A granny summary of an article by Dror Dotan and Noa Handelsman (it’s here)
The Role of Syntax in Numerical and Mathematical Processing
The word “syntax” probably reminds most of us of high school language classes. It is usually used it to describe the rules that combine words into sentences. What you might not know is that syntax is also a pretty important aspect of mathematics and numbers. So what exactly is the syntax of numbers and calculations, and why does it even matter?
Syntax is a term that describes systems of rules responsible for combining basic symbols into more complex structures: words into sentences, digits into multi digit numbers, mathematical symbols into algebraic expressions, and so on. Think of a sentence like the boy ate an apple – it is syntax who dictates that the boy is the one who did the eating, and the apple is the one being eaten, not the other way around. It might also be helpful that we know that usually its boys that eat apples and not apples that eat boys, but if you think of a similar sentence, like hope lost hope, we defenitly need syntax to figure it out. In school we learned that in such a sentence the boy is the subject, ate is the verb, and apple is the object. The idea of syntax in numbers is quite similar. Take a number like 34,560 – syntax tells us that 4 is the thousands digit and 0 is the units digit, and also that we do not need to say the 0 out loud. What about algebra? Who do you think said that in an expression such as 4e2 + 5, e is the base and 2 is the exponent? That’s right, syntax. In short, syntax is what allows us to decode structures that contain more than one symbol. In mathematics, that is the name of the game. We take “building blocks” and combine them into more and more complex expressions that represent more and more complex ideas.
One of the fascinating things about syntax is that it is a highly complex ability. Many aspects of syntax appear to exist only in humans. Some researchers argue that the ability to handle syntax is a kind of human “superpower” that distinguishes us from other animals. According to this view, there is one general syntactic ability that enables combining words into grammatical sentences, digits into multi digit numbers, sounds into a harmonic mekody, lines into a shape that looks symmetric, and more. In this sense, syntax is like an abstract organ that humans have and other animals do not. It helps us speak, calculate, and recognize melodies.
But let’s not get too content – it is not that simple. Other studies suggest that “syntactic ability” is not one single thing. It is a collection of many, and we mean many, distinct mechanisms in the brain. For example, researches show people who cannot apply syntax in one domain, perhaps due to a cognitive impairment, but have no problem applying syntax in another domain. In one study in our lab, we identified people with a syntactic impairment in language, who struggled to understand sentences like “the boy who ate an apple walked” – they thought that the apple is the one who walked. At the same time, the very same people had no trouble with syntax in other domains. For instance, they could easily combine digits into multi digit numbers. Cases like these suggest that syntactic abilities in different domains are separate. If there were just one general ability, we would expect the same level of syntactic performance across all domains.
The story gets even more complex. It is not only that syntax differs between domains, it can also split within the same domain. Some people with a syntactic impairment struggle to read the number 3,406 out loud as “three thousand four hundred and six,” but have no problem doing the reverse process – they can hear “three thousand four hundred and six” and write 3,406. This shows separate syntactic abilities for reading and writing numbers. And even if we focus only on reading numbers, we find that it involves several different syntactic mechanisms, each responsible for a slightly different type of structure.
Why should we care whether syntax is one super ability or a collection of many separate abilities? First, because we are researchers, and these questions matter to us. But there are also practical reasons, especially when it comes to learning. If syntax is one general ability, then training a child’s syntax in one domain, for example practicing on multi digit numbers, should also improve their syntactic abilities in other domains, like understanding sentence structure or algebraic expressions. But if each syntactic ability is separate, we will need to work with the child separately in each domain.
So what’s the bottom line here – is syntax a uniquely human superpower, or a mix of many distinct mechanisms? We think both answers are right. We do believe syntactic ability is a human superpower, but not as a single mechanism or one specific brain area. Instead, it is the human brain’s ability to organize itself in a way that can handle complex kinds of expressions. This ability is manifested in different systems in the brain, each responsible for a different domain: language, number processing, music, and maybe more. In each of these, it allows handling expressions far more complex than those handled by other animals.