Contemplating Infinity

I would like to do what I can to help anyone who has tried to contemplate what infinity is. This is being reposted because more has been added to it.

Infinity is supposedly a number, the highest number that there is. Yet, it is a realm in which numbers have absolutely no meaning. At the other end of the number line, zero is also a number. 

This reveals something about numbers, to have meaning we have to be at a point on the scale of numbers where there are numbers both above and below us. If we have numbers on one side but not the other, at either zero or infinity, then numbers become meaningless. The definition of a number depends on the other numbers as a number is defined by what it is not, which is why each number requires another number both above and below it.

Numbers are themselves infinite, meaning that they continue indefinitely, they must be or else infinity could not be the supposed number that it is. That is at least the theory. But the limitation lies in ourselves. To be meaningful to us numbers must be manifested in some way, if only as figures on paper. A number has no real meaning until it is manifested. 

But that creates an impenetrable barrier between us and infinity. We could fill the whole universe with numbers on paper. But since the universe that we inhabit is finite, whatever number we could thus create would also have to be finite and so would fall short of infinity. To be infinite, a number must just be. It can never be infinite if it must be generated or manifested in any way.

Any finite number not only falls short of infinity, it must fall infinitely short of infinity. No matter what we do with finite numbers, we can never get even an iota closer to infinity. We can spend our whole lives multiplying numbers until we have a number that fills the whole universe, and we will be not a bit closer to infinity than when we started. If we could somehow get closer to it, then infinity would not be infinite. You can only make progress to a destination if it is a finite distance away. There can never be any common ground between the finite and the infinite.

In geometry, we are taught that parallel lines are sets of lines that are in the same plane but which never meet in our finite realm. They do, however, eventually meet at infinity. 

Parallel lines must meet somewhere. To claim that they do not is for the finite to reach the infinite. Parallel lines may never meet in the geometry textbook illustrations, or in the world, or in the universe. But infinity is so far, in fact infinitely far, that nothing finite like a pair of parallel lines can ever reach it. 

The most perfect pair of parallel lines that our universe can manifest must eventually meet. The parallel lines do not have to meet in the finite universe to which they belong. But for the parallel lines of a finite universe to reach infinity without meeting is to reach infinity by finite means, and we know that such a thing is impossible.

Another way to think of infinity in terms of geometry is as a perfectly straight line being an arc of an infinite circle. There cannot really be any such thing as an infinite circle because any arc of it would have to be a perfectly straight, and infinite, line. 

Defining a point as the center of an infinite circle doesn't make any sense either because it would have to cease to be the center if it was moved a finite distance in any direction and a finite number subtracted from infinity would still equal infinity. There is no such thing as an infinite circle because a circle must have a definite center and and the center could be defined as anywhere in the circle if there was an infinite circle.

Infinity actually can be expressed with finite numbers, but we must go to the opposite end of the number scale to do it. Any fraction with zero as a denominator is representative of infinity, such as 1/0, just as any fraction with zero as the numerator represents zero. 

Since zero contains nothing, one divided by zero must be infinity. An infinite number of zeros can fit into 1. If 1/0 was not tantamount to infinity, then zero would have to equal something and if it did then it wouldn't be zero. This reveals that a finite something is as far removed from zero as the finite something is removed from infinity. This is why we can only express infinity with finite numbers if one of those numbers is zero.

The opposite of the infinite is the infinitesimal. The infinitesimal is the reciprocal of infinity. Something that is infinitesimal is something that is just about zero. In fact, any finite quantity can be divided into an infinite number of infinitesimal divisions. Like the infinite, the infinitesimal can never be described with finite numbers. All finite numbers are just as meaningless with the infinitesimal as with the infinite. 

Just as the concept of infinity is used in geometry this concept of the infinitesimal is used in Calculus. On a curve of continuous change any point on the curve represents an infinitesimal section of change at a constant rate.

If we can apply numbers to something, it is neither infinitesimal nor infinite. Just as we are limited by the fact that we are composed of matter in a universe of space and matter from reaching infinity, we are also prevented from reaching the infinitesimal. An electron, a mere point particle with no discernible internal structure, is the closest we come to the infinitesimal, just as the entire universe is the closest we come to the infinite.

Upon reaching infinity, we would find that numbers have become utterly meaningless. If any number has any meaning at all, then we have not reached infinity. Numbers are meaningless at the other end of the scale, at zero, because there is nothing to manifest numbers and numbers, or any mathematical entity, must be manifested in some way to be real. 

Zero does not mean the same thing as nothing, zero means there could potentially be something, which would be 1, but there isn't. Zero is not nothing but it is information that there is nothing. Neither would numbers make any sense at infinity, because no finite number could be manifested. 

If we have zero at one end of the number scale, and infinity at the other end, there should be some halfway point between zero and infinity. The obvious halfway point would be the number 1. This is because any number, denoted as X, that is between zero and infinity has a reciprocal, denoted as 1/X, that is between zero and 1.

The halfway point could also be considered to be the number 1/2, one half. First of all consider the time version of infinity, which is eternity. An eternal being, which has existed for eternity past and will exist for eternity future, will always be at the halfway point of it's existence. No matter how far into the past or future, the eternal being will still be at the halfway point of it's existence. A truly eternal being, meaning both past and future, can never be anywhere but at the halfway point of it's existence.

For another example of how the number 1/2 relates to eternity, consider the statistics of repetitive odds. If you play a game in which there is a 1/2 chance of winning, and you play the game twice, your odds of winning are 3/4. This is because your chance of winning the first play is 1/2. That leaves 1/2 remaining, and your chances of winning that one the second play is 1/2. So, 1/2 + 1/2 of 1/2, or 1/4, = 3/4. 

Now, suppose that we play another game in which the odds of winning are only 1/4, but we play it four times. The odds of winning become 1/4 + (3/4 x 1/4) + (1/2 x 1/4) + (1/4 x 1/4) = 10/16, or 5/8. Thus, the odds of winning are less than if we played the game of 1/2 odds twice. As the number of the odds game gets higher, for example the odds of 1/100 played 100 times, the odds of winning get progressively lower. But the odds of winning never go below 1/2, no matter how high the number. 

If the odds of winning were one in a million, but we played a million times, our odds of winning would be a shade over 1/2. When we get to infinity, and played a game in which the odds of winning were infinitesimal, or 1/infinity, but we played the game an infinite number of times, the odds of winning would be exactly 1/2. This is another way in which one-half relates to infinity as the halfway point one the number scale between zero and infinity.

What if the finite could be made infinite? It would mean that everything would have to exist. If the universe was infinite, there could be nothing which could possibly exist which did not exist somewhere, as long as the number of things that could possibly exist is finite.

There would have to be exact copies of our earth and solar system out there, in fact, an infinite number of exact copies of our earth and solar system. There would also have to be copies of the earth and solar system with every possible variation, such as solar systems with earth and Venus exchanging places and earths with Australia attached to the coast of Africa. This is because anything that could possibly exist, but with the odds against it, would effectively have an infinite number of attempts to overcome the odds.

THE ILLUSION OF INFINITY

Infinity isn't really a number. Saying that there is an infinite number of something isn't really an answer, even if it is the best answer that we can give.

Numbers are a tool that we use to describe the world and the universe around us. But it is also true that numbers are our own creation. We are more complex than the surrounding inanimate universe but we are of finite complexity and that inevitably shows up in the number system that we create. The way that it shows up is in our concept of infinity.

If we are of finite complexity and create a system of numbers that never ends, it will have to end in the nebulous concept that we call infinity. Infinity is a reflection of our finite own nature, rather than a real number.

I define complexity as the value of the denominator when something is expressed as a fraction or ratio. If we are of finite complexity ourselves then there has to be a limit to the numbers that we can effectively conceive of and measure. If numbers go on forever they must thus terminate in this concept that we call infinity.

We have developed numbers to describe the universe that we live in. But that universe is, as far as we know and as far as we can see, finite. Yet our numbers can go on forever. For that reason we have to perceive numbers as terminating in this concept of infinity.

We are of finite complexity, although more complex than our inanimate surroundings. If something was more complex than we are we would have to see it as being infinitely complex. To describe something fully with numbers we must completely understand it, such as we do with the calendar. We use words, rather than numbers, to describe what we do not completely understand. "Infinity" or "infinite" is actually a word, rather than a number.

To completely understand something it must be less complex than our brains. We can never describe something fully with numbers that is of equal or greater complexity than us. We may describe events as "random" but there is really no such thing as random. Like infinity it is a matter of our finite perspective.

Somewhere out there is a mathematical formula that completely describes us and our behavior. But to grasp it we would have to be "smarter than ourselves", which is impossible. We could not see the formula as being of any finite complexity, because then we would be on our way to grasping it. We would have to see it as being of infinite complexity, as we would anything that is more complex than we are.

So our sense of infinity is a matter of our own perspective and we have to perceive something as being infinitely complex if it should be more complex than we are.