Sec­tion 15 begins in the qui­et of a reflec­tive evening, mark­ing the final day of the 1999th year. The steady rhythm of the rain had already wel­comed the night, and I sat in silence with my wife as we antic­i­pat­ed the arrival of a new age. With our chil­dren and grand­chil­dren already retired to their rooms, the moment held a kind of rev­er­ence, a solemn appre­ci­a­tion for the cycles of time. There’s some­thing pro­found about wit­ness­ing not just the end of a year, but the close of a mil­len­ni­um. It invites ques­tions about what has passed, what has changed, and what might come. In that hushed space, my mind returned to an ear­li­er con­ver­sa­tion with my grandson—a bright young Hexa­gon, unusu­al­ly pre­cise and full of promise. A les­son shared dur­ing the day con­tin­ued to echo in my mind, tying num­bers to shapes, and tra­di­tion to insight.

The day’s teach­ing had start­ed like many before, with rota­tion­al drills in Sight Recog­ni­tion. Each of us—his uncles and I—took turns rotat­ing at var­ied speeds, chal­leng­ing him to guess our shapes and ori­en­ta­tions with accu­ra­cy. His respons­es were swift and cor­rect, reveal­ing a keen mind already sur­pass­ing his years. Want­i­ng to encour­age that bril­liance, I intro­duced him to a geo­met­ric puz­zle root­ed in basic arith­metic. With nine one-inch squares arranged into a per­fect three-inch square, I demon­strat­ed a con­cept that remains cen­tral to geom­e­try: the rela­tion­ship of parts to a whole. It was a sim­ple dis­play, yet it sym­bol­ized some­thing larger—the pow­er of abstract think­ing and how new under­stand­ing can emerge from famil­iar ideas. This wasn’t just about shapes; it was about help­ing him see the invis­i­ble threads that con­nect log­ic, space, and num­ber.

Even in Flat­land, where dimen­sions are lim­it­ed, there’s always room for intel­lec­tu­al expan­sion. As I reflect­ed on our inter­ac­tion, I real­ized how impor­tant it is to fos­ter such minds ear­ly. Though our world is bound to two dimen­sions, our think­ing does­n’t have to be. Curios­i­ty, when nur­tured, becomes a force capa­ble of press­ing against the bound­aries of per­cep­tion. Teach­ing isn’t only the trans­fer of knowl­edge; it’s a way of light­ing a spark that may lat­er grow into rev­e­la­tion. This becomes espe­cial­ly true in eras of tran­si­tion, like the one we stood on the brink of that evening. A new mil­len­ni­um offers not just a cal­en­dar change, but a chance to reset how we imag­ine our real­i­ty.

That evening’s qui­et was inter­rupt­ed not by noise but by the grav­i­ty of thought. In teach­ing my grand­son, I had glimpsed what lies ahead—not only for him but for all of us. His ques­tion, which had seemed so inno­cent at first, now returned to me with deep­er weight. Could there be some­thing beyond the plane we inhab­it? Is it pos­si­ble to imag­ine a truth beyond our sens­es? Those ques­tions don’t arrive suddenly—they begin in moments like these, sparked by lessons that seem sim­ple but con­tain the seeds of trans­for­ma­tion. That real­iza­tion brought both joy and unease, for every new truth has the poten­tial to unmake the old. And in Flat­land, where order is sacred, such change is not wel­comed eas­i­ly.

As we wait­ed for mid­night, the rain con­tin­ued its steady cadence. I felt the pres­ence of time mov­ing for­ward, not in sharp bursts, but in the soft, per­sis­tent flow of reflec­tion and antic­i­pa­tion. My wife remained silent, per­haps sens­ing the same shift that I did, a qui­et ten­sion between the known and the pos­si­ble. The future, for all its uncer­tain­ty, always starts in the present moment of thought. If my grand­son con­tin­ued to ask, and if he were guid­ed with care, per­haps he would one day see beyond our plane. Not because he was told, but because he had rea­soned it him­self. That would be the true promise of the new millennium—not tech­no­log­i­cal progress, but the progress of per­cep­tion.

In a soci­ety where every­thing is mea­sured and mapped, allow­ing space for the unknown can be rev­o­lu­tion­ary. That’s what I felt on that rainy night—the slow turn­ing of an idea, much like we turned our own bod­ies for recog­ni­tion. Yet this idea could not be seen or touched; it had to be grasped through reflec­tion, deduc­tion, and belief. The lega­cy we leave is not in the forms we pass down, but in the ques­tions we help the next gen­er­a­tion to ask. If he could won­der, per­haps oth­ers would too. And maybe, just maybe, we would no longer be flat in mind, even if we remained flat in form. The moment passed, but its weight stayed with me, mark­ing the turn of not just the year, but of under­stand­ing.