yequalsx: yes, almost by definition, memory made up of bits should be modeled with a field of characteristic 2. That seems the most "natural" way to do it. Ho

yequalsx: yes, almost by definition, memory made up of bits should be modeled with a field of characteristic 2. That seems the most "natural" way to do it. However, the authors of this paper are thinking about "computers" in a broader sense. Take a look at these two papers: * "Neural Turing Machines:" https://arxiv.org/abs/1410.5401 https://arxiv.org/abs/1410.5401 * "Hybrid computing using a neural network with dynamic external memory:" http://www.nature.com/nature/journal/v538/n7626/full/nature20101.html http://www.nature.com/nature/journal/v538/n7626/full/nature2... and a related blog post at https://deepmind.com/blog/differentiable-neural-computers https://deepmind.com/blog/differentiable-neural-computers The memory space of these "neural" computers is formally modeled as R^n (n being the total number of parameters and memory addresses), and implemented approximately with 32-bit floating point numbers in practice (i.e., with a memory space of (2^32)^n bits). As you read the paper linked to by the OP, think about these neural computers instead of the one atop your desk. EDITS: removed sloppy math and lightly edited some sentences.