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A visual sense of number
David Burr & John Ross The University of Florence Burr & Ross Current Biology 2008
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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).
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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).
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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.
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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).
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Brain imaging A B C Right hemisphere Left hemisphere Top view L
CS 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.
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Neurons in monkey pre-frontal and parietal cortex
B 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
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Number neurons cover a large range
Nieder & Merten J Neuroscience 2007
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Could numerosity be a visual attribute?
If so it should be subject to adaptation.
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Adaptation demo
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Adaptation demo
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Where did the other dots go? (We’ll come back to that)
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Adaptation: 45 sec + 8 sec top-up
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Test stimulus (500 ms)
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0.5 sec pause
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Probe stimulus (500 ms)
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Psychometric functions with adaptation
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Adaptation vs dot number
Adapt to 400 dots
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Effect of number of adaptor dots
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Adaptation: magnitude estimation
No adapt Adapt 120
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Numerosity or texture?
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Size of rectangular elements: paired comparisons
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Adaptation does not depend on element orientation
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Effect of the test contrast
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Effect of adaptor contrast
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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
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Colour-contingency after-effect
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Colour-contingency after-effect
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Colour-contingency after-effect
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What are the neural mechanisms underlying numerosity adaptation?
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“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)
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LIP neurons respond in graded fashion to total number in RF
Roitman, Brannon &Platt PLoS 2007
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Implications for adaptation
LIP VIP
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Data
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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
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Attention and subitizing
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Weber’s law for numerosity
25% Weber fraction explains the subitizing limit of 4 Ross, Perception, 2003
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The attentional blink: slow motion Giovanni Anobile
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Attention affects subitizing but not estimation
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Spatial attention: slow motion demo Marco Turi
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Attention affects subitizing but not estimation
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Attention affects subitizing but not estimation
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Mental abacus represents large exact numerosities using pre-existing visual resources Frank, M.C.., & Barner, D.
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Abacus
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Mental abacus
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