Felicitous Geometric Algebra. A Kindle ebook carefully demystifying Euler's Identity. Full Unified Geometric Algebra. Another Kindle ebook expounding on Grassmann's idea: "In extension theory there appears a characteristic method of calculation which is inexhaustibly fruitful and consists in subjecting spatial structures (points, lines, and so forth) directly to calculation." Fixing Nothing. After mathematicians finally came up with a symbol for Nothing, they couldn't stop. These various vacuities prevent things from really vanishing, which prevents dimension from being well defined. Even worse, disparate kinds of Nothings inhibit a unification of disparate kinds of numbers. Such numbers are generated by Geometric Algebra, and they must be allowed to really vanish to avoid accumulating numeric garbage that would clog its machinery. This hygiene can be achieved by reverting to the primordial economy of just one Nothing in mathematics. After that is achieved, programming languages can acquire the same hygiene. Strangely, the early C language started with it, then degenerated. Meandering Toward Geometric Algebra. Here is the key to Geometric Algebra: points are numbers—geometric numbers—and their extension generates lines, planes and on up, which are also numbers. Grassmann’s path to that idea was so esoteric and meandering that few have untangled it over the last two centuries. Surprisingly, it can easily be untangled by anyone willing to acquire the seldom articulated dimension of a point, not the widely discussed one. There’s the rub: our own path toward that dimension has been as meandering and baffling as Grassmann’s path was. To untangle both paths we shall have to go back several millennia and proceed straight and narrow. This will be quick: we’ll be flying low over the winding river of ideas leading toward formal geometric dimension.
