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### Magnitude systems

Mikael SkagenholtMoreover, we documented a striking asymmetrical interaction between numbers and time processing, such that time can either be modulated by numerical magnitude in control participants and in patient CB, or it can be dramaticallyimpaired by the mere presentation of numerical stimuli in JT. Our data can be explained by the hypothesis of a partly shared magnitude system between magnitude dimensions, and endorse the proposal that asymmetries between number, time and space may relate to intrinsic, paradigm-free differences between these dimensions, with number being the strongest.Magnitude systems -

*Mikael Skagenholt*

However, parietal lesions can often result in space impairment (see Rorden et al., 2006), therefore more cases need to be examined before reaching firm conclusions on the role of the parietal lobes in space processingMagnitude systems -

*Mikael Skagenholt*

Space processing was spared in our two patients.Magnitude systems -

*Mikael Skagenholt*

The locus of the magnitude system shared among number, time and space processing has been originally proposed in the right inferior parietal cortex (e.g. Walsh, 2003). However, the selectively impaired numerical and temporal processing shown here, together with preserved space processing in both patients are difficult to accommodate within this proposal.Magnitude systems -

*Mikael Skagenholt*

Finally, the idea that time is a vulnerable dimension found support in JT?s performance in temporal tasks showing that her temporal processing was destroyed by numerical stimuli even when they were task-irrelevant. Notably, such impairment did not emerge in case of space, again reinforcing the proposal that magnitude dimensions differ intrinsically, with time but not space or number being a weak dimension.Magnitude systems -

*Mikael Skagenholt*

Whether numbers are a more salient dimension also relative to space remains to be established as our paradigms only explored the effect of numerical magnitude on length but not the opposite.Magnitude systems -

*Mikael Skagenholt*

we suggest that asymmetric relations between magnitude dimensions are due to intrinsic differences between these dimensions, with numbers thought to be a more salient dimension or more automatically accessed relative to time.Magnitude systems -

*Mikael Skagenholt*

we have shown that the asymmetry in the interaction occurred between dimensions whose representation is considered abstract, namely numbers and time, rather than between ?abstract? and more ?concrete? concepts such as space. We have also shown that numbers interacted with spaceMagnitude systems -

*Mikael Skagenholt*

However, we showed that the same interaction of number on time occurred in very different paradigms requiring temporal estimation and discrimination respectively.Magnitude systems -

*Mikael Skagenholt*

This suggests that both symbolic and non-symbolic number stimuli seem to modulate time processing.Magnitude systems -

*Mikael Skagenholt*

These asymmetries between dimensions are not in line with the original proposals of a fully shared mechanism, which predicts that time and numbers would only interact symmetricallyMagnitude systems -

*Mikael Skagenholt*

Our data suggest that the relation between dimensions is asymmetrical, with numbers appearing as the most dominant dimension and time the weakest.Magnitude systems -

*Mikael Skagenholt*

A partly shared mechanism would account for interactions as well as dissociations among dimensions, which can be explained by dimension-specific processes being impaired rather than the common magnitude system.Magnitude systems -

*Mikael Skagenholt*

Instead, we suggest that our results are best explained by the proposal of a magnitude system partly shared among dimensions. This is the idea that besides sharing an approximate magnitude system number, time and space are also implemented by dimension-specific processesMagnitude systems -

*Mikael Skagenholt*

Our results indicate that: (i) number processing was impaired in JT but not in CB; (ii) in JT time processing was preserved unless numbers were part of the experimental paradigm even as taskirrelevant stimuli; (iii) in CB selectively impaired time processing was nevertheless modulated by numerical value, similar to controls; and that (iv) space processing was preserved in both patients.Magnitude systems -

*Mikael Skagenholt*

Despite this impairment, CB?s temporal estimation and discrimination were influenced by the magnitude of the numerical stimuli, similar to control participants: small numerical stimuli or small numerical primes resulted in a significantly more underestimation of temporal durations relative to larger numerical stimuli or larger numerical primes. Contrasting with his time impairment, CB?s number and space processing were spared. He was accurate at estimating the numerosity of sets of stimuli, regardless as to whether these consisted of coloured circles or of numbers. Spatial processing was also entirely preserved, as CB was accurate at indicating the longer of two lines irrespective of the prime used.Magnitude systems -

*Mikael Skagenholt*

In contrast, CB with a right hemisphere lesion was selectively impaired in processing time whereas number and space processing were preserved. His time impairment affected the ability to estimate temporal intervals as well as the ability to discriminate between temporal durations. For instance, CB?s underestimation of temporal intervals could be up to 1/3 of their veridical duration (e.g. 18 s for a veridical 60 s interval) and he was equally impaired irrespective of the stimuli displayed, i.e. coloured circles or Arabic numbers.Magnitude systems -

*Mikael Skagenholt*

JT was equally accurate at discriminating the length of two line stimuli whether they were preceded by task-irrelevant numerical primes or by a non-numerical prime.Magnitude systems -

*Mikael Skagenholt*

Strikingly, the same temporal interval was correctly judged as lasting approximately 1 min when coloured circles were displayed. Similarly, JT could correctly discriminate which of two line stimuli lasted longer in the presence of task-irrelevant symbols or letter primes, but she performed at chance when the identical stimuli were preceded by numerical primes.Magnitude systems -

*Mikael Skagenholt*

Our results indicated that JT with a left parietal lesion was selectively impaired in processing numbers as indicated by the lack of the classical distance effect when comparing Arabic numerals, by her poor performance in arithmetic tasks and in numerosity estimation. Time processing was entirely accurate unless it was tested in the context of numbers even if these were taskirrelevant.Magnitude systems -

*Mikael Skagenholt*

Similarly, CB was accurate in length discrimination relative to controlsMagnitude systems -

*Mikael Skagenholt*

JT was accurate when comparing the length of two stimuli preceded by numerical primes, with no significant difference from controlsMagnitude systems -

*Mikael Skagenholt*

Experiment 9: which line was longer in length (with Arabic number primes)Magnitude systems -

*Mikael Skagenholt*

Similarly, CB was accurate in spatial discrimination relative to controlsMagnitude systems -

*Mikael Skagenholt*

JT was accurate when comparing the length of two stimuli preceded by a non-numerical prime, with no significant difference from controlsMagnitude systems -

*Mikael Skagenholt*

Experiment 8: which line was longer in length (with non-numerical prime ?#?)Magnitude systems -

*Mikael Skagenholt*

It is possible, however, that JT?s impaired performance was not due to the presence of numbers per se but rather to the fact that they may have acted as distractors. This may be because there were two primes appearing randomly across trials, which may have made it difficult for JT to concentrate on the temporal task. This was not the case for Experiment 6 where only one type of prime (?#?) was used across all trials. To test whether JT?s impaired temporal discrimination in the presence of numbers may have been caused by the numbers acting as distractors, we used an identical time discrimination task where the primes were two non-numerical stimuli, i.e. the two letters of the alphabet ?A? and ?Z?, appearing randomly in exactly the same fashion as the number primes.Magnitude systems -

*Mikael Skagenholt*

Results of Experiment 6 suggested that JT could perform the time discrimination task when a non-numerical prime was displayed. This contrasted with JT?s impaired time discrimination when the identical task was used in the context of numerical primes, suggesting that time discrimination was preserved except in the context of numbers.Magnitude systems -

*Mikael Skagenholt*

Results of Experiments 5?7 showed that JT?s time processing was impaired only when tested in the context of numbers, but that it was otherwise preserved. This suggests that numbers may have interfered with time processing in JT. To test whether numbers had a similar impact on space processing, we tested space judgments in the context of both numerical and non-numerical primes. If numbers have such disrupting effect on JT?s spatial processing similar to time, a difference should be expected between conditions with numerical and non-numerical primes. In contrast, if numbers have no impact on space processing, the type of prime used should not change performance. Moreover, we aimed to test whether CB?s performance in a spatial task could be modulated by numerical magnitude similar to the time tasks.Magnitude systems -

*Mikael Skagenholt*

Experiment 7: which line lasted longer (with letter primes)Magnitude systems -

*Mikael Skagenholt*

JT was accurate at comparing the duration of two stimuli preceded by letter primes (see Table 4), and did not differ from controlsMagnitude systems -

*Mikael Skagenholt*

irrespective of whether the prime was a number or the symbol ?#?Magnitude systems -

*Mikael Skagenholt*

In contrast, CB was impaired in temporal discrimination relative to controlsMagnitude systems -

*Mikael Skagenholt*

In striking contrast with JT?s performance in the same task with number primes (Experiment 5), here she showed normal accuracy when comparing the duration of two stimuli preceded by a nonnumerical primeMagnitude systems -

*Mikael Skagenholt*

only JT showed a discrepancy in the temporal discrimination task with numerical and non-numerical stimuli, the letter prime condition was only investigated in JT and not CB.Magnitude systems -

*Mikael Skagenholt*

we administered another task which was identical to Experiment 5 except that primes were no longer Arabic numbers but the non-numerical symbol ?#?.Magnitude systems -

*Mikael Skagenholt*

The previous results suggested that JT was impaired at time discrimination when numbers were presented even as task-irrelevant stimuli. This is consistent with her poor performance at interval estimation in the presence of task-irrelevant numbers (Experiment 4) but is in contrast with JT?s performance in Experiment 3 where she was accurate at estimating temporal intervals displaying coloured circles. However, it is unclear whether this difference is due to the stimuli used (task-irrelevant numbers vs. coloured circles) or the type of temporal task performed (estimation vs. discrimination).Magnitude systems -

*Mikael Skagenholt*

Experiment 6: which line lasted longer (with non-numerical prime ?#?)Magnitude systems -

*Mikael Skagenholt*

CB was impaired when comparing the duration of two stimuli preceded by a numerical primeMagnitude systems -

*Mikael Skagenholt*

JT performed near chance when asked to compare the duration of two stimuli preceded by a numerical prime, with a significant difference from controls across priming conditionsMagnitude systems -

*Mikael Skagenholt*

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