Logic

Zellweger

A rogue mathematician named Shea Zellweger has created a notation he calls the logic alphabet.

We need a better set of signs for and, or, if
[⋯]
These three are themselves only a small part of the 16 binary connectives.

As a big math nerd and symbol nerd, I fell in love after looking at this for all of five minutes. The fundamental structure of the system is immediately apparent — as are its advantages over ordinary logical notation.

The 3-d “chessboard” above is a kind of diagram of the relationships of the different symbols, which should properly be rendered in 4-dimensional space. I could not resist doing a mapping of my own, taking advantage of an orthographic hypercube projection that I learned in high school and have been obsessed with ever since. I think it makes the patterns in Zellweger’s notation even more apparent.

Since Zellweger is a maverick, with no academic math credentials, his system has had almost no impact on the world of mathematics. But the art world has taken a little interest, because some of the artifacts of his work are so beautiful. So I discovered him through a science-art museum that Indri of Waterbones turned me on to, and they in turn point to a fascinating interview with Zellweger in the art and culture magazine Cabinet.

his notebooks (made between 1953 and 1975) have remarkable visual appeal, passing through phases reminiscent of Russian Constructivism, outsider art, concrete poetry and pop

In the Cabinet interview, Zellweger asserts a kind of Sapir-Whorf hypothesis of mathematics ...

Yes, you only see the symmetric patterns in the system when you look at the whole thing with all 16 elements together. When you use only a few, you don’t see the beautiful crystalline structures. My notation is designed to highlight these wonderful patterns, not obscure them, as most notations do.

... and goes on to make interesting comparisons with the cool math manipulatives used in Montessori education.

Frege

a much later addition

In 1879, the mathematician Gottlob Frege proposed his notation Begriffsschrift, “logicwriting”, which has a delicious two-dimensional quality a bit like diagrammed sentences.

It did not stick.

I discovered it through Matthew Attoparsec Dockrey, a nerd’s nerd who created a programming language based on it. A daring step far beyond fonts with ligatures for common programming operators!