### 453. Infinity Is An Attribute of God And Is Not the Meaning of 'Nothing.'

In my last blog, I say that all things in the universe are finite and that all finite things are different and come from a different infinite (or not-finite) thing, which is in God.

Physical scientists say that a universe begins with

*nothing*. (click) They say that

*nothing*implies

*infinity*. This implication eliminates God from the universe because physical scientists link

*time = 0*and

*infinity*to the notion of

*nothing*. I say that mathematics cannot define the beginning and ending times of the universe. I also say that the infinity of God is absolute whereas the infinity of the universe is variable and is never maximum.

__See the thoughts of Andrew M. Ryan below.__(click)

The first thing to notice is that infinity is an inherently irrational concept. Though we may understand in a strictly formal sense

__what the word__

__infinity____means__, it is not possible to conjure up an accurate representation of the idea in our minds. The best we can do is acknowledge that, however far we go, we can always go farther. But man can’t wrap his head around anything truly boundless. Moreover, the machinery of logical and mathematical reasoning also breaks down when applied to infinity. The crux of this breakdown comes from the observation that the

*cardinality*(size) of all infinite sets is the same, regardless of how those sets are defined. For example, the set of all integers is the same size as the set of all odd numbers, even though, intuitively, it seems like there should be twice as many of the former as the latter. The even numbers are missing from the set of odd numbers, but not missing from the set of integers. Therefore, the set of integers must, in some sense, be the larger of the two, even if we concede that both are infinite. But how could one infinite set be any larger than another? They both go on forever.

*Infinite Hotel*is one example. In it, we are to imagine a hotel with an infinite number of rooms, and then wrestle with various notions of vacancy and occupancy. Specifically, would an infinite number of guests result in full occupancy? The answer appears to be no. If a new guest arrives, we simply move the guest in room one to room two, the guest in room two to room three, and so on, making room for the new guest. Since there is no end to the number of rooms, even an infinite number of guests cannot fill them all. In this and every other paradox of infinity, the issue revolves around treating infinity simultaneously as a

*number*and as the concept of

*unboundedness*. A number is a discrete, definable entity, while unboundedness is exactly the opposite. All numbers are unique, their values rigorously determined, whereas all unboundedness,

*qua*infinity, is the same. But because we can define infinite sets in much the same way that we define particular numbers, it appears as though different infinities are equal and unequal at the same time.

**(fig. 1)**; being infinite, the void can contain any number of infinite sub-regions, just as we can define any number of infinite sets using only a subset of the integers (odd numbers, for example). Now, any discrete point selected anywhere inside of this infinite sphere is, by definition, an infinite distance from the perimeter. And because all infinite quantities are equal (equally boundless), every point in the sphere is also an equal distance from the perimeter. However, the only point in a sphere that is equidistant from every point on the perimeter is the very center of the sphere. Therefore, the line connecting any point inside the sphere to its perimeter is a radius of that sphere. That is, every point in the sphere, no matter where it is, is the same point, namely, the center. The paradox is obvious—every point in an infinite sphere is the center of the sphere, the same point. There is a clear logical contradiction between infinite geometry and Euclidean geometry. Indeed, there is a contradiction between infinity and every variety of math and logic, because every infinity must be treated both as a particular number as well as an equally unbounded quantity. Or again, infinity can be defined in many different (and mutually exclusive) ways, but always ends up equally infinite just the same.

Figure 1—While only one point (the center) is equidistant from every point on the perimeter of a finite, Euclidean sphere (a) every point in the interior of an infinite sphere (b) is equidistant from the perimeter. Hence, every point in an infinite sphere can be thought of as its center.

**(fig. 2)**and vary the height. As the height increases, the angle at

*a*decreases, and if the height becomes infinite, the angle becomes zero. However, if this angle becomes zero, oints

*b*and

*c*become the same point. This is true regardless of how far apart, in absolute terms,

*b*and

*c*really are. That is,

*b*and

*c*, from the standpoint of infinity, are the same point, even though they aren’t

*really*the same point. Under normal, finite conditions, these sorts of paradoxes are no more than interesting intellectual observations, having no relationship to reality. But, if we are agreed that the void is genuinely and unavoidably infinite, we can’t simply leave this problem unaddressed. The points in an infinite sphere are either all in the center or they’re not. Points

*b*and

*c*either have a particular separation or they don’t. The void is either infinite or it isn’t. In none of these examples can we have it both ways.

*really, really big*, on the one hand, and

*infinite*, on the other. As we increase the height of our triangle, the distance of

*a*from

*b*and

*c*is not merely great enough to make

*b*and

*c*look the same, it is great enough to render them, mathematically, as the exact same point. The angle at

*a*, from an infinite distance, is not just very, very small, it is exactly zero. And this is true whether we initially choose the base to be an inch or a light year wide. This results in a real, intractable mathematical contradiction. There appears to be a kind of

*tension*between the Euclidean and infinite characters of the points

*b*and

*c*. The question now is, do we treat this tension as entirely theoretical, or is it, in some sense, real.

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