Abstract
A fascinating research program in neurophysiology attempts to quantify the amount of information transmitted by single neurons. The claims that emerge from this research raise new philosophical questions about the nature of information. What kind of information is being quantified? Do the resulting quantities describe empirical magnitudes like those found elsewhere in the natural sciences? In this article, it is argued that neural information quantities have a relativisitic character that makes them distinct from the kinds of information typically discussed in the philosophical literature. It is also argued that despite this relativistic character, there are cases in which neural information quantities can be viewed as robustly objective empirical properties.
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Notes
The entropy associated with a single value of some random variable is given by the log of the reciprocal of its relative frequency. \(\hbox {Log}_{2}(1/.5)\) = 1 bit. \(\hbox {Log}_{2}(1/.25)\) = 2 bits. To find the entropy of an entire distribution, we take a weighted sum over all individual entropies. So, the marginal entropy \(\hbox {H}(\hbox {X}) = .5(1) + .25(2) +.25(2) = 1.5\). The computation required to find the marginal entropy H(Y) is identical to that required for H(X). To compute the joint entropy H(X,Y), we take a weighted sum over the individual entropies associated with each of the six terms in the center of the table. Three of those terms evaluate to 0. Once they are removed, the remaining terms constitute an expression that is identical to that for H(X), which, as we just saw, is equal to 1.5 bits.
It is worth noting here that the hair-in-the-wind argument exploits a perfectly contingent fact about humans. Filiform hairs on the legs of crickets move with the local air currents too. But in that case, neural receiver mechanisms use the hair-air correlation for predator detection (Magal et al. 2006). In that case, hair direction really is an informational signal. At least in principle, the amount of information transmitted in this case could be quantified.
I have not given a definition of the term “function.” As the size of the philosophical literature on the subject suggests, it is not easy to say exactly what it means for an object or process to have a biological function. For many aspects of biological theory, including the kind of function discussed here, I favor the modern history theory of functions, as expressed in Godfrey-Smith (1994). But my view is compatible with other theories of biological function as well. It is important, however, that the notion of function have some relation to natural history. Without that connection, it loses some of the objectivity that I argue is worth retaining in neurophysiological theory. See section “Is neural information cbjective?” for further commentary on this point.
I have suppressed the role of time in this discussion because it complicates the mathematics without changing the conceptual issues under consideration. Notice that the argument doesn’t change significantly if we consider two non-identical strings sent from one location to another over time. If strings share statistical properties, their transmission may achieve the same information rate expressed in bits/s. This is still no reason to think that the two strings have the same meaning.
Another, more controversial, reason to resist the semantic interpretation of information theoretic estimates is that the activity in a single neuron seems to be too low-level for semantic properties to emerge at all. If there are no semantic properties at the level of individual neurons, then, clearly, information estimates describing the behavior of individual neurons cannot be interpreted semantically. Rosa Cao has defended this anti-semantic position on the basis of an interesting dilemma. The signals transmitted by individual neurons either lack sufficiently robust connections to the external world to carry content on their own, or the connections they exhibit are too inflexible too deserve an informational, as opposed to merely causal, mode of description (Cao 2012).
See, for example, Cover and Thomas (1991).
The phrase “For Shannon” in this definition might be misleading. Shannon was many things, but he was not a metaphysician. He was not interested in trying to divide the world into informational phenomena and non-informational phenomena. In fact, in a short paper entitled “The Bandwagon,” Shannon warns that information theory is easily misused when applied outside the realm of communications technology (Shannon 1956).
Although their article is focused on genetic information, they suggest that their definition can be extended to include neural information quantities.
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Acknowledgements
Funding was provided by the National Science Foundation (Grant No. 1430601). Thanks to Peter Godfrey-Smith, Rosa Cao, Ron Planer, Matteo Colombo, Daniel Kostic, and Gualtiero Piccinini for their insightful criticisms of my initial writings on this topic. Thanks also to two anonymous referees for their detailed commentary on an earlier draft of this manuscript.
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Rathkopf, C. Neural information and the problem of objectivity. Biol Philos 32, 321–336 (2017). https://doi.org/10.1007/s10539-017-9561-7
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DOI: https://doi.org/10.1007/s10539-017-9561-7