The Mental Number Line February 9, 2007
Posted by Johan in Cognition, Mathematical Cognition, Neuroscience.4 comments
If you close your eyes and imagine the numbers 1 through 9 on a line, what does the image that appears in your head look like? Most people will say that they imagine a horizontal line, with 1 on the left, and an orderly progression to 9 on the right. Naturally, this finding could be an effect of cultural convention in societies that use arabic numerals, but research indicates that there may be more to it than that. In this post I will outline some research in the field of mathematical cognition (sometimes known as numerical cognition), which suggests that this anecdotal finding may reveal a fundamental characteristic of how numbers are represented in the brain.
If you ask participants to press a key to the left for numbers larger than a reference number, and to press a key to the right for smaller numbers, an interesting pattern appears, after counterbalancing with the converse condition. On average, participants respond faster to smaller numbers with the left key, and to larger numbers with the right key. This is known as the Spatial-Numerical Association of Response Codes (or as its more catchy acronym, SNARC) (Dehaene et al, 1993). This finding has been interpreted as evidence that numbers are coded spatially in the brain. The coding appears to be relative: the same number will show a left-side advantage if it is smaller than the reference number in one condition, and a right-side advantage if it is larger than the reference in the next condition. The effect appears when numbers are presented as arabic digits or as written words, suggesting that the effect is mediated by abstract representations, rather than any characteristics of the visual form of the stimuli (Fias & Fischer, 2005).
At this point, you might think that the SNARC effect has something to do with lateralization: perhaps the left hemisphere is simply better at small numbers, and the right hemisphere is better at larger numbers. Aside fomr the difficulty in joining such a notion with the previously described relative coding, Dehaene et al (1993) showed convincingly that the effect is not a mere consequence of slower processing when information has to cross the corpus callosum: when participants responded with their hands crossed over, the left-side advantage for smaller numbers still appeared, even though the participant was now responding with the right hand, and vice versa. Other investigators have found SNARC effects when participants respond with a single hand (Fias & Fischer, 2005).
Turning to the brain, the hunt for a tidy line of neurons arranged in a line from left to right, has, unsurprisingly, been fruitless (Fias & Fischer, 2005). Still, some evidence suggests that the intraparietal sulcus is involved in number comparison tasks (Göbel et al, 2004). However, this area also responded to the spatial control task that was used in this particular experiment. The same pattern emerged when repeated transcranial magnet stimulation was applied to a nearby area, in order to disrupt neural activity. The SNARC effect was diminished, and so was performance in a visuospatial search task (Göbel, Walsh & Rushmore, 2001).
The failure to find specific neural activity for number comparison tasks in contrast to visuospatial tasks is not necessarily bad news for the idea of a mental number line: if number comparison and visuospatial search tasks activate the same areas, it could be viewed as converging evidence for a spatial organization of numbers. Same areas, and thus, the same form of processing. This sounds good, but runs into conceptual problems, as you are essentially trying to prove your hypothesis with a null result. The core of the problem with current paradigms appears to be that the control conditions which show no SNARC effect (e.g., visuospatial search) still produce activation patterns in fMRI that are not significantly different from that produced by the number comparison task.
Regardless, this area of neuroscience is in its infancy. It will be interesting to see if a neuroimaging approach can inform mathematical cognition in general and the SNARC paradigm in particular, beyond providing a probable brain location.
If you’d like to learn more about the mental number line, the chapter by Fias and Fischer (2005) is a good starting point.
References
Dehaene, S., Bossini, S., & Giraux, P. (1993). The Mental Representation of Parity and Number Magnitude. Journal of Experimental Psychology: General, 122, 371-396.
Fias, W., & Fischer, M.H. (2005). Spatial Representation of Numbers. In J.I.D. Campbell (ed.) Handbook of Mathematical Cognition. Hove: Psychology Press.
Göbel, S.M., Johansen-Berg, H., Behrens, T., & Rushworth, M.F.S. (2004). Response-Selection-Related Parietal Activation during Number Comparison. Journal of Cognitive Neuroscience, 16, 1-17.
Göbel, S., Walsh, V., & Rushworth, M.F.S. (2001). The Mental Number Line and the Human Angular Gyrus. Neuroimage, 14, 1278-1289.
You Make Pearson Cry #2: Deadly Mobiles? February 8, 2007
Posted by Johan in Rants, You Make Pearson Cry.add a comment
While international media appears to have been spared so far, Swedish media decided to go creative when interpreting results from studies by IARC (the International Agency for Research on Cancer) on the possible dangers of mobile phone use. National tabloid Expressen goes for the big guns with a headline that roughly translated goes “cell phones damage your child’s brain.” In the article, it is claimed that the risk of “brain tumour” increases by 39 percent if you have used your mobile phone regularly for over 10 years. There’s no mention of children being at risk, so I presume this bit of the story was inspired by the fact that the risk only appears over the long term.
So is there truth to this? Yes, and no. If you go to the source, it turns out that people who have used cell phones for over 10 years do have an increased risk of cancer, and the difference is on the order of 40 percent.
But the increase is not for brain tumours in general. Rather, there is an increased risk of acoustic neurinoma, which IARC describes as “slowly growing benign tumours that generally have a good prognosis, as they only rarely undergo malignant change.” Now that’s interesting enough in itself, but wait, it gets better: the IARC report also states that the incidence of acoustic neurinoma in adults is on the order of 1 per 100 000 per year.
Let’s do some numbers on that. If the incidence for the normal population is 1/100 000, or a risk of 0.00001 percent per year, and regular mobile phone use over 10 years increases the risk by 39 percent, the incidence for these people is 1.39/100 000, and the risk grows to a whooping 0.0000139 percent.
So to summarise, heavy mobile phone use over a long period of time increases the risk that you will catch a benign, slow-growing tumour by a number that is, in real terms, somewhere on the order of being struck by lightning in your pinky.
The real, undiscovered danger in mobiles lies in their use as throwing weapons. I’m willing to bet that the risk of getting a mobile thrown at your head with deadly results is at least 39 percent greater than the risk of the mobile causing you cancer. Of course, such an argument relies on treating proportions as absolutes…. and that would just be silly, wouldn’t it?
By the way, this particular case has nothing to do with misinterpreting correlations, so from now on, I guess You Make Pearson Cry will concern rants on any bad science reporting, correlational or not.
Ah, the humanity February 7, 2007
Posted by Johan in Evolutionary Psychology, Off Topic.add a comment
Found near Mantua in Italy. The remains are estimated to be roughly 6000 years old (Source, in Swedish).
The other year I got into a long debate with a guy who firmly believed that humans generally behaved worse to one another a few hundred years ago and back: his argument was that because resources were scarce, people generally had to be more selfish in order to survive. He felt that there must have been more violence, more betrayal, more exploitation and opportunism.
I’m not so sure. Humans are social animals, so in true evolutionary psychology-style, I would argue that it is generally more adaptive to stick together in hard times than to see to yourself first. There are obvious short-term benefits to cheating the system, but I don’t think these would be substantial enough to make up for the consequences of social exclusion – which would naturally affect the reproductive fitness of your offspring in turn.
I tend to think that we live in one of the most individualistic societies that have ever existed. In modern society, you have perfect anonymity, and thus perfect irresponsibility. In the bad old days, people lived closer to one another. You couldn’t pack up and move if you fell out with the neighbours. So by necessity, people must have acted in more socially desirable ways.
I know I read a paper where someone argued that the incidence of antisocial personality disorder (aka ‘psychopathy’) is on the rise for this very reason.
Anyway, I think that’s enough evolutionary psychology musings for today.
Completely off-topic February 7, 2007
Posted by Johan in Off Topic.add a comment
But I’m with overwhelmed coursework and lab stuff, so proper postings will have to wait.
Meanwhile, watch this youtube video about web 2.0. It’s good. No, I’m not joking. If you’re even the slightest bit of a geek, this will make you choke up.
Tools of the Trade: Neuroscience Links February 3, 2007
Posted by Johan in Behavioural Genetics, Neuroscience.add a comment
There is a host of free neuroscience resources online, but it can be surprisingly difficult to find them yourself. Here are a few I find useful:
- Brain Voyager: Brain Tutor is a free program which lets you zoom around a brain in 3d. It will highlight lobes, gyrii, fissures. Good for getting a general idea of where things are, roughly. I wrote a brief guide to Brain Tutor, which may be helpful if you have a hard time getting started with the program.
- When you have a specific area that you need to locate or learn more about, try the free version of Gray’s Anatomy over at Yahoo.
- Sylvius is also a free anatomical dictionary, but more specific to neuroanatomy. Note that they’re offering their database in iPod format for a measly $10. Impress your friends!
- Brainmaps offers a giant database of prepped brains in all flavours: humans and non-human animals. Nissl stains, cytochrome oxidase, you name it. It’s like Google Maps but with brains, and at least twice as addictive. Brainmaps also features connectivity maps and some downloadable programs, which go a little bit beyond Brain Tutor in content.
- Finally, OMIM (Online Mendelian Inheritance in Man) is a database which offers comprehensive records of genetic components in various diseases. This resource is not exactly one you play around with like Brainmaps, but OMIM can nevertheless be hugely helpful if you see a gene getting tossed around in an article. A quick check at OMIM lets you see if it is also implicated in other conditions. Likewise, you can (theoretically) plug in a condition and see if it has been linked to any genes. Before you budding behavioural geneticists out there get too excited, it’s worth noting that this database is largely focused on medicine, as that is also the general focus of genetic research in humans… So unless your topic of interest is abnormal psychology or psychiatry, this may be less helpful than it first seems.
If you know of any cool resources, feel free to share them in comments.
