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

2. 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).

3. 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).

4. 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.

5. 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).

6. 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.

7. 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

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

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

10. Adaptation demo

11. Adaptation demo

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

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

14. Test stimulus (500 ms)

15. 0.5 sec pause

16. Probe stimulus (500 ms)

17. Psychometric functions with adaptation

18. Adaptation vs dot number
Adapt to 400 dots

19. Effect of number of adaptor dots

20. Adaptation: magnitude estimation
No adapt
Adapt 120

21. Numerosity or texture?

22. Size of rectangular elements: paired comparisons

23. Adaptation does not depend on element orientation

24. Effect of the test contrast

25. Effect of adaptor contrast

26. 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

27. Colour-contingency after-effect

28. Colour-contingency after-effect

29. Colour-contingency after-effect

30. What are the neural mechanisms underlying numerosity adaptation?

31. “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)

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

33. Implications for adaptation
LIP
VIP

34. Data

35. Interim conclusions
The capacity to estimate number is built into vision.
Numerosity is a primary visual attribute: a dozen ripe cherries look twelvish, just as they look reddish.
Like other visual attributes, numerosity obeys Weber’s Law, is subject to spatially local adaptation and contingency aftereffects.
See Burr & Ross Curr Biol 2008 And Butterworth Curr. Biol. 2008

36. Attention and subitizing

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

38. The attentional blink: slow motion Giovanni Anobile

39. Attention affects subitizing but not estimation

40. Spatial attention: slow motion demo Marco Turi

41. Attention affects subitizing but not estimation

42. Attention affects subitizing but not estimation

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

44. Abacus

45. Mental abacus