The Narrow Road to the Complex Plane　複素平面の細道

As I tread deeper upon the Imaginary Path, the sun no longer deigns to rise or set; it merely drifts, shifting its argument in an endless cycle. What I deem to be morning resembles the eve, and what I take for evening still clings to the shadows of high noon. My footsteps have lost all sense of "before" and "after"—to advance is but to rotate, and to tarry is but to oscillate.

虚の道を進むほど、日はもはや昇りも沈みもせず、ただ角度を変へて巡るのみとなれり。朝と思へば夕に似、夕と思へば未だ昼の影を残す。我が歩みは、もはや前後を失ひ、進むとは回ること、留まるとは揺らぐこととなりぬ。

At a certain hamlet, I came upon a pond clear as a mirror. The figure reflected on the water stood with left and right reversed. When I raised my hand, the shadow responded with a slight lag; I could no longer discern which was the master and which the reflection. A villager spoke: "This is the Land of the Conjugate. The form is cast, yet the essence remains distinct."

ある里にて、鏡のごとき池に出づ。水面に映る我が姿は、左右入れ替はりて立てり。手を挙ぐれば、影は遅れて応へ、我が動きと、影の動きと、どちらが主とも定めがたし。里人いはく、「ここは共役の地なり。姿は映れど、実体は異なる」と。

"Conjugate"—the word lingers heavy in my breast. In my travels, did I too once possess one who formed my perfect pair? Yet, when I strive to call that name, my voice merely dissolves into the imaginary void. As I venture further, the path begins to trace a circle. Upon the third encounter, the truth dawned on me: to advance is to return; to return is to advance. In this realm, "distance" is but a deception. At night, I record these thoughts in the traveler’s register: One step forward, the Origin recedes; One turn around, and it draws near.

共役──その語、胸に重く留まりぬ。我が旅にも、かつて対をなす者ありしや。されど名を呼ばんとすれば、声は虚に溶けて消えたり。さらに進めば、道は円を描き始む。三度目に至りて、我は悟れり。進みて帰る。帰りて進む。ここにて距離とは、欺きに過ぎず。夜、宿帳に記す。一歩進めば 原点は遠のき回れば近づくと。

Upon a certain mountain pass, I encountered a shadow-like guide. He had no name, called only "i." His form was never fixed—at times a boy, at times an old man. When I walked, he stood ahead; when I tarried, he appeared by my side. i spoke thus: "On the path of the Real, to square is to increase. On the path of the Imaginary, to square is to invert." I understood not even the half of these words, yet my very footsteps began to sense this inversion.

ある峠にて、案内人めいた影と行き合ふ。名はなく、ただ i と呼ばれたり。姿は定まらず、時に少年、時に老人なり。歩めば先に立ち、止まれば隣に現る。i は言ふ。「実の道にては、平方すれば増す。虚の道にては、平方すれば反転す」と。その言葉、我には半ばも解せず。されど歩みは、確かに反転を覚え始めたり。

Beyond this point, the Real fades thin, the Imaginary grows thick. I arrived at the ruins of an ancient capital. It was said to have flourished once, yet now only its absolute value remains high, while its essence is void. The towers stand uncollapsed, yet no soul dwells within. Their values are vast, but their meaning is small. I find myself thinking: Perhaps the world of men is much the same. Fame, status, records—all of these may be nothing more than aliases for "Distance."

ここより先、実部薄れ、虚部濃し。ある古き都の跡に至る。今は絶対値のみ高く、中身は空なり。塔は崩れず立てど、中には誰も住まず。値は大なれど、意味は小さし。我は思ふ。人の世もまた、かくのごときものか。名声、地位、記録──すべては距離の別名に過ぎぬやもしれず。

At midnight, i declared: "Henceforth, should you wish to return to the Origin, you must first conjugate yourself." To conjugate—does it mean to turn one's self inside out? Or does it mean to face the shadow one has long since lost? Only my footsteps have begun, slowly, to wind inward, and further inward still.

夜半、i は告げたり。「この先、原点に戻らんと欲すれば、一度、己を共役せねばならぬ」 共役するとは、己を裏返すことか、失ひし影と向き合ふことか。ただ歩みのみが、徐々に内へ、内へと巻き始めたり。

Imaginary, Real --
A single, seamless thread
On a spring evening.

虚も実もひとつらなりの春の宵

（Guskuma Gregory Akinori ＋ いしみねかんと）