Today, we are going to talk about two related abstract quantities and their developmental course: time and number.
There are objects in the physical world that the brain is able to sense; on the contrary, there are abstract concepts such as time or numbers that the brain represents in a way that is difficult for scientists to access, especially in infancy. How can we be sure when children develop a sense of time and number as well as whether these are inherent abilities or learned ones? Both being abstract quantities, do time and number rely on the same mechanisms or are they only functionally similar?
Time perception is a difficult concept to unpack: anything ranging from being able to tell how much time has passed to bodily reactions to time (such as circadian rhythms) and projecting thought into a past or future time can fall under time perception. However, the origins of time perception is primarily studied through the lens of perceiving time durations, such as being able to tell whether one activity took longer than another or specifically triangulating how much time has passed.
Some of the most relevant research began with Brackbill and Fitzgerald (1972), who state that infants are ideal to work with because they are “uncontaminated” by things adults worry about and can respond purely to the temporal intervals they are shown. The authors worked with infants at 1 month and used Pavlovian temporal conditioning to produce autonomic constrictions of the pupils at 20 second intervals through a change of illumination of a lightbulb. Then, even with the source of light removed, infants’ pupils continued to constrict at the same 20 second intervals (Brackbill and Fitzgerald, 1972). It appears that the infants’ brains encoded the interval of illumination change and continued to reproduce it even when the stimulus was removed, suggesting that they are able to respond to short intervals of time.
An ERP study by Brannon et al. (2007) found that infants and adults show a similar brain response to temporal changes in a series of auditory tones (for example, when a habituated 1500-ms interval was replaced with a 500-ms interval). Authors concluded that 10-month-old infants can detect temporal changes to a 2:3 ratio, suggesting that their brains perceive time according to the same principles that guide adult timing (Weber/ Fechner laws).
Have you ever thought that time was passing more slowly than it really was? Children misperceive time in this way, too, if even more so than adults. Gautier & Droit-Volet (2002) found that 5 and 8-year-olds both had more difficulty estimating duration for visual and auditory signals than adults. These results support the theory that time processing, while present at an early age, continues to improve with experience – a very developmental perspective.
What about number? It is known across the scientific community that numerical reasoning has roots in the approximate number system (ANS), a system that helps form non-exact representations of quantities and is as equally affected by Weber/ Fechner laws as time perception. Can the ANS be trained? A study by Halberda and Feigenson (2008) revealed that ANS acuity increased due to neural maturation as well as experience, such as practice at numerical discrimination. However, this neural maturation truly peaks around early adolescence: 3-year-olds could discriminate numbers with a 3:4 ratio, 6-year-olds could discriminate numbers with a 5:6 ratio, while adults can discriminate numbers up to a 10:11 ratio.
Interestingly, research has shown that impairment of the ANS and impairment of time perception are both correlated with developmental dyscalculia in children (Mazzocco et al., 2011; Vicario et al., 2012). This makes intuitive sense, given that they are both, in some aspect, estimation of quantity. However, in a study with adults, Cappelletti et al (2011) found that time perception was not significantly damaged in adults with dyscalculia. Is this a case for children being able to grow out of a time perception impairment?
Time and number have several commonalities, such as their innate origin, adherence to a scalar property, and similar veins of development as well as their reliance on two main executive functions: working memory and inhibition. Additionally, the two abilities both reside in a common area in the parietal lobe and demonstrate similar neuronal activation in approximation tasks (Bueti & Walsh, 2009). This was the basis for a generalized magnitude system that pitched number, time, and space as having a common underlying structure.
Perhaps next, we can investigate spatial perception?
Brackbill, Y., & Fitzgerald, H. E. (1972). Stereotype Temporal Conditioning in Infants. Psychophysiology, 9(6), 569–577. https://doi.org/10.1111/j.1469-8986.1972.tb00766.x
Brannon, E. M., Libertus, M. E., Meck, W. H., & Woldorff, M. G. (2007). Electrophysiological Measures of Time Processing in Infant and Adult Brains: Weber’s Law Holds. Journal of Cognitive Neuroscience, 20(2), 193–203. https://doi.org/10.1162/jocn.2008.20016
Bueti, D., & Walsh, V. (2009). The parietal cortex and the representation of time, space, number and other magnitudes. Philosophical Transactions of the Royal Society B: Biological Sciences, 364(1525), 1831–1840. https://doi.org/10.1098/rstb.2009.0028
Cappelletti, M., Freeman, E. D., & Butterworth, B. L. (2011). Time Processing in Dyscalculia. Frontiers in Psychology, 2. https://doi.org/10.3389/fpsyg.2011.00364
Gautier, T., Droit-Volet, S. (2002). Attention and time estimation in 5- and 8-year-old children: a dual-task procedure. Behavioural Processes, 58(1), 57–66. https://doi.org/10.1016/S0376-6357(02)00002-5
Halberda, J., & Feigenson, L. (2008). Developmental change in the acuity of the "number sense": The approximate number system in 3-, 4-, 5-, and 6-year-olds and adults. Developmental Psychology, 44(5), 1457–1465. http://dx.doi.org.ezproxy.library.tufts.edu/10.1037/a0012682
Mazzocco, M. M. M., Feigenson, L., & Halberda, J. (2011). Impaired Acuity of the Approximate Number System Underlies Mathematical Learning Disability (Dyscalculia). Child Development, 82(4), 1224–1237. https://doi.org/10.1111/j.1467-8624.2011.01608.x
Vicario, C. M., Rappo, G., Pepi, A., Pavan, A., & Martino, D. (2012). Temporal Abnormalities in Children With Developmental Dyscalculia. Developmental Neuropsychology, 37(7), 636–652. https://doi.org/10.1080/87565641.2012.702827