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Continuous vs. Discrete Across the Sciences
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I'm currently listening to Walter Isaacson's biography of Albert Einstein, and it's always interesting how similar disputes and controversies happen in parallel disciplines. Around the turn of the century, there were debates regarding the nature of matter, whether it was continuous, or made up of discrete elements (i.e. atoms and molecules). Also, the nature of light was at issue. Was it continuous, like a wave, or made up of discrete elements? What ramifications did each of those views have?

When it came to the nature of matter, statistical methods were being used around the turn of the century to be able to describe various phenomena in terms of the random motion of very small elements. In 1905, Einstein's "miracle year", one of his papers focused on explaining Brownian motion, the random motion of particles suspended in a gas or liquid (such as water). Einstein's paper described the mathematics behind large numbers of discrete units randomly bumping into one another, and how that would give rise the Brownian motion, providing further evidence for the idea that matter is composed of discrete elements.

It reminded me of the debate in neuroscience around the same time. Camillo Golgi championed the reticular theory, the idea that the brain was a continuous web. On the other hand, Santiago Ramón y Cajal theorized that the brain was composed of discrete elements. It wasn't until electron microscopes were invented in the 1950's and we could see neurons and the tiny synaptic spaces between them before Cajal was definitively proven correct.

The distinction between continuous and discrete is virtually the same as that between digital and analog, and when it comes to brain function, that debate is still very much alive.

Over at Chris Chatham's blog, one of his most popular entries is entitled 10 Important Differences Between Brains and Computers. Guess what #1 is?

Difference # 1: Brains are analogue; computers are digital

It's easy to think that neurons are essentially binary, given that they fire an action potential if they reach a certain threshold, and otherwise do not fire. This superficial similarity to digital "1's and 0's" belies a wide variety of continuous and non-linear processes that directly influence neuronal processing.

For example, one of the primary mechanisms of information transmission appears to be the rate at which neurons fire - an essentially continuous variable. Similarly, networks of neurons can fire in relative synchrony or in relative disarray; this coherence affects the strength of the signals received by downstream neurons. Finally, inside each and every neuron is a leaky integrator circuit, composed of a variety of ion channels and continuously fluctuating membrane potentials.

Chris is highlighting the idea of "rate coding", that the primary means of information being transmitted by neurons is in the rate at which they fire, which he's right in saying is a continuous variable.

But he ignores "temporal coding", the idea that information is conveyed by the specific timing of individual spikes, rather than just an average rate of firing. For example, barn owls are able to use the relative timing of incoming signals from each ear to locate an object (such as prey) in space. When one ear is closer to the sound source, the sound waves will generate auditory input in the closer ear first, and take a very small amount of time to reach the ear that's further away. The owl's nervous system is able to calculate the difference between those inputs in order to localize the sound source.

Also, there is a large amount of evidence for spike-timing dependent plasticity being an important, if not the most important, basis of learning. This is a form of learning where the strength of a synapse is modified based on the relative timing of the presynaptic and postsynaptic neurons.

So, one could make a very strong case that the brain is not essentially analog. However, there's no reason to categorically stereotype brains as being either digital or analog. Rate codes are obviously used. But then, so are temporal codes. So is the brain digital or analog? Well, as with matter, in a sense, it's both.

We certainly don't perceive or interact with water as if it is made of discrete units. When we pour a glass of it, or go swimming in it, it functions as a continuous quantity. But if you shrunk down small enough, you'd see that it's really a bunch of molecules bumping around into each other.

The history of modeling nervous systems has predominantly focused on neuron models that model rate coding. However, if the discrete actions of individual neurons is important in explaining brain function, then it should not be averaged or abstracted away into a continuous function. And to describe the brain in an all-or-nothing manner as either digital or analog is, I believe, a conceptual mistake.

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