Hi:

I just wanted to remind everyone of the limits of reductionism. Space can only exist with matter/ energy and time. Matter/ energy and time can only be described in terms of space. We are forced to describe each in terms of the other- and conclude that, in our universe, they are part and parcel of the same thing...energy.

This fact gives very important clues to their essential nature, topological relationships, and the grand proportions which give them meaning- and permits us to understand what they are...and what we are.

Though the universe has geometric properties, Karl Schwarzschild found out while studying the massed photon (see special topics) in his search for solutions to Einsteins formulae, that the universe is, well more complex. His two/ sphere, closed universe is unbounded to 10 to the 40th Cm. from anywhere and his "singularities" are not geometric singularities...they are black holes. The Schwarzschild universe resolves to two /spheres, (not a geometric point or points) at the Planck length. From our frame, 10 to the -35th or so of the Schwarzschild universe, by volume, is singular (see mathematical exercises on this site)...and wow, do these calculations account for the universal "missing mass"!

If we could look AROUND the singular condition, (actually a bounce at 180 degrees), we could view the other half of the universe. Even at a distance of 60 billion light years, the other (photonic) hemisphere of the universe does have a small, but detectable mass (photons), from our frame, just as singularity at a vast distance in scale has mass- and a "gravitational attraction". Singularity in the real universe has geometric characteristics, but consists of energy- and has mass.

The existence of the singular condition as it is observed in our universe implies something very important, namely that our frame of reference is 3+1=4 dimensional. It also is geometric PROOF that what we see of the universe, dimensionally, is not all there is to it...that there IS another side to the reality we view day by day.

Let me once again stress, our universe is so constructed that there is an actual location where the cosmos we understand does not exist. Depending on the frame from which the universe is observed on 4D surfaces, this location, a tiny two/ sphere may have actual dimensions relative to us, of 10 to the minus 33rd Cm (NOT a geometric point!). From another frame, this tiny, irreducible, almost massless, near timeless, near spaceless energy location is observed by us to encompass the universe. ..to a radius of 10 to the 40th centimeters in every "direction".The 4D projection is viewing the Earth from its surface, where it is huge and seems to fill half our field of vision, and viewing the same Earth from Jupiter where it seems little more than a point of light in the sky.

The "size" of this topologically almost nowhere location as observed from our frame is determined by energy concentrations. Its nature is confined and shaped by the existence and relationships of fictitious forces related to areas of varying energy density, also as observed from our frame.

The surfaces of these energy spheres, cosmologically, actually amorphous (phase solid) singularity, create the world we know, and separate us from the equally real unknown. These surfaces are called "event horizons", geometrically, sphere flakes. Taken together, everywhere, they form "space", a matrix... a space/ time foam which like soap bubbles in a bathtub does have mass (dark energy) as observed from our frame. On this site, I refer to this matrix collectively as "sub-microscopic singularity".

At the bottom of our reality, these event horizon surfaces (topological defects: solitons) form atomic particles, quarks, protons, antiprotons, neutrons, electrons and atoms. If enough energy is concentrated in one "place", we can observe large or even huge singularity of stellar, or galactic mass. From our frame, if we got "close" to such singularity and its all important event horizon, we would be torn apart by unbalanced forces. Our universal parameters forbid an "approach" to such a monster.

Still there is nothing to stop us from imagining what would happen if we could stand beside a Schwarzschild two/ sphere singularity with an event horizon surface the size of a basketball from our frame. Such a sphere in geometry is called a throat, or gorge sphere. (see http://www.jp-petit.com).../Extensions/pres_questionable_en/PQ3trad.htm for details...part of the site is in French, part in English)

If we stuck our left arm into such a throat or gorge sphere, our right arm would come out for geometric reasons, on the other side of time, perpendicular to the event horizon surface. As I say elsewhere on the site, it would "bounce" and undergo geometric inversion. If we jump into the sphere, we come out the inverse of the way we went in.

The nature of the universal geometry is to protect and conserve both entropy and order. One 3 space is absorbed while the other 3 space emerges.

Note how I say that...very carefully! We don't go in and come out, singularity with respect to our frame expands and absorbs us, while our other self emerges. From a single frame, any black hole SEEMS to grow in size as it attracts matter from space. However, if we could see the universe as a whole, we would also see a process of emergence (white hole/ big bang) on the other side of time.

From our frame then, black holes seem to gain in mass over time as they "attract" matter. However, cosmologically, if we could see around to the other side, we would view a white hole ejecting matter. The cosmic result is +1 + -1= 0, a static or quasi-static universe. Each frame of reference remains in the same invariant location, while the momentum of General Relativity, NOT as a single gorge sphere, but a universal singular phenomenon, in energy, space and time exposes, covers and re-exposes each of our two/ selves over and over- forever. The analogy of a sand bar being covered and uncovered by the tides is probably the best we can do in 4D.

The dual structure of the universe makes our controlled approach to the universal singular condition possible- in fact, we exist only 10 to the minus 33rd Cm above the abyss! The secret to our preservation, and the existence of cosmological time is Schwarzschilds two sphere geometry! Since we have a dual existence, it is possible for us to watch our second self from a safe distance (remote frame) on the other side of time (cosmological time separation)...from what seems to us the same place! The mass of the universe acts as a great magnet, perfectly and evenly distorting space/ time and slowing the process of our existence. Rather than being torn apart in an instant, we observe time to take almost an eternity (cosmological time) to pass. We are remote observers of our own universe.

The careful reader might react with alarm at my assertion that "we watch ourselves from a remote frame on the other side of time, in cosmological time separation from what seems to us to be the same place!" On this site, I have over and over stated that in a dual universe we are superposed on our antimatter other self in energy and space (inverse mapping) and yet our two bodies are cosmologically separated in time.

Lets stop and consider for a minute. Our lives are expressed in electromagnetic energy...and they process electromagnetic information. In that sense, our TRUE existence is in the photonic "hemisphere"! Yet the bodies, and universe we OBSERVE undergo the time dilated descent into the cosmic abyss...in the singular "hemisphere". Whether we have an after "death", "life" in the other "hemisphere" where time and entropy are "reversed" from our frame is conjecture. Nevertheless we, as creatures of energy do observe the opposite antipode of our existence, and ARE cosmologically separated from the body we so securely feel we inhabit! Remember, any geometer will gladly remind us that the seemingly vast universe, is a cosmic illusion...in a sense, the universe, as complex as it is, boils down to US, and any other observing frame in the universe. Even a blade of grass observes in the sense that a satellite observes; it receives, stores (and here is the scary part), transmits or conveys information.

Still not convinced? At the speed of light, and from the frame of electromagnetic energy, time ceases to pass according to STR. This means that the photons we observe from our frame exist in all parts of the universe simultaneously as part of the photonic, white hole "hemisphere". The information processing part of us, so far as a photon is concerned, is in the same location as the event horizon part of our physical existence which is creeping toward the singular antipode in time dilation! Both sides of our existence ARE, because of the nature of light, and the electromagnetic energy of which our bodies consist...superposed.

How about "naked" singularity? Naked singularity is an infinitely dense singularity at a geometric point, without an event horizon. In a finite universe, this is not possible, nor is the geometric point more than a mathematical and geometric tool. Stephen Hawking and Kip Thorne have had a bet, Hawking asserting basically what I have just said. Kip Thorne thinks he has found a naked singularity, but I'm not at all sure Hawking has given him his $100 yet!

In a sense, since universal singularity is everywhere at a certain place in scale, such singularity can be described as "naked"...from a cosmological frame. Such singularity is important, because we "bounce off", and are actually living slightly above its event horizon. However, so far as we, from our 4D perspective are concerned, if there is no defining surface, there is no singular condition, because all singularity stops and accumulates light at a certain, well defined surface from our frame (particulation). We speak of rain, as it approaches, as coming down in "sheets" or filaments. The universe at the lowest scales appears the same way, as it emerges from the undefined to the clearly defined reality we understand in 4D. The key, of course is free fall, something observed only from a 4D frame.

Because the universe can only be described in terms of a finite set of components- time, space and energy- with energy at the bottom line, the universe itself is a finite entity and cannot be reduced or expanded beyond clearly defined limits. A universe without any of these three items cannot and does not exist...it is a hole cut in a piece of paper.

Best Wishes,

Sam Cox