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White laboratory mouse (Mus musculus ) crawling on a clay pot. Uttarakhand India
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Mice Can’t Do Calculus But Their Brains Can

Neuroimaging and mathematics showed that a simple Stop! signal in the brain would not allow a mouse to stop as quickly as it in fact did

Science writer Kevin Hartnett tells us that, based on experiments with mice, the brain sharpens control of precise maneuvers by using comparisons between control signals rather than the signals themselves:

[The research] explores a simple question: How does the brain — in mice, humans and other mammals — work quickly enough to stop us on a dime? The new work reveals that the brain is not wired to transmit a sharp “stop” command in the most direct or intuitive way. Instead, it employs a more complicated signaling system based on principles of calculus. This arrangement may sound overly complicated, but it’s a surprisingly clever way to control behaviors that need to be more precise than the commands from the brain can be.

Kevin Hartnett, “The Brain Uses Calculus to Control Fast Movements” at Quanta Magazine (November 28, 2022) The paper is open access.

The researchers observed, via neuroimaging and mathematics, that a simple Stop! signal in the brain would not allow the mouse to stop as quickly as it in fact did. There had to be another signalling system in the brain as well. So they decided to have a closer look at it.

Between the cortex where goals originate and the [mesencephalic locomotor region] MLR that controls locomotion sits another region, the subthalamic nucleus (STN). It was already known that the STN connects to the MLR by two pathways: One sends excitatory signals and the other sends inhibitory signals. The researchers realized that the MLR responds to the interplay between the two signals rather than relying on the strength of either one.

Kevin Hartnett, “The Brain Uses Calculus to Control Fast Movements” at Quanta Magazine (November 28, 2022).

The MLR pays attention the difference between the two signals more than the signals themselves. A bigger difference means a faster change and a quicker command to Stop!

The researchers cast the stopping mechanism in terms of two basic functions of calculus: integration, which measures the area under a curve, and derivation, which calculates the slope at a point on a curve.

If stopping depended only on how much of a stop signal the MLR received, then it could be thought of as a form of integration; the quantity of the signal would be what mattered. But it doesn’t because integration by itself isn’t enough for rapid control. Instead, the MLR accumulates the difference between the two well-timed signals, which mirrors the way a derivative is calculated: by taking the difference between two infinitesimally close values to calculate the slope of a curve at a point. The fast dynamics of the derivative cancel out the slow dynamics of the integration and allow for a fast stop.

Kevin Hartnett, “The Brain Uses Calculus to Control Fast Movements” at Quanta Magazine (November 28, 2022).

So mice can’t do calculus but their brains can. Assuming that the human brain works similarly to the mouse brain when it comes to sudden stops, then — if the researchers are correct — our brains do calculus too, even if, despite applying ourselves personally, our minds are not very successful at it.

Neuroscientist Sridevi Sarma, who was not involved with the paper, notes that “it allows you to anticipate and predict.” If we must stop suddenly, it may be more useful to know how fast we are speeding up or slowing down than to know how fast we are going. The obliging brain’s calculus gives us that tool.

Fun fact: Mice actually like to run. Even wild mice will run in wheels, given a chance:

You may also wish to read: Researchers: The [human] brain’s claustrum acts as a router for thoughts. Francis Crick thought the claustrum might be the “seat of consciousness,” an inherently materialist concept. The researchers think he was wrong. Of course, seeing the claustrum as a router is more consistent with the immaterial nature of consciousness than seeing it as a seat. (Denyse O’Leary)


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Mice Can’t Do Calculus But Their Brains Can