And so our perfect numbers, wisdom’s boast, Are faint, uncertain shadows in the mind, That we can never picture to the eye, Nor truthfully apply to anything. We use a ragged, ill-drawn substitute, That answers all the purposes of life. The truths of mathematics, so sublime, Are never true to us, concretely known; And in the abstract so concealed are they, No man can swear he has their perfect form. We can’t conceive a line without some breadth-- The perfect line possesses length alone; Earth never saw a pure right-angle drawn, Pythag’ras cannot prove his theorem, The finest quadrant is but nearest truth, The closest measures but approximate, And all from Sanconiathon to Pierce, With grandest soaring into Number’s realms, Have only fluttered feebly o’er the ground, Their heaven-strong wings by feebling matter tied. Man is a pris’ner, but the prison walls Are very vast; so vast the universe Lies, like a mote, within their mighty scope. Most are content to grovel on the earth, Some rise a little way, and sink again; And some, on noble wing, soar to the bounds, And eager beat the bars. Beyond these walls The abstract lies, and oft the straggling rays, Through crevices and chinks, stray to our jail; And these we fondly hug as truth. Poor man! The glimpses of the great Beyond have roused, For centuries, his curious soul to flight. With eagle eye fixed on the distant goal, He cleaves his way, till dashed against the walls; Some fall with bruiséd wing again to Earth, And some cling bravely there, so eager they To reach the untouched prize, and so intent Their gaze upon its light, they notice not The bounds, till Hamilton, with wary eye, Discovers the Eternal bounding line, And sadly shows its hopeless fixity.