Integral--AQAL--Psychology is not simply a bio-psycho-social-spiritual model of consciousness that partly develops through the life span. It is not multi-disciplinary or inter-disciplinary, but, as the quadrants show, Integral Psychology is an organization of some universal constituents of moments of awareness, including in you and in me across the time of my writing and your reading this, in the context of the myriad events in the quadrants.
The LL shared we-space is made up not just of our agreements or shared values, but also the shared assumptions that might even allow disagreement to happen. We probably agree on the importance of logic in my statements, for example, and this is in part the result of the modern and post-modern world view that Wilber often mentions. The many implicit agreements are communicated (at least in the everyday realm) through LR quadrant patterns of verbal and non-verbal communication.
Logical materialists might say that LR quadrant physical appearance and behavior, including mirror neurons, creates or causes LL shared experience. Philosophical idealism gives consciousness primacy over physicality. Using the quadrants, we can bypass the chicken and egg question about brain and mind, science and spirituality, by noticing that they are simply experienced differently, and that, logically, they influence each other.
Because of the Integral research meta-theory called IMP, Integral Methodological Pluralism, we can, and need to, build valid and reliable conceptual bridges between science and spirit (and states of consciousness), and especially between the conventional adult levels of psychological development, and advanced psychological development. If advanced maturity is recognizable and accessible, then there is something we adults can grow to--there is more to life after all.
I think other Wilber readers will agree that his books are not just intellectually stimulating but are also at times poetic and evocative of state experiences. Integral theory is based on perspective-taking, and science is one important, but not the only, perspective.