Peirce and de Morgan
In the Single Algebra a symbol denotes a process either forwards or backwards, pictured as segments on a line. In order to deal with numbers of the form $a + ib$ de Morgan introduced the Double Algebra, where a line is given a direction in the plane. For a long time de Morgan tried to develop a Triple Algebra in the same spirit of pure logic, even after Hamilton showed that the Quadruple Algebra of quaternions was the next natural geometric step.
It was the originator of Category Theory, C. S. Peirce, who remained inspired by de Morgan's ideas and went on to develop the Theory of Signs and the triad philosophy. The under-appreciated Peirce is now recognised to have, amongst many other things, axiomatised arithmetic before Peano and to have discovered the ability of electrical circuits to do Boolean algebra.