mapping: condition 1: shape, color, and size of
each element; condition 2: overall area (
summation of the areas of all elements depicted in each
stimulus); condition 3: overall perimeter (
summation of the perimeters of all elements depicted
in each stimulus) and density (the mean distance
among the elements). Moreover, in condition 3,
there was a negative correlation between overall
area and number: The overall area of the 8
elements was larger than that of the 32 elements.
Furthermore, the elements of each stimulus
occupied the same overall spatial frame in
conditions 2 and 3. If the overall area, in the
presence of the same perimeter, was the crucial
factor underlying number-space mapping, chicks
would have chosen the right panel in the small
number test and the left panel in the large
number test. The results showed that in the
small number test (8 versus 8), chicks chose
the left panel 69.46% and the right panel
30.54% of the times. In the large number test
(32 versus 32), chicks chose the left panel
25.27% and the right panel 74.73% of the times
(Fig. 3). Therefore, the results of experiment 3
demonstrate that spatial mapping relates to
the abstract numerical magnitude, independently of non-numerical cues.
Our results indicate that a disposition to
map numerical magnitudes onto a left-to-right–
oriented MNL exists independently of cultural
factors and can be observed in animals with very
little nonsymbolic numerical experience, supporting a nativistic foundation of such orientation. Spatial mapping of numbers from left to
right may be a universal cognitive strategy available soon after birth. Experience and, in humans, culture and education (e.g., reading habits
and formal mathematics education) may modulate or even be modulated by this innate number sense.
During evolution, the direction of mapping
from left to right rather than vice versa, although in principle arbitrary, may have been
imposed by brain asymmetry, a common and
ancient trait in vertebrates (22), prompted by a
right hemisphere dominance in attending vis-uospatial and/or numerical information. Recent
studies have suggested that numerical knowledge constitutes a domain-specific cognitive ability, with a dedicated neural substrate located
in the inferior parietal cortices (1, 23). Moreover,
number-space mapping is implemented in humans through a topographical representation
in the right posterior parietal cortex (24). Such
topography has not yet been found in neurons
responding to number in animals (25, 26).
Because nonverbal numerical cognition is
shared by many animal classes (1, 27, 28), we
suggest that a similar predisposition to map
numbers onto space is embodied in the architecture of the animal neural systems.
REFERENCES AND NOTES
1. S. Dehaene, The Number Sense (Oxford Univ. Press, New York,
2. R. S. Moyer, T. K. Landauer, Nature 215, 1519–1520 (1967).
3. J. F. Cantlon, E. M. Brannon, PLOS Biol. 5, e328 (2007).
4. D. Scarf, H. Hayne, M. Colombo, Science 334, 1664 (2011).
5. E. S. Spelke, K. D. Kinzler, Dev. Sci. 10, 89–96 (2007).
6. S. Dehaene, S. Bossini, P. Giraux, J. Exp. Psychol. Gen. 122,
7. M. Zorzi, K. Priftis, C. Umiltà, Nature 417, 138–139 (2002).
8. C. Umiltà, K. Priftis, M. Zorzi, Exp. Brain Res. 192, 561–569
9. The SNARC effect refers to the fact that humans respond
faster to small numbers when responses are executed on the
left side rather than on the right, but they respond faster to
large numbers when responses are executed on the right side
rather than on the left.
10. S. Zebian, J. Cogn. Cult. 5, 165–190 (2005).
11. S. Shaki, M. H. Fischer, W. M. Petrusic, Psychon. Bull. Rev. 16,
12. M. D. de Hevia, L. Girelli, M. Addabbo, V. Macchi Cassia,
PLOS ONE 9, e96412 (2014).
13. R. Rugani, L. Regolin, G. Vallortigara, J. Exp. Psychol. Anim.
Behav. Process. 33, 21–31 (2007).
14. R. Rugani, D. M. Kelly, I. Szelest, L. Regolin, G. Vallortigara,
Biol. Lett. 6, 290–292 (2010).
15. C. B. Drucker, E. M. Brannon, Cognition 132, 57–67 (2014).
16. R. Rugani, G. Vallortigara, B. Vallini, L. Regolin, Neurobiol.
Learn. Mem. 95, 231–238 (2011).
17. G. Jewell, M. E. McCourt, Neuropsychologia 38, 93–110 (2000).
18. B. Diekamp, L. Regolin, O. Güntürkün, G. Vallortigara,
Curr. Biol. 15, R372–R373 (2005).
19. L. Regolin, Cortex 42, 101–103 (2006).
20. I. Adachi, PLOS ONE 9, e90373 (2014).
21. Materials and methods are available as supplementary
materials on Science Online.
22. L. J. Rogers, G. Vallortigara, R. J. Andrew, Divided Brains
(Cambridge Univ. Press, New York, 2013).
23. A. Nieder, D. J. Freedman, E. K. Miller, Science 297, 1708–1711
24. B. M. Harvey, B. P. Klein, N. Petridou, S. O. Dumoulin, Science
341, 1123–1126 (2013).
25. J. D. Roitman, E. M. Brannon, M. L. Platt, Front. Integr.
Neurosci. 6, 25 (2012).
26. A. Nieder, J. Comp. Physiol. A Neuroethol. Sens. Neural Behav.
Physiol. 199, 1–16 (2013).
27. E. M. Brannon, H. S. Terrace, Science 282, 746–749 (1998).
28. R. Rugani, L. Fontanari, E. Simoni, L. Regolin, G. Vallortigara,
Proc. Biol. Sci. 276, 2451–2460 (2009).
This study was supported by the University of Padova (Progetto
Giovani 2010, to R.R., GRIC101142; and Progetto di Ateneo 2012
to R.L., CPDA127200) and by European Research Council (ERC)
Advanced Grant PREMESOR ERC-2011-ADG_20110406 to G.V.
Raw data are provided in the supplementary materials.
Materials and Methods
Figs. S1 and S2
References (29, 30)
22 October 2014; accepted 12 December 2014
IDENTITY AND PRIVACY
Unique in the shopping mall:
On the reidentifiability of
credit card metadata
Yves-Alexandre de Montjoye,1 Laura Radaelli,2 Vivek Kumar Singh,1,3 Alex “Sandy” Pentland1
Large-scale data sets of human behavior have the potential to fundamentally transform
the way we fight diseases, design cities, or perform research. Metadata, however, contain
sensitive information. Understanding the privacy of these data sets is key to their broad
use and, ultimately, their impact. We study 3 months of credit card records for 1.1 million
people and show that four spatiotemporal points are enough to uniquely reidentify 90%
of individuals. We show that knowing the price of a transaction increases the risk of
reidentification by 22%, on average. Finally, we show that even data sets that provide
coarse information at any or all of the dimensions provide little anonymity and that
women are more reidentifiable than men in credit card metadata.
Large-scale data sets of human behavior have the potential to fundamentally transform the way we fight diseases, design cities, or perform research. Ubiquitous technologies create personal metadata on a very large
scale. Our smartphones, browsers, cars, or credit
cards generate information about where we are,
whom we call, or how much we spend. Scientists
have compared this recent availability of large-
scale behavioral data sets to the invention of the
microscope (1). New fields such as computational
social science (2–4) rely on metadata to address
crucial questions such as fighting malaria, study-
ing the spread of information, or monitoring pov-
erty (5–7). The same metadata data sets are also
used by organizations and governments. For ex-
ample, Netflix uses viewing patterns to recom-
mend movies, whereas Google uses location data
to provide real-time traffic information, allowing
drivers to reduce fuel consumption and time spent
The transformational potential of metadata data
sets is, however, conditional on their wide availability. In science, it is essential for the data to
be available and shareable. Sharing data allows
536 30 JANUARY 2015 • VOL 347 ISSUE 6221 sciencemag.org SCIENCE
1Media Lab, Massachusetts Institute of Technology (MIT), 20
Amherst Street, Cambridge, MA 02139, USA. 2Department of
Computer Science, Aarhus University, Aabogade 34, Aarhus,
8200, Denmark. 3School of Communication and Information,
Rutgers University, 4 Huntington Street, New Brunswick, NJ
*Corresponding author. E-mail: firstname.lastname@example.org