Foraging for food, remembering, and mathematics

On April 16 Scientificamerican.com reported on research that links hunting for words with foraging for food.

Our brains may have evolved to forage for some kinds of memories in the same way, shifting our attention from one cluster of stored information to another depending on what each patch has to offer. Recently, Thomas Hills of the University of Warwick in England and his colleagues found experimental evidence for this potential parallel. “Memory foraging” is only one way of thinking about memory—and it does not apply universally to all types of information retained in the brain—but, so far, the analogy seems to work well for particular cases of active remembering.

The report describes how researchers led by Thomas Hills of the University of Warwick used verbal theme clusters to investigate the possibility that the body (or the brain) searches for information in much the same way that a creature searches for food.  They used something called verbal fluency, tasks that have been designed to study memory and to test for the breakdown of memory from diseases.  It has often been observed that when people are asked to name members of a category (like animals, vegetables, or movies) their lists develop in clusters of related items.  In naming animals, for example, when a subcategory is exhausted (like animals that can be pets) they move to another subcategory (like large predators, or ocean animals, etc).  The question researchers were trying to answer was whether the moves among subcategories were analogous to the moves an animal might make among food sources.  Biologists have mathematical models that describe optimal foraging, and these was used to write software that would characterize the shifts among themed clusters that were made by participants in the study.

Hills coded a computer program that first decided the probability that a student would name a particular animal, given what the student had already named. If someone started with “cat,” for instance, they are much more likely to next type “dog” than “zebra.” When the program encountered a pair of words that were unlikely to appear together, followed by a pair of words with a much higher chance of coupling, it interpreted the pattern as a jump from one themed cluster to another—such as from pets to savanna.

Then the program compared the responses of participants to what optimal foraging models predict.  The students whose mental activity most closely matched the model were actually the ones who made the longest lists.

Hills’s program further revealed that the most successful students abandoned one category of animals for another when it took too long to name a new animal, just as a foraging animal leaves behind a patch of food when its time would be better spent at a more fruitful patch. The findings appear online in the February 13 issue of Psychological Review.

While the study addresses only a particular kind of memory, or remembering activity, the significance of the investigation may not lie only in the questions it answers about memory function. The results support the more general investigation of whether higher level cognitive abilities evolve from more fundamental ones, like spatial foraging mechanisms.  According to Hills,

Before we had abstract thinking, we had brains that helped us get around physical spaces—some of those abilities may be co-opted to search in information space.

Foraging mechanisms have already been used to explore how we search for information, on the web for example.

But in October, I discussed a related idea described in an article on vision at Physicsworld.com.  The piece contrasted the fractal pattern of the searching eye with the restrictive stillness of digital imaging technology.

Richard Taylor and his colleagues at the University of Oregon investigated this movement or how we search for information in a complex scene.  By tracking the motion of the eye they found that the eye searches one area with short steps before jumping a larger distance to another area, which it again searches with small steps, and so on, gradually covering a large area.

And there is the work done to investigate how the body represents spatial information in the activity of what neuroscientists call grid cells in the brain:

Grid cells provide geometric coordinates for locations and help the brain generate an internal grid to help in navigation. Along with place cells, which code for specific locations, head direction cells, which act like a compass, and border cells, which define the borders of an environment, grid cells enable to brain to generate a series of maps of different scales and help with recognition of specific landmarks.

One of the keys to how these things may be related to mathematics lies in the observation of planned action, studied by cognitive scientists and cited by Yehuda Rav (in his essay on Mathematics and Evolutionary Epistemology

When we form a representation for possible action, the nervous system apparently treats this representation as if it were a sensory input, hence processes it by the same logico-operational schemes as when dealing with an environmental situation.

I have little doubt that mathematics emerges from all that the body knows and all of the ways that it can act.   Looking at how the nervous system interacts with conceptual or internally generated worlds can tell us quite a lot, not only about the content of mathematics, but also about how it is motivated and, perhaps, what it means to be human.

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