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Manifold initiatives try to utilize the operational principles of organisms and brains to develop alternative, biologically inspired computing paradigms. This paper reviews key features of the standard method applied to complexity in the cognitive and brain sciences, i.e. decompositional analysis. Projects investigating the nature of computations by cortical columns are discussed which exemplify the application of this standard method. New findings are mentioned indicating that the concept of the basic uniformity of the cortex is untenable. The claim is discussed that non-decomposability is not an intrinsic property of complex, integrated systems but is only in our eyes, due to insufficient mathematical techniques. Using Rosen's modeling relation, the scientific analysis method itself is made a subject of discussion. It is concluded that the fundamental assumption of cognitive science, i.e., cognitive and other complex systems are decomposable, must be abandoned.