At a time when many people see numbers, arithmetic, and mathematics as mere oppression, others are intrigued by the basic question, how did the human race learn to do math? There are some clues, as a new project called Quanta is trying to establish.
First, while no animals use abstract numbers in the wild, some animals can do rough figuring:
Although researchers once thought that humans were the only species with a sense of quantity, studies since the mid-twentieth century have revealed that many animals share the ability. For instance, fish, bees and newborn chicks can instantly recognize quantities up to four, a skill known as subitizing. Some animals are also capable of ‘large-quantity discrimination’: they can appreciate the difference between two large quantities if they are distinct enough. Creatures with this skill could, for example, distinguish 10 objects from 20 objects, but not 20 from 21. Six-month-old human infants also show a similar appreciation of quantity, even before they have had significant exposure to human culture or language.Colin Barras, “How did Neanderthals and other ancient humans learn to count?” at Nature (June 2, 2021)
The difference between 1 and 4 is not difficult for a hungry animal. The difference between 20 and 21 is more like an abstraction — you need some pattern of organization to even keep track of it. And it only matters if you are already doing things that require intellectual engagement. All we know for sure is that ancient humans had “sophisticated cognition” hundreds of thousands of years earlier than researchers used to think.
For humans, as Colin Barras notes, it’s often a practical matter. How important are the distinctions?:
In a 2013 study,[Karenleigh] Overmann analysed anthropological data relating to 33 contemporary hunter-gatherer societies across the world. She discovered that those with simple number systems (an upper limit not much higher than ‘four’) often had few material possessions, such as weapons, tools or jewellery. Those with elaborate systems (an upper numeral limit much higher than ‘four’) always had a richer array of possessions. The evidence suggested to Overmann that societies might need a variety of material possessions if they are to develop such number systems.Colin Barras, “How did Neanderthals and other ancient humans learn to count?” at Nature (June 2, 2021)
Probably so. We could probably keep track of our children without numbers. But if we had one hundred chickens, we would soon be scratching some kinds of information on the walls. Emotional memory won’t work as well with chickens.
But once we get serious about numbers, they are really remarkable, and not at all boring. For example:
Most real numbers are not real or not in the way you think. (Robert J. Marks)
We can add new numbers to mathematics. (Jonathan Bartlett)
Yes, you can manipulate infinity — in math (Jonathan Bartlett)