“The Maths Gene”, Keith Devlin

This book had been on my shelf for months, but I’d been looking forward to the promised explanation of “why everyone has it, but most people don’t use it”. Devlin is quick to point out that the maths gene is of course a metaphor for an innate ability and he then provides lots of evidence for our inherent number sense and mathematical mind.

Cool baby experiments (hooray!) illustrate his points by showing that in a human’s first year of life, “number is apparently a more important ‘invariable’ than color, shape or appearance”: A baby’s surprise, measured by amount of time spent looking at a presented object, is much greater when two objects turn into one than when, say, a ball turns into a rattle.

Another memorable example of how deeply anchored our sense of arithmetic is invokes the mental number line that most people “see” when picturing numbers. Although for most of us this is subconscious, it is nice to find out that I am one of 14 % of people who are aware of doing it. I felt personally addressed again when Devlin mentions how people who become fluent in a second language keep doing arithmetic in their native tongue because it is remembered by sound patterns.

One of his most important messages is the distinction between arithmetic and higher mathematics. While many people (proudly) claim to be “terrible at maths”, the times tables have little to do with mathematics. Maths is instead the science of patterns; patterns like fractals, for example, self-similar figures like broccoli or the Koch snowflake, made of ever-smaller triangles stuck onto the middle of each side of an equilateral triangle. This is fascinating stuff and it’s great to have mathematics pointed out in everyday phenomena: Animal fur, flower shapes and even wallpaper all get fair mention. Elsewhere, Devlin offers a slightly cheesy mathematical soap opera and a fake missing person story to make the reader take note. Maybe he keeps his examples deliberately down-to-earth to fight against the stereotypes of the head-in-the-clouds mathematician, but I don’t care – it works.

A lot of effort is spent on linking maths to language, because Devlin’s main argument is that mathematical and linguistic ability are two parts of the same coin. This is a nice concept but given that I was slightly bored with The Language Instinct, there were too many language syntax trees in this book for me.

Devlin advances his own theory of why all humans have the capability for abstract thought, which he equates to mathematical ability, and it goes something like this: during evolution, the brains of hominids grew and changed structure, which allowed for off-line thought, which was a great advantage and led to maths and language. It takes several chapters to arrive at this point and I’m in no real position to summarise but I think those are the bones of the theory.

As weak Homo sapiens became able to recognise and act on more and more intricate (abstract) patterns, he didn’t have to spend as much time and effort on just surviving and hence we can spend our time today reading, painting, travelling and carrying out other useless activities.

“I do not believe that a basic mathematical ability is any more unusual than an ability to talk”, Devlin says, but people are put off by the notation and, often, teaching methods. “It is a great pity that for so many years our teaching methods have obscured one of humankind’s greatest conceptual inventions”.

This book is really quite the declaration of love to higher mathematics and should be of considerable interest to non-mathematicians. Hopefully you’ll come out of reading “The Maths Gene” convinced that mathematics, rather than being all about numbers and equations, is the discovery of fundamental facts in an abstract world invented by the human brain.

“The Language Instinct”, Steven Pinker

I was excited to read this classic and the introduction sounded really ambitious.

Chapters One and Two were very interesting and give the reader plenty of stuff to talk about at a party, if you can remember anecdotes. Like Leroi’s “Mutants”, these chapters relate unusual phenotypes, like well-spoken but mentally retarded teenagers. It’s nice to find out about pidgin and creole languages as well.

When compared to Diamond’s “Guns, Germs and Steel” at first I thought this book was much more accessible, because it deals with concepts familiar to everyone, rather than abstract theories, and it was easy to connect with Pinker’s line of reasoning, even if you had never thought about these topics before. Later on, though, I felt myself comparing “part read” to “part left to read” and hoping the latter was smaller a lot!

As soon as Pinker hits syntax trees in Chapter Four, he just loses me in the forest. It is uninteresting, dry and not crucial for understanding the rest of the book. There is so much technical stuff here I’m sure it can only interest the most hard-core theoretical linguists.

Much like with many intellectuals, Pinker’s opinion blazes through that he is much more intelligent than the average man. Which is probably true but I would like to figure that out on my own.

There are some fascinating bits, though, that I will take away from this book. I love all the baby experiments showing innate understanding of certain events and ideas (no babies were harmed…) and can’t wait to observe those things myself some day (cringe, I know!). I also got a strange urge to learn the variant of Lardil, an Australian language, with a unique 200 word vocabulary that is allegedly learnable in a day and can express “the full range of concepts in everyday speech”.

Overall, though, I was slightly disappointed at yet another “masterpiece” that just dragged and dragged. Fascinating topic, no doubt, but maybe I should have started on the Language Instinct for Dummies.