We've had plenty of discussion of the Stroop Effect on Cognitive Daily, and a cool effect it is -- but it's not the only effect with a catchy name. How about the *spatial numerical association of response codes effect*? Not catchy enough for you? The scholars researching the effect have taken to calling it the SNARC Effect. Now if that isn't an effect named to win a blogger's heart, I don't know what is.

First identified by Dehaene, Bossini, and Giraux in 1993, the SNARC Effect suggests that people represent numbers in the form of an imaginary number line. When asked to indicate if a digit is odd or even, people respond faster to large numbers with their right hand, and faster to small numbers with their left hand. Dehaene et al. reason that this must be because respondents are imagining the numbers on a number line, where smaller numbers are always to the left.

More recent research has confirmed the SNARC Effect, so now study is focused on details of the effect. Samuel Shaki and William Petrusic wondered if we respond to negative numbers the same way.

Negative numbers are obviously very different than positive numbers. Most importantly, they don't have real physical correlates -- though I can have 3 golf balls, I can't have –3 golf balls (I can assure you: with my unique talent for hitting golf balls into water hazards, if it was possible, I'd have done it).

Shaki and Petrusic devised a simple test to see if response times for negative numbers were also bound by the SNARC Effect. They showed viewers a computer indicating either "larger" or "smaller." Then two numbers between –9 and +9 were displayed. The two numbers were always just one apart (e.g. 1,2 or –3,–2). The task was to press the button corresponding to the digit which matched the instructions (so, if "larger" flashed, followed by "1,2", the correct response would be to push the button on the right, with the right hand). Participants understood that "larger" always meant "greater" in the mathematical sense -- thus –3 is larger than –4. Here are the results:

These results support the SNARC effect: reaction to smaller numbers is faster with the left hand. However, when the experiment was run in a slightly different format, the results changed. If the experimenters grouped negative numbers together, so participants only had to compare two negative numbers, a kind of reverse SNARC effect was observed:

With negative numbers, the right hand responded faster to smaller numbers, while the traditional SNARC Effect still applied with positive numbers. Shaki and Petrusic argue this result shows that we process numbers differently depending on context. If we're only considering negative numbers, we skip a step and represent the negative numbers increasing in absolute value from left to right. We only use the traditional "number line" representation when considering both positive and negative numbers.

Shaki, S., & Petrusic, W.M. (2005). On the mental representation of negative numbers: Context-dependent SNARC effects with comparative judgments.

Psychonomic Bulletin & Review, 12(5),931-937.

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Not only do I think of numbers on a number line, but I imagine the years of a century arranged sort of like a snakes and ladders board (though with some interesting decade reversals), days of the week and months of the year in oval loops (with distortions that make summers and weekends seem much more significant than they are, a likely holdover from my school years).

I always thought I was rather odd but perhaps I'm quite a bit more common than I realized.

Are any theories offered as to the association of right with larger and left with smaller? Were the participants all good readers in a language in which writing is presented left to right? Are there any cultures in which there is the equivalent of the number line in the reverse direction? Or might this result from the bias towards right-handedness, right seeming stronger/larger/better?

As Lakeoff has pointed out, we often use metaphors, particularly spatial metaphors, in our language. I would not be surprised if our spatial processing capabilities have been co-opted by other types of thinking. But is there a genetic bias to associate left with smaller and right with larger?

Magista, I also have a similar image in my mind. I have long suspected that I do this with both numbers and dates because when I was in kindergarten I remember we had a poster with a 10 x 10 table of the numbers 1 to 100 that was used to help us learn the numbers. But since I can't remember how I thought about numbers before my formal education, I can't really compare.

Looking at this effect across cultural and age boundaries would, I think, reveal a lot of interesting information about how we perceive numbers. Do our metaphors vary between societies or is the visual/spacial number metaphor universally the same in humans?

Interesting. It's not entirely true that negative numbers don't have real physical correlates. Any directional measurement (e.g. how far North is London from here?) has a potential negative value with a real physical correlate. This is why we're able to conceptualize where negative numbers belong on the number line. And I think it might also explain why removing positive numbers has the opposite SNARC effect, because removing positive numbers leaves negative numbers with no direction to be inverted, making them a complete abstraction. Everyone knows "-3 miles north" is the same as "3 miles south" because south is negative north, but "-3 miles" by itself is only an abstract concept because there's no direction to invert.

Magista, you may be a space-time synaesthete:

http://www.cs.uwaterloo.ca/~mjrenss/syn.ppt

Seconding Bob's question (sort of): does this also affect people who read and write right-to-left?

A pang:

That would depend on whether they represent the number line that way. A cursory search online suggests that the number line goes left to right, regardless of the way words are read. Can anyone confirm this?

James, that PPT was fascinating! Slide 8 had almostexactlythe proportional representation of the months as I visualize them.What I don't do, however, is attach any colour perceptions to days/months/years. Maybe to one or two numbers...

Veryinteresting.I am visiting from Tangled Bank..I hope you don't mind a question from a VERY mathematically challenged person (I am lucky to figure out numbers at all, much less on a number line - joke), but I saw a special on TV not too long ago (numerically challenged, remember?) and it was about mathematically brilliant people. One of the people rapidly does very large calculations in his head. He was asked how he sees numbers and to try to describe them. The jist of the show was that this individual sees numbers as images - shapes and colors instead of the arabic numbers. He was attempting to describe a little bit of how he puts the shapes together to quickly form the answers. The shapes were not squares, or other regular shapes - they were often free-form.

I hope I have described this well enough that someone here may have thoughts about this and also if something like this could be the "next" concept in mathematics.

Thanks

Here is a link to a website about Mr. Tammet (the person who sees numbers as shapes, colors, textures, etc that I was writing about above). The website has a link to Mr. Tammet's own website, too.

http://www.wisconsinmedicalsociety.org/savant/tammet.cfm

Although this is an acquired savant talent, it still begs questions...can we all do this? Is this the next step in mathematics?

Thanks

but if the right-brain controls the left hand and the left-brain controls the right hand, what does it all mean?

About the SNARK effect- did you know that it doesn't apply to people who write in languages from right to left?!

such as Hebrew and Arabic!!

(since the SNARK effect relates not only to numerical representation but also to reading words)

actually, the snarc effect does apply to cultures who read from right to left, but the effect is reversed so that left hand is associated with large numbers and vice-a-versa. The effect does not exist in illiterate individuals, suggesting it is an association aquired through reading. I did my honours thesis on this topic, an interestingly found that the snarc effect is also eliceted by auditory stimuli, suggesting an amodal association.

give me the simple answer to the question, for sixth grade level

describe how you would compare two negative numbers

Tell me

@14

Say you have $10.00 and someone steals either $5 from you (i.e., -5) or $10 from you (i.,e -10). Which amount of money stolen is worse?

Just wondering... couldn't you have -3 golf balls if you had had 3 and someone stole them?