Blockchains have become immensely popular and are high on the list of national and international research and innovation agenda's. This is partly caused by the numerous interesting applications, combined with the promise of full decentralization and high scalability (among others). Keeping that promise, however, is technically extremely demanding and has already required substantial scientific efforts, which so far have not been overwhelmingly successful. In this paper, we provide a laymen's description of what may turn out to be a fundamental hurdle in attaining blockchains that combine scalability, high transaction processing capabilities, and are indeed fully decentralized.