At this moment an objection may arise: since the Thomas-Yau-Joyce picture is beset by some vagueness and plenty of technical difficulties, why is it useful as a guiding principle at all? Besides the supportive evidence that we shall soon discuss, the main answer is that the Thomas-Yau philosophy transforms a PDE problem (the existence of special Lagrangians) into a categorical framework, which if better understood is in principle checkable by algebraic means. A Bridgeland stability is the interplay between a category and a numerical property. In the analogous problem of Hermitian Yang-Mills connections, the existence criterion is formulated by $\mu$-stability, which compresses the information of the Kähler form into only certain intersection numbers/cohomological integrals (cf. section 2.5). Likewise, the stability condition responsible for the existence of special Lagrangians, even though it is not adequately specified, is in principle a compression of the analytic data of a holomorphic volume form, and quite plausibly enters only through cohomological integrals of $\Omega$, as will be discussed more fully in Chapter 3. As an indication of the possible predicative power of the Thomas-Yau picture, here is a sample question as food for thought: