What is the prospect of developing artificial general intelligence (AGI)? I investigate this question by systematically comparing living and algorithmic systems, with a special focus on the notion of "agency." There are three fundamental differences to consider: (1) Living systems are autopoietic, that is, self-manufacturing, and therefore able to set their own intrinsic goals, while algorithms exist in a computational environment with target functions that are both provided by an external agent. (2) Living systems are embodied in the sense that there is no separation between their symbolic and physical aspects, while algorithms run on computational architectures that maximally isolate software from hardware. (3) Living systems experience a large world, in which most problems are ill-defined (and not all definable), while algorithms exist in a small world, in which all problems are well-defined. These three differences imply that living and algorithmic systems have very different capabilities and limitations. In particular, it is extremely unlikely that true AGI (beyond mere mimicry) can be developed in the current algorithmic framework of AI research. Consequently, discussions about the proper development and deployment of algorithmic tools should be shaped around the dangers and opportunities of current narrow AI, not the extremely unlikely prospect of the emergence of true agency in artificial systems.