1. Numbers

1
Disruption of the mental number line in
hemispatial neglect Marco Zorzi,
Konstantinos Priftis, Carlo Umiltà
University of Padova and University of Trieste

2
Numbers Visuospatial Images

• Numbers could be
• represented in
• the human brain as
• a continuous, left-to-right
• oriented number line
• (Galton, 1880, Nature
• Seron et al. 1992, Cognition).

3
Spatial effects in number processing

• The Distance effect (Moyer Landauer, 1967,
  Nature)
• In number comparison tasks, reaction times
  decrease as the distance between numbers
  increases (e.g. 1-2 slow ? 1-9 fast).
• Spatial Numerical Association of Response Codes
  (Dehaene et al., 1993, JEPHPP)
• During parity judgement, healthy subjects are
  faster in classifying small numbers using the
  left hand (e.g. 1) and big numbers using the
  right hand (e.g. 9).

4
Do spatial disorders affect number processing?

• Patients with hemispatial neglect ignore the
  perceptual and/or conceptual space contralateral
  to their brain lesion.
• In line bisection tasks, neglect patients shift
  the line midpoint as a function of line length
• (Halligan Marshall, 1988, Cortex).
• Does neglect disrupt the number line as in the
  case of visually presented lines ??

Midpoint deviation
Line length
Line bisection is affected by line length
(Halligan Marshall, 1988).
5
Methods

• Participants
• Four right brain damaged (CVA) patients with left
  neglect (age 64.5, edu. 9.7).
• Four right brain damaged (CVA) patients without
  neglect (age 58, edu. 5.2).
• Four healthy controls matched for sex, age and
  education to the neglect patients.
• All participants had intact numerical and
  arithmetic skills (counting, number comparison,
  parity judgement, addition, subtraction,
  multiplication).
• Stimuli and Procedure
• Forty-eight number intervals (e.g. 1 - 9, 11 -
  13, 25 - 29) were presented orally to the
  participants. The majority of participants was
  also tested using a backward presentation of the
  same number intervals (e.g. 9 -1).
• The length of the numerical interval was of three
  (e.g. 1 - 3), five (e.g. 1 - 5), seven (e.g. 1 -
  7) or nine (e.g. 1 - 9).
• Each number interval was presented within the
  units (e.g. 1 - 5), the teens (e.g., 11 - 15) and
  the first ten (e.g. 21 - 25).
• Participants were asked to detect the mid-point
  number of each number interval
• What number is halfway between 1 and 9 ? ?
  5 .

6
Results
7
Effect of interval length on bisection errors
Y axis 0 midpoint. Positive values indicate
right shifts, negative values indicate left
shifts. Regression analyses Length (3 vs. 5 vs.
7 vs. 9). OV ? .54, p lt 0.001 GZA ? .62, p
lt 0.001 GZE ? .36, p lt 0.01 GS ? .39, p lt
0.001. Number size (units vs. teens vs. tens) was
not significant in any of the groups.
8
Discussion

• 1. Neglect patients make many bisection errors,
  in spite of their normal numerical and
  arithmetical abilities.
• 2. For all neglect patients, errors consist in a
  rightward shift that increases as a function of
  number interval length.
• 3. For patients who make errors at the shortest
  interval (e.g. 5-7), there is a crossover effect
  with a significant leftward displacement of the
  bisection point.
• 4. There is no effect of number size. This
  suggests that the number line is not compressed,
  in contrast to most models of number
  representation (e.g., Dehaene et al., 1998, TINS
  but see Zorzi Butterworth, 1999, CogSciSoc, and
  Stoianov, Zorzi, Umiltà, Bressanone 2002).

9
Conclusions Numbers and space

• The discovery of this new form of
  representational neglect reveals the intimate
  relationship between numbers and space.
• The mental number line has a spatial nature that
  renders it functionally isomorphic to real
  physical lines. This suggests that the notion of
  a mental number line is much more than a
  metaphor.

In my thought. . . words do not seem to play
any role but there is associative play of more
or less clear visual images - Albert Einstein