Conceptualizing infinity is impossible. The human mind, bound by the five senses it can perceive and conditioned its entire operational career to deal with limits and boundaries, simply cannot encompass infinity. Even the bare concept of infinity defies the imagination. Try to imagine, if you will, a never-ending universe, going on and on in every direction without end. Those last two words are the meaningful ones, innocuous as they sound. Without end. Try to imagine anything without end, really and truly limitless, and the imagination exhausts itself. The mind runs in circles.
There is always something bigger or something smaller, something closer or something farther away. Outside our solar system is a galaxy, and millions and millions of miles away are more galaxies, and outside of those spheres of existence there is the universe, and outside of that...? Some argue that our universe is just one in a boundless sea of other universes, just as our galaxy is one in a limitless sea of other galaxies. Others contend that ours is the only universe, and it encompasses everything that ever was or ever will be, and quite a bit more: infinity, in fact. The human mind, as has already been stated, is blinkered by its perceptions, and has a tendency to impose limits on what it perceives. It has been the trend for humanity to imagine that our universe, our plane of reality, our dimension, our world (whatever it may be called) must end somewhere. But that answer only brings up another question: if we go to the ends of the universe and hit a wall, then what is on the other side?
Even a consideration of the finite but staggeringly huge distances between stars and planets is a strain on our thinking capacities. Numbers get so large as to become meaningless. We know that a billion miles is an exceptionally long way, but we really don't appreciate that kind of distance. Even if we walk five miles and consider that we'd have to walk that same distance 200 million times again in order to travel a billion miles, we just can't grasp it. You can put a bowling ball on the grass of your front yard, walk 26 paces away and put down a peppercorn. Your imagination will be stretched when you attempt to visualize the ball as the Sun and the peppercorn as the Earth.
That represents a distance of only 94 million miles or so. For the mind to envision infinity (millions, billions, trillions, and quadrillions of miles) is impossible. We are limited in our perceptions. Were we omniscient beings, perhaps we could more easily see or imagine infinity. Restricted as we are to a small terrestrial planet and its immediate vicinity, we can only think so far as we can see or imagine. Given the nature of our perceptions (outlined above), we are limited in the mental arena as well as the physical one.
Norton Juster demonstrated the impossibility of infinity in his book "The Phantom Tollbooth." The protagonist, a boy named Milo, meets the Mathemagician, the keeper of all things having to do with numbers. The Mathemagician, in trying to explain the idea of infinity to Milo, tells the boy to imagine the highest number he can think of. Milo answers with a ponderously large one. The Mathemagician then tells him to add one to it. Milo does so, and the Mathemagician tells him to add one to it again, and again, and again.
"But when can I stop?" asks Milo, exasperated.
"You can't," the Mathemagician replies.
Visualizing infinity is impossible, but seeing it is ridiculously easy. Just look up at the night sky. When you gaze into the heavens and the twinkling stars glinting trillions of miles away and the uncharted blackness in between, you gaze into infinity. You are looking that something that appears flat and finite, but is truly boundless and infinitely deep. You can see it, but you can't imagine it.