This file as pdf here.
A little stirring in the conceptual soup:
The model here departed from a very elementary geometrical view
on Big Bang as a point (Zero) in the sense of a first center (0).
Big Bang as a triple point between metaphysics, mathematics and
physical concepts.
The complementary pole (00) becomes really "undefined"
by definition.
The 4th dimension degree (ddegree) as Direction(s) has here been
regarded as created between these "poles".
In later years and decades the Big Bang theory has been established
as proved, and black holes as consequence of collapsing stars
has been intensely discussed.
Singularities, Zeropoints and infinities as
00poles are incorporated as concepts in physical discussions.
Yet, it seems that physicists still find it
difficult to accept infinities when they appear in their functions.
They are regarded as "absurd" answers in their calculations.
The String theory was developed as a way to avoid such "absurd"
answers when particles were treated as points.
In which sense if any are such answers absurd?
All right, certain kinds of physical calculations may demand that
both entities in a relation be well defined within limits.
However, methods or conceptual structures to
interpret infinities when they show up, not neglecting them, seem
necessary to develop from the viewpoint of our model.
Two first things to say:
 The redefinition in our model of "infinity" to "anticenter"
implies at least that infinities get indirectly defined through
their complementary poles, representing centers.
 The 5th dimension degree, here introduced for the Entirety,
polarized into poles 0 and 00 makes a difference. The fact that
established physics only count on 4 dimensions seems to be an
essential part of the problem. The infinities said to appear among
the equations in Einstein's general relativity theory may just
point towards one such not recognized higher ddegree.
Black holes:
To begin with the singularities connected with theories about
"black holes":
"Spacetime breaks down" in black holes. This
statement or description becomes quite natural if we replace the
concept of a "4dimensional spacetime" with the 4dimensional
vector fields in our model, defined through the polarization of
the Entirety into the poles 0 and 00. (Of course Space is created
through the Big Bang, doesn't exist "before", and the
concept "before doesn't exist either.)
The replacement implies only that a formulation
in ddegrees 3210/00 (0/00 for Motions, here Time) are raised
( = deepened) one ddegree to 4th ddegree as non polarized At
the poles all structure disappears.
In words from Hawking: singularities are found where spacetime
has a beginning or an end. 0<===4===>000 (4 for spacetime).
That's obviously at the "outer poles" 0 and 00 of ddegree
4 in our model.
(This picture should be turned
upside down.)
In other formulations:
"The singularity is the point where the whole mass of
the black hole is gathered and crushed to infinite density".
"SpaceTime breaks down and a so called
singularity is created. The density of matter becomes infinite
in a place which has no extension".
Mass→Gravitation
→ Density:
First, why talk about matter or mass
in this context? The problem some authors find in this occurrence
seems to depend on their wish to limit themselves within the frame
of a 4dimensional world and the concept of Mass  which in our
model isn't identified before ddegree step 43.
That the property of mass as a structure breaks
down is quite natural at the poles of ddegree 4. An analysis
in terms of a change in dimension degree seems necessary to introduce.
Second, it's said that gravitation seems to grow towards
infinity (00) inside black holes. We have identified the vector
fields when polarized as F_{A},
the outward acceleration force
(cf. Space, now recognized as expanding) and F_{G},
Gravitation as the inward acceleration force. With the definition
of gravitation as the direction inwards, (Vconv) this growth sounds
natural. One aspect on this infinity is the infinite number of
directions towards a point. Observe that the infinity here concerns
the "strength" of the force.
Third, "density becomes infinite":
Density is in our model suggested as the physical concept
in ddegree step 5  4. In next step polarized into Mass
and Vacant Space (as E = +/ mc^{2}). (Density
as Mass/Volume here implies that a fractional expression may be
interpreted as a relation of complementarity.)
The suggestion is well in agreement with statements
about the conditions in black holes. Density of vectors at a Zero
point becomes infinite.
Density, it's said too, is inversely proportional to Mass squared:
D ~1/M^{2}
Expressed in this way it may seem odd that Density grows when Mass
is reduced.
Yet, accepting that the formula conceals a border
between ddegrees and implies a relation between higher and lower
ddegree, it's more understandable. (Note the inversion too, see
below.)
Singularities of opposite kinds, 0 and 00?
The suggestion that Big Bang was a singularity of the 0type and
black holes are singularities of 00types seems very natural from
the viewpoint of the model here. (It is attributed to Weyl [Wikipedia].)
The 00pole has here also been interpreted as
manyfold in relation to the 0pole as a unity. Black holes as
the death of big stars are naturally a manyfold
In terms of forces:
Singularities are presumed as points "since no known forces
can resist the enormous force created when stars collapses".
The poles 0 and 00 are identified as first binding
and polarizing forces in ddegree 4 in our model. Which connections
exist between the infinities and singularities in physics and
these conceptual definitions?
In the theories about black holes the antigravitational
force F_{A} is regarded as absent.
Gravitation, the force of the 00pole in this model, when acting
alone in the collapse of stars, obviously acts as a destructive
force since mass disappears. Hence, black holes could be regarded
as results of Gravitation in its most primary form. Aggregating
but fragmenting or destructuring.
It implies that the property of Mass also, not
only "Matter", need a factor from the
F_{A} force for its construction.
(Cf. our suggestion to use matter for the atomic structure developed
in ddegree step 32, mass as concept for the deeper property
developed in ddegree step 4→3.)
[At the same time the singularity may be interpreted as a secondary
defined Zeropoint, as we have assumed a "pole exchange"
in the last step of a dimension chain where motions inwards, "towards
each other" indirectly defines a 0pole again. This 0pole
could be attributed the property of a binding force of secondary
order (equivalent with what Weyl calls of "00type"?.
In that case we have connected the interpretation
of black holes with motions, with the last step in the dimension
chain instead of aspects in ddegree 4. (Cf. ddegree "0/00"
as the meeting of the outer poles in ddegree 4)]
About curvature of spacetime:
A factor that may complicate the physicists' analysis is
their wish to connect gravitation with curvature of space. Even
in ddegree 4.
In our model a point as the singularity of Big
Bang is the opposition to an infinity and gravitation in ddegree
4 is identified as a radial inward directed vector field  and
curved space is introduced first in step 4→3.
In the view of astronomers and cosmologists
of today a point represent an infinite curvature, a really selfcentered
infinity! Such a definition points to the alternative analysis
at the end of our dimension chain.
(Rotating black holes may justify aspects from
the lower ddegree. Cf. about rotation.)
As to this curvature:
Would it be possible to replace a gradually increased curvature
with repeated steps from an Euclidean to an elliptic
geometry? (See file "43
IIIIV", No. 5)
An Euclidean plane (as an angle) may be represented
by an elliptic line, an Euclidean line by an elliptic point. Applying
this description of elliptic geometry in relation to the Euclidean
one as a stepwise lowering one ddegree, we may from volumes arrive
toward a point in 3 steps.
Space and Time "shifting place":
According to one statement "SpaceTime becomes so curved
that space and time in some way shift place". It sounds as
if we in that case had something remembering of what we have called
a "pole exchange" in last step of the dimension
chain in our model, where motions from each other define anticenters,
motions inwards, towards each other, define centers. (Distance
and Time as entities in last step.) In connection with the view
on dimension chains of Motions and of Structures as in opposite
development, we could perhaps imagine such a change.
Ddegree of Motions: 00/0 1
2
3 4 5
Ddegree of structure: →5 →4 →3 →2 →1 →0/00
In other words: space becoming the imaginary factor (instead
of √ 1 for Time), Time or Motions
(ddegree "0/00") realized  perhaps connected with
the wild fluctuations of quantum mechanics in microcosm? (Space
as "imaginary" could perhaps be thought of as corresponding
to human memory, rooms inwards, the world in dreams when a person
sleeps and represent "an entirety" in itself.)
What happens at the singularity in black holes  if anything?
Is there any possibility of transformations in the imagined centers
of black holes? Any hidden connections with other parts of Universe?
The most logical with our model in mind would perhaps be a transformation
to the opposite force F_{A} the
outward acceleration force, a hidden connection with expanding
Space? With the world of negative energy (E = mc^{2})?
Apart from black holes:
Definitions:
Within mathematics the concept poles are used as in our model
(also replaced as "partial structures").
A point Zo is said to be a pole to a function
if the limit of the function goes towards 00 when Zo goes towards
0. It's a simple expression for the polarity in ddegree 4 in
the dimension chain.
Within physics a singularity is a point in time and/or space
where one or several physical entities are undefined "since
their value becomes infinite".
Here the connection between the properties "undefined"
and "infinite" is expressed  with the explanation
that "we don't know any laws of nature which are valid
with infinite values on physical quantities".
A general question: Could some of the problems with singularities
and infinities depend on a mixup of different kinds of infinities
and of different aspects or definitions of "singularities"?
One may ask:
What is the essential property of an infinity?
· That it is immeasurable?
· Infinite in number of something?
· Or just unlimited?
· Or just undefined or badly defined just
in this special relation to some other quality?
· Or the reference to its relation to
a center, a 0pole, its property as an "excluded center"
in relation to an "enclosed" one? Its character of "anticenter"?
· Or the event that some zero point has
become inverted?
The several different kinds of infinities and definitions seem
unclear or disputable.
Infinity in numbers is one thing, but there
are essential infinities as anticenters that don't concern numbers.
Infinities in "strength" of forces, in the property
Mass or in Charge are hardly of the same kind; the
only common property may be the that they are immeasurable.
Some other examples:
 3rd degree is undefined for an existence in
ddegree 2. We have that higher ddegree is undefined in relation
to a lower one, but it could hardly be described as infinite?
 In simple geometry a lower ddegree represents
infinity in relation to or included in the next higher one  as
a potential number of surfaces in a volume.
 A spherical surface is closed and measurable
as such but unlimited, in this sense infinite.
We could add a question if singularities may have any connections
with the "superpositions" in quantum
mechanics?
A superposition is perhaps not infinite but
undefined with respect to 2 possible answers. However, on the
xaxis in a coordinate system the yaxis is undefined and could
be regarded as representing an "anticenter" and as such
all possible but potential values, including +/ infinities. Equivalent
with the 3rd ddegree in relation to an existence in the 2nd ddegree.
If a superposition when released is regarded
as a collapsing yaxes, giving answers Yeas or No, it's equivalent
with probability 1 or 0. And probability is perhaps the only physical
concept that is infinite at a welldefined number 1 (!).
What does a probability on the other side of
this border 1 imply? It's said that physicists have met such
peculiarities. In connection with Schrödinger's wave functions
the probability to find the electron somewhere is the amplitude
squared. Then the amplitude must be below 1 (something) in order
not to give probabilities >1.
Could this problematic infinity be selfinflicted?
Depending on some wrong border to the possible amplitude? Or
on the other side of 1 represent something that already has
happened? Backward in Time? )
Does the redefinition of infinity to anticenter imply any contribution
?
It follows from the starting point of Big Bang, all right, but
then?
Infinity leads the thought to size, immeasurable
things, while the concept anticenter allows much broader references
and points toward a relation.
Transformations:
Everywhere where the 0pole becomes the denominator, these difficult
infinities must show up. There must be something wrong with applying
this mathematical convention to physical realities, since the
Zero point and Big Bang naturally is a common "denominator"
for everything in Universe.
It seems necessary to analyze what a mathematical
fractional number really corresponds to in physical terms. (Cf.
fractals.)
The natural thing would be to see them as relations
and indirectly arrive at new definitions.
Again, within mathematics a singularity is an undefined point
in a curve, a surface or else analytical function: a point as
a break, a corner or such things. It's classified as undefined
since some other mathematical concept, whatever it may be, isn't
defined in that point.
A simpleminded view would be to look at these
points or corners as polarizing ones, indirectly defined through
the continuous or analytical parts that they divide. (Why should
every concept which physicists or mathematicians invent have to
exist in all other contexts? Not to exist is also a property!)
Such points or singularities of different kinds are related to
structural changes as phase changes or to what happens
at bifurcations (with reference also to Hirsch and Smile).
In terms of our model reasonably with jumps, with dimension degree
steps, may it be fractals or whole steps.
In the latter case it would imply a change,
a transformation to another physical quantity. We have the general
truth that concepts only can be defined through one another. Hence,
it's quite natural if physical concepts will have to be transformed
into one another for a definition.
Two possibilities:
Yet, there are two possibilities: with respect to a dimension
chain: in the model here:
 Either to find the singularity and infinity of some entity as
pointing out a relation to the complementary pole in the same
ddegree, or to identify it as expression for a change in ddegree
as in a phase shift.
The interpretation may be confused by the general ambiguity regarding
the 00poles in the dimension chain: Each lower ddegree in relation
to the higher represents geometrically an infinity. We can also
regard a whole chain as "haploid", as a development
from the first 0pole to the 00 at the end of the chain, the 00pole
debranched to a surrounding, an anticenter, in each step of the
0pole towards lower ddegrees.
At the same time  or when the dimension chain
is regarded as "diploid", all complementary poles in
lower ddegrees have inherited some features from the 0and 00poles
respectively. There is some character of the opposition center
 anticenter in each degree (as Mass versus Space, Electric versus
Magnetic fields, as protons versus electrons.
Furthermore, we have assumed as a general view
that the anticenter pole, as the "surrounding", is stepwise
builtin during the development of the 0pole towards higher levels.
Hence, we can expect infinities builtin everywhere in our ordinary
world.
It's perhaps not strange then that physicists
some decades ago found that the positive charge
in nuclei seemed to rise towards infinity inwards the center.
(Charge in this model regarded as a 2dimensional property in
relation to Mass as 3dimensional.)
The found infinity of charge could depend on
a mix of ddegrees. It could imply that the analysis should be
moved one step deeper to the physical quality Mass,  or outwards
put in relation to the physical concept of Distance  in order
to get defined values?
(Cf. the convention to put the negative charge
of the electron to 1, and the partial builtin negative charge
1/3 of one quark in the proton in the quark theory. And the family
connection assumed here between negative charge and F_{A
} and Vacant Space in higher ddegree.)
Inversions:
A usual, simple illustration of a singularity is the point x
= 0 in the function
y = 1/x.
This is the inversion of the function y = x,
of a straight line from the origin, a "radius".
One aspect is the value of y, rising
towards infinity when x approaches zero 0. Infinities are
of the asymptotic kind. The jump to an interpretation of what
these coordinate axes eventually represent in physical concepts
seems to be appropriate.
Another aspect could be expressed as the opposition
between "excluded" and "enclosed" center,
derived from our first polarization in 0 and 00.
From the viewpoint of first origin in the coordinate
system it's the curve that represents the excluded center, connected
with infinities, and the origin (x = 0) with the real "enclosed"
center. However, from the viewpoint of the curve, the origin x
= 0 becomes an excluded center, and the curve of the inverted
function, indirectly defining a new center, represents the enclosed
one.
The functions y = x and y = 1/x illustrates geometrically
the complementary poles radial  circular which we have
assumed as the polarity from polarization in ddegree 3.
(See presentation
of the model.)
Geometrically it's possible to identify inversions of
different kinds.
 The negative and positive halves of the coordinate axes
may be regarded as inversions of each other around zero 0.
 Directions inwards and outwards may be regarded as inversions
in a similar sense  along the vector lines.
 A part of a curve, inverted along a tangent, would represent
the complementarity concave  convex. Equivalent with an
inversion of the viewpoint: from outside to inside.
Hence, the complementary poles in our dimension chain may be
regarded as inversions  geometrically.
We could repeat here that one of the poles (or
partial structure in all ddegrees has inherited some feature
of infinity or anticenter.
Connecting such different inversions with dimensions and dimension
degrees, it could imply that also simple inversions of numbers
as such around number 1 could content a possible relation between
them in a physical context.
Generally it seems necessary to identify "around what"
the inversion occurs,
sometimes possible to express as "on the other side of a
border".
One could conclude that it should be possible to handle some
infinite factors through an analysis of the inverted form and
the kind of inverted relation to the complementary pole. If not
going underground  to higher ddegrees.
Concerning the physical quantities connected to the poles,
in which way if any could these be regarded as inversions of each
other: protons and electrons? Mass and Space ? E and M? FG
and FA? Surely not in a simple manner.
A vector field or force as outward directed
should certainly have to be turned or "inverted" through
the 5th dimension degree, the entire Universe, to become an inward
directed one.
And we can go on assuming that Mass as a property
should demand 2 such inversions or reflections, also the one between
positive and negative Energy
(E = +/ mc^{2}) to disappear as Mass and reappear as
empty Space.
What physicists call antimatter as antiprotons
versus protons demands probably 3 inversions through the higher
ddegrees.
Protons and electrons as antimatter to each
other on another level and grandchildren of F_{G}
and F_{A} surely demand 4 inversions
to transform to their complementary pole, the change in mass relation
included.
In general words it sounds reasonable that transformations between
complementary poles demand reflections as inversions in a different
number of steps.
How does this assumption agree with the suggestion in files about
Mass and Charge
that these properties could be interpreted in some terms of negative
(inward) and inverted acceleration (1/a) and velocity (1/v)
respectively? It may agree in the case of Mass but Charge should
need the addition of some more complex operation.
(As to the relation between reflection and inversions, compare
about quaternions in file
43: VVI.)
In lower ddegrees where degrees of motions become dominating,
"inversions" may be regarded as repeated processes.
In light beams we have the continuous transformation of the Efield
to Mfield to Efield during the propagation. Motion as such,
even identifiable in elliptic rotation, implies a repeated "pole
exchange", (ddegree 0/00 in our model) as inwards/outwards;
so too in longitudinal waves, so in the gait of living individuals.
As to the expression for velocity, Distance/Time (D/T) and last
step in our dimension chain, it's possible to regard it as a transformation
 or translation  between complementary poles in itself. With
the illustration from file Motions:
*
