# The Redefinition of a Point

##### By Bruce Camber Initiated: October 22, 2018 Related: Quantum Gravity, Dark Matter Dark Energy, Basics

Introduction. In high school math back in the 1960s, the old classic definition of a point was that it had no width, no length and no depth. It’s 0-dimensional and has position only. Though it defined the two ends of a given line, it was all quite axiomatic, based on postulates and logic; we were expected to “accept it as a given” so we did.

Over the years, a pointfree mathematics emerged — no points! Some would say rather humorously, “It’s totally pointless!” Yet, two very real categories have been defined: noncommutative geometry and pointless or pointfree topology. Both actually help us to redefine points by defining the meaning of point free. Both are important within our struggle with definitions and we will return to each over time.

The Planckpoint. Here, now (today), we would like to add a third category: planckpoints. Then, we’d like to consider two forms of a planckpoint: a planckvertex and the plancksphere. Hopefully the definitions of all three will become increasingly clear as we write each subsequent article.

Scaling Points. That old, classic high school definition of a point (above) may end up becoming just a group of words with no application to anything. The ubiquitous period at the end of this sentence, a symbol of the point, can be easily measured to be about 1 millimeter (10-3) wide. Though small, it is rather large in the face of an atom. There are one million nanometers along the diameter of that one millimeter period (or symbolic point). Hard to believe. Looking more closely at just one nanometer (10-9), you might see a stack of ten hydrogen atoms. Then, looking even more deeply, you can see many different large atoms within one angstrom (10-10 meters).

If atoms were all there is, we could stop here and start dancing; but, the nucleus of an atom is in the range of 10-14 meters, and then comes the particle zoo and even all the hypothetical particles in the ranges of 10-15 meters and possibly 10-16 meters. That’s at the limits of measurement even at CERN labs. Yet, we know there is a Planck Length (1.6×10-35meters). Shouldn’t we should know what is in between the CERN measurements and those Planck units?

Key Question: We could continue to try to validate any number of hypothetical particles, but why guess when we know the Planck base units appear to be proper calculations and they do represent the beginning of something?

Facts & Guesses. Since 2011 we’ve been asking, “What are these Planck base units and how do they come to be?” We’ve danced around the question for almost seven years. Our tools of measurement are Max Planck’s calculations for his four base units, base-2 exponentiation or doublings, commonsense, and logic. Because we have redefined the infinite as continuity, symmetry and harmony, we are not shy about guessing that the Planckspheres are the first manifestation of a space-time moment and each manifests as the most infinitesimal sphere there is and all are defined by the Planck base units and all the dimensionless constants that define them.

Here is a point with a length, a mass, a charge and a transaction speed (time); it has no less than three-dimensions and it is the first manifestation of the finite-infinite transformation and this nexus of transformation is our Notation 0.

It is here that I believe the first real point is defined. Thank you -BEC

The Notational Groups That Scale The Universe. Starting at the bottom with Planck-size measurements, we progress up to the size of the universe. A challenge for every student prior to high school graduation would be to know “something” in each of the 71 groups.

An online question“Is there such a thing as a Planck Point, or are Planck lengths basically just points?”

Answer by Bruce Camber: “To answer such a question might be useful in mathematics, logic and physics. Perhaps we should attempt to redefine a point, then possibly define a planckpoint, a planckvertex and a plancksphere (probably interchangeable). BTW, there is a physical place called, “Planck Point” but it has nothing to do with Max’s work.

A planckpoint would be a new understanding of points because it would, by definition, be three-dimensional. It would be defined by all four of the Planck base units along with the dimensionless constants that define them. It would have a known width, length and depth. It might best be imagined to be a sphere or a “construction vertex” to create the first geometries. If you take as a given that the Planck units are the first instance of space-time (see: https://81018.com/c/), you can now build an integrated chart of the universe. So, if we were to double the first unit and continue doubling each result, within 202 doublings we would be at the age and size of the universe. Here’s a chart to demonstrate that fact: https://81018.com/chart/ That’s base-2 notation or exponential growth (See Euler’s perfect equation). By the 65th to 67th doubling, CERN labs is able to pick up its measuring. So, between the first doubling at Notation #1 and the 64th doubling, there is a rich possibility for mathematics, logic, string theory, and some kind of unified theory of mathematics, i.e. Langlands programs.

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