Let me count the ways

I found an article on the history of counting the other day, but I don’t think it was entirely serendipitous. I am intrigued by history of any sort, of course, but more so if it bumps against me softly -if it seems to have been searching for validation in the same world in which I find myself. In me, in other words.

I have long thought that a pencil, or a piece of paper becomes a part of my brain if it helps me consolidate a thought, or whatever. Could History itself have such a requirement? Am I equally essential for History? Does it require me -or at least somebody– for consolidation: the hearer of a tree falling in the forest that verifies the noise it is making? History, after all, requires the retelling of an event, otherwise it is forgotten. Lost… or might never have been…

And what does any of this have to do with counting I can almost hear you asking with your similarly extended selves? Well, the doddery part of me has recently fixated on counting things. It all started, I think, with a design flaw in my electric toothbrush. A dentist somewhere decided that teeth, to be properly attended to, required 2 minutes of cleaning, so the makers of the toothbrush decided to signal the two minutes by turning it off. I accept that a 2 minute vibrator -for the teeth, you understand- is a kind of low-level technological breakthrough. I also reasoned that the two minutes might best be expended equally on all teeth, and not just the ones in front that are easier to reach in the morning. And since teeth are readily divisible into four quadrants that I don’t have to belabour, I started to count in 30 second aliquots to signal me when to switch. And it just ballooned from there.

Now, I can’t walk up or down steps without counting them and I can’t pass a flower without counting the petals. In fact, on a good day, I can tell how many buttons there are on a store clerk’s blouse without blinking or appearing to stare if one of them is undone. Admittedly, knowledge derived from counting has its survival benefits -it is between 15 and 23 steps in total darkness from bed to bathroom, depending on the urgency- but feeling the need to count the number of trees in my yard, even if it occupies time that is otherwise rather empty, seems a little obsessive: a sure sign that what few neural pathways remain intact in my brain are just flaunting their synapses in a pointless attempt at bravado.

At any rate, I found the article about the history of counting interesting, although if anything, it merely served as a justification for my as yet unmyelinated neurons to go rogue. It was written by Colin Barras, who, apart from being a science journalist, and one time technology news editor, life science, and biomedical news editor of New Scientist, also holds degrees in geology, palaeobiology and science communication, plus a PhD in palaeontology. I mention his credentials to dispel any temptation to blame him for any conclusions or sundry foibles of his readership. https://www.nature.com/articles/d41586-021-01429-6?

And anyway, it’s not numerical skills or even the ability to approximate quantities that appealed to me -at my age I no longer have any illusions about acquiring them; my interest focussed on number-words and the need for them. Counting, in other words. Humans may be the only creatures that have learned to count in the wild, but ‘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.’

And, not to be outdone and without meaning to blow my own horn, I, too, am capable of these things. So, nothing new there…

It is the history of numbers and being able to count with them that interested me. As Barras points out, ‘many aspects of numbers, such as the spoken words and written signs that are used to represent them, must be produced by cultural evolution — a process in which individuals learn through imitation or formal teaching to adopt a new skill… Although many animals have culture, one that involves numbers is essentially unique to humans. A handful of chimpanzees have been taught in captivity to use abstract symbols to represent quantities, but neither chimps nor any other non-human species use such symbols in the natural world.’ In other words, there is a difference between ‘innate ‘quantical’ cognition seen in animals and the learnt ‘numerical’ cognition seen in humans.’

Barras goes on to enumerate various (competing) theories as to numbers, but I will admit that the most interesting one (to me as a compulsive counter) was the one about ‘counting-words’ proposed by Evolutionary biologist Mark Pagel at the University of Reading, UK, and his colleagues. As they see them, ‘words are treated as entities that either remain stable or are outcompeted and replaced as languages spread and diversify. For instance, English ‘water’ and German ‘wasser’ are clearly related, making them cognates that derive from the same ancient word — an example of stability. But English ‘hand’ is distinct from Spanish ‘mano’ — evidence of word replacement at some time in the past. By assessing how frequently such replacement events occur over long periods, it is possible to estimate rates of change and to infer how old words are… low-value number words (‘one’ to ‘five’) are among the most stable features of spoken languages… they seem to have been stable for anywhere between 10,000 and 100,000 years.’

I’ll omit the arguments as to whether or not that really suggests ‘the numbers from ‘one’ to ‘five’ derive from ancient cognates that were first spoken tens of thousands of years ago’, but allow me to report that ‘In societies with complex number systems, there were clues to how those systems developed… it was common for these societies to use quinary (base 5), decimal or vigesimal (base 20) systems. This suggested… that many number systems began with a finger-counting stage.’ I feel comfortable in confessing that my subliminal counting rarely uses the vigesimal system because my toes are seldom visible for reference; I am an obligate quinary man and once the available bimanual resources are used up, I start to think about what I am going to have for dinner that evening.

Okay, I know it’s not much, or anything, but Barras did make me feel more comfortable about myself. I mean there was a long line of counters before me and just look at what their determination led to. I’m not sure what obligate quinaries would think of the 2 minute toothbrush, though…


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