Infinity and Definition of a Point

From Nathan Carlson, a reader of my first paper on IUT (http://scientificphilosophy.com/Downloads/IUT.pdf):

Mr. Borchardt,

I was reading your paper on the Infinite Universe Theory, and it reminded me of something I had been pondering for quite some time now, a logical accounting for gravity.  I had a rather interesting idea that if something exists as an atom (by the Greek meaning, an indivisible subject) then inevitably, it exists as a point.  I then set about defining a point, starting with the idea of a small sphere, and found that unsatisfactory.  I then had it as the meeting between two lines, but that does not properly define it either, as it accounts for two dimensions.  So I came to my third definition which becomes useful hereafter.

A point can be defined as the intersection between an infinite number of infinite planes.  This becomes more interesting when you bring a second point into that interaction.  the intersections between these infinite planes become potential points as well.  The closer the two points are, the greater the density of these potential points.  I will call these I-points.

Now give the point mass (not realistically of course, because it would of course be made of an infinite number of smaller particles.)  If these two points have mass, and an inclination to move, then this point field, (to me at least) is the plot of likely paths that the particles can take, and may even be an exact representation of possible paths the particles can take, though still an infinite set of paths, they are denser with two particles than one, with three than two, and in expansion to a possible infinite number of particles.

However, I'm not interested in calculating an infinite number of particles possible point paths.  What interests me here is the logical explanation of gravity.        I will redefine force here, not as push or pull but as an inclination of matter to move, (which could be proved by proving that it is impossible for matter to be without motion, also a talk for a later time I hope.)

Mass (m1m2) I will define as a collection of M-points (M-points being defined as a collection of I-points that have/constitute mass). 

As these M-points get closer the I-points they are made of generate increasing point sources to exist in.  In other words, Mass approaching Mass creates more possible spaces in the "etherosphere" for the Mass to exist in.  Given an inclination to move, mathematically a point will over time take (and remain in) the path with the most options.  Hence increasingly massive objects have an increasingly denser set of possible points for matter to exist in. 

Massive objects instead of being attracted to each other are instead falling into a denser etherosphere.  Hence your "Push", but not exactly.  Instead it is the motion of mass (still relying on proof of impossibility of mass to remain stationary).  The points generate their own increasing number of options for movement. 

[[don't take this as a relation to the theory above, rather take it as an interesting spin tweaking one dimension]
Take the I-points and instead of having the infinite planes have only two dimensions, have them three dimensional with the X and Y infinite and the Z approaching zero (or infinite smallness)  and then you have room for an interesting type of mass that is literally being squeezed through potential point paths generated by the density of the etherosphere. 

Take those two :) and you can see that the system cannot collapse in on itself into an entropic state of stillness because the closer any mass (made of M-points) gets to another the more potential places it will have to move into, increasing the potential for motion.  The only way to approach that is to increase the density of the points, the farther a single point gets from a dense core (-singularity or not singularity but close in definition) the less options it has. 

I hope that is a sufficiently interesting conversation starter, your paper was thought-provoking and I believe closer to the Truth than science has come in years.  There are other things I'd like to discuss, like the law of Conservation of Mass, and the religious possibilities of an etherosphere; I don't believe that mass or even mass-energy cannot be created or destroyed, I believe that they cannot be created or destroyed by physical means or means known through things that exist with mass and physical existence.  And I believe in the soul, if the etherosphere exists, then I believe that a soul could be a complex mapping of potential point spaces constituting an intelligence, or more grossly a computer.

My Sincere hopes that you find this useful, and an interesting hello,


Nathan Carlson

Post Script:  Please don't feel insulted by this, but I would hope that this leads to an interesting conversation and not a footnote in a paper.  I would not imply, having not met or become familiar with you beyond your 2007 paper that you would plagiarize, or steal an idea.  It is my intention rather to believe that you are an interesting and intelligent individual that, should this be of use to science, would detach any significance of personal recognition from you or I and leave the significance to the fascinating theory which shakes science and reshapes our understanding of our reality. I personally believe that science is hindered by the desire for personal recognition, and that better science develops from open source with excellent documentation.


Hello and thanks for your comments on infinity. You have quite the imagination! Since writing the IUT paper, Steve Puetz and I have just completed our definitive work on the subject (Puetz and Borchardt, 2011). As you may recall from the IUT paper (Borchardt, 2007), we consider microcosms (x,y,z portions of the universe) to be infinitely subdividable as well as infinitely integrable. None of these could be considered true points, because a true point in mathematics is the imaginary intersection of imaginary lines from all three directions. Neither the lines nor the point could exist, for existence is defined as that which contains matter, has the 3 dimensions (x,y,z), and has location with respect to other things. You are correct, therefore, that a true point cannot be a sphere. What you have realized, in essence, is that math is no match for the infinite universe.

BTW: In all our work at PSI, we consider force to be neither matter nor the motion of matter. Instead, force, like momentum and energy, is a calculation or matter-motion term in which we multiply a term for matter times a term for motion. Despite the claims of regressive physicists, force neither exists nor occurs. What we describe as force is our observation and description of matter in motion. Your definition of force as “an inclination of matter to move” is slightly better than the usual, but will not get you the correct theory of gravity. This Steve and I got by giving up matter-motion terms entirely. We don’t consider gravity to be a “force,” but the result of a Gravitational Pressure Gradient due to aether density and activity being greatest where complexed aether (baryonic or ordinary matter) is least. If you are serious about this, you can practice by substituting “matter-motion” for “force” whenever you come across it. Then the definition of “force as an inclination of matter to move,” becomes “matter-motion as an inclination of matter to move,” which clearly makes no sense. It’s best simply to stick with matter and the motion of matter, or in shorthand, “matter and motion.”

BTW2: Sorry that I can’t help you calculate souls from the aetherosphere. The Progressive Science Institute is an “organization that sponsors education and research on scientific philosophy free of political and religious influence.” 


Borchardt, G. (2007). "Infinite universe theory." Proceedings of the Natural Philosophy Alliance (http://scientificphilosophy.com/Downloads/IUT.pdf) 4(1): 20-23.

Puetz, S. J. and G. Borchardt (2011). Universal cycle theory: Neomechanics of the hierarchically infinite universe. Denver, Outskirts Press (www.universalcycletheory.com).

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