The universe, for some, is as unfathomable as the concepts of infinity itself; and rightly so, for the definition of our universe is bounded within the traditional fourth dimensional reality of our existence. Indeed, anything outside of our traditional fourth dimensional reality is not part of our universal existence. In fact everything we know about the universe is based on our ability to observe and measure varying degrees of luminosity/radiation within this fourth dimensional confinement; i.e., this is our known universe. Our known universe has many imposed limitations, based on our ability to observe and measure it, but no one can really estimate as to the actual age and size of the universe beyond the interpretation of empirical evidence that we are able to gather and collate. As of matter of contention is whether these measures for age and size have any real meaning outside our observable universe. This is partly because the dimensional boundaries of our SpaceTime are always evolving and partly because within our demensional boundaries of SpaceTime it is ever-expanding, per our ability to observe and measure it. Another aspect for consideration is whether this small pocket within our observable universe is representative of the universe as a whole.
What we believe we know of the universe is captured and documented in a variety of theoretical interpretations and principles. Physics is the scientific study of matter, energy, force, and motion, and the way they relate to each other. Physics traditionally incorporates mechanics, electromagnetism, optics, and thermodynamics and now includes modern disciplines such as quantum mechanics, relativity, and nuclear physics. This is how we relate to our immediate physical environment. Beyond our immediate physical environment is the medium of the observable or known universe. Cosmology is both the scientific study of the origin and structure of the universe and the philosophical study of the nature of the universe. Cosmology itself is subdivided into specialized fields like cosmogony, cosmism, and cosmography. Still another alternative view, cosmometry, is the art of measuring the universe; or perhaps more to the point, is the study and application of the fundamental patterns, structures, processes and principles that are at the foundation of all manifestation in the Universe, physical and metaphysical. In its essence, cosmometry is about synergetics. However cosmometry is not the reference used to provide an age or size to the universe, because this study views the universe as bounded both by SpaceTime and its metaphysical being rather than just its traditional fourth dimensional containment of existence.
Prior to our universal reality within a fourth dimensional existence, the instance of universe is modeled within the creation event called the Big Bang. The pre-Big Bang is a theory, in which all the essence of our universe was previously defined within or as a singularity, is really an extreme condition of our fourth dimensional reality in SpaceTime providing for a temporal confinement in the unification of all the primary forces of the physics (i.e., gravitational, electromagnetic, strong and weak). In other words, the Big Bang is not considered to have transitioned from a true one dimensional perspective of SpaceTime. Therefore, it can be assumed that the actual instance of creation that preceded the Big Bang creation event was an unfolding evolution of dimensional realities in degrees of SpaceTime. Per the online wikipedia reference, Stephen Hawking has addressed this peculiar connection between time and the Big Bang. In ‘A Brief History of Time’ and elsewhere, Hawking says that even if time did not begin with the Big Bang and there were another time frame before the Big Bang, then no information from these events then would be accessible to us; i.e., nothing that happened pre-Big Bang would actually have any effect upon the present time-frame. Upon occasion, Hawking has stated that time actually began with the Big Bang, and that questions about what happened before the Big Bang are meaningless.
A true one dimensional consideration maintains that all the physical manifestations of our fourth dimensional reality, like the fundamental forces or primary interactions of the physics (i.e., gravitational, electromagnetic, strong and weak) and the individual attributes of Space and Time itself, were all defined within a one dimensional SpaceTime continuum. From our fourth dimensional subsistence, it is difficult to imagine other varying dimensional states, or transitions from these states. As understood of spacial dimensions, a corollary for varying dimensions of SpaceTime can be assumed. The consideration for a one dimension SpaceTime continuum is a line; for indeed, a point would be dimensionless relative to Space and Time. The four spacial dimensions in which SpaceTime could be considered would be as follows: unbounded linear space, unbounded surface space (or combined linear spaces), unbounded volumetric space (or combined surface spaces without density), and finally bounded space (or combined volumetric spaces for SpaceTime density). Still physical theories that incorporate an aspect of Time within the dimensional abstraction of a traditional fourth dimensional reference to SpaceTime, such as Einstein’s Theory of General and Special relativity, provide three ordinary dimensions of Space combined with a single dimension of Time to form a four-dimensional manifold for representing SpaceTime (a.k.a, Minkowski space). Still other research has provided for an alternative view of a multidimensional Time consistent with dimensions of Space; i.e. one dimensional time (linear velocity), two dimensional time (curved acceleration), three dimensional time (spherical jerk), fourth dimensional time (density bounded within fundamental forces that make up our dimensional reality).
Upon the introduction of the concept of a singularity, as representative of the Big Bang, the tendency is to consider a gravitational singularity as the appropriate modeling for this condition. Notably scientists have explained Black Holes using this very model of gravitational singularity (i.e. a SpaceTime continuum reflective of Maximum Space Density, or near infinite density within near zero volume, and Minimum Time Density, or near infinite temporal dilation – a.k.a No Time). This misleads one to conjecture upon the possibilities of Black Holes as the epoch of another Big Bang. However, there is more than one type of singularity. An alternative perspective on the notion of a singularity, as representative of the Big Bang, is more aptly modeled upon the notion of a (for lack of a better adjective) ‘dark energy’ singularity (i.e. a SpaceTime continuum reflective of Minimum Space Density, or near zero density within near infinite volume, and Maximum Time Density, or near infinite temporal expansion – a.k.a All Time). This would be more in line with the expectation of a reality before baryonic matter. This alternative concept is somewhat analogous to the abstraction of a White Hole, or the concept of a reverse Black Hole, and is expressed as the reverse of a gravitational singularity. White holes appear in the theory of eternal black holes; i.e., speculation of white holes are that they must have existed upon creation of the universe and they emit matter until they finally explode and disappear.
With this background, what would then be the shape of our cosmos? A fourth dimensional perspective of the cosmos would imply a spherical rendering. In this abstraction, the universe would fit within a finite sphere as long as the sphere is ever-expanding, consistent with the Inflationary Theory and observations. The spherical model is representative of a “closed” universe, expressing all of the local curvature and local geometry as positively curved. Then there is the donut theory of the universe. The doughnut theory of the universe is an informal description of the theory that the shape of the universe is a three-dimensional torus. The name comes from the shape of a doughnut, whose surface has the topology of a two-dimensional torus. This is only one considered solution to the consensus that the universe is flat; i.e., in a “flat” universe, all of the local curvature and local geometry is flat. Finally there is the hyperbolic universe, which can be thought of locally as a three-dimensional analog of an infinitely extended saddle shape. The hyperbolic model is representative of an “open” universe, expressing all of the local curvature and local geometry as negatively curved.
So why is it important to know the shape of the universe? Within the consensus of the Friedmann–Lemaître–Robertson–Walker (FLRW) model (of Inflationary model) of the universe, the common description for the Big Bang (and even the terminology used) may mislead some to believe that there exists a physical, cosmographical center to the cosmos. Indeed the equations of classical general relativity indicate a singularity at the origin of cosmic time, although this conclusion depends on several assumptions (which I will not expound on in this article). And if the Universe is contained within an ever-expanding sphere (which may have started from a single point), it can still appear infinite for all practical purposes. Still for the universe to be homogeneous and isotropic, its evolution cannot be inviolate; i.e., that is to say that the creation event cannot co-exist within the created product, or for that matter it cannot co-exist for the same reference in SpaceTime as the termination event). Consequently, the universe maintains a consistent, but independent, evolutionary persistence throughout its existence.
As the considered point of origin was the singularity of the Big Bang, it persisted as the whole of Time and Space within a dimensional framework in which the fundamental forces were unified. Both general relativity and quantum mechanics break down in describing the pre-Big Bang consistence, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths. Upon creation, the unification of forces within the singularity evolved/transformed towards their current fourth dimensional condition. In this way, the SpaceTime continuum is merely the vessel of our universe. As positive density matter began to interact within our traditional fourth dimensional boundaries, it provide for the displacement of the zero density medium and allowed for the complimentary condition of negative density matter. So where the order of the universe was absent of positive density, creation has messed with its balance. Subsequently the evolution of large structures versus small structures for positive density matter is random at best, or the universe would have almost immediately collapsed in on itself. Instead it is expanding and becoming more ordered with time. Therefore there is no real center to the universe; rather there is only the unfolding of SpaceTime into varying evolutionary conditions. It is not a center which can be viewed, or even measured, as its very reality is subject of debate. It is this persistence that purports, in our dimensional measure of being, a flow of influence to and from center. Thus the notion of a universal singularity is derived, not from its focus of centricity, but from within its ambit of containment. It is not a fixed location in Space, but rather a fixed condition in Time. These are the conditions of our creation and termination.
As you can imagine, our current interpretations for shape, size and age of the universe will forever remain a mystery and a constant miracle of discovery as we continue to further our knowledge.
1^ Fuller, Buckmister. The Designers and the Politicians" (1962), later published in Ideas and Integrities : A Spontaneous Autobiographical Disclosure (1969), and The The Buckminster Fuller Reader (1970).
2.^ Hawking, Stephen (1996). "The Beginning of Time". University of Cambridge. Retrieved 2012-07-08. "Since events before the Big Bang have no observational consequences, one may as well cut them out of the theory, and say that time began at the Big Bang. Events before the Big Bang, are simply not defined, because there's no way one could measure what happened at them. This kind of beginning to the universe, and of time itself, is very different to the beginnings that had been considered earlier."
3.^ Hawking, Stephen (1996). "The Beginning of Time". University of Cambridge. Retrieved 2012-07-08. "The conclusion of this lecture is that the universe has not existed forever. Rather, the universe, and time itself, had a beginning in the Big Bang, about 15 billion years ago."
4.^ Hawking, Stephen (27 February 2006). "Professor Stephen Hawking lectures on the origin of the universe". University of Oxford. Retrieved 2012-12-05. "Suppose the beginning of the universe was like the South Pole of the earth, with degrees of latitude playing the role of time. The universe would start as a point at the South Pole. As one moves north, the circles of constant latitude, representing the size of the universe, would expand. To ask what happened before the beginning of the universe would become a meaningless question because there is nothing south of the South Pole."
5.^ Ghandchi, Sam : Editor/Publisher (16 January 2004). "Space and New Thinking". Retrieved 2011-04-09. "and as Stephen Hawking puts it, asking what was before Big Bang is like asking what is North of North Pole, a meaningless question."
6.^ Bauer, Stephen (2004). "The Evolutioning of Creation – Volume 2". ISBN 978-1-4628-8759-0. Retrieved 2013-01-28. "I would like propose a universe that is motivated via its evolution from ‘minimum Space’ and ‘maximum Time’ to ‘maximum Space’ and ‘minimum Time’.
7.^Wheeler, J. Craig (2007). Cosmic Catastrophes: Exploding Stars, Black Holes, and Mapping the Universe. Cambridge University Press. pp. 197–198. ISBN 978-0-521-85714-7.
8.^ Carroll, Sean M. (2004). Spacetime and Geometry (5.7 ed.). Addison Wesley. ISBN 0-8053-8732-3.
9.^ Bauer, Stephen (2004). "The Evolutioning of Creation – Volume 2": Author’s Note, pp 11. ISBN 978-1-4628-8759-0.
10. ^ a b Overbeye, Dennis. New York Times 11 March 2003: Web. 16 January 2011. “Universe as Doughnut: New Data, New Debate”
11.^ Hawking, Stephen. "The Beginning of Time". Stephen Hawking: The Official Website. Cambridge University. Retrieved 26 December 2012.
12.^ Zebrowski, Ernest (2000). A History of the Circle: Mathematical Reasoning and the Physical Universe. Piscataway NJ: Rutgers University Press. pp. 180. ISBN 978-0813528984.
13.^ Bauer, Stephen (2004). "The Evolutioning of Creation – Volume 2". ISBN 978-1-4628-8759-0. Retrieved 2013-01-28. “Per the ‘Machining of Materiality’ in volume one, the concept of gravity is the representative result of the opposition of existence to a state of nonexistence, while the concept of antigravity (or dark energy) is the representative result in the affinity of existence toward the state of nonexistence; i.e., respectively a more positive mass is attained via gravity versus a more negative mass incurred via dark energy.”
14.^ Bauer, Stephen (2004). "The Evolutioning of Creation – Volume 2". ISBN 978-1-4628-8759-0. Retrieved 2013-01-28. “Time and Space express measure via their direction towards a maximum and minimum. If the squeezing of Space into a subsistence of discrete mass density manifests an inward force of attraction, then the expanding of Space into an insistence of discrete absence of mass density should manifest an outward force of repulsion via its force of deceleration. In maintaining the balance of the universe via such a measure in Space and Time requires that there must be a way to represent this measure unit of non-mass, i.e., there must be a way that Time can be stuffed into Space.”
15.^ Bauer, Stephen (2004). "The Evolutioning of Creation – Volume 2": A Universal Centric Singularity, pp 46-48. ISBN 978-1-4628-8759-0.