
In a world where everything is measured to finite time, a finite amount, or a finite frame of reference, it’s very hard to grasp the concept of what something means to be infinite. Sometimes, we just accept the biblical domination of interpretation, and say to ourselves in the back our mind, “Well, we know what forever is– but I don’t want to think about it because that’s not what we’re dealing with. Plus, it’s too hard to fathom.” I think this is a realm of something that might seem like speculation of something people would rather not delve into. However, it’s fundamental principle of the physical world around us. We use infinite quantities to solve problems, describe physical phenomena, and for me and probably most importantly at this time– to pass my math classes.
Truman G. Madsen, in talking about how long eternity was in a lecture I once listened to, had to use a worldly and finite definition which has always made me think. Paraphrasing, he said that an eternity (or infinite time) is like a seagull that flies to the top of Mount Timpanogos every so many years (100 or 10 or 1000 years, I don’t remember) and sharpens his beak on a rock. The seagull would then do this every period of years until that mountain is whittled down to nothing. He then went on to say, that that amount of time is like eternity. No offense to the late Mr. Madsen but to me, this is a forced simile that doesn’t doesn’t even come close to eternity or a precise description of what forever is. You see, a time frame was placed on the time it took for the mountain to break down. There was a beginning, there was an end. Not infinite, but finite.
In my mind, infinity = eternity = forever = never ending = without bounds. Can we quantitatively describe what we or anyone else has never experienced? It sure is hard. Don’t get me wrong, I’m not speculating anything here, just stating fact. The mathematical quantity of infinity is treated as a number, yet it is not a number, or at least any real number. You see, it cannot be defined because it is increasing constantly, decreasing constantly, or it is all the numbers in existence with is a never ending sequence. Wait a minute– all numbers? How many is that? Why, infinite, of course! Kind of hard to wrap your mind around? Well lets have some practical application.
∞ is the symbol we’ll use to represent infinity. Okay. Let’s say a we have two men. One man is 53 years old. The other man is 25 years old. How many years older is the first man than the second? Well, we take 53-25=28. 28 years is pretty significant when talking about age. There are quite a lot of things one can learn in a span of time lasting 28 years from start to finish. Now, let me ask you this. What is 53+∞? It’s just plain old ∞. What’s 28+∞? Same thing. Just ∞. Now, assuming these two men live forever, or to ∞, What’s the difference in age between them? Let’s work it out this way. (53+∞)-(25+∞) = what? It’s not 28 anymore– it’s and indeterminate answer. This means that it’s not a finite amount. It’s an infinite amount, or in other words, how can you take something that doesn’t end and subtract something else from it that doesn’t end? Impossible. The amount you find is also never-ending. If there are no bounds set on anything, then there is no difference between different quantities. The differences disappear. What does that say about the two men? Is one still older than the other? Not with an infinite definition, and this is again because infinite things can’t be bounded– that goes for age. In fact, age is irrelevant when talking about infinite time. Time itself is not useful either, seeing that there would be no need for a measurement of time if there is no end to it. You might also note that if there is no end, there couldn’t have been a beginning because if you go infinity backwards, you just get -∞. Forever the other way.
I like to think of things this way: if people lived to be 1,000 years old, would you still say a 98 year-old woman is old? What about someone who’s 98 years old who lives 1,000,000 to years? would that person still be called old? What about 1×10^100 years old? Would the 98 years even matter? Something to think about.