28 April 2006

Logic

A rogue mathematician named Shea Zellweger has created a new logical 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 is its superiority to 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 couldn't resist doing a mapping of my own, taking advantage of an obscure hypercube projection that I learned in high school and have been obsessed with ever since.

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.

5 comments:

Kate said...

Your Dad would love this.........please show it to him!

christine said...

An exhibition of Shea Zellweger's Logic Alphabet models and diagrams will open in February at the Museum of Jurassic Technology in Culver City Los Angeles......a pre-view pic of the show attended by none other than Brittany Spears is available on flickr...just type logic alphabet into google and you'll get the link....

Anonymous said...

Thats disgusting - the following is cool:

www.flickr.com/photos/hexadecimal_time/2254800793/

Jonathan Korman said...

Awww ... you shouldn't say my diagram is disgusting. But your variant notation is indeed cool, Anon.

Anonymous said...

Another Anonymous

Dumping with "disgust" does not even a little bit reduce the Beauty of the Chess Set Logical Garnet shown above.