If pointfree is pointless, shouldn’t we go back to the very beginning?


The Redefinition of a Point

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 in the Antarctica 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.

Your comments and questions are encouraged.

Challenge us. Help us. We need all the help we can get:

Key documents that were recently homepages:

October 16: Looking in the dark for Dark Matter & Dark Energy
October 12: What would you do with this model of the universe?
October 1: The first 64 notations out of the 202
September 28: An Open letter about nature of light
September 20: “Gravity, Oh Gravity… Why Such Gravity?”
September 19: On Validating The Efficacy of our Model.
September 17: Open Letter (email) – Many similar notes are sent to scholars everyday.
September 14: Your critical review is encouraged.
September 12: Questions – Frequently Asked Questions.
September 5: Commonsense – It is not common and it is not a sense.
August 31: Reviews – You are invited to review an alternative to Big Bang Cosmology.
August 26: Problems – We all must become problem solvers.
August 5: On embracing the functions of our Universe
August 2: This Simple Scale of the Universe
July 23: Big Bang Theories Unnecessary In Light Of A Natural Inflation
July 12: An addendum to the Standard Models and for all algorithms
July 8: Compilations of concepts that could give rise to the 202 doublings
July 4: Revolutions: Foundational Concepts & First Principles

June 21: Planckspheres, dimensionless constants, doublings
May 18: Alternative to the Big Bang theory

April 30: Emergence & Growth from the first moment in time
April 21: More about emergence, growth, and imagination
April 18: Einstein’s Postulates

An excellent resource to translate any of our pages by its URL:

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Editor’s Notes about Navigation and Other Points of Interest:

  1. Navigation: Scroll to the top of the page. Cursor over the word HOME and a very long drop down menu will be displayed. It can be scrolled. There is a link to every homepage within this site from its beginning in September 2016.
  2. Homepage. Click on Our Universe in 202+ Doublings to go to the current homepage.
  3. In that “second header” there are links to the past 25 homepages. “Just Prior” always goes to the most recent, then each number is active to the next prior homepage. The image goes to the horizontally-scrolled chart as does its tagline.
  4. Values and ethics: Within our study of universals and constants, there is a sense of value that gives rise to values and ethics. The antithesis is nihilism which eventually opens us all to the various forms of dystopia we are experiencing today.

The current struggle: Who will lead us? Who can break the impasse?

Might the seven First Ladies of oldest trade routes of our world break the impasse?

Sphere to plane