My Plastic Brain

  Soon afterward, though, my number sense seemed to float away. I don’t know how or why. All I know was that I stopped being top of the class in math and started slipping a good way down toward the bottom. Ever since, I’ve pretty much opted out of the whole thing, and by and large I’ve gotten away with it. But since math underpins most if not all of the science I report on, and comes up more in everyday life than I would like, I would really like to be good at it again.

  Perhaps surprisingly, a basic understanding of mathematics comes as part of the package for humans, along with most other animals, from monkeys to rats, dogs, and even some fish. The fact that, at the very least, most creatures can tell the difference between “many” and “not so many” suggests that it must be a key survival skill favored by evolution. We humans have the added benefit of being able to manipulate numbers in the abstract to turn vague ideas about numbers into actual quantities. French neuroscientist Stanislas Dehaene has found that the less accurate, “there or thereabouts” bits of math processing uses visual and spatial brain areas, whereas the exact stuff requires the same areas as language processing.2 So to some extent, being a words person and a numbers person are kind of the same thing. No excuses there, then.

  Oxford math professor Marcus du Sautoy also argues that there is no such thing as a non-math brain. Even if you count people with dyscalculia, the math equivalent of dyslexia, which affects around 5 percent of the population, we are all mathematicians, he argues, because mathematics is basically the ability to spot patterns in the world. You might not be good at arithmetic, in other words, but pattern-spotting is such a general skill that there is a lot about math that you can master. Pattern-spotting is such a key survival skill that it has been selected for time and again by evolution, says du Sautoy. “If you saw something symmetrical, it was likely to be the face of an animal, and either you could eat it or it could eat you. Either way, those sensitive to symmetry survived,” he wrote recently in the Guardian newspaper, in an article that pooh-poohed the whole idea of there being such a thing as a non-numbers brain.3 “Similarly, humans with a good sense of numbers could tell whether their tribe was outnumbered or not, which would inform the decision to fight or flee.”

  Clearly, though, people do vary in their math ability. We are not all Oxford professors of mathematics, after all. The question of why we differ so much is something that interests Roi Cohen Kadosh, a cognitive neuroscientist also at Oxford University. He studies how these hardwired tendencies get shaped by learning and also how factors like personality, reasoning skill, and attention affect mathematical ability. After hearing my experiences, he suggests that loss of confidence is probably the main problem—as I have heard a few times now, freaking out about not feeling capable of doing something is a sure-fire way to rob the brain of the resources it needs to do it. Could it really be that my conviction that I am terrible with numbers is the reason that I am? And could that be the reason why a recent report by the Organisation for Economic Co-Operation and Development (OECD) found that 54 percent of boys and 65 percent of girls consider math to be stressful.4

  If that's the case, then perhaps a bad head for numbers will be easier to turn around than I thought, and it might not even require too much messing with my brain at all.

  Roi puts me onto one of his students, Amar Sarkar, who recently did a study into how brain stimulation might help people to get over their math aversion enough to unleash their hidden math genius.5 Amar wouldn’t put it like that, though. When we meet at Oxford University, he is cautious and reserved, and he speaks slowly and deliberately to make it impossible to draw any overhyped conclusions from his research so far. He is particularly keen to underline the fact that what I am doing—trying things out on myself—is not science. “It will be scientifically invalid, but still, an interesting experience for you,” he says. Amar is young and just beginning his scientific career and hasn’t even run the gauntlet of being misquoted many times in the science media, so I’m impressed that he seems to inherently understand that, given the wrong information, a journalist might well claim that he is unleashing people's hidden math genius. So I probably shouldn’t. But it isn’t actually too much of an exaggeration. In a recent study where Amar compared two groups of people—one group with an emotional aversion to math, and the other without—he found that, while the low math-angst group were a bit better at math in real life, the high math-angsters were also pretty good: well above average, as you might expect from Oxford University students, who made up most of the study volunteers. The reason they struggled at math seemed to have very little to do with their actual ability.

  Nevertheless, when asked to work out whether a simple sum (for example, 8+2 = 10) was true or false, people who were scared of math were significantly slower. And when they measured levels of the stress hormone cortisol, the math haters had significantly higher levels than their more confident counterparts. But—and this is where it gets interesting—when they boosted the electrical signals in the right prefrontal cortex with electrical stimulation (this is above the eyes, at the top of the forehead, and involved in control of emotional reactions), they found that it not only reduced their cortisol levels significantly but also allowed them to react about fifty milliseconds faster to the math questions. As Lila Chrysikou told me in Kansas, fifty milliseconds is quite a lot to a psychologist—but in terms of using this in real life, the cortisol changes are far more impressive. Lower cortisol means feeling less stressed out, which is something that you could definitely feel. Might this simple intervention, shutting down stress a little bit, really help people love math? Or at least not hate it quite so much?

  Here's where I find out. Having tested me out and concluded that I fit into the category of a math-anxious person, Amar offers to give me a week's worth of stimulation and a bit of cognitive training, just for fun, to see if it changes anything in not only my scores but also how I feel about math.

  I have been stimulated in the brain lots of times now, and it never stops making me feel a bit nervous, especially when Amar tells me that he is going to use a more powerful and long-lasting version called tRNS (transcranial random noise stimulation).

  I’m cheered up, though, by the fact that Amar is strapping the electrodes to my head with a lovely bright-blue-toweling sweatband. I comment that it's going to be a fabulous Dire Straits look, then wonder if this will make any sense to Amar, seeing that he was born four years after the classic Money for Nothing video came out; plus he grew up in India, where I have no idea if Dire Straits were even a thing. But he grins broadly and tells me that, although Dire Straits weren’t huge in India when he was growing up, his parents are big fans of stadium rock, and he was raised on the likes of Bruce Springsteen and Dire Straits. I briefly glimpse a less reserved side of Amar as we chat about the joys of dad music, and ponder what Mark Knopfler is up to nowadays.

  Then it's onto the familiar routine of baseline tests (pages of basic arithmetic questions that get harder and harder, and I’m not allowed to skip any), plus various measures of my working-memory capacity.

  Then he straps me into the brain stimulator and turns on the current. “Do you feel enhanced?” he asks. “No,” I reply. “Should I?” “No,” he says mysteriously, and then I start the test.

  Unlike when I was in Kansas, I don’t feel any kind of wonkiness, buzz, or other changes in myself. That might be because when Lila plugged me in, she was turning down activity in the prefrontal cortex, whereas Amar is turning it up. Perhaps it's easier to notice when you lose brainpower, but a bit extra doesn’t necessarily seem that different. I certainly don’t feel like any kind of genius, that's for sure. Even so, I quickly settle into the test, and, once it becomes clear that I can manage the level of mathematics required to tell whether a sum is true or false (for example, 9 x 3 = 27), I relax and start racing through them. It seems to help if I say the sums out loud, so I start muttering to myself whenever Amar leaves the room.

  I do the same for the next few days—and on days
two and three, Amar gets me to do some cognitive training that, in an experiment he has just finished and which isn’t published yet, has also had some effect on math ability. It's quite fun—I have to pretend to be a worker in a robot factory and have to make various on-the-spot decisions about what to do with robots that come along the conveyor belt: if it has broken arms, press left; if it is red, press right. If it has a yellow light around it, press nothing. I recognize it as taxing working memory plus some of the mental-control skills I lacked back in the early days in Boston, and I am struck by how much easier I find it to make these kinds of fast mental decisions.

  In the Betty test, I found it impossible to change my mind about pressing a button once my hand had started moving. Now it's not a problem. Perhaps this is no coincidence: pretty much everything I have done since has been relevant to the prefrontal executive control bits of the brain. Coping with the robot task might be proof that I have gained a small amount of control. Or it might be that I am getting a boost in this area from the stimulation, which I am today using via a rather fetching rubber cap. I later learn that the theory behind this is that training working memory transfers to a skill that needs working memory (math). It's back to working memory again, albeit in a slightly more interesting game format. It's perhaps no surprise. I mention to Amar that executive functions keep cropping up. “Most of your book is executive functions,” he confirms.

  After that, I have a whole afternoon to kill in Oxford, so I head to one of the city's many bookshops to look for a math revision guide. Amar isn’t keen on this idea because it adds another factor to the experiment that he didn’t plan for, but concedes that since this isn’t a proper study, and given that I’m only having two robot-factory training sessions—rather than several weeks, as they would in the real study—adding a few minutes of math practice here and there probably won’t make much difference. Amar tells me that sometimes you don’t see transfer for several weeks after training anyway, since it takes time for the changes to make themselves apparent.

  I had thought of picking up a revision guide a few weeks earlier at home, but I didn’t want to ruin my baseline scores by practicing too early. I had also been thwarted by the full force of my aversion to math. I walked into my local bookshop, headed to the revision guide section, and pulled out a math book aimed at teenagers. I opened it to a random page and…well, the pages might as well have contained images of rotting corpses. I physically recoiled, shoved the book back on the shelf, and found myself walking out of the shop before I realized I had even told my legs to move.

  This time, in Oxford, I decide to ease myself in more gently and so pick an exam revision guide aimed at ten-year-olds. That night, on the train to see a friend in nearby Didcot, I have a go, one question at a time, taking it slowly, and being sure to check the answers on the cheat sheet as I go along. It could be that having been zapped earlier that day did something to my brain, but weirdly I find myself actually enjoying it. And every time I get the answer right, my confidence grows. My final score is 96 percent. Not bad at all.

  Sure enough, a few weeks later, when Amar sends me my results, they seem to suggest that my skills have indeed improved. On the baseline math tests, where I had to wade through pages of multiplications, long divisions, and the like, my baseline score was 98. After the stimulation and training, it jumped to 106 (see figure 6.1). It doesn’t sound like a big improvement, but Amar seems impressed. “It's an 8.1 percent improvement. For just two sessions, that seems pretty sizeable.” Based on other data, he tells me that a rough estimate for the practice-effect is around 2 percent.

  He is, however, keen to point out that this doesn’t necessarily mean that the other 6 percent came from the intervention. “This is a sample size of one, and there could have been any number of reasons that you would want to improve in the second session,” he says. Expectation or regression to the mean (a strange law of statistics that says that a second score on anything will be closer to average than the first, whether you do anything to change it or not) could have played a part.

  One thing I hadn’t paid a huge amount of attention to at the time was that, before each sum appeared on the screen, a word with either negative or positive connotations (a “prime”) flashed up briefly in front of me. In a previous study that Amar's is based on, people with high math anxiety were quicker to respond when the prime was a negative word like “useless” or “failure.”6 This result was a surprise: usually, having a boost of positive thinking helps people to do their best work. Instead, with math anxiety, it seemed to resonate with how the people saw their own abilities, which somehow made them perform better when the prime was negative.

  Figure 6.1. Numerical operations score.

  When Amar repeated this study, he didn’t find the same effect in his sample (he says that it might be because his sample was mixed sex while the original was women only; women are known to be more likely to be math anxious than men). For this woman, though, the negative words didn’t make any difference: my reaction time was more or less the same whether the word was a compliment or an insult.

  The fact that negative primes do affect some people suggests that they are working as another kind of unconscious bias. In chapter two, I found that my focus was being tugged toward disapproving faces, while skipping over the happy ones. Practicing doing the opposite, using online training, seems to have done the trick in rewriting that bias. The ultimate aim for math-anxiety training is to do something similar with the way people feel about their math ability. “This will be the really interesting thing…. Can we cause people with high math anxiety to stop benefiting from the negative prime and start benefiting from the positive prime?” Amar says. It hasn’t been done yet, but that's definitely the aim of this kind of research—to make people maybe not love math but at least not have a negative emotional reaction to numbers, whether that be conscious (“I don’t do math”) or unconscious (“Oh, look, I seem to be walking away from the math section of the bookshop rather quickly”). Amar agrees. “Yes. I guess that would be the ideal outcome,” he says, cautious as ever.

  While I didn’t show any sign of being affected by the positive or negative words that came before the sums, during stimulation, the speed at which I decided if the sum was true or false increased by two hundred milliseconds compared to baseline. Again, this is more impressive than it sounds. “A two-hundred-millisecond improvement at no cost to accuracy in performance is considered huge. In comparison, the improvement in my math-anxiety paper was just about fifty milliseconds,” says Amar.

  Again, there are a whole heap of caveats to add here. To quote Amar when he sent me my results, “The main thing is that performance on the second session was much better than the first. Of course, this doesn’t mean that it was due exclusively to stimulation. To truly determine whether it was the stimulation, we would need about 120 participants, sixty of whom complete the sessions with real stimulation, and sixty of whom complete the same thing with placebo/sham. If the improvement is greater following real compared to sham, then we can say that stimulation produced the effect.”

  We didn’t measure my cortisol levels and so don’t know if I, like the volunteers in Amar's study, would show a lowered stress response after being stimulated. I certainly felt less terrified about the sums in the “after” testing, but that could just as easily have been because I was more familiar with them and knew that I could handle some if not most of them. And getting 96 percent in the revision guide didn’t harm my confidence either.

  Figure 6.2. Reaction time in milliseconds before and after stimulation and training. My accuracy score was the same before and after (93.5 percent versus 93 percent), suggesting that I didn’t speed up at the cost of accuracy.

  In the end, though, it doesn’t matter whether it was the stimulation or practicing math that made me feel less terrified of the test. As Amar points out, doing math puzzles is a form of brain stimulation. In other words, you don’t need to wire your brain into a battery, but it seems to hel
p.

  Whatever starts it off, once that confidence starts to build, it sets up a virtuous circle. And if Amar is anything to go by, it is absolutely possible to get better at math with a bit of effort. On day two of testing, as we head to the testing room, he admits that, until recently, he had a pretty bad phobia of mathematics—something that is not terribly useful if you want a career in science. Thankfully, he tells me, it's not a problem anymore. “What did you do?” I asked, hoping for a pearl of wisdom that will inform what I do from now on. He grins at me as the elevator doors open, and raises his eyebrows. “I practiced.”

  Practice, then. That's about as high tech as it needs to be as far as math is concerned. Sean the sub was right all along: I just need to stop being fatalistic about having a “non-math brain” and do something about it. It harks back to the idea of a growth mind-set, which I encountered in the debate about working-memory training. Whether people benefit from cognitive training or not has a huge effect on whether they think it is possible to improve, whatever their current ability. On the other hand, if you don’t think you can do anything about a skill, you probably won’t bother to work on it, and your predictions about being bad at it will come true.

  Nevertheless, the stimulation did seem to have an effect, and I’m intrigued to find out what exactly it might be doing to help things along. After my trip to Oxford, I call Roi Cohen Kadosh and ask him. “It's a really good question,” he says, suggesting that no one else knows either. “I can say what we think….

  “There are some results showing that we can modify neurochemicals in the brain—some of them are associated with neuroplasticity,” he tells me. “Then we are affecting connectivity between different brain regions with stimulation as well [and] affecting the consumption of oxygen and metabolites.” Is this all happening at once, or does one thing happen first and set off a domino effect of brain change? “It's hard to know,” he says. “Maybe it's all of them working at the same time.”