Our Amazing World
by Joe Selzler
"What is infinity? Can it be described? Can it be studied or observed? Can it be measured or weighed? Can it be timed?"
"To Infinity and Beyond!" So cried the favourite children's character Buz Lightyear in the movie Toy Story. When I heard that cry I could think back to when I was a child and what I thought about infinity. I was fascinated with the concept of infinity. I wanted to know just what it was. I couldn't imagine something that didn't have an end point. To me everything had to end somewhere and we should be able to find it. But I have to admit that I didn't do much to pursue the matter much further. I just accepted that some things were infinite as a matter of course, leaving my doubts to another day.
Where was I first introduced to the concept of infinity? Well, actually it was not in school but in church. I was raised in a Catholic home and so we went to church nearly every Sunday. In the Catholic church, as indeed in Protestant churches, God is seen as being infinite. So I was taught in my catechism classes that God is infinite. That he is, always was, and always will be.1 It was to be a concept I would not readily accept. I always questioned how someone or something could be "is, always was and always will be." I could not get my head around it.
When I got to school I learned that some things go to infinity; such as the number Pi. (3.14159265358979323846...) The three dots at the end of the number here indicate that it goes to infinity. Other numbers, such as the fraction one third, go to infinity as well. (.33333333 ) I won't list them all here but I think you get the idea. The trouble was, my questions about infinity never got answered. Even though my math teachers could show me how Pi goes to infinity because you could keep on doing calculations that added to the numbers after the period, I still wanted to see that there was no end to it. The greatest problem for me was that I wanted to see the entire number right to its infinity before I was really sure that it didn't end.
Now I know that for most of us the concept of infinity doesn't occupy too much thought or time. On a scale of one to ten of important concepts for us to consider in our daily lives it rates about --1. There are related concepts that we do consider much more often. Take for instance the concept of eternity. We know it is a very long time. Indeed it is infinite time. When something takes a very long time to reach us, such as a letter from a pretty girl or handsome guy, or some money we are owed, we sometimes say, "This letter took an eternity to get here."
So, just what is infinity? Can it be described? Can it be studied or observed? Can it be measured or weighed? Can it be timed?
The Oxford dictionary defines the word infinite as "boundless, endless, very great, innumerable, very many, (In Mathematics) greater than any assignable quantity or countable number."2 The word infinity comes from Latin: "infinites" unboundedness.3 If you think about it a bit the very definition of the word suggests something that cannot be measured in any way. If something is infinite it requires some other infinite something to measure it. For if something is bounded it certainly cannot measure something that is not bounded.
But here we have a paradox. If something is truly boundless it is impossible for any other boundless thing to exist. That's because something that is boundless necessarily places boundaries on everything else. Indeed, that which is boundless gives to everything else all that is necessary for those things to exist.
George Soslovsky writes: "we must accept that SOMEWHERE under all these layers there is a positively infinite thing that all other infinities are dependant on."4 By layers he means concepts such as -- an infinite line in space requires that space be infinite, an infinite idea requires that thought be infinite, a dynamic function in time requires that time be infinite. He describes this positive infinity as being all there is, that it does not change because it already contains any changes that could take place.
In other words he is saying that there exists something that does not change and is unaffected by everything else that exists but upon which everything else we know of is dependent. Therefore, we cannot have a number such as Pi that is infinite unless there exists some one thing that transcends Pi and all else. Things are beginning to sound more reasonable to me. However, I am still brought back to that concept I learned in church. If it is true that infinite time is dependent on some positive infinity, then could it be that an "is, always was and always will be," exists outside of time as something time is dependent on?
We sometimes look back on ancient people as being simple, unable to understand the more advanced concepts of our day. But actually, there are a number of men and women from antiquity who did indeed understand advanced concepts and who have pointed the way to our modern understanding of infinity. For example: "For I am the LORD, I change not; therefore ye sons of Jacob are not consumed." - (Malachi 3:6) And: He is before all things, and by him all things exist. Colossians 1:17 (King James Version). These ancient men understood that there is one who exists outside of that which we can sense. And the things we can sense depend upon that one. They considered him to be the one who made it all.
Can I understand how it is that this Creator "is, always was and always will be?" No, I cannot because I am limited, finite. But modern mathematics has shown that some things are infinite and that those things depend on one, all encompassing infinity. The Bible explains that infinite thing as being a God, and a personal God at that. He does not change. Our world may be changing. Many people fear that global warming will change our world irrevocably. But it is not just global warming that affects us. We may lose our jobs, our friends, or our loved ones. A storm may take our house or a war may take our land. We may be loved one moment and persecuted the next. Indeed, our very lives will only last about 70 years. However, there is one thing that will never change. I suggest that we can count on that one, positively infinite thing, which many call the Lord, as the one thing that will never change and will always be there, even at our death, when we pass to the other side.
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