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The leading supercomputers in the Top 500 list are based on a traditional, monolithic architectural approach. They all use complex nodes consisting of different elements such as CPUs and GPUs or FPGAs with common I/O interfaces. It is a well-known difficulty with such systems that one often encounters underutilization, because the more complex the node, the more prone the overall system becomes to inefficiencies. A second problem is the cost of scalability, because a node must be able to perform very complex calculations for problems that are often not scalable, and the same node must perform scalable calculations for problems that would not require such complex nodes. This make the system extremely costly. A third difficulty is the composability of resources, as for instance future computing systems like quantum computers. In order to try solving these problems, we propose a disaggregation of resources and their dynamic recomposition by a programming paradigm called modular supercomputing. We motivate the approach by relying on computer-theoretical considerations for a generalization of Amdahl's law. We present arguments for for the usefulness of modularity for important applications such as Earth System simulations, continuous learning and data analysis problems. FInally, we are presenting first results of test problems.