Without Begining, Without End...

Before retiring for the evening I came across this Carl Sagan quote while reading the book, "A Short History of Nearly Everything" by Bill Bryson and I got so excited I had to sit down and capture all the ideas that came to me while reading it:

"Carl Sagan in Cosmos raised the possibility that if you traveled downward
into an electron, you might find that it contained a universe of its
own...

"Within it, organized into the local equivalent of galaxies and smaller
stuctures which are themselves universes at the next level and so on forever --
an infinite downward regression, universes within universes, endlessly.
And upward as well."

This statement nicely articulates a sentiment I've had for a very long time but haven't been able to express. I've often wondered about the scriptural phrase, "no beginning and no end". I think it's a pretty difficult concept for our mortal minds to understand. No beginning? How is that possible? Everything has a begining... doesn't it?

The closest I've come to understanding the concept of "no beginning" is to consider a simple illustration. (Keep in mind that every example I can come up with applies the abstract concept to some concrete thing, i.e. space or time...)

Imagine cutting a standard piece of 8.5" X 11" paper in half; now, discard one of the halves and cut the remaining half into half again. Discard one of the halves and cut the remaining half in half again. Repeat this process infinitely. You may think that eventually you are left with nothing... but this can never be. By definition you are only ever cutting the paper in half, and therefore you will always have half of what you had previous to the cut. Always! Theoretically, the cutting never stops because you're always left with one half of what you started with.

Obviously this illustration breaks down when considered practically, i.e., we don't have tools to cut paper in half infinitely -- eventually the paper becomes too small to handle properly. But consider the example with respect to the concept of no beginning and no end. It is conceptually possible to spend the rest of eternity cutting a single 8.5" X 11" in half. No end.

Now I admit this next part requires a bit of a mental leap, but I haven't been able to verbalize it any other way yet. Compare the paper cutting example above to tracing back to the beginning of the piece of paper -- not the day the paper came out of the mill, but rather the root of the paper ie: the exact point at which the paper ceases to occupy space, and instead there is a void. By cutting the paper in half in an attempt to get to this beginning... you will never get there, there will always be some infinitley small portion of the paper left. Effectively, there is no beginning. (I know, I know... it still needs some work -- but it make complete sense in my mind.)

Now another example.

Imaging that after cutting the paper into some ridiculously small halves, say 1 X 10^-100 millimeters squared you were magically able to shrink yourself small enough such that the dimensions of the piece of paper were, in proportion your new miniscule size, 8.5" X 11". Keep this image in your mind... and gaze around you. Now look up into the space above you to the place where the enormous you once stood and consider how big you once were. It's basically unimaginable.

I think it's remarkable that 21st century astronomers look out into the heavens and see some very small fraction of the totality of space (if there is such a thing); similarly particle physicists stare into the most powerful electron microscopes mankind has ever devised, and observe only largest particles we know exist.

No beginning? No end? Definitely.