Laws of Form Simulator

June 2021

In 1969 George Spencer-Brown published the work »Laws of Form«, in this work he tried to build arithmetic, algebra, and logic based on a single operation, the distinction. This distinction, also called mark or cross, is at the same time an operator as well as an operand, which is applied in space (here it's an infinitely large white area). If there is a cross in space, i.e. a distinction has been made, then this space is marked. However, if one goes into the area that was distinguished by the distinction (inside and outside), it will be unmarked again unless you introduce another distinction there.

Screenshot of the simulator Every mathematical system is based on axioms, simply accepted and fixed rules. In LoF there are exactly two axioms. Making a distinction twice is equivalent to making a single distinction and a distinction inside a distinction annuls both distinctions. Each expression can be transformed into exactly one of two states, the marked or unmarked space.

LoF also offers non-negligible epistemological implications in the field of radical constructivism. It provides a solid basis for explaining autopoietic systems (Humberto Maturana and Francisco Varela), deriving theories of observation and system theory (Niklas Luhmann), and cybernetic concepts (Heinz von Foerster). Moreover, there are opinions that the statements presented in Laws of Form are the basis of all cognition.

This simulator offers several functions to get an intuitive understanding of the dynamics of Laws of Form.