Noumenal Rings and Badges. One of the things I didn't do before was to make a proper ring/badge distinction between alpha/anti-omega and omega/anti-alpha, since the concept of circles within squares in the one case and of squares within circles in the other case is only valid on the basis that, under the objective vacuum of a female hegemony, both squares and circles will be ringful, i.e. vacuous, in complete contrast to the badgeful nature, as it were, of squares and circles existing in relation to the subjective plenum of a male hegemony. Hence merely to distinguish circles within squares from squares within circles is not enough. Neither will exist except in contrary relation to rings and badges, vacuums and plenums. Thus the notion of a plenumous circle in a square would be no less of a contradiction than the contrary notion of a vacuous square within a circle. Circles only exist within squares in consequence of a vacuous precondition hailing from a female hegemony in metachemistry over antimetaphysics, and have a right to be termed ringful. By contrast, squares only exist within circles in consequence of a plenumous precondition hailing from a male hegemony in metaphysics over antimetachemistry, and have a corresponding right to be termed badgeful. Rings and badges are, in general terms, the alpha and omega of, in this case, a noumenal antithesis between absolute rectilinearity (coupled to absolute anti-curvilinearity) and absolute curvilinearity (coupled to absolute anti-rectilinearity). They can also exist, as I will show in the next essay, on the basis of a phenomenal antithesis between relative modes of rectilinearity and curvilinearity.