# Bit Twiddling

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*.