An essay based on my 15-vear old explorations on the nature of everything. 

A THEORY for the INFINITE AGE of THE UNIVERSE

The Birth of Infinity

I

The infiniteness of the Universe, at least in regard to age, is a well-respected concept in much of historical philosophical thought. There have been, however, not that many theories to support the position, and in fact, a good number of the theories introduced prove just the opposite, that the Universe's age is finite. The position on the problem is basically 1.)that the Universe is finite (of limited age), or 2)that on the contrary the Universe has always existed and has infinite age. The first theory states that the Universe has existed for a definite amount of time (10 billion years, for example) and that nothing existed before then, while the second professes that the Universe is already infinitely old. The implications of the argument are profound, for if the infinite age can be proven, it means that it obviously didn't have a temporal beginning. Without a beginning in time, there could not be a temporal creation, a fact which is quite important to certain aspects on Judaic-Christian thought.

This paper will present two theories to prove that the Universe is infinite. Actually the theories to be presented are not proofs but rather disproofs -­ the first dealing with the concept of a Basic Cause, and the second with the position that the Universe does not necessarily need a cause to begin, but rather just came into existence of its own accord (self­ causing). The first proof will attempt to show that the possibility of the Universe being created by an infinite Basic Cause is impossible, and the second will prove the invalidity of the claim that either the Universe or a Basic Cause is not necessarily infinite as it could be self-causing. However, even though these theories are basically disproofs, the infinity of the Universe will be proven in the process.

II

Before we can begin though, we must first set down the meaning of our terminology and assumptions. First, what do we mean by infinity? There are two concepts of infinity which can best be expressed in the following equation 1/∞ > 0 and 1/∞ = 0. The first equation refers to an ever-increasing number that will never reach an end. In other words, you will never be able to reach a number or point, a greater than which could not be conceived or created. No matter how great a number might be, a greater finite number does exist. Therefore, the first equation could never equal zero, because this concept of infinity never really transcends the finite, no matter how great the denominator of the equation becomes there will always be a greater possibility. In short, this concept refers to an ever­ greater sequence of numbers. The second interpretation regards infinity in the absolute sense, where it totally transcends finiteness. No matter how large the concept of infinity is in the first interpretation the equation could never equal zero, but in this interpretation the matter of largeness is unimportant, we have gone beyond it, and the equation now equals zero. Magnitude is no longer important. If we substitute a two or a million in the equation (2/∞ or 10⁶/∞), it will still equal zero.¹ We are referring to an absolute infinity.²

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1. It appears that the second concept, absolute infinity, makes the first interpretation possible. The only· reason that we can constantly create greater numbers is because we can draw upon the concept of absolute infinity. Only because there is such an absolute can there be an infinite sequence of numbers, which in turn can never reach the limit of the absolute.

2. At this point it should be stated that I am not claiming the ability to fully understand, conceive, or appreciate the concept of absolute infinity. That is not the question. It is unimportant here whether or not I can truly conceive or have a “feel" for such a concept, but what is important is that I can talk about it, use it, and subject it to the laws or logic. 

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Both of these concepts of infinity I think are legitimate in their own right, depending for what they are used. The first concept could be applied to an active state, while the other is applicable to passive states. What I mean by this can best be shown in the following examples. Power is in the active state and the first interpretation of infinity is applicable to it. For example, power can never reach such a state where a greater power could not be produced. No matter how powerful something is, there could always be something more powerful, since power can only be expressed in finite terms. If we assume that time, which is passive, is infinite, we can show how absolute infinity is applicable. Imagine time in the present stretching ad infinitum into the past. The past, however, unlike power cannot be expanded any further.³ Since we have said that time is infinite (which also implies that the past alone is infinite.) and that the past cannot be expanded, the infinity must be absolute. In other words, since in the past an infinite amount of time has already passed and that this “past-time” cannot be expanded (e.g. passive), it must, therefore, be absolutely infinite.

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3. The present is always moving forward and therefore in a sense the past is expanding. What I meant was that the past does not expand in the “past" direction (vs. the future direction toward which the present moves). The example works even if we assume the present to be stationary.
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It is this assumption, in fact, that time is infinite, that is the major premise we must assume. Our premise is that time, no matter how tautological it may sound, is infinite in a temporal sense. That is to say that time is linear or sequential. In other words, it is comparable to the definition of a straight line, that extends to infinity in both directions. One direction of time being the past and the other the future, or rather the infinite possibility of future time. In this way, time is temporal in the sense a line is linear. Also, time is made of a series of sequential events just as a line is a series of points.⁴

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4. This assumption that time is infinite in a linear sense; that is to say that it is a temporal series ad infinitum, has certain implications. Since I am not ready at this time to prove this statement as being valid, I make it a premise, therefore there exists the possibility that time is not infinite. The resulting implications are many: 
       a.) If there is no Universe, there is no time. That is before the Universe existed (if it has a beginning) there was no time. Time cannot exist apart from the Universe.
      b.) There is also the possibility that the Universe had a beginning and that time is still infinite. For example, if we could travel back in time, we could traverse half the temporal distance to the beginning. We could then travel half the remaining distance, and in turn traverse again over the new remaining distance. In the first case we are 1/2 the distance away, then 1/4, and then 1/8 etc. ad infinitum. We will come closer and closer to the beginning of time but never reach it. We are always one-half the remaining distance away. Therefore time can be infinite and still have a beginning in that the diminishing sequence would never reach its limit {e.g. the beginning). It is most similar to this example: Take the umber 1. Take 1/2 of 1 and add it together - 1 + 1/2 = 1 1/2.  Take 1/2 of 1/2 and add it to the other sum – 1 1/2 + 1/4 = 1 3/4. If you continue the process a number very close to 2 will be produced, but you will never actually reach 2. In the same sense you can have infinite time and a beginning (the limit). This theory, however, is paradoxical in the same sense as Xenon’s paradox of a man walking a mile.
     3) If we assume that time is infinite there might be an inherent paradox. For if this premise that “time is absolutely infinite” is true, then it is possible that time as we know it does not exist. Let us for convenience sake apply man's arbitrary units of time to all of time. Therefore, if we use the years as a measure of unit, time consists of an absolute infinite number of years. Now, if we compare one year to the total amount of time, it takes on the appearance of our former equation: 1/∞ = 0. If this is the case, the equation says that our unit of time, the single year does not exist. There are two ways out of this di- lemma. First, as we said before, absolute infinity transcends magnitude, therefore the comparison is illegitimate. Comparisons must be made in the same frame of reference. The numerator of the equation is quantitative and the denominator is not in that it transcends quantity. The other possibility is that our units of time do not exist and that all measurements of time are totally relative. Our measurements of time are not truly applicable to time in itself and only has value from our human perspective. If this is the case then time is totally relative and no measurements have objective meaning. For example, note this mathematical problem (remembering that we are using absolute infinity):

 If x/a = C and y/a = C then x=y, now let a = ∞; c = 0; x = 1; x = 2, substitute 1/∞ = 0 and 2/∞ = 0 ∴1=2.

The fact that 1 = 2 seems paradoxical, but not if all our temporal measurements are totally relative. Our units of time are valid for our subjective perspective, since we always use the same perspective, but our units have no objective validity in regaled to time itself. If this is the case, can we justify the use of sequential time? It might be true for man but not valid in itself.
         I want to emphasize that that these alternatives and consequences of my premise, that time is sequentially or linearly infinite as well as the premise itself cannot be proven, at least for now. The only basis I have for my premise is that it is a rather popular notion of what time is. 

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III

We are now ready to begin the examination of why the Universe is necessarily infinite. The first theory derives from the assumption that the Universe was caused by a Basic Cause. It is an old theory used to prove the existence of God. It states that since every event has a cause and that you cannot have an infinite regression of events there must have been a First or Basic Cause, and this Cause is God. It is God by which the Universe was caused, derived, or evolved from. While I hope to disprove the argument, it is not for the sake of destroying the Basic Cause doctrine, but to give at least a partial proof in the process of why the Universe must be infinite.⁵

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5. I believe that my second theory is much more conclusive than the first and that it could stand alone. I include this one for the sake of completeness.

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What is actually meant by the fact that the Universe was caused by a Basic Cause? Since the Universe is defined as everything that exists, it necessarily includes the Basic Cause, whether it is God or a primeval atom. Since by definition the Basic Cause is a part of the Universe (and assuming for the moment that it is infinite and not self-causing), it could not have possibly caused itself, meaning that in reality the Basic Cause could not have been the cause of the Universe. This, of course, is mere haggling over semantics. Actually, I only want to get the terminology straight. It would be better to say that the Universe was evolved or derived from the Basic Cause, instead of caused. There is a subtle difference. By saying that the Universe was caused, it is implied that the Basic Cause is not a part of the Universe, while by definition it is. When we say that it is derived or evolved from the Basic Cause, the Basic Cause is included in the Universe. There is not that much difference, and in effect the rest of the Universe is caused by a Basic Cause.

Now let us make a small diversion into the nature of stability. If an absolutely stable object is placed in an absolutely stable environment, it will last for an infinite amount of time. This stability I speak of can best be explained by the example of a rock. Let us take a rock, but not an ordinary one, one which has been frozen at the theoretical absolute zero temperature, so that  all the energy has been removed, thereby none of the internal components (e.g. molecules, atoms, electrons, etc.) are in motion. There is no possibility of any internal motion or change.             Not even the bonds can break down to cause change. It is totally unchanging, or as I prefer, stable. If it is now placed in a likewise totally motionless, unchanging, static, stable environment (and if we accept the principle of causation), the rock will last for an infinite amount of time and not turn to dust. What I am saying is almost tautological. Stability is the same as unchanging, or in a stronger form, incapable of self-caused change. Therefore, anything that doesn't change and is not subject to any outside instability will necessarily last to infinity. It is stable.

The converse is also true -- for anything to be infinite it must be stable. This is is true because anything that is not stable given enough time (which infinity guarantees) will necessarily lose its identity. For example, if the rock was not absolutely stable, un­changing, the random motion of its internal self or of its environment will cause it to change so that it will lose its identity. If we add heat, or if erosive forces are brought in the rock, will eventually become dust: This might not be apparent as a general principle at first because the rock is an isolated case. Stability does not necessarily exclude motion or change. For example, if a certain motion occurs in a continually repeating pattern, it is stable, but once it is subject to instability (possibly from its environment), it will necessarily lose its identity because the pattern will change. In this case it is erroneous to speak of it as non-changing. There is internal change, but its overall pattern of change or motion is not changing; it is stable. Motion and a degree of change are also possible in an infinite object as long as the essence of the object is stable. A limited analogy of this is chemical equilibrium. If we put a lump of sugar into a solution already saturated with sugar a chemical equilibrium will form. Some sugar molecules from the lump will go into solution, while other sugar molecules already in the solution will adhere to the lump. There is an e1uillibrium. There is change, but the basic essence and identity of the lump of sugar is stable.  An object can have motion, it can have change, but if the overall view of the object is stable, its identity will be insured for infinity.

Now we can return to the original theory. It was said that the Universe evolved from (or was caused by) an infinite Basic Cause. If this is so then the Basic Cause must be stable, which means one of three things: 1) that it is totally lacking change; 2) that there is motion or change but it forms a stable pattern; 3) that the essence of the Basic Cause is stable. In any event, the Basic Cause is infinite and thereby stable, implying that it is incapable of any major change. Since the 8asic Cause has already lasted for an infinite amount of time, it must have reached a stability, which insured its identity as well as its infinity. Also, since it has lasted for an infinite time, it must necessarily be stable in regard to its environment too. Therefore, since it has reached this absolute stability (unchanging), it cannot suddenly change and become unstable so that the rest of the Universe could evolve. If something is totally stable it will last for infinity, and since the Basic Cause is already infinite and thereby stable, it is incapable of a change (from within itself or the likewise stable environment) that would bring about the cause or evolution of the Universe. Finally, it becomes obvious that the Universe could not have been caused by an infinite Basic Cause.

If there is no Basic Cause one might assume that an infinite regression of events is possible and that the Universe is infinite. However, there still remain the objections that: 1)the Universe does not necessarily need, cause to begin, it just began and that; 2)the Universe is self-caused (or that the Basic Cause is self-caused which is actually a part of the Universe and that the rest of the Universe evolved from this now finite Basic  Cause). It is these objections that lead to the second theory as to why the Universe is necessarily infinite.

 IV

Before we can begin, we must first recall that we have assumed that time is sequential, being very similar to a straight line. So similar in fact that for the sake of clarity, I have represented time as a line. (See Diagram 1 above).

Line BC represents time extended to infinity in both directions. C represents the past and D the future, or rather the infinite possibility of future time. A is the present which is continually moving forward to the future. Line AC is the actual past representing an infinite amount of time, as is AB represents the future. What I now intend to do is prove that the Universe cannot possibly be finite and must be infinite.

If the Universe is not temporally infinite it must have had a beginning, and if we assume that the Universe exists in the present, we know that the Universe began (something came into existence) at some particular point in the past -- D (Fig. 2). But this is impossible. It was stated that the Universe began at point D. Even though the Universe did not exist previous to point D, the possibility of its existence must have. For how could anything occur unless the possibility of its happening existed previous to its occurrence?  In Figure 2 we see what the situation is supposedly. AD is the supposed finite age of the Universe. The line CD supposedly represents the time -when the Universe.  The line CD represents the time when the Universe did not exist: nevertheless, the possibility of the beginning must necessarily exist. What is important, however, is that line CD is also infinite. The implications of this are quite interesting. No matter how small the probability of an event, given enough time which infinity guarantees, it will necessarily occur. Since the possibility of the beginning of a Universe existed before D, that is in the realm of line CD, and since line CD is infinite, the possibility had to have come about prior to D. The Universe must have begun before D. So we set the "beginning" back to the arbitrary point E (Fig. 3). Even so, the possibility of the "beginning" still naturally exists prior to E also,  under the realm of line DE; but line DE is also infinite, meaning that infinity necessitates the happening of the possibility before point E. The “beginning" had to have occurred prior to E also. No matter how far back in time we place the beginning of the universe, the possibility of its existence naturally existed prior to that point. Since from that point to the infinite past, there will also be an infinite amount of time,  there will also be an infinite amount of time, the possibility will have to occurred prior to that point. It is happen -- the process will continue ad infinitum into the past.  The result being that Universe could not have had a temporal beginning. It is the case then, the Universe is Infinite.

I fear to explain any more for I am unable even to explain the theory in a positive sense. I can only show that no matter how far back in time the Universe supposedly begins, there must necessarily be a beginning prior to it (e.g. farther back in time). It appears that what is happening, is something similar to what was described in Footnote 1 (page 3). The fact that line AC, the present to the past, is absolutely infinite creates the possibility of always having a "beginning" farther back in time, thereby never being able to reach the oldest "beginning" for there will always be one older. It is a conjoining of the two interpretations of infinity, one making the other possible. The result being that the Universe is necessarily infinite.⁶

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6. By the same line of thinking, the Universe can never come to an end or cease to exist. If the Universe could come to an end, the possibility must necessarily exist in the present. Since, however, an infinite amount of time has already passed, the end would have to have already come. Therefore, due to the fact that the Universe still exists, the possibility of an end does not exist. An interesting point is that the Universe could have never existed if the possibility of an end did exist. For is it did, the same process concerning the beginning of the Universe would occur. There would be a constant moving of the end point farther and farther into the past.

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The implications of an infinite Universe as we have shown are: 1)the Universe was not caused by an infinite Basic Cause; 2)it was not caused by a finite Basic Cause; 3)it did not suddenly occur of its own accord (either self-caused or not). Also, while the implications of an infinite Universe would have little effect on philosophical thought, it would be important to some aspects of religious thought concerning the belief in a temporal beginning. The possibility still remains though that the Universe was created in an infinite state in itself.

V­­

Since it would be nice to assume that both theories are true, they would necessarily have to fit together and bear each other out. The second theory proves that the Universe is temporally infinite. If this is so then according to the first theory it must necessarily be stable which means one of three things: l)it is totally unchanging; 2)it forms stable patterns; 3)its essence is stable. The first possibility seems unlikely because so much of the Universe appears to be unstable. While we cannot prove this beyond doubt, we can probably assume that it is unstable. The second possibility of a changing pattern seems more applicable. (It even correlates to t e theory of an expanding-collapsing Universe). However, one wonders just how exactly must the pattern be repeated -- as the cycle begins to be repeat will we be reborn and live our exact lives over again(a complete determinism)? I prefer the third possibility that the essence of the Universe is infinite. How can we discover the essence of the Universe and how it is stable? A possibility is that the Universe's stability lies in its uniform-instability. If everything around us appears to be so unstable, in such change and flux, then possibly there is stability in the fact that everything is constantly changing. The condition of constant uniform instability never changes. In a sense it is stable. The uniform instability is a kind of stability. This is just possibly the identity or essence of the Universe -- its instability. ⁷

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7. A quite interesting but highly doubtful theory comes from this if we accept t e instability of the Universe as fact -- a temporally infinite God cannot exist. If God is infinite he must be stable, and since the Universe's necessary stability is based on its total instability, a stable God could not possibly fit in. One might argue, however, that God like the Universe could be uniformly unstable. This is not possible, for if God was unstable, God would eventually lose his identity and there would be no God. One counters that the Universe is unstable yet retains its identity. God, however, by definition is part of the Universe. The Universe's essence is instability. If God was unstable, he would be like all the other parts of the Universe -- forever losing their identity. If we assume that God is temporally infinite, he cannot exist as a part of the Universe. However, if this is our definition of God, that he is infinite, he then becomes by definition equated with the only truly infinite thing - the Universe itself.