might seem strange. But in Flat­land, such recog­ni­tion is impos­si­ble. All fig­ures appear only as straight lines, regard­less of their true form. A Tri­an­gle, Square, or even a Cir­cle can’t be iden­ti­fied just by looking—at least not from the Flatlander’s per­spec­tive. Vision is restrict­ed to a hor­i­zon­tal plane, mak­ing depth and angle com­plete­ly invis­i­ble. To under­stand this, one can use a sim­ple exper­i­ment. Place a coin on a table and look down—it appears cir­cu­lar. But as the eye is low­ered clos­er to the table’s sur­face, the coin becomes an ellipse, and even­tu­al­ly, a flat line. When the eye is per­fect­ly lev­el with the table’s edge, only a nar­row strip is vis­i­ble, indis­tin­guish­able from a line. This is how Flat­landers see each other—nothing more than vary­ing shades of lin­ear bright­ness.

Because of this lim­i­ta­tion, iden­ti­fi­ca­tion in Flat­land depends not on sight but on sub­tler sens­es. Indi­vid­u­als must rely on oth­er meth­ods such as voice recog­ni­tion, touch, or even advanced tech­niques learned through edu­ca­tion. While geo­met­ric vari­ety exists, it remains visu­al­ly hid­den unless one devel­ops the skill to inter­pret slight dif­fer­ences in bright­ness and length. In essence, Flat­land oper­ates under a com­plete­ly dif­fer­ent under­stand­ing of space, where what you see can’t be trust­ed as a full rep­re­sen­ta­tion of real­i­ty. The absence of ver­ti­cal per­cep­tion has deeply influ­enced the society’s devel­op­ment, shap­ing not only its meth­ods of recog­ni­tion but also its entire world­view. A Square doesn’t just see the world in straight lines—he lives in a soci­ety where every­thing is mea­sured in lines, judged by lines, and lim­it­ed by them.

Even their belief sys­tems and social order are formed around this dimen­sion­al con­straint. Since no object can be observed from above, con­cepts like height or vol­ume don’t exist. The very idea of a cube or a sphere would be incom­pre­hen­si­ble to most Flat­landers. Their world is rich in struc­ture, yet bound by what they can per­ceive. Just as a shad­ow gives hints of a three-dimen­sion­al object, Flat­landers only expe­ri­ence faint clues of the broad­er dimen­sions they can­not access. This lim­i­ta­tion, while accept­ed by most, begins to feel restric­tive for those who think deeply. The nar­ra­tor, now aware of dimen­sions beyond Flat­land, reflects on this bound­ary with a sense of loss and dis­cov­ery. What was once cer­tain­ty now appears incom­plete.

Inter­est­ing­ly, this mir­rors how human under­stand­ing often works. We live with­in the lim­its of what our sens­es and tools can detect, assum­ing that to be the whole truth. But his­to­ry shows us that deep­er lay­ers always exist beyond our first impres­sions. Just as Flat­landers must learn to ques­tion the real­i­ty they see, so must we chal­lenge our assump­tions to grow in knowl­edge. The narrator’s jour­ney begins here—not with rebel­lion or rev­o­lu­tion, but with a reeval­u­a­tion of what seemed obvi­ous. It’s a reminder that truth often starts at the edges of per­cep­tion, where imag­i­na­tion meets obser­va­tion. And in Flat­land, that edge is a lit­er­al one—the line they see, and the world they think they under­stand.