Grand­son, whose casu­al remarks on the mean­ing of 3, 4, and even 5 dimen­sions had met with the approval of the Sphere? This idea was, at first, with enthu­si­asm; but I soon dis­cov­ered that, while the the­o­ry was com­pre­hen­si­ble enough, its appli­ca­tion baf­fled me. Every attempt to demon­strate the con­cept of upward, not North­ward, by analo­gies from the world of sight, total­ly failed; for in the realm of Flat­land,
the very idea of “upward” as opposed to “North­ward” or any oth­er “ward” was incom­pre­hen­si­ble.

Despite my con­fu­sions, I attempt­ed to share my rev­e­la­tions with my Grand­son, hop­ing his fresh per­spec­tive and pre­vi­ous curi­ous com­ments on
dimen­sions might ease the teach­ing process. As my plans unfold­ed, the moment came to put my the­o­ry to the test. Call­ing upon my Grand­son, I
endeav­ored to enlight­en him about the three dimen­sions, employ­ing var­i­ous means of prac­ti­cal demon­stra­tion to elu­ci­date the the­o­ry of
“Upward, not North­ward.” My efforts, ini­tial­ly met with inter­est, soon turned to dis­may as he strug­gled to grasp the abstract con­cept utter­ly for­eign to his two-dimen­sion­al per­cep­tion.

The more I per­sist­ed in my expla­na­tions, invok­ing geo­met­ri­cal fig­ures and the exam­ple of the Sphere’s vis­i­ta­tion to enhance my argu­ments, the more bewil­dered he became. His inabil­i­ty to per­ceive or even to imag­ine the upward dimen­sion I so ardent­ly described, made our con­ver­sa­tions increas­ing­ly frus­trat­ing for both. Towards the end of our dis­cus­sions, my Grand­son’s tem­per flared, and he reproached me for what he deemed non­sense, claim­ing it impos­si­ble to believe in the exis­tence of any­thing beyond the famil­iar two dimen­sions of Flat­land.

Res­olute yet dis­heart­ened by this ini­tial set­back, I con­tem­plat­ed the mon­u­men­tal chal­lenge that lay ahead in my mis­sion to edu­cate Flat­land about the third dimen­sion. Rec­og­niz­ing the her­culean task of alter­ing the ingrained per­cep­tions of an entire soci­ety, I pon­dered over the
meth­ods I could employ, con­sid­er­ing the resis­tance and skep­ti­cism I encoun­tered from my own Grand­son.