One of the most compelling problems in science consists in understanding how living systems process information. After all, the way they process information defines their capacities to learning and adaptation. There is an increasing consensus in that living systems are not machines in any sense. Biological hypercomputation (BH) is the concept coined that expresses that living beings process information non-algorithmically. This paper aims at proving a positive understanding of “non-algorithmic” processes. Many arguments are brought that support the claim. This foster, it is argued, a brand-new understanding of information processing among living beings.One of the most compelling problems in science consists in understanding how living systems process information. After all, the way they process information defines their capacities to learning and adaptation. There is an increasing consensus in that living systems are not machines in any sense. Biological hypercomputation (BH) is the concept coined that expresses that living beings process information non-algorithmically. This paper aims at proving a positive understanding of “non-algorithmic” processes. Many arguments are brought that support the claim. This foster, it is argued, a brand-new understanding of information processing among living beings.