Bit operations preserve De Morgan’s laws. Bit values are sequences of symbols. What makes them behave like booleans? Where does the essence of a boolean lie?
In mathematics, sometimes the parts pass behaviours to the whole: the properties of a scalar field influence those of a vector space constructed over the field.
Surprises are typical: although we can define the derivative of complex functions with real functions, if we can differentiate a complex function once, we can differentiate it an infinite number of times, which isn’t the case at all on the real field. This sort of complex function is called holomorphic.
Dated 21 July 2014. I have found this fragment while rummaging in my old notes; it might pique someone’s curiosity.