This is an extended summary of an invited talk given by the author at Graph Drawing 1999. The text contains some of the basic ideas together with an outline of the whole lecture. As an appendix we included Nesetril - Naceradský 1995 Manifesto. This paper does not contain any of the extensive illustrations which accompanied the lecture (of course this is a paradox in itself: a paper on drawing without drawings). This is necessary due to the format of these proceedings. Moreover the lecture was conceived as a multimedia show (with slides, CD projection and transparencies accompanying the lecture on three different screens) and this is hard in any case to reproduce in the print form. Thus, with a single exception, there are no accompanying figures here. For the benefit of the reader we included the list of our exhibition and an interested reader can get more complete information from the preprint KAM-DIMATIA Series 99-437 (). One can also consult the two-volume set  and related works of the author ,  and  (and references given there). This text was prepared especially for the conference on Graph Drawing.