Mathematical behavior without a brain?

I have made the argument on more than one occasion that a refreshed look at mathematics may help illuminate the relationship between our experience of the physical and our experience of the thoughtful. Mathematics is a discipline characterized by complex relations among abstract things but, as has been explored from many directions, the action of the brain itself looks mathematical –

*In vision, individual neurons respond to abstractions (particular abstract visual properties contained in an object) like the verticality of edges.

*In navigation, neurons fire in grid-like patterns, internally marking locations.

*In learning, Bayesian probabilities accurately model the development of our intuitive understanding of physical things (like the interplay of  the weight of an object and its size, stability, speed) as well as our expectations of the social behaviors we perceive.

Even more broadly, research led by cognitive and computational neuroscientist Anil Seth supports the idea that all aspects of the brain’s construction of the world are managed through probabilities and inference, where sensory signals are combined with expectations based on prior experience to form the best hypothesis of what’s out there. He defines perception as controlled hallucination, and further argues that this kind of predictive processing can help us understand the nature of consciousness itself, where our sense of self is also generated by the brain’s ‘best guess’ processing. In this light, conscious experience is one of the consequences of the brain’s predictions about sensory signals from within and around the body. In a recent TED talk, Seth says the following:

So our most basic experiences of being a self, of being an embodied organism, are deeply grounded in the biological mechanisms that keep us alive. And when we follow this idea all the way through, we can start to see that all of our conscious experiences, since they all depend on the same mechanisms of predictive perception, all stem from this basic drive to stay alive. We experience the world and ourselves with, through and because of our living bodies.

and later

Finally, our own individual inner universe, our way of being conscious, is just one possible way of being conscious. And even human consciousness generally — it’s just a tiny region in a vast space of possible consciousnesses. Our individual self and worlds are unique to each of us, but they’re all grounded in biological mechanisms shared with many other living creatures.

I don’t think that we have reason to assume that the basic drive is to stay alive. I’m fairly well-convinced that it’s more creative than that. But this also echos the view that was pioneered by biologists Humberto Maturana and Francisco Varela. In their book, The Tree of Knowledge. they describe cognition as “an ongoing bringing forth of a world through the process of living itself.”

These and other studies in cognitive science lend strong support to Yehuda Rav’s argument that at least the bones of mathematics, on which more culturally driven mathematical themes develop, emerge from cognitive processes that have been genetically fixed and driven by natural selection. And the way I see it, questions about these genetically fixed, mathematics-like processes are approached from another direction when brainless creatures seem to demonstrate behaviors that we associate with the presence of consciousness (like learning), or when consciousness is considered very broadly in an evolutionary context.  Studies suggest that the thing we call ‘thought’ exists outside the brain.  Recent New Scientist articles address these issues. Bob Holmes published a piece in May with the title Why be conscious: The improbable origins of our unique mind. Holmes surveyed studies aimed at identifying at least the elements of consciousness that can be found among a diverse set of creatures.

Unlimited associative learning requires an array of brain functions, not only selective attention, but also the ability to combine sensations into one perception, perform compound action patterns and distinguish between self and environment. Scientists have found evidence that this complex learning is surprisingly widespread throughout the animal kingdom. Already, researchers have documented it in almost every vertebrate (except, possibly, lampreys), some arthropods such as insects and crustaceans, a few molluscs including octopuses and, perhaps, some snails. The jury is out on other groups, such as worms, since we don’t have enough evidence to be sure.

…There’s no doubt that human consciousness is special. Whether it is unique in some way or simply richer than that of other animals is still up for debate. However, it is becoming clear that the rudiments of consciousness are all around us.

Then, in July, Erica Tennenhouse contributed an article with the title, Smart but dumb: probing the mysteries of brainless intelligence. Here, findings in various experiments support the idea that “organisms with tiny brains or no brain at all are capable of amazing feats.”

A slime mold, for example, which is neither plant, nor animal, nor even fungus, seemed to learn not to be deterred by compounds like caffeine that were placed strategically in the way of a path toward nutrients. These deterrents were not concentrated enough to harm the slime mold but they were enough to stop them. After several hours, however, they moved through the threat.  And, as time passed, they moved through it more quickly.  After a few days, they almost completely ignored.

Tennenhouse provides a list of organisms, with their neuron count, and one of their feats:

A pea plant, with 0 neurons, when given the option of growing roots in a pot with a steady food supply or one with a “boon-or-bust” supply, will prefer the former but try the latter if they are starved.

Box jellyfish (with 13,000 neurons) “use four of their 24 eyes to peer through the water’s surface at tree canopies, which they use to help them navigate mangrove swamps.”

Bumblebees (1,000,000 neurons) will learn to pull a string to get a sugary treat by watching another bee perform the task.

But here’s something interesting about the slime mold – the abstract of a paper published in Nature in September of 2000 reads:

The plasmodium of the slime mould Physarum polycephalum is a large amoeba-like cell consisting of a dendritic network of tube-like structures (pseudopodia). It changes its shape as it crawls over a plain agar gel and, if food is placed at two different points, it will put out pseudopodia that connect the two food sources. Here we show that this simple organism has the ability to find the minimum-length solution between two points in a labyrinth.  (emphasis added)

And here’s another strategy used by researchers that was reported by Tim Wogan in 2010 in Science.

They placed oat flakes (a slime mold favorite) on agar plates in a pattern that mimicked the locations of cities around Tokyo and impregnated the plates with P. polycephalum at the point representing Tokyo itself. They then watched the slime mold grow for 26 hours, creating tendrils that interconnected the food supplies.

Different plates exhibited a range of solutions, but the visual similarity to the Tokyo rail system was striking in many of them… Where the slime mold had chosen a different solution, its alternative was just as efficient.

A 2012 Scientific American article by Ferris Jabr (How Brainless Slime Molds Redefine Intelligence) sums the point up nicely:

In other words, the single-celled brainless amoebae did not grow living branches between pieces of food in a random manner; rather, they behaved like a team of human engineers, growing the most efficient networks possible. Just as engineers design railways to get people from one city to another as quickly as possible, given the terrain—only laying down the building materials that are needed—the slime molds hit upon the most economical routes from one morsel to another, conserving energy. Andrew Adamatzky of the University of the West of England Bristol and other researchers were so impressed with the protists’ behaviors that they have proposed using slime molds to help plan future roadway construction, either with a living protist or a computer program that adopts its decision-making process. Researchers have also simulated real-world geographic constraints like volcanoes and bodies of water by confronting the slime mold with deterrents that it must circumvent, such as bits of salt or beams of light.

And what about time?

Another set of experiments suggests that slime molds navigate time as well as space, using a rudimentary internal clock to anticipate and prepare for future changes in their environments. Tetsu Saigusa of Hokkaido University and his colleagues—including Nakagaki—placed a polycephalum in a kind of groove in an agar plate stored in a warm and moist environment (slime molds thrive in high humidity). The slime mold crawled along the groove. Every 30 minutes, however, the scientists suddenly dropped the temperature and decreased the humidity, subjecting the polycephalum to unfavorably dry conditions. The slime mold instinctively began to crawl more slowly, saving its energy. After a few trials, Saigusa and his colleagues stopped changing the slime mold’s environment, but every 30 minutes the amoeba’s pace slowed anyway. Eventually it stopped slowing down spontaneously. Slime molds did the same thing at intervals of 60 and 90 minutes, although, on average, only about half of the slime molds tested showed spontaneous slowing in the absence of an environmental change.

…Somehow, the slime mold may be keeping track of its own rhythmic pulsing, creating a kind of simple clock that would allow it to anticipate future events.

While none of these reports say so directly, it does begin to look like slime molds have a mathematical way about them.

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