Time and the Finite Universe

Les Bill Gates
14 min readJun 8, 2022

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A Dialogue between the Philosopher Sto Méllon and the Scientist Ross E. Forp

Author’s Note: The following is not meant to be scientifically accurate. I am a mathematician, not a scientist, and my knowledge of General Relativity, Quantum Mechanics and Cosmology is quite limited. The dialogue is rather an attempt to explain some aspects of Science and Religion by way of analogy. Please bear this in mind when offering criticism.

Méllon: What do you know about the Universe?

Ross: Everything there is to know.

Méllon: Well Ross, what do you understand by ‘Infinity’?

Ross: The Universe is infinite in size and infinite in time — it goes on forever and it’s been here forever.

Méllon: That’s where you are wrong. It is neither infinite in size nor infinite in time. Tell me, what you know about time?

Ross: Some scientists believe that the Universe is cyclic. It starts with a Big Bang, the Universe expands until it cannot expand any further, then contracts under the force of gravity until there is a Big Crunch. Then there is another Big Bang and the whole process is repeated — indefinitely. They believe this goes on forever, and hence the Universe is infinite in time.

Méllon: Nonsense. Do you believe in God?

Ross: Yes, of course. How else can one explain the creation of the Universe? The probability of an ordered Universe coming into being out of nothing without divine intervention is zero. Any mathematician would tell you that.

Méllon: Well, doesn’t it say in the Bible, in Genesis 1:1: “In the beginning God created the heavens and the earth.”1?

Ross: Yes.

Méllon: So there was a beginning, right?

Ross: Er … yes.

Méllon: So time began and, therefore, cannot be infinite?

Ross: I suppose… But what about space? Everyone knows the Universe is infinite in size.

Méllon: Another misconception. The Universe is unbounded, but not infinite.

Ross: Unbounded? What do you mean by that?

Méllon: It is very simple for me, but more difficult for you to understand. We are constrained to live in a world with an incomplete dimension.

Ross: A what?

Méllon: I am talking about time. Time is an incomplete dimension because it only goes one way. Let me try and explain. Can you imagine a crawling insect that lives on the surface of a balloon that is expanding?

Ross: Yes, that’s not hard.

Méllon: Can you see that the insect can crawl anywhere it wants around the surface of the balloon, but it can never escape from the surface?

Ross: Because it can’t fly?

Méllon: Yes, that’s right. Well, what do you think would happen if the balloon stopped expanding?

Ross: The insect would fall off?

Méllon: Not exactly. What happens is that time stops for the insect. And that’s exactly what happens to us when we die. Time stops. But the real question is, can time start again?

Ross: Yes, I suppose it can if the balloon starts expanding again.

Méllon: Balloon? Oh, no don’t get too caught up in my analogy. You’re right, of course, the balloon could start expanding again … or it could start contracting.

Ross: You mean like time goes backwards?

Méllon: Wrong. Time cannot go backwards, not in the way you mean. You can’t get younger again; nor could you travel through time. That’s impossible. But time could go in the opposite direction. Direction? That’s not quite the word I want, but you know what I mean. But this is all rather irrelevant; what is important for you right now is that time will stop.

Ross: So what does happen to the crawling insect?

Méllon: The insect stands at the crossroads. My friend, Rev. Eals calls it ‘The Crossroads of Time’, and one of three things can happen. The first is that the insect learns to fly and flies down inside the balloon where it becomes trapped in a land of eternal darkness. The second is that it learns to fly and flies up above the balloon into a world of everlasting light and freedom.

Ross: You used the words ‘eternal’ and ‘everlasting’. Don’t they mean the same thing as infinite?

Méllon: Not in the sense you are thinking. What it means is the insect leaves the incomplete dimension (time) and enters the complete fourth dimension. This fourth dimension is unbounded, not infinite. I’ll explain this more later.

Ross: What’s the third thing that can happen to the insect?

Méllon: The third thing that can happen is that the balloon starts expanding again, and the insect continues to exist as a crawling insect. His perception of time begins again as the balloon expands.

Ross: But a crossroads has four exits, doesn’t it?

Méllon: Very remiss of me. Of course, there are four ways. The fourth is that the balloon starts contracting, and the insect continues to exist as a crawling insect. His perception of time begins again as the balloon contracts, but the direction of time is reversed. That’s what I meant when I said time could go in the opposite direction. But don’t get confused. This would be indistinguishable from the time we know. We would not notice any difference, and we would certainly not get younger. We wouldn’t return to an earlier time. In other words, time travel is impossible.

Ross: But what happens when the balloon deflates to nothing?

Méllon: Don’t get too caught up in the balloon analogy. It would simply mean the end of the Universe as we know it.

Ross: You mean “In the end God will destroy the Heaven and the Earth.”?

Méllon: Maybe you are right, or maybe it’s not quite as final as that. In Revelation 21:1 the apostle John wrote “Now I saw a new heaven and a new earth, for the first heaven and the first earth had passed away.1” So, yes, the Universe as we know it will cease to exist, but that’s not the end of the story. However, these are not things for us mere mortals to understand.

Ross: Okay, so how does the balloon come into this?

Méllon: A balloon is three-dimensional and expansion (or contraction) of the balloon adds another uni-directional dimension for the insect. But please try to forget about the balloon. I believe there is a simpler analogy. Imagine you are a flat two-dimensional being living on the surface of a three-dimensional sphere. You have no conception of the third dimension — up away from the surface of the sphere has no meaning to you since you are flat. But, what if the sphere were expanding, like a balloon being inflated? Then you would experience a third dimension and it would be uni-directional. That’s your ‘time’. And, if the sphere starts to contract, your ‘time’ will be reversed. Now answer this — is the surface of the sphere infinite?

Ross: No, of course not.

Méllon: But it is unbounded, right?

Ross: What do you mean by that?

Méllon: You (remember you are a flat being) could move anywhere you like on the surface of the sphere. Let’s think about the Earth we live on. Many ancient civilizations believed that The Earth is a disc and therefore flat. The consequence of such a theory is that the Earth has a boundary and, if you reach the boundary, then you will fall off the edge.

Ross: That’s nonsense. Nobody believes that any more.

Méllon: You would be surprised. There are even some people today who adhere to conspiracy theories and believe that the spherical Earth is a lie. However, these people are in the minority. Science and geographical discovery have proved that the Earth is a sphere, further validated by video taken by astronauts and cosmonauts over the last sixty years. Given that the Earth is a sphere, there is no boundary and no edge to fall off.

Ross: That’s scientific. So, get to the point.

Méllon: A consequence of the spherical Earth theory is that there is no boundary, so the Earth is finite and unbounded in 2-dimensional space. You can move around the 2-dimensional surface of the Earth as you please. Here I am ignoring physical boundaries that may impede your journey such as mountains, but you can work your way around these and carry on on the other side as if there had been no diversion. So, ignoring these physical boundaries, if you move in a straight line in any direction, then you could keep going until you arrived back at your starting point. Think of a journey around the world that follows the equator. If you start at Singapore and travel east along the Equator, you will follow what appears to be a straight line and travel approximately 40,000 kilometres until you arrive back at Singapore — back at your starting point. Of course, you don’t really move in a straight line. You move around the equator which is the circumference of a sphere — this is what we call a geodesic. Suppose you live on a sphere like the Earth but there is no sea or mountains — it is a smooth perfect sphere. You are flat i.e. you have no sense of the third dimension, no height. You can move around the 2-dimensional surface of the sphere. If you move in a straight line in any direction, then you will never meet a boundary and you could keep going until you arrived back at your starting point, just like the journey around the world described above. A geodesic generalises the idea of a straight line to curved space. The circumference of a sphere is a geodesic in 2-space. In other words, the surface of the Earth is finite, but unbounded, in 2-dimensional space. The important thing to understand is that the surface of the sphere is unbounded and finite in 2-space. You could keep going around the geodesic as many times as you like without ever meeting a barrier — so it is unbounded — but the surface itself is finite since its area can be measured.

Ross: Okay, that makes sense.

Méllon: Similarly, the Universe is finite, but unbounded, in 3-dimensional space. Try to step up a dimension from the scenario I described above. We three dimensional beings, have no sense of the fourth dimension, unless we include time for the fourth dimension. If you travel into Space and move in a straight line in any direction, then (ignoring stars and other Space debris) you will never meet a boundary and you could keep going until you arrived back at your starting point, just like the journey around the world described above. Of course, you don’t really move in a straight line. You move along a geodesic. If we were to travel out into space in a straight line (which is really a geodesic in 3-space), then we will never meet a boundary and could (theoretically, if we could live that long), eventually arrive back at our starting point (just like the journey around the equator of the Earth). The Space that makes up the Universe is the surface of a four-dimensional sphere which is unbounded and finite in 3-space. You could keep going around a geodesic as many times as you like without ever meeting a barrier — so it is unbounded — but space itself is finite since its volume can be measured.

Ross: So, how do you explain time?

Méllon: Remember the insect — his time is directly related to the expanding (or contracting) of the balloon. Things are similar for us three-dimensional beings living on the surface of a four dimensional Universe. Our perception of time is directly related to the expanding Universe. When the Universe stops expanding and starts contracting (even as the cyclic theory predicts), then our time will stop before it is reversed. That does not mean that we will get younger, or that we can travel in time. It simply means that time will go in the opposite direction.

Ross: How can time go in the opposite direction?

Méllon: We are assuming that the Universe exists in three dimensions only. If we introduce a fourth dimension, then that would be time. A two dimensional being living in 2-space on the surface of a sphere will perceive the third dimension (his ‘time’) only if the sphere is expanding or contracting. Similarly our perception of the fourth dimension (our ‘time’) is a direct consequence of the expanding (or contracting) Universe. Think of a walk from point A to point B. If you walk back from B to A, you don’t walk backwards and place your feet on the same spots as before. You simply reverse the journey. So it is with time. You will not revisit events from your past. You won’t even notice that it has reversed — it’s just the direction that’s changed.

Ross: So how can I gain a conception of the next dimension?

Méllon: Whereas we can understand and experience the fourth dimension as time, the greatest challenge for us as 3-dimensional beings living in a 3-dimensional world is that it is impossible for us the conceive or visualise the fourth space dimension in the same way that we conceive and visualise the other three dimensions. In his novel ‘Flatland: A Romance of Many Dimensions’2, Edwin A. Abbot makes an effort to bridge the concept from the perspective of one dimension to two dimensions, and then from two dimensions to three.

Ross: What does Abbot say?

Méllon: In Section 13 of his novel, Abbot describes a meeting between the narrator from Flatland (the 2 dimensional world) and the Monarch of Lineland (the 1 dimensional world): “It seemed that this poor ignorant Monarch — as he called himself — was persuaded that the Straight Line which he called his Kingdom, and in which he passed his existence, constituted the whole of the world, and indeed the whole of Space. Not being able either to move or to see, save in his Straight Line, he had no conception of anything out of it.”

Ross: Where is all this going?

Méllon: In Section 16, Abbot tackles the problem of how a being from Spaceland (our 3 dimensional world) can explain the third dimension to the being from Flatland (the 2 dimensional world): “You are living on a Plane. What you style Flatland is the vast level surface of what I may call a fluid, on, or in, the top of which you and your countrymen move about, without rising above it or falling below it. I am not a plane Figure, but a Solid. You call me a Circle; but in reality I am not a Circle, but an infinite number of Circles, of size varying from a Point to a Circle of thirteen inches in diameter, one placed on the top of the other. When I cut through your plane as I am now doing, I make in your plane a section which you, very rightly, call a Circle. For even a Sphere — which is my proper name in my own country — if he manifest himself at all to an inhabitant of Flatland — must needs manifest himself as a Circle.”2

Ross: I don’t follow.

Méllon: Think of a sphere cutting through a plane. All the being from Flatland sees is a circle that changes size.

Ross: Can you get to the point? Forgive the pun.

Méllon: The circle he sees seems to appear from nowhere, then starts as a single point before increasing in size until it is equal in size to the circumference of the sphere; and then it decreases in size again until it becomes a single point again, and disappears. In other words, the circles he sees are cross-sections of the sphere. They are only there in the Flatland being’s experience fleetingly, like a shadow.

Méllon: Following this example, a being from FourDland (the 4 dimensional world) can explain the fourth dimension to us beings who live in the 3 dimensional world as being like a four-dimensional sphere. A four-dimensional sphere is an infinite number of spheres, one placed on the top of the other (in the fourth dimension sense) that can cut through space, with a three dimensional section that appears to us as a series of three-dimensional spheres of varying sizes. This concept is very difficult for us to envisage.

Ross: You just used the word infinite. Didn’t you say infinity doesn’t exist?

Méllon: In the Mathematical world, yes, it is convenient for us to say that infinity does exist, but infinity does not exist in the Physical world.

Ross: That all sounds very ‘convenient’. Isn’t Mathematics real?

Méllon: Of course it is, as a tool. Can you let me get back to the point I was trying to make?

Ross: Okay, but I’m a little sceptical.

Méllon: When we think of the fourth dimension as the expansion of 3-dimensional space, we can envisage a being living in four dimensions as a fleeting shadow. We do not see the shadow, but we can sense that it has passed through our 3-dimensional world, just like the circle passed through Flatland.

Ross: Like a ghost?

Méllon: Not a ghost! Not the ghost of a dead person that comes back to haunt us. But rather an entity from the spirit world — maybe an Angel, or even some aspect of the Holy Spirit of God Himself. It’s not for me to say, less still for me to try to explain it. God’s ways are not our ways. However, there seems to be some hint that God exists in the fourth dimension (or maybe a still higher dimension) and His Spirit enters our three dimensional world by passing through our world — as I said, like a shadow. Or as the apostle Paul said in 1 Corinthians 13:12, “ For now we see in a mirror, dimly, but then face to face. Now I know in part, but then I shall know just as I also am known.”1

Ross: What evidence do you have to support this claim?

Méllon: No tangible evidence. It’s just a matter of faith.

Ross: That’s not very scientific.

Méllon: No, nothing I have told you today has any scientific proof; yet I do not think it is speculation. These ideas make a lot of sense and give us a taste of how the spiritual world interacts with the physical world.

Ross: Do you believe in the Multiverse?

Méllon: Of course not. There is only one God, and therefore only one Universe. The existence of a Multiverse would demand the existence of a multitude of Gods, which is clearly wrong. As the apostle Paul wrote in Ephesians 4:4–6: “There is one body and one Spirit, just as you were called in one hope of your calling; one Lord, one faith, one baptism; one God and Father of all, who is above all, and through all, and in you all.”1

Ross: Have you heard of Dark Matter?

Méllon: Yes

Ross: So, how do you explain that with your theory?

Méllon: I’ve heard it said that dark matter is the invisible glue that holds galaxies together, but think of it as the rubber.

Ross: Rubber?

Méllon: Yes, the rubber of the expanding balloon.

Ross: Oh, it’s back to the balloon, is it?

Méllon: You should know by now that the balloon is just an analogy. The rubber of the balloon is the boundary between the inside of the balloon and the outside of the balloon. It also holds the 3-dimensional balloon together. Without the rubber, there would be no balloon. In the same way it’s the dark matter that holds the four dimensional universe together. It is the boundary between the inside of the four dimensional sphere and the outside of the four dimensional sphere. Remember the Crossroads of Time.

Ross: Fair enough, I suppose you might be right. What about Black Holes? According to Britannica.com “a black hole can be formed by the death of a massive star. When such a star has exhausted the internal thermonuclear fuels in its core at the end of its life, the core becomes unstable and gravitationally collapses inward upon itself…”3

Méllon: Let me try and explain. Imagine there is a massive crawling insect on the surface of the balloon; then it will break the rubber and fall through, taking other less massive insects with it. Time will stop for them. They reach the Crossroads of Time. In other words, the insect learns to fly and flies down inside the balloon where it becomes trapped in a land of eternal darkness. That’s an analogy of a black hole.

Ross: This whole discussion has been a load of analogies, hasn’t it?

Méllon: Yes, but maybe you will have learned something; or at least have been given food for thought.

References:

1. The Holy Bible, New King James Version (NKJV)

2. ‘Flatland: A Romance of Many Dimensions by Edwin A. Abbot’, The Project Gutenberg edition, 2008

3. ‘Black Hole’ https://www.britannica.com/science/black-hole

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Les Bill Gates

I was born in England in 1949. I have an Honours degree in Mathematics from Oxford University. A former teacher and High school Principal, I am now a writer.