Math Skills
The highest form of pure thought is in mathematics. ~ Plato
An essential skill for survival is applied mathematics. Time, space, and numbers allow animals to forage, find their way home, and migrate daunting distances. Knowing the number of immediate predators, or the size of a neighboring group, can lead to life-or-death judgments.
Many species are sensitive to quantity. Spiders know how many prey they have tucked away on their webs.
Numerous cues keep ants on the navigational straight and narrow, including counting their steps, sensing the polarization of sunlight, as well as keeping track of visual, olfactory, magnetic, and vibrational landmarks. An ant’s mental map of terrain is at least as intricate as any other animal. It has to be, as an ant’s life is forfeit if it loses its way.
Honeybees can tell quantitative differences. They can rank quantities according to the rules “greater than” and “less than.” Honeybees also understand the concept of nothing. Children do not grasp the symbolic number zero until they are 4 years old.
“Nothing” can be informative. ~ German zoologist Andreas Nieder
Several ancient human civilizations lacked the full understanding and importance of zero, leading to constraints in their numeric systems. ~ Australian zoologist Scarlett Howard et al
Newborn chicks understand both relative and absolute quantities. Their mental number line – running left-to-right small-to-large – is identical to innate human conception. Chicks also have a good sense of ratios.
Monkeys and birds can not only distinguish numerical quantities but also grasp the empty set as the smallest quantity on the mental number line. ~ Andreas Nieder
Road Signs
It’s all about context. ~ American ethologist Ted Stankowich
Cars on the highway traveling at unnatural speeds kill a lot of birds. Those birds that do manage to live learn the rules of the road.
From observation, birds figure the average speed of vehicles on a section of roadway and adjust their flight patterns to accommodate traffic. Speeders are an especial danger, as birds do not expect breakneck drivers.
Optimal Foraging
Animals prefer habitats that contain a higher percentage of preferred food items and avoid habitats containing a higher proportion of predators. ~ Canadian psychologist William Roberts
Foraging for nectar may not seem too complex, but it is a craft to perform it efficiently. The traveling salesman problem (TSP) – efficient multiple-stop route formulation – has vexed human problem solvers since first considered in 1832. TSP is a computationally difficult (NP-hard) problem to solve. But bumblebees manage it.
Bumblebees optimize their nectar collection. Individual flowers vary in nectar content, especially considering those already recently harvested. A bumblebee remembers visited flowers and selects the most easily accessible flowers that have the highest probability of rich reward. Bumblebees solve TSP using spatial memory and a bit of trial and error learning.
Sea Star Geometry
Sea star larvae swim about for 2 months before settling down. They propel themselves by controlling thousands of beating, hair-like cilia on the edges of their bodies.
By selectively coordinating some cilia to beat opposite the direction they are swimming in, larvae dynamically create vortices in the water. These whirlpools pull algae and other foodstuffs from far away into a sea stars’ path. Sea stars optimize the number and effect of the vortices to maximize currents toward them. Sea star larvae are experts in the applied 3d geometrics of fluid dynamics.
Whipping up whirlpools slows a sea star down, but even a little larva knows the importance of a good meal. With full bellies, young sea stars give the whirlpool making a rest and get along.
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Math skills are analogous to social skills. One would not be effective socially without a decent sense of numbers. Gregarious animals need to discriminate numerically and gauge probabilities, at least intuitively, to successfully cope within a group, and especially to lead a tribe.
Lionesses live their lives in prides of female relatives. They share cub-rearing. Lionesses recognize each other’s roars. When hearing the roars of unfamiliar lions, they count how many there are.
Even though spotted hyenas live in clans of up to 90 individuals, they spend most of their day in smaller, more vulnerable groups. Like lions, hyenas count unfamiliars and assess odds.
Spotted hyenas are more cautious when they’re outnumbered and take more risks when they have the numerical advantage. ~ American zoologist Sarah Benson-Amram
Children as young as 3 years spontaneously discover algorithms for addition which allow them to make counting decisions in the same way as chimpanzees. This is precocious knowledge manifesting at a developmental stage. How those mental mechanics work, in either chimps or children, is not understood. What is known is that chimps and humans both have similar sociality and have an innate ability for numeracy.
Innate aptitude may require a cultural kick for an ability to manifest. Because basic math is ubiquitous in modern societies, the common assumption is that humans naturally comprehend simple numeracy. That is not so. The Piraha tribe of hunter-gathers in Brazil cannot count at all. Their word for 1 also means “a few,” while 2 does double duty for “not many.” Anything else is simply “many.” They also have no way to say “more,” “several,” or “all.” American linguist Daniel Everett tried to teach the Pirahas math basics, but not a single Piraha could count to 10 or add 1 and 1 after 8 months of diligent instruction.
