In 2001, Yamamoto and Kitazawa showed that the perception of temporal order can be reversed when subjects cross their hands. Subjects closed their eyes and had their hands mechanically touched in quick succession (with stimuli separated in time by a variable amount - from 1500 ms to 0 ms). Subjects were asked to raise the finger of the hand that was first stimulated. The results showed that subjects were accurate in reporting the temporal order of these stimuli when separated by as little as 70ms - but when their arms were crossed, subjects showed a tendency to reverse the temporal order when the stimuli were separated by 100 to 200ms.
Subjects were not merely confused due to the arm-crossing, since the responses were unspeeded, since subjects could respond correctly to a single stimulus, and since subjects behaved correctly even with crossed arms when the stimuli were separated by 1500ms.
In general, subjects showed a larger tendency to report the right hand was stimulated first when in fact the left hand was, as opposed to the opposite confusion. The authors speculate this may have to do with hemispheric asymmetry.
Arm position was also parametrically manipulated by evaluating 6 arm positions - in the first, hands were extended to occupy the ispilateral hemifield, and were progressively crossed in 45 degree increments. Critically, two of these conditions were matched for hand placement but differed in terms of whether the arms were perpendicularly crossed, or merely parallel in space. The results here showed that only arm crossing was associated with temporal order reversal - a contralateral arrangement of the hands is not by itself enough to explain the effect.
The authors explain these results by suggesting that subjects determine temporal order by reconstructing external events in terms of their spatial locations in the external world - and that with short separation intervals between stimuli, "the second stimulus is given before the first stimulus is adjusted for the crossed position of the hands", and creates errors based on a default or prepotent assumption that the hands are not crossed.
However, it's not clear under this explanation why subjects should not reverse temporal order when the hands were placed contralaterally - remapping should be required in both cases. One possibility is that the use of parallel arms (rather than arm crossing) when placing the hands in the contralateral hemifield actually provides additional spatial information which lessens the requirement for remapping.
New work shows that this temporal order reversal can be substantially ameliorated merely by viewing uncrossed rubber hands whose finger pressing was visibly yoked to their own - perhaps by remapping subjects' proprioceptive representations of their hands to the actions of the visibly uncrossed hands. In other words, subjects were able to utilize the visual feedback from uncrossed hands to "reverse" their mental representations of which hand was which - yielding less reversal of temporal order. Similarly, other work shows that crossing the hands behind the back has less of an effect than doing so in a way that is plainly visible to the subjects.
This is just one of many demonstrations that arm crossing can affect cognition. For example, the standard spatial compatibility effect in manual responses (subjects respond most quickly with the left hand to stimuli presented on the left, and with the right hand to those presented on the right) is fully reversed with arm crossing: in that case, subjects respond more quickly with the right hand to stimuli presented on the left, and vice versa. This is also accompanied by a general slowing of responses, putatively the time for a remapping process to take place.
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...and that is why the flux capacitor is in the shape of a Y.