AbstractAnalysis and Modeling is the first “phase” of understanding or developing a system. It is also, maybe more importantly, the foundation of understanding a natural science or system. It's abstract and conceptually difficult but, being foundational, contributes the most to the quality of understanding of (designed or natural) systems. Complex Systems have a natural hierarchy of levels and multiple subsystems. The character and functionality of each level or subsystem “emerges” across its boundaries. Both sides of these boundaries must be understood within that side's natural thought patterns. Integrated interdisciplinary collaboration is essential for making sense of complex systems; but collaboration among disciplines is difficult, because of their different ways of thinking. This creates a dilemma, “understanding complex systems” is one horn; “integrated interdisciplinary collaboration” is the other. This dilemma in complex system analysis/modeling and interdiscipline collaboration, is currently addressed by “grabbing the bull by the horns.” This takes on this doubly complex problem, by painstakingly building up abstract “bull wrestling” skills in and across domains and disciplines. There's another wrinkle; complexity requires interdisciplinary collaboration at deeper, more dissimilar, levels. The usual approach, finding a way to “pass between the horns of the dilemma” will not work here, due to this cross coupling. Rather than trying to pass between the horns, by abstracting away the coupling, we overtly organizing this coupling. We weave a semantic unification space of conceptual connections linking each side of a boundary to its appropriate way of thinking. This allows us to abstracting away the dilemma and iron out the wrinkle. The threads of common image schemas, cognitive metaphors and conceptual interfaces, weave a bridge between the semantics foundations and organizations of each problem. These allow addressing the problems synergistically. This paper presents and explores a naturally valid way for discipline specific and discipline integrating addressing complex systems. We start with the methodological insights from analysis and modeling from the perspective of object orientation, with its ontologies, organizing lexical semantics. We advance from there by integrating in imagistic, imaginative semantics and affordance based interaction methodology, as the keys to addressing complex systems analysis, modeling and integration. © 2007 Wiley Periodicals, Inc. Complexity, 2007