1. A visual sense of number
David Burr & John Ross
The University of Florence
Burr & Ross
Current Biology 2008

2. Many agree, that besides a mechanism for precise calculation based on symbolic representation, there exists an evolutionarily ancient approximate number system shared by and non-human animals for rough estimation of numerosity.

3. Estimation of numerosity in rats
(A) The probability of rats breaking off a sequence of lever presses as a function of the number of
presses in the sequence and the number required to get the reward. The inset shows the mean number
of lever presses (circles), standard deviation (squares). The coefficient of variation (CV), which is the
ratio between the mean and the standard deviation, is constant, indicating Weber’s law (redrawn from
Mechner, 1958 and from Gallistel & Gelman, 2000).

4. Monkeys: same/different task
(B) Behavioral performance of two monkeys in a same-different task where they judged whether a test stimulus contained the same or a different number of items as the sample display. Each curve represents the percentage of “same” response as a function of test numerosity, for a given sample numerosity (modified from Nieder, 2003).

5. Number production by key-press
0.15
0,30 CV 10 20 30
Mean SD 2 4
Number of level presses
Behavioral performance of human adults that were asked to produce a given number of key presses. The mean number of presses (circles), standard deviation (squares), and the coefficient of variation are striking similar to the rats’ performance drawn above.

6. Human estimation of prices
Frequency (%) 2 4 6 8 10 12 14 16 18 20 1 3
Normal distribution.
Log-normal distribution.
Normalized price (linear scale) D
Distribution of human adults’ estimates of prices of items, after normalization by the mean price. The distribution is consistently skewed and is better fitted by a log-normal than by a normal curve (from Dehaene & Marques, 2002).

7. Brain imaging A B C Right hemisphere Left hemisphere Top view LCS
IPS
Right hemisphere
Left hemisphere
left angular gyrus (AG)
bilateral posterior superior parietal lobe (PSPL)
bilateral horizontal segment of intraparietal sulcus (HIPS)
Top view A L C B
(A) Three-dimensional representation of the three parietal sites of major activation in number processing individuated by a recent meta-analysis of fMRI studies of number processing. CS, central sulcus; IPS, intraparietal sulcus. (from Dehaene et al., 2003). (B) Regions whose activation increases with number size during calculation (from Stanescu et al., 2001), including left HIPS, left premotor, and left inferior prefrontal areas. (C) Region of reduced grey matter in a population of subjects with developmental dyscalculia (from Isaacs et al., 2000). The location of impairment coincides with the left HIPS.

8. Neurons in monkey pre-frontal and parietal cortexB
Time N u m b e r o f i t s ( l g c a ) 2 5 7 1 z d p n % 3 4 A C D
Fixation
500 ms
Sample
800 ms
Delay
1000 ms
Test
1200 ms
Match
Non-Match
P=0.25
P=0.50
Spike rate (Hz)
Selectivity follows a log scale

9. Number neurons cover a large range
Nieder & Merten
J Neuroscience 2007

10. Could numerosity be a visual attribute?
If so it should be subject to adaptation.

11. If so it should be subject to adaptation.
Is numerosity a primary visual attribute, or quale, like colour or motion?
If so it should be subject to adaptation.
John Mollon (1974). After-effects and the brain. New Scientist 61:
‘If you can adapt it, it’s there.’

12. Complementary after-images
If you fixate a strongly-coloured image on a constant region of the retina, the sensitivity of the absorbing cones will be temporarily reduced and they will respond to the incident light much less.
It’s very important that you fixate the image. The treshold of sensibility of your blue cones are increased in this part.

13. Complementary after-images
If you fixate a strongly-coloured image on a constant region of the retina, the sensitivity of the absorbing cones will be temporarily reduced and they will respond to the incident light much less.
It’s very important that you fixate the image. The treshold of sensibility of your blue cones are increased in this part.

14. Complementary after-images
If you fixate a strongly-coloured image on a constant region of the retina, the sensitivity of the absorbing cones will be temporarily reduced and they will respond to the incident light much less.
It’s very important that you fixate the image. The treshold of sensibility of your blue cones are increased in this part.

15. Adaptation demo

16. Adaptation demo

17. Where did the other dots go? (We’ll come back to that)

18. Adaptation: 45 sec + 8 sec top-up

19. Test stimulus (500 ms)

20. 0.5 sec pause

21. Probe stimulus (500 ms)

22. Psychometric functions with adaptation

23. Adaptation vs dot number
Adapt to 400 dots

24. Effect of number of adaptor dots

25. Adaptation: magnitude estimation
No adapt
Adapt 120

26. Numerosity or texture?

27. Size of rectangular elements: paired comparisons

28. Adaptation does not depend on element orientation

29. Effect of the test contrast

30. Effect of adaptor contrast

31. Numerosity or texture Neither PSE nor Weber fractions depend on:
Size or shape of elements
Orientation of elements
Fourier sprectra of stimuli
Contrast, or contrast sign
Chromaticity

32. Colour-contingency after-effect

33. Colour-contingency after-effect

34. Colour-contingency after-effect

35. What are the neural mechanisms underlying numerosity adaptation?

36. “Number-neurons” in monkey pre-frontal and parietal cortex
Time N u m b e r o f i t s ( l g c a ) 2 5 7 1 z d p n % 3 4 A C D
Fixation
500 ms
Sample
800 ms
Delay
1000 ms
Test
1200 ms
Match
Non-Match
P=0.25
P=0.50
Spike rate (Hz)

37. LIP neurons respond in graded fashion to total number in RF
Roitman, Brannon &Platt
PLoS 2007

38. Implications for adaptation
LIP
VIP

39. Data

40. Attention and subitizing

41. Weber’s law for numerosity
25% Weber fraction explains the subitizing limit of 4
Ross, Perception, 2003

42. Numerosity and subitizing
Rather than counting them, economist William Jevons estimated numbers of beans thrown into a dish, and made errors when there were more than 4 beans. Errors in estimate varied with bean number: Weber’s law.
William Stanley Jevons

44. The attentional blink: slow motion Giovanni Anobile

45. The attentional blink: real time Giovanni Anobile

46. Attention affects subitizing but not estimation

47. Spatial attention: slow motion demo Marco Turi

48. Spatial attention: real time demo Marco Turi

49. Attention affects subitizing but not estimation

50. Attention affects subitizing but not estimation

51. Attention affects subitizing but not estimation

52. Mental abacus represents large exact numerosities using pre-existing visual resources  Frank, M.C.., & Barner, D.

53. Abacus

54. Mental abacus