The Geometric Nature of the Kunal Kishor Verma’s Infinitely Self-Referential Field!
By!
Ian Beardsley!
December 19, 2025"
In a recent paper by Kunal Kishor Verma and myself, it is suggested in Kunal’s Timeless Energy
Principle (TEP) that the universe is an infinitely self-referential field of models that only resolve
when we choose one, and it then collapses into an abstract theory that is incomplete, but
allows the mind to model the Universe from one point of view. It is incomplete in the sense that
all theories are incomplete to date because they are formulated with mathematics which is a
formal system. Formal systems are incomplete because they are self-referential and thus
based on at least one assumption (Godel’s Incompleteness Theorem).!
As such, in our paper, we model this infinite regress to get around the inability of physics to tell
us what reality actually is. The model we collapse from the infinite regress is determined by our
assumptions, like the assumption by relativity of curved spacetime, in the sense that curved
spacetime is inferred by its measured effects. All measurements are really inferences because
they are done with devices based on the same principles we are measuring.!
In light of this we often choose a model based on the assumptions that suit our needs because
any assumption opens particular doors, and closes others. Often the most versatile theory for
the moment is the one that keeps the most doors open (Dr. Richard Allen Miller). The draft of
the paper by Kunal and Ian (the final has been submitted for peer review) is at:!
Nature as Infinite Regress: A Unified Framework of the Timeless Energy Principle and the
Collapse of Abstract Modeling!
https://www.academia.edu/144939647/
Nature_as_Infinite_Regress_A_Unified_Framework_of_the_Timeless_Energy_Principle_and_the
_Collapse_of_Abstract_Modeling!
We see that all theories are incomplete due to the assumptions by the following illustration…If
we want to say what space is, or to keep it simple, what distance is, we say it is given by
velocity over time, or!
x=vt!
We want to say what x is, so we must say what velocity is. It is distance per time:!
v=x/t!
We put this expression for v in the equation for distance and we have!
v=(x/t)t!
This returns!
x=x!
Which is to say distance is distance, or more generally space is space. Thus we see physics
makes assumptions, which does not allow us to say what reality is, here the reality of space
because the language is self-referential.!
The Geometric Nature of the Infinitely Self-Referential Field!
Here I suggest the field is characterized by the equilateral triangle. If the left corner of its base
is our thesis, then the right base corner is the anti-thesis. The apex is the synthesis of the
thesis and the anti-thesis. But this synthesis becomes a new thesis. It in turn has an anti-
thesis, and these latter two form a new synthesis. This new synthesis has an anti-thesis, and
this new pair of thesis and anti-thesis has a new synthesis. So we see the infinite self-
referentiality of the field, geometrically. Since the equilateral triangle tessellates, we have an
infinite array of triangles, each node can be taken as a thesis, and has an anti-thesis node, with
this pair of nodes having a synthesis. We can choose any node in the infinite array as a thesis,
find its anti-thesis, and form their synthesis.!
If the tessellations go out to infinity symmetrically, they do so in six-directions, because the
dual of the equilateral triangle is the regular hexagon (as shown in the drawing).!
We see this why in physics , , , are so important. Because the fundamental
unit of the field, the equilateral triangle, if you draw in its altitude, form a 30-60-90 triangle. And
we have!
!
!
!
The regular hexagon is important to characterize the field because its radius is equal to its side
and we can take the side and radius as 1, each. This is why six-fold symmetry is so
fundamental as well. This is analogous to the speed of light in relativity having the property of
infinity and being taken as 1. The speed of light is often taken as c=1 giving one the property of
infinity, because at the speed of light time is zero, so in its reference frame it takes no time to
travel any distance giving v=c=1 is infinite velocity. Similarly the self-referential field is
described by the unit regular hexagon having side to radius equal to 1, describes the field
continuing out to infinity with six directions,!
The square is important because it tessellates as well like the equilateral triangle and the
regular hexagon. It is the basis of all coordinate systems, in that for instance while in it a point
is given by (x,y), in polar coordinates a point is given by ( ) where r and theta are given by!
!
!
This is also the source of appearing so much in physics because!
!
45 degrees is half of 90 degrees. 90 degree angles are formed by bisecting a line into two
equal angles.!
In the hyperbolic geometry of spacetime where clocks are described by hyperbolas, the world
line of light is t=x giving an angle of 45 degrees and this is the asymptote of the hyperbola.
1/2
1
2/2
3/2
cos(30
∘
) =
3
2
cos(60
∘
) =
1
2
sin(90
∘
) = 1
r, θ
x = rcos(θ )
r = x
2
+ y
2
2/2
cos(45
∘
) =
2
2
