An introduction to infinity and the infinitesimals

Can we further define these two?

Throughout history, the finite-infinite debate has been fraught with emotion between those who “believe” and those who do not. Those old debates are ignored here. How do we start with a clean slate, a tabula rasa?  Are there simple concepts of infinity that defy a finite label? Some of the most advanced work to control the concept of the infinite is in physics, i.e. the work within renormalization and regularization. These highly-technical descriptions of infinity have yielded concepts with highly-specialized language. Although some of that work will be engaged, our goal is to explore alternatives to Newton’s absolutes of space and time.

To start simply and modestly, qualities of pi are analyzed. Within her sphere we begin to see much more. And then, her most basic qualities shine through.

Then, turning to the classic studies of the electron defined as a point particle with a point charge and no spatial extent. The radius formula is:


Within our base-2 chart, this “point” particle falls within Notation 60. There are 60 doublings of the Planck scale numbers prior to reaching the size of a “point” particle. Denying this infinitesimal range seems a bit too sure that particles and waves are our fundamental building blocks with which to construct our universe. A key concept of this website is that the most simple sphere, the plancksphere, is the most basic building block and that once it begins stacking, it is simple no longer.

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Also see: The Physics of Infinity, GFR Ellis, KRY. Meissener, HERMANN Nicolai.