**∞**

**THERE IS NO REALITY WITHOUT INFINITY**

Recently, a physicist
said to me: “While infinity may be a useful concept, it does not actually
exist.” I respectfully disagree. Let me see if I can explain why.

In TDVP, using the logic
of the calculus of dimensional distinctions (CoDD) and Triadic Rotational Units
of Equivalence (TRUE) Analysis, we may investigate the question of whether the
concept of

*infinity*is an existential reality (I use the word ‘existential’ here as it’s root meaning, not in the more diffuse sense of the philosophy of existentialism), or a convenient mathematical and theological fiction.
Why is the mathematical
logic of the TDVP appropriate for investigating this question about infinity?
Because it combines the basic concepts of pure mathematics with the basic concepts
of physics. It does this by defining the basic distinction of pure mathematics as
equivalent with the smallest mass of quantum entity, the electron. This ties
the mathematics of the CoDD to the mathematical structure of the physical
universe.

__Infinity as a useful concept in mathematics__
In
contemporary mathematics, infinity is the

*concept*of a state or object being larger than any number of units of measurement, no matter how large or small the units are. When used in the context of “infinitely small," infinity is the*concept*of an object that is*smaller*than any single measurable unit, no matter how small the unit is. Special care must be taken to be sure that infinity is**not**erroneously treated as a number, because attempting to treat infinity as an actual number can lead to paradoxes. So, for contemporary mathematicians, infinity exists only as an abstract concept. The symbol
Infinity is also used in the definition of the
cardinality of a set of objects as in a list, array, or ordered sequence of objects
that does not have a finite number of elements. The set of positive integers is
a good example. Again, one must be careful to avoid thinking of infinity as an actual
number, because doing so can lead to confusion. For example, the set of
integers and the set of even integers are both infinite, despite the second set
being contained within the first set. Infinity is also used in the theory limits.
Some functions approach a specific finite value as the independent variable in
the function approaches zero infinitely closely, while other functions may
approach infinity as the variable approaches zero. The concept of a function
"approaching infinity" means that it grows larger without bound.

For macro-scale analytical geometry,
with applications of integral and differential calculus, the concept of
infinity is very useful, if continuity of space and time can be assumed. Determination
of rocket trajectory and satellite orbits are good examples. In problems involving
finite discontinuities in variables of extent and content, however, integral
and differential calculus cannot be used, and contemporary mathematicians must
resort to cumbersome finite-difference equations.

__Georg Cantor’s Infinities__
From antiquity, many philosophers
and mathematicians contributed to the study of infinity, but it was Georg
Cantor in the nineteenth century who established infinity as a respected mathematical
subject, even though he didn’t get the recognition he deserved in his lifetime.
Most of the other mathematicians of his time denounced his work as “religious
philosophy”, not mathematics. Despite the disdain of his peers, Cantor created
modern set theory single-handedly by defining the concept of one-to-one
correspondences between sets. He started by demonstrating that the set of integers
(whole numbers) can be aligned in a one-to-one correspondence with the set of fractions,
and concluded that these two sets have the same infinity. This led to his most important
discovery, when he proved that there are infinitely many infinities, of
different sizes. For example, the infinity of points in three-dimensional space
is much larger than the infinity of points on a line because three-dimensional space
contains an infinite number of lines.

__Infinity as used in Theology__
For theologians,
God's infinity is defined as something distinctly different than mathematical infinity. In mathematics, the concept of
infinitely large is derived from the concept of enumeration in the finite world
of our experience by recognizing the impossibility of ever coming to the end of
being able to add one to any number, no matter how large it gets; and the
concept of infinitely small is conceived of by dividing unity by those larger
and larger numbers obtained by the process of addition to get smaller and
smaller numbers,

*ad infinitum*. On the other hand, theologians claim that our ability to build infinity from the finite, to understand that we can keep applying the fundamental operations of addition and division over and over, getting a new result each time, is grounded in the idea of the theological infinite as an attribute of God.
Theologians
believe that God is infinite in a way that the finite mind can never understand;
and that God's qualities cannot be determined by the addition of parts. Thus,
God is not a completed whole, but rather, a Whole Being without limits'.

^{ }[Leibniz,*New Essays on Human Understanding,*trans. Peter Remnant and Jonathan Bennett (Cambridge: Cambridge University Press, 1981), 157ff.]

__Infinity as a necessary concept in TDVP__
In the CoDD, the quantum
mathematics of the TDVP, we have shown by the mathematical process of Dimensional
Extrapolation, that any domain of n dimensions is embedded in a dimensional
domain of n+1 dimensions. This means that the nine mathematically-definable finite-dimensional
domains of the reality we experience is embedded in infinity. The forms that
make up the elementary vortices that we can observe and quantify in 3S-1t, are
conveyed from the logical structures of infinity (the mind of God, if you will)
across the six dimensions of consciousness and time by conveyance equations containing
gimmel, into the three-dimensional domain of everyday observation. However, as
shown by quantum experiments like the double-slit and delayed-choice
experiments, these forms are non-local (i.e., existing as potentials throughout
infinity and the finite domains embedded in infinity) until specific distinctions
are drawn by a conscious observer.

**CONCLUSION**

*In the ultimate scheme of things, Infinity is real, not just a mathematical fiction. Without Infinity, there would be no gimmel, and, as demonstrated in the TDVP with the logic of the CoDD, without gimmel, there would be no universe.*
Is this an infinity of content or empty dimensions or both? Is time from a higher dimension represented as a "block universe"? The latter seems to be the experience of some stories of NDE's, as if they had moved to a higher dimension(s) in time -- but that is what I am asking.

ReplyDeleteI can ask the question but its hard to know if its meaningful! :)

From the TDVP point of veiw, real Infinity is an infinity of content because everything is embeded within it. Space, as Einstein said, does not have any existence of its own, and in TDVP it's likewise for space-time and all other dimensional domains. In an NDE, consciousness is expanded to an awareness of a higher dimensional domain that includes the 3S-1t domain embedded within it. That is why they are able to see what is going on around their physical body even there is no brain function or physical sense activity.

DeleteInteresting.

DeleteI got in contact with a math professor but it appears he is not aware of any journals FLT65 could be submitted too. I will keep trying though!

Thanks Wayne.

Delete