This is an old matter of debate in neuroscience, going back to the 1940s. The question has never been properly resolved. In my opinion, the question has never even been properly formulated.
A recent study in Nature provides evidence that “in some sensory organs and invertebrate systems, neurons can also communicate in the absence of action potentials by grading their transmitter release according to the presynaptic membrane potential, which is directly determined by the barrages of synaptic activity arriving in the cell. This graded synaptic transmission was thought to be irrelevant at the vast majority of synapses in the brain, because the electrotonic distance between the presynaptic cell and its axonal terminals was considered to large.” (The quote is not from the paper but from this summary.)
This result is an interesting and straightforward challenge to the classic view according to which neural impulses are all-or-none. But when the result is formulated in terms of the digital vs. analog question, it misleadingly suggests that neural signals are both digital and analog in the sense of those terms that are used in computer science and engineering.
The notions of “digital” and “analog” that are used in computer science and engineering are relatively well defined, and in my opinion they do not map onto the homonymous but vaguer notions employed in the debate about brains. So, the brain might well be both digital and analog in some loose sense, but that has relatively little to do with digital and analog computers. (For more on this, you a draft that I’ve written on this here.)
Acknowledgments: Thanks to Corey Maley for telling me about this study.
Is the Brain Digital or Analog?
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I don’t think it’s all that bad. If spikes are all that matter, then the random variable describing the spikes takes on one of two values, i.e., it is a discrete signal, which is one well-worn use in electrical engineering (i.e., the neural signal is a string of zeros and ones). If we also need to know the voltage value in the cell, not just whether it spiked or not, then we are sampling from a continuous distribution, i.e., an analog distribution. This is how we discuss analog versus digital thermometers or speedometers, for instance. Similarly, analog computers use continuous variables while digital computers sample from a discrete set (typically 1’s and 0’s).
However, this well-defined sense does not map onto debates sparked by Dretske, who quite deliberately defines the terms ‘analog’ and ‘digital’ quite differently than in the engineering literature. You would be right to criticize anyone for suggesting that the study of graded versus spike-mediated synaptic transmission is addressing Dretske’s framework.