We tend to think of sensory receptors (photoreceptors, inner hair cells) or sensory neurons (retinal ganglion cells; auditory nerve fibers) as measuring physical dimensions, for example light intensity or acoustical pressure, or some function of it. The analogy is with physical instruments of measure, like a thermometer or a microphone. This confers a representational quality to the activity of neurons, an assumption that is at the core of the neural coding metaphor. I explain at length why that metaphor is misleading in many ways in an essay (Brette (2018) Is coding a relevant metaphor for the brain?). Here I want to examine more specifically the notion of biological measurement and the challenges it poses.

This notion comes about not only in classical representationalist views, where neural activity is seen as symbols that the brain then manipulates (the perception-cognition-action model, also called sandwich model), but also in alternative views, although it is less obvious. For example, one alternative is to see the brain not as a computer system (encoding symbols, then manipulating them) but as a control system (see Paul Cisek’s behavior as interaction, William Powers’ perceptual control theory, Tim van Gelder’s dynamical view of cognition). In this view, the activity of neurons does not encode stimuli. In fact there is no stimulus per se, as Dewey pointed out: “the motor response determines the stimulus, just as truly as sensory stimulus determines the movement.”.

A simple case is feedback control: the system tries to maintain some input at a target value. To do this, the system must compare the input with an internal value. We could imagine for example something like an idealized version of the stretch reflex: when the muscle is stretched, a sensory feedback triggers a contraction, and we want to maintain muscle length constant. But this apparently trivial task raises a number of deep questions, as more generally the application of control theory to biological systems. I suppose there is a sensor, a neuron that transduces some physical dimension into spike trains, for example the stretch of a muscle. There is also an actuator, which reacts to a spike by a physical action, for example contracting the muscle with a particular time course. I chose a spike-based description not just because it corresponds to the physiology of the stretch reflex, but also because it will illustrate some fundamental issues (which would exist also with graded transduction, but less obviously so).

Now we have a neuron, or a set of neurons, which receive these sensory inputs and send spikes to the actuator. For this discussion, it is not critical that these are actually neurons; we can just consider that there is a system there, and we ask how this system should be designed so as to successfully achieve a control task.

The major issue here is that the control system does not directly deal with the physical dimension. At first sight, we could think this is a minor issue. The physical dimension gets transduced, and we could simply define the target value in the transduced dimension (eg the current). But here we see that the problem is more serious. What the control system deals with is not simply a function of the physical dimension. More accurately, transduction is a nonlinear dynamical system influenced by a physical signal. The physical signal can be constant, for example, while the transduced current decays (adaptation) and the sensory neuron outputs spike trains, i.e., a highly variable signal. This poses a much more serious problem than a simple calibration problem. When the controlled physical value is at the target value, the sensory neuron might be spiking, perhaps not even at a regular rate. The control system should react to that particular kind of signal by not acting, while it should act when the signal deviates from it. But how can the control system identify the target state, or even know whether to act in one or the opposite direction?

Adaptation in neurons is often depicted as an optimization of information transmitted, in line with the metaphor of the day (coding). But the relevant question is: how does the receiver of this “information” knows how the neuron has adapted? Does it have to de-adapt, to somehow be matched to the adaptive process of the encoding neuron? (This problem has to do with the dualistic structure of the neural coding metaphor).

There are additional layers of difficulty. We have first recognized that transduction is not a simple mapping from a physical dimension to a biological (e.g. electrochemical) dimension, but rather a dynamical system influenced by a physical signal. Now this dynamical system depends on the structure of the sensory neuron. It depends for example on the number of ionic channels and their properties, and we know these are highly plastic and indeed quite variable both across time and across cells. This dynamical system also depends on elements of the body, or let’s say more generally the neuron’s environment. For example, the way acoustical pressure is transduced in current by an inner hair cell depends obviously on the acoustical pressure at the eardrum, but that physical signal depends on the shape the ear, which filters sounds. Properties of neurons change with time too, development and aging. Thus, we cannot assume that the dynamical transformation from physical signal to biological signal is a fixed one. Somehow, the control system has to work despite this huge plasticity and the dynamical nature of the sensors.

Let us pause for a moment and outline a number of differences between physical measurements, as with a thermometer, and biological measurements (or “sensing”):

• The physical meter is calibrated with respect to an external reference, for example 0°C is when water freezes, while 100°C is when it boils. The biological sensor cannot be calibrated with respect to an external reference.
• The physical meter produces a fixed value for a stationary signal. The biological sensor produces a dynamical signal in response to a stationary signal. More accurately, the biological sensor is a nonlinear dynamical system influenced by the physical signal.
• The physical meter is meant to be stable, in that the mapping from physical quantity to measurement is fixed. When it is not, this is considered an error. The biological sensor does not have fixed properties. Changes in properties occur in the normal course of life, from birth to death, and some changes in properties are interpreted as adaptations, not errors.

From these differences, we realize that biological sensors do not provide physical measurements in the usual sense. The next question, then, is how can a biological system control a physical dimension with biological sensors that do not act as measurements of that dimension?