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Numerical cognition

3 points by rtplasma ↗ HN
Since early childhood I have visualized numerical constructions [1] (and other discrete abstract objects) in an "imaginary" space, in a particular way. That is, when imagining ordinary numbers, I have "seen" them along a particular path in space. In fact, its representation in space is so permanent, and established, that I am able to draw its path on a paper.

I not only visualize ordinary neutral numbers (the number line), but also visualize calendar-cycle/seasons (months), clock (24 hour line), and the alphabet -- each system with its own and dedicated path in space.

I have always taken this for granted. Only recently I began wondering whether other people visualize numbers, and how. I made a quick search online and found that this property of the human mind has in fact been known for along time [2], and it has been studied recently as well [3], [4].

Do any of you perceive numbers in a particular way, e.g. with a number-space association? Do you create number-forms (as explained in [1])? I am interested if any of you have any thoughts about this issue. Is it subject to change, or has it remained unchanged since early childhood?

[1] https://en.wikipedia.org/wiki/Numerical_cognition#Relations_between_number_and_other_cognitive_processes [2] http://www.nature.com/nature/journal/v21/n543/abs/021494e0.html [3] http://www.nature.com/nrn/journal/v6/n6/full/nrn1684.html [4] http://link.springer.com/article/10.1007/s00426-015-0741-2

6 comments

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tgflynn
Could you explain a bit more about how you "visualize numbers" ? You say you see them along a path. How exactly does the path represent the number ? Is it the length, or the number of segments ?
rtplasma
To clarify, I visualize the number line. It is actually a curve which extends into space like a meander, and certain distinct numbers are located on points with large curvatures (e.g. 10 and 20). It is somehow "logarithmic-cyclic", so that the shape of the curve starts over for every 3-power -- 10^0, 10^3, 10^6. The shape of the number space from 10^3 to 10^6 looks the same as for 10^0 to 10^3, except the representation in space appear scaled-up or larger. I do not know how common this perception is :)
rtplasma
I do not perceive a "high-resolution"-curve (for example, 14 and 15 is hard to distinguish on the curve, but 12 and 18 is easy to distinguish). So, when I think about a number I approximately know where on the curve to assign it.
brudgers
I don't think I visualize numbers in an unusual way, but I'm curious if there are any diagrams of your visualizations that you're comfortable sharing.
rtplasma
At the moment, I have no drawing available. But it would be a version of what is drawn on p. 439 in [3].
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