Colorful T Algebra

Step Four to Games of Thing:
Colorful T algebra

In my last blog I have shown the possibility of formulating the Boolean algebra as colorful V Algebra. But due to the incapability of it to represent expressions containing a sequence of ORs, we have to create another pictorial algebra overcoming such difficulties: the colorful T algebra.

T arithmetic

As in the Box Arithmetics, the logical constant FALSE is represented by

VOID

and TRUE is drawn as a black T

We can also represented the NOT and OR operation as drawings in the Bar Algebra.

NOT a is represented by

a OR b is represented as

The logical primitives of logical T arithmetic is the Law of Negation (or Cancelation) and the Law of Disjunction (or Condensation).

Law of Cancelation is drawn as

Law of Condensation is drawn as

T Algebra

The axioms of Brownian Cross algebra is Position and Transposition.

Law of position [[a]a]=     is drawn as

Law of transposition [[ac][bc]]=[[a][b]]c is drawn as

Simplifying T Algebra

The axiom pair can be replaced by single axiom: the Huntington axiom.

the Huntington Axiom [[a][b]][[a]b]=a,  as it is used by Louis Kauffman in his box algebra can be drawn as

Last remark

I like the colorful T pictorial symbolism better than the the V algebra, but watching the Ts more deeply, we will see that it can be be more simplified by replacing T with the more simple I to get Stick Algebra that we will discuss in the next blog.