Is Information in the Brain Represented in Continuous or Discrete Form?
<i>Rushton (1961) concluded that the neural signaling of a typical human myelinated nerve fiber spanning, say, between a finger and the spinal cord cannot employ a continuous representation due to the presence of noise. Despite these seminal works, computational models based on continuous representation dominate present day neuroscience literature –
for example, continuous attractor networks (Eliasmith, 2005; Wang, 2009).</i><p>Sure, we know from basic information theory that any noisy system is inherently discrete. However, depending on the magnitude of the noise, I don&#x27;t see why we should not describe models in terms of continuous variables.<p>As an analogy, consider the average numerical computer program. We often derive the underlying math in terms of real-valued vector spaces. However, when implementing the program on a computer system, all variables are ultimately discrete. A reason for not thinking about our problems in terms of discrete objects is that math just tends to get incredibly complicated as soon as objects are discrete; and that the computational substrate is fine-grained enough (in most cases).<p>Similarly, if noise limits the effective resolution of individual signals or representations in the brain to 5 bits (number taken from the paper), that (in my opinion) still does not mean that we should stop describing computational neuroscience models in continuous spaces -- at least not, if they are validated with the empirically measured amount of noise; which is exactly what Eliasmith&#x27;s lab (cited above) does (full disclosure: I&#x27;m one of his students). Furthermore, as soon as you code information in populations of neurons, the noise on individual connections becomes less important; one could argue that whenever the brain needs precise computations, it dedicates more neural resources to that problem; then, the noise will &quot;average out&quot;.