ABSTRACT
The biological basis for mathematics is present in many living creatures other than human beings, making mathematics very different from reading and writing (that even for human beings can be regarded as “unnatural acts” or cultural artifacts). Many vertebrates, even fish and frogs, display behaviors that signify some kind of number sense, because their decisions show ability to “count” or respond to greater or lesser number sets; described by terms like “numerosity” or “subitizing,” number sense is a deeply embedded ability across many species, mammals and birds included, and is considered to be conserved for its useful survival properties. Fish are able to “count,” in that guppies will gravitate towards swimming with larger schools of fish rather than smaller ones; a frog can count how many noises its rivals are making in a mating situation and will try to outmatch the mating calls up to the number seven. (Amazingly, spiders have been found to actually count up their “savings” by number rather than the total mass of accumulated prey caught in their webs!) Some animals in fact appear to be able to make discriminations between groups of numbers up to ten, although it is more difficult if the groups differ by only one or two and are easier for the birds and mammals to discriminate if the difference within the first nine total numbers are at least three items apart. Chimpanzees are able to learn to associate actual Arabic numerals with a number of items, up to the Arabic numeral “9.” They can arrange the Arabic numerals as well as the groups of items in ascending order from the least to the most! In fact, chimpanzees have been found to have better working memory for numbers than human beings do, showing the ability to remember the locations of numerals that have been 95presented to them in a random sprinkled array after a delay when blank boxes come up for them to tap. (It is thought that some of this wonderful visually based working memory has been preempted or repurposed for language in human beings, and it can be argued that what we have gained is more important than what we have lost in terms of this working memory for spatial arrays of numerals.)
