|Orthodox Outlet for Dogmatic Enquiries||Science and Atheism|
The Universe, probabilities and Goedel
He who has never wondered about the beginning of the world, is NOT a human being.
Unsubstantial excuses for rejecting God
Several years have gone by, since the definitive proof that the Universe has a beginning was announced - a proof that locked away once and for all in the closet of History all the Atheist and Paganist positions that the Universe is beginning-less; a proof that finally and triumphantly vindicated the Christian Faith, which has always maintained that our Universe has a beginning. And yet, some people remain incorrigible. There will always be some uninformed fanatic who will insist on “beginning-less” universes, on “multiple” universes, on “recyclable” universes… anything that might justify their disbelief in the Creator.
The Universe is neither beginning-less (as has been PROVEN), nor recyclable (as also PROVEN even more recently, by the fact that its expansion is ever-accelerating – which signifies that it will NEVER return to a contracting phase, so that it can re-expand.) Thus, the only recourse left to those who continue to deny the Creator, is to IMAGINE infinite other universes, which differ in Time-Space to ours (but in which our own universe supposedly belongs), and in which we are supposed seek the cause of our universe’s existence…. The only problem is, this theory requires tons of imagination and UNSUPPORTED DOGMATISM, for someone to assume that other “Space-Times” exist! Because if, BY DEFINITION, our Time-Space contains “everything that exists in Creation’, it is like claiming that one can find existence….beyond existence! And if we were to theorize that another Time-Space gave birth to ours, then it wouldn’t be ANOTHER one; it would be a PART of our own, which likewise extends back into the past! In other words, from the moment that we agree to any kind of ASSOCIATION between “two” Time-Spaces, then we would not be looking at two separate Time-Spaces, but a “supra-Time-Space”, and our Universe would just be a part of it. Even so, one will still be left wondering about the creation of all these and the question would again be transferred TO THE PAST, without being solved. Thus, if we were to accept the (already proven) fact that our Time-Space has its BEGINNING 13,7 billion years ago, then, quite simply, NOTHING MUST HAVE EXISTED, PRIOR TO that moment, consequently, every supposed association with any other supposed extra-universal Time-Space is NONEXISTENT.
In other words, whereas it cannot be proved (even though it does not conflict with any scientific data) that God is the initial, UNCREATED beginning, in which our Time-Space EXISTS, to assert that “other” Time-Spaces supposedly exist, not only is equally improvable, it actually even conflicts with the scientific data which has confirmed that our Time-Space has a BEGINNING and that beyond it, nothing else created exists, since there is no spatial or temporal “beyond”. And this is something that the “theoreticians” of “multiple universes” are well aware of, which is why they admit that their assertion cannot be proven, since, “for our Time-Space, every other Time-Space is simply…..nonexistent”!!! They are more or less telling us that “...there is an infinite number of…. nonexistent Time-Spaces, in which, however, resides the cause of our own Time-Space”!
The probability of existence
Naturally, no serious Physicist can ever accept the above “charlatanisms” as a solution to the issue of the Universe’s beginning. That is why there is such an intense intellectual struggle going on, for approaching (as much as is possible) that “first cause” of the existing Universe, beyond any improvable and contradictory conjectures regarding supposed “other” Time-Spaces. This, of course, is not only an acceptable thing; it is also a desirable one, in the attempts to comprehend Creation.
In the framework of this attempt, we AGAIN resort to the matter of probabilities. To the basic question: “Why does something exist, when it could have equally not existed?” some respond with the following idea: “Given that nonexistence is ONLY ONE condition, whereas existence could manifest itself in countless ways, then, it is possible that existence is far more probable than nonexistence”!!! What an amazing concept!!! At least the undersigned bows to the genius of this thought!! This answer may not -of course- explain HOW everything came to be, but it certainly explains why “existence” could be the prevailing condition. However, the more important aspect of this theory is that –once again- it places probabilities at the root of the problem!
Based on the above reply, we are now faced with the ensuing, very important question: “And by what is the law of probability determined?” or even: “What is more fundamental? The actual existence of Time-Space, or the probabilities thereof, or perhaps the mathematics by which the laws of probabilities are adjusted?”
These are all extremely significant questions, which, when investigated, we are led – from another path now – to conclusions that we have already encountered, in older articles.
We have already spoken of the important role played by probabilities in the mystery of existence, when we addressed the matter of quanta and the laws that govern their appearance and disappearance. And now, we are encountering the exact same issue once again, only this time, it is from the point of view of necessity of existence! Finally, it looks like “probabilities” are the key to everything – from the laws of thermodynamics and the definition of “what can possibly occur”, even to existence itself!
On investigating the question, “what is more fundamental: probabilities, or Time-Space?”, we reach certain equally important conclusions:
Since matter and energy are nothing more than “waves of probabilities”, and Time-Space is composed of materializations and de-materializations of such waves of probabilities that are dependent on the laws of probabilities, it becomes obvious that we should consider probabilities as being the fundamental ingredient of the Universe.
But then, the question that is automatically posed is: “Who is the Lawmaker that imposed this law?” Who determined the laws of probabilities, so that they would function exactly as they do, thus making existence more probable than nonexistence?
The philosophical demand now arises, for the existence of a certain entity – which is not only beyond Time-Space, but also beyond probability! An entity that is not in the least subject to the law of probabilities, but is in fact the determinant of those probabilities! This entity cannot possibly be located within this probability-governed Universe of ours…..
The next issue that is raised is the following: If the laws of probabilities are governed by mathematics, then, are mathematics even more fundamental than the laws they govern? Or are mathematics simply the means by which the laws of probabilities are expressed?
This question is reminiscent of the assertion made by many Christians, that: “Natural laws are simply the MEANS by which God expresses Himself within His Creation, and, because He is steadfast and consistent, these (means) are perceived as automated natural laws.” According to the Christian Faith, behind these natural laws are hidden the ‘logos’ (reasons) of beings, which are the far deeper causes of existence of each and every being and which are made evident, only to someone who has transcended the created world and who thenceforth perceives it from the standpoint of the Uncreated God, through his union with Him.”
This matter, albeit seemingly irrelevant to mathematics and physics at first glance, essentially refers us to the familiar Theorem by Goedel. According to this Theorem, any system of axioms whatsoever includes proposals that cannot be investigated as to whether they are true or false, with the means made available to us by that same system. In other words, in order for us to be able to prove these axiomatic proposals, we need to utilize another system of axioms – an even broader one – that will contain the previous one. But even thus, we continue to be left with our inability to prove this broader system, and will need to resort to something even broader! As one can easily perceive, this entire situation is endless! Our knowledge of things will forever demand even more data, which, necessarily, will be given to us ONLY by something outside the system being studied.
This leads us to the realization that ALL world theories and philosophies (without exception), that wish to confine the “existent” to the material universe alone, or Time-Space alone, or only to something created (whatever that may be), will always find themselves exposed in the end, inasmuch as they will be unable to prove, or to document, or to explain something in their world theory! Every philosophy and every materialistic view of the world will, necessarily, end up at an impasse; at a DOGMATIC view, which does not make any allowances for proof! Thus, whether this dogmatic view is a God, or a Universe without any answers explaining the cause of its existence, they will both end up at the same impasse, of Goedel’s Incompleteness Theorem.
To use a more vivid presentational means, this Theorem says that, for someone to view the Universe in its entirety, without any deficiencies and blanks, it must be viewed by observing it from a place OUTSIDE of it! Only then, will he be able to comprehend exactly what is going on! As long as we exist INSIDE it, there will always be something that escapes us! But such a preferential place OUTSIDE the Universe simply cannot exist in this world, since all of Creation is incorporated INSIDE the Universe!
Hence, as long as we are living INSIDE our Time-Space, we shall never be able to prove anything overall about the Universe, and we shall never find the ultimate answers that are hidden inside it, since that secret is safeguarded “OUTSIDE” it! (No, the word “outside” was not used inadvertently, nor as a “figure of speech”, as we shall see further down.). Goedel’s Theorem DEMANDS the existence of an exo-Universal entity, Who will FILL IN the blanks of our theories on the Universe! The existence of this entity is no longer a simple conception or a simple sophistry for mathematics. It is now a MATHEMATICAL REQUIREMENT!
So, we turn once again to the Christian view of the Universe, which we spoke of previously, and ask: In what does the Christian Faith’s teaching differ to Goedel’s Theorem?
Contrary to the materialistic and Paganist world theories, the Christian Faith PERSISTS in a First Cause that is found OUTSIDE of Time and Space! We call it “God”. The Christian persistence in acknowledging an EXO-COSMIC GOD and not an endo-cosmic one, as the other (Paganist mainly) religions do, is a characteristic trait. The materialists’ philosophy that only a material world exists, and the Paganists’ worldview that God (or gods, according to them) are found INSIDE the world, are both in direct conflict with Goedel’s mathematical theorem! Both of them are, in other words, nothing more than anti-scientific convictions!
It is our view that God did not simply create the Universe once upon a time and then abandoned it – as poor Epicurus had speculated in his ignorance - but that He continues to work within it, giving it a hypostasis, at every single moment, “weaving it” at (literally) every point of Time and Space, within a “foam-filled void” comprised of potential particles called the “quantum vacuum” in modern Physics. These particles are obeisant to the LAWS of probabilities; however, what is beyond our ability to determine, is FOR WHAT REASON these laws function the way they do!
The only way that one can see the "logos of beings" according to the Christian Faith, (the ultimate logos/reason for every single thing in the Universe), is to “exit” from it!
And how can something created “exit” from Creation? By means of theosis!
It is not necessary for a created being to “physically” exit Creation. Its union with the Uncreated renders it a communicant of the EXPERIENCES of Divinity, which are, in themselves, beyond Time and Space. The Universe is essentially embraced by Divinity, and not the opposite! Thus, through its union with God, the created is rendered capable (according to Goedel’s Theorem) of having an “outsider’s” view of the world, now able to perceive that which it could not perceive, prior to its “exit”, i.e. the logos/reasons of beings! Isn’t it amazing, how the Christian experience of the saints is so harmoniously in accord with a Mathematical view of the world?
Naturally, when speaking of a “union with God”, we are not implying that the created will ever be able to comprehend God Himself! On the contrary! If we ventured to apply Goedel’s Theorem to God also (something that cannot be done anyway), we would see that there is nothing beyond that “Omnipresence”, consequently, we cannot go past God in order to study Him, hence, we will never be able to comprehend God in His entirety, even if we do manage to attain theosis! Indeed, as far as God is concerned, given His infinity, it is obvious that the infinite can NEVER be fulfilled in our understanding, since we are finite, spatial-temporal beings. For all eternity, we shall continue to learn about Him and approach him, increasing our knowledge of Him, without, however, ever completing it!
Returning, however, to the matter of the Universe, we come to realize that the thing we lack in order to comprehend it (which is precisely what makes us have an incomplete view of it), is our inability to see that EXTERNAL factor which constantly caters to its continuing existence; that factor which determines the mathematical expressions of its probabilities, and which also gave it a beginning in Time.
Mathematical and natural approaches are just other ways of making us realize the futility of our materialist stance; of making us see more clearly the impasses of our life when alienated from God, and the INCOMPLETENESS of our existence without the One Who created us. Without Him, we will forever be one step away from the answer; the answer will forever escape us. We will focus on the law, but the lawgiver will elude us. We will stare at the result, but the cause will elude us. We will ponder over the prevalent probabilities, but the reasons for their functions will escape us. We will gaze at the problem, but the answer will elude us.
And yet! “He who sustains all things, by the word of His might” (Hebrews 1:3) “stands before the door (of our heart) and knocks! And if anyone hears His voice and opens the door…” (Revel. 3:20) then He shall share with him such common experiences, such divine exo-cosmic experiences, that very few people have lived in History on “exiting” this world, and who are still unable to even vaguely describe them:
“I know someone in Christ who, fourteen years ago (whether in the body or out of the body I do not know, God only knows), was caught up to the third heaven. And I know that this person (whether in the body or out of the body I do not know, God only knows) was caught up into Paradise and heard unspoken of things, which befit no man to utter. ” (2 Corinthians 12:2-4)
Doesn't wisdom cry out? And doesn't prudence raise her voice?
She stands atop high places, higher than the road, in the middle of the crossroads.
She cries out loud near the gates, at the entrance to the city, at the doorways.
"Men, to you I cry out! And my voice is directed to the sons of men.
You simple ones, understand prudence. And you foolish ones, acquire a heart that understands.
Hearken, for I will speak of superb things, and my lips shall speak correctly.
For my mouth shall tell the truth, and my lips abhor irreverence.
All the words of my mouth are with righteousness; in them, there is nothing insidious or perverse.
Everything is clear to him who understands, and proper, to those who find knowledge.
Receive my instruction, and not silver; knowledge, rather, than choice gold.
Translation by A. N.
Article published in English on: 16-3-2007.
Last update: 16-3-2007.