she encountered herr traurig, who was known to know the cause of the screens — herr traurig had first come into ubiquitous notoriety by defying the previously held wisdom of the screens involving the conjecture of shadows, in which screens were held to be mere shadows of other invisible screens : herr traurig ridiculed the conjecture on the basis that it was nonsense, that it added things to things that need not be added, that it unnecessarily complicated the already complicated matter of the infinite system of screens — he offered the analogy, in parody, that it was as if those who postulated the conjecture were to begin learning how to count, and they found that they had too few objects, and that, in order to begin counting they decided the objects must be made more numerous : if the screens were infinite, he held, why must they be made twice infinite in order to be understood : but timsh saw some lurking truth, if counter-intuitive, to the previously-held conjecture of shadows, although he was not able to articulate this truth to herr traurig, and even if he could, traurig's dialectic was suffciently developed to easily refute her vague notion of the truth of the shadows — indeed it was her sense that the truth of the shadows depended on its vagueness, so that the truth's existence was by its nature indefensible through dialectic : the affirmation of her belief in the conjecture of the shadows despite herr traurig's formidable arguments unexpectedly came from herr traurig himself. this happened when traurig, in a particularly haughty and ridiculing temper, laid in against the conjecture's reliance on concepts concerning the line: herr traurig's invective against the line went like this: the conjecture of the shadows fails in describing the dimensions of the screens by elevating the line above the point — whereas, he argued, the shadows would maintain that 'the indivisible lines' are the ultimate principle, obviously the point needs to be accounted for, after all, images are composed of points, and screens are composed of images, so to abandon the point and embrace the line is insanity : but her faith in the conjecture of the shadows and its ultimate principle of 'the indivisible lines' was unshaken. in fact, herr traurig's invective concerning the insanity of the lines further strengthened her intuition regarding both shadows and lines. indeed, were lines not able to encompass both empty space and solid substance? can a line not be constituted both by the oblique space between two objects and by the change in surface quality of a single object?