“Linear”, “Linearity”

One of the defining peculiarities of this work is that the term “linear”, and the derived term “linearity”, occur in this work with two very different meanings. These two meanings almost never occur together in human activity, because of the gulf that usually separates the artistic and the mathematical worlds.

To the graphic artist, “linear” means “having the properties of a line”. The artistic property of a line is that it has a pull in some direction, and also in the opposite direction, but not in any intermediate direction. The better an artist is, the more difficulty he/she would have in providing an objective definition of linearity.
To the mathematician, “linear” means that if you multiply what you put into an expression by some amount, what you get out is multiplied by the same amount. To the computer programmer, “linear” means “free of surprises”. In contrast, Chaos Theory is the study of non-linear processes.

The basic strength of quadrupole convolution is that it unambiguously defines linearity in the artistic sense, both in direction and in magnitude. Yet, quadrupole convolution is completely linear in the mathematical sense, and in the computational sense.

To Quadrupole Convolution.