Infinity

Where is the infinite? It seems to lie in two directions simultaneously – outer space and inner molecules. Capt. Kirk and Star Trek were some of the first to point us to deep outer space, to venture far beyond our own solar system and galaxy. In fact, it was not until sometime in the 20th century that we even knew that there was more than our own galaxy. Kirk, Spock, Nimoy, and the numerous “Red Shirts” took us to a new planet every week, sometimes two, and demonstrated that creates there were strange and familiar. They were like us because we imagined them. But they were unlike us because we did our best to make them unique. Opening this doorway to thought leads to the question – how many stars, planets, and creatures can possibly exist in the universe? Is the answer 1, 100, or 1 million? So far we are still wondering about that question. Is there any reason that the number of stars and planets cannot be infinite? Is there a number so large that it is the same as infinity for all practical purposes (like Bill Gates’ net worth)?

The second direction seems to be downward into the animal cell and the structure of atoms. The universe seems to exist in their in exactly the same way it exists in outer space. Atoms look like little galaxies or solar systems. But, kids now learn that electrons are probability spaces and not little tiny planets orbiting the nucleus. They also learn that the electron field is not a sphere around the nucleus, but is a space that is shaped by the other atoms in its vicinity. This tiny inner infinity is complex, and the more complex it becomes, the more it looks like the giant outer infinity.

Is infinity useful? It is more than I can eat, own, earn, or carry. I understand that ancient man had a very primitive counting system that went something like “none”, 1, 2, “many”. If you had more than 2 of anything you were rich to the point that it was not necessary to count it all. I might have nothing, one for myself, one for me and one for you, or more than that. 3 or 30 were both the same. How can this primitive person use infinity? Today we count things a little higher – and usually focus on our money. I might have 1 dollar, 100, 1000, or 100,000. We can count as high as we like and there are two numbers that we are particularly interested in – one million and one billion. When we make our first million we begin to hope to be rich. When we make our first billion, then we have made it. Is anyone concerned with trillion? It appears that only the computer people are looking that high. The storage on a hard drive, the RAM in a computer, and the operations per second – these are all interested in trillions and higher.

Infinity … does anyone really care?