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So, the addition and multiplication we are used to using are commutative .
In the 1840s, the Irish mathematician William Hamilton found that multiplication was not commutative in all number systems.
The second difficulty was more damaging and, to a degree, commutative with the first.
This is a consequence of large rotations not being commutative in three dimensions, so the averages are not accurate in regions of high variability.
Of course, the relationship between painting and philosophy is not entirely commutative .
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