Apeiron

Have you heard of the demon that came to the boy as a fly? Night had well established itself and the shadows within the room made the boy feel confined and lonely. His mind was racing preventing him from falling asleep. A sliver of moonlight escaped into the room and illuminated the fly on the opposite wall. The boy had an eerie feeling that the fly was staring back at him, meeting his gaze.

The fly was.

Then it spoke, but the boy surprised at it's ability to speak made the words inaudible. So again the fly uttered,"This what you are feeling, do you hate it?"

"Yes..."the boy was hesitant to answer.

"What if I were to tell you that this that you are feeling you will feel again innumerable many times over an infinite amount of time. All of your life, past and future, your suffering and your falling in love; all of it will happen again in the same sequence of events over and over again. This moonlight that reveals my presence will fall into the room and splash against the wall in the same fashion infinitely many times." There was silence."Well? How does it feel?"

"You are a god...never have I heard anything more divine."

A vile smile, "Fitting. Do you believe it?"

"No, but the thought itself is no less divine."

Unlike Nietzsche the boy was not afraid. I too do not fear this reality. The idea of an infinite universe, unending and forever repeating is a terrifyingly beautiful thought. With ease the idea quickly becomes infectious of the mind. When the theory first came before me it did so with an air of euphoria.

The observable universe that we know of is constantly expanding, this was first discovered by Hubble and further found to be true by modern astrophysicists. The most well known astrophysicist of our time, Stephen Hawking, found it to be true that the universe was in fact expanding but disproved the theory that the universe was infinite in time. This was also found to be true by Einstein many years before when he discovered the theory of relativity. Einstein was the first to find out that time itself was not constant but changed with matter and pockets of great gravity. The idea brought about the theory that time and space were two different directions in a grid like setting where matter and the universe sat and impressed into it a spherical curvature. Hubble also found that matter in the universe exists in different densities, so that there is no equal distribution. Though some modern astrophysicists still currently believe that given a large enough scale the matter would statistically take on an even distribution. Either way, the observable universe has a definite volume, though it is changing with time due to expansion, and is even accelerating as time continues forward.

The french 19th century mathematician Henri Poincare came up with the idea that the universe took on the shape of a dodecahedron. To calculate the volume of the observable universe one can assume the shape to be spherical, and thus the equation would be that of a volume of a sphere.

V=4/3*(PI)*R^3

We know that in order to calculate the volume, one cannot use the 13.7 billion light years as a radius since Hubble discovered that the universe is expanding. Taking into account the expansion one can safely assume a radius of 46 billion light years. In that case the volume can then be calculated to be:

V=4/3*(PI)*(46 billion light years)^3=4.077*10^32 cubic light years.

It is a common belief that the universe is much larger than what we can observe, and if Poincare is correct in his shape, the assumed diameter of the total universe is 150 billion light years, and so the volume would be 1.2*10^33 cubic light years. Some even believe that the universe is infinite in space, and that the expansion is the proof of that belief. But until we know for sure, what is definite is the current volume of the observable universe and that it is distinct and real. This is an important fact for what is about to follow. 

Max Tegmark of the MIT Kavli Institute of Astrophysics calculated that given a large enough scale, matter in the universe is actually evenly distributed. Just as explained above the observable universe has a measurable and real volume though it is not definite. Again because of the expansion of the universe the volume is always changing, but if what Hubble also found to be true is in fact correct then the portions of the cosmos with denser sections of matter are not expanding, but riding the expansion like a wave. So that is to say that if the universe did in fact stretch far beyond the borders of the observable, then some cosmic viewer would see that matter was spread evenly throughout. 

Imagine your the cosmic viewer and can see the full volume of the observable. Now back up to a point where the Poincare dodecahedron is but a fraction of the view. Whatever the new dimensions of your view are, the volume can still be found. Let us imagine this simply. Imagine if you will that you are looking at the view so that it is flat before you. One can then take the space and divide it into equal portions of a volume that we know of. 

Fig. 1

Figure one shows a basic outline of the simple calculation. Simply by knowing the values of x and y the universe's new volume can be calculated. But in reality space is not a 2-D plane, but three dimensional and so another factor, z, coming out of the page is necessary to know. Either way though it can be said that the volume of the new view would be:

Vt=V*(x*y*z).

Unless of course the universe is in fact infinite in space, then the new volume would be easy. Infinite.  For the sake of the argument, let us say that Stephen Hawking is correct in assuming that the universe is not infinite, but has boundaries despite us never knowing what lies beyond them. The point being made though leads to theorem 1.

Theorem 1: The universe has a definite (when compensating for expansion) volume, and is not infinite in space, and with a large enough scale matter is distributed evenly. 

The other important theorem is the one proposed by Heisenberg's uncertainty principle. 

Theorem 2: There is only a finite number of configurations within a finite volume possible

These two theorems when combined form an obvious assumption. If there is a finite volume that is measurable, with only a limited amount of configurations then it is completely possible that one of those configurations will repeat itself. In fact, it becomes a mathematical certainty that identical instances of our Earth's entire history will occur just by chance and that the nearest twin could be found 10^10^115 meters away from us. That is a double exponential function which produces a number much larger than that of a googolplex. Remember, this is only true because of the even distribution of matter within a finite volume that contains limited atomic configurations.

The universe is a dynamic system and undergoes constant flux. Throughout all of space as everything is expanding the small pockets of attracted matter that is galaxies and galaxy clusters undergo radical change. When lighter elements like Hydrogen and Helium are condensed due to gravity they are condensed so much that nuclear fusion begins. Here in this furnace of life the lighter elements are becoming heavier, turning into all of the matter that exists. When those stars die that matter is spewed out into the empty space where gravity once again pulls them in but instead of forming stars, the heavier particles of matter form planets. Eventually though, everything returns into chaos. This is a view not only held by astrophysicists but even Buddhism. Buddha often expressed the believe in rebirth. But rebirth is only achievable if there is an end. So there is a constant cycle of disorder, and order. In this cycle thousands of worlds are constantly being formed and destroyed. Who knows the complexities of life that could exist, or how similar the worlds were to ours? This catastrophic exhibition and the always changing and becoming is cyclical. According to Newton the conservation of energy is such that energy is neither created nor destroyed, just transferred to new systems. So with the constant flux and the conservation of energy the constant reconfiguration is something that can be modeled and even predicted.

Stephen Hawking in his lecture pertaining to the creation of the universe says that the safest assumption is that there is a beginning. The way he explains it is that of a globe, and the beginning rests directly on the south pole of the globe. All of the longitudinal lines climbing north represent the expanding universe, the further north one travels the wider the expansion. But it starts at one point, and Hawking says that to ask what was before the beginning does not make sense, because just like the globe there is no point further south then the south pole. Hawking also shares the belief with Einstein that time is relative so that there is not really a beginning in time but a beginning in space, because time is dependent on our observation of it. But in our observation, we can see no end to the universe and are plagued with the question of what lies before it. So in relativity, time to us IS in fact infinite. For the following theories to be true, a third theorem must also be true.

Theorem 3: Time is infinite in both directions, just as most pre-socratic philosophers theorized.

Again imagine the universe at it's current state. Eventually even the universe as a whole will endure the unraveling and find itself empty once again. Everything will degrade and cease to be eventually, but the same atoms will be brought back together once again in perfect harmony. For the flux to remain true, the universe must begin again. So however long it would take, the galaxies would reform under new configurations and the process will repeat, the new state is state B and the prior is state A. This will continue n amount of times if time is finite. But if Theorem 3 holds to be true, then this process will occur infinitely many times.

Figure 2

Each transition in between represents the destruction and rebirth of the new universe. And a widely accepted theorem of the creation of the universe is that of the big bang. So believe if you will a big bang occurring in between each new universe.

To further understand this theory one must next look at another contribution from Henri Poincare, and that is his mathematical model of the time recurrence theorem. Given that the universe is a dynamical system it follows common Ergodic Theory that given a finite amount of time within an infinite window of time, all points within any subset of a dynamical phase will return to a state very close to it's initial state. In other words, within a finite amount of time there is a mathematical certainty that one of those configurations will repeat itself. That means, after all of the possible configurations have been done, though maybe innumerable, one will eventually repeat. This is like a cosmic game of chess, because of the odds, one game given that it is played over an infinite amount of time will repeat itself.  This is just like Heisenberg's theory that there exists a twin within a certain distance based off of calculable odds. Though modern theory ties this to the idea of multi-worlds that co-exist in the same infinitely spaced universe. I do not believe that. I think that it follows that Poincare and Tegmark are correct.

If so, if over an infinite amount time there exists a finite window in which the limited configurations will eventually repeat itself. Then the linear cycle as seen in figure 2 actually becomes a flat circle.

Figure 3

This model is significant because it also implies that there is no beginning or end to the cycle. If time is in fact infinite in both directions a fascinating result arises. If the initial state continues to be revisited in a circular fashion, then one can say that universe A will convert to B infinitely many times into the future, but at the same time it is true that the transition from A to B HAS happened an infinite amount of times. 

You, sitting right here have existed innumerable many times and will for an infinite amount of time. This is a mathematical certainty. 

Theorem 4: The history and future history of the universe is a constant and unending series of finite configurations with no real end or beginning and no definitive way to even know where exactly on the cycle we exist. All that can be said, is that "I am here, and will be here once again infinitely many times."

If theorem 4 is correct, then it holds true that the demon was right.  Every pain and every joy, every friend and foe, every moment that made you fall in love and each one that broke your heart you will have to experience again, and you have experienced them innumerable times. This also implies that there is no real purpose other than for the cycle to continue. Even still, for us humans the only purpose becomes then to just exist so that we can act as finite systems within the infinite. It also implies that fate and destiny in essence do exist, as much as I hate to admit it. This lack of purpose, this aimless existence is what struck fear into the heart of Nietzsche, who claimed that that type of existence is dreadful and terrifying. In the Gay Science Nietzche writes: 

"...The eternal hourglass of existence is turned upside down again and again, and you with it, speck of dust!" Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: "You are a god and never have I heard anything more divine"? If this thought gained possession of you, it would change you as you are, or perhaps crush you.

I became fascinated at the concept. Mostly because many other philosophies that had captured my imagination in the past such as the karma and chaos of Buddhism, the absurdity of life from Albert Camus' The Myth of Sisyphus,  and the theory of St. James (as seen attempted in the Movie "Cloud Atlas") proposed by my father. But the first concept of this was achieved in the 6th century BC in Greece by the philosopher Anaximander. 

The apeiron is everything and it is nothing. It has always been and always will. It is the crucible in which all things are created and the darkness in which those things are consumed. Unending and indestructible, the apeiron is infinite in time and space. There are no defining qualities and it is completely unchangeable. It was proposed to be another element of life, only the one that governs all of the machinations of the cosmos. Mystery surrounds it as many different philosophies define it to be different things. 

The philosopher Thales in 5th century BC attributed the apeiron to be the element water as the universal element. But Anaximander offered a different opinion, saying that the element of water is governed by apeiron, and so the apeiron is an element in itself just without form and has always existed in the universe. Others have attributed apeiron to be God. This unchangeable force that is unending and indestructible, that which governs all things, wills them to be and causes for their existence to cease, is just the hand of Jehova. Modern astrophysicists, though they do not believe it to be an element of sorts, but do believe that it is an invisible force that holds things together and rips them apart, like that of anti-matter.

Buddhism teaches the philosophy that all knowledge is already within ourselves and we are simply awoken into it. If Theorem 4 is true, then yes that makes sense because you have already lived a life time of those experiences. You have infinitely many times in the past learned whatever you will learn in the future. So yes, you know everything that you will ever know because you have lived through innumerable times. Perhaps that is why when that piece of information invades your brain and allows a breakthrough of understanding we feel that "Aha!" moment. That burst of understanding is not an alleviation of the stress that it took to learn it, it is a realization that you already knew it and you were simply remembering it again. 

My heart swells with the thought of revisiting my joys but breaks at knowing that I will have to relive every moment of suffering in my past. But without that "Aha" moment to breakthrough every possible thing to know, we do not know whether or not this is true. We do not know because from state to state we are not conscious of the finite time in between because relatively it seems infinite. That means if the cycle does hold true, a person who dies will only become conscious again when they are reborn. What a beautiful and terrifying reality.