Small Medium at Large

That is the punch line to an old joke:

 A very petite clairvoyant escaped from prison. The newspaper headline said, “A small medium at large”.

For the second time you will read here my not so favorite of all human beliefs – anthropocentricism (“ánthrōpos, "human being"; and Ancient Greek: κέντρον , kéntron, "center") the belief that considers human beings to be the most significant entity of the universe and interprets or regards the world in terms of human values and experiences”. So everything must be reckoned from our points of view. And for that, when we look around us, something is either small or large and everything in between, in the purely human context. Human nature, such as it is, is naturally self-centered so that our everyday experiences are framed by the world we know. And what we know is limited by what we observe; then we ponder, we think and even conclude based on those limitations. Our ideas therefore of what is small and what is large and everything in between are confined within or restricted by those limitations.

This may not altogether be such a truly human deficiency if it were not the wellspring of hubris, condescension, self-adulation, vanity and arrogance, when we think large of our status or position and look down upon those of small stature or of insignificant rank in the social ladder.

If that might seem harsh of an indictment on the nature of man, it can also be this: there are little problems, sometimes too small we ignore them; and there are seemingly insurmountable challenges that we don’t bother to face. Little problems sometimes turn into big ones, often after it is too late to grapple with; huge challenges are not met because we don’t even try.

Circumspection aside, some very serious people spend their career or their entire adult lives looking into the very small and looking up to the incomprehensibly and insanely large. Since Antonie van Leeuwenhoek first laid eyes on the then unknown living microorganisms and when Galileo first glanced at Jupiter’s moons when he improved the telescope’s magnification, much of man’s perspective had been altered.  

Astronomers cannot help themselves as they marvel at the size of the universe while many of us merely shrug at how it is beyond our comprehension. Then we are told that everything in it is actually made up of very small stuff.  Here is the thing though. We really don’t know how truly large the universe is and how small are the really small, despite how much advances scientists have come to find out about either one.

What has all these got to do with anything?  To make us properly grounded to our place in this world, a different kind of perspective from what we’re typically used to must be called upon in order for us to appreciate what is far more profound than the ever so human idea of small, large and in between.

Let’s see about how large the universe is. Keep in mind this is just our vision of it based on what the most powerful Hubble Space Telescope can discern so far and what mathematics from cosmology can estimate: If our entire solar system (which would include the sun that is 1.3 million times larger than the earth) were the size of a grain of sand, the universe would be all the sand contained in all the shorelines around the world. And I think I am being conservative about that analogy.  Because we truly cannot know about what is beyond what is observable from where we are.  This brings us to the idea of the infinite size of the universe. Mind boggling, perhaps, but someone had a clever idea on how to deal with that.

A German mathematician, David Hilbert, in his famous 1924 lecture, “Über das Unendliche", which roughly translates into, “on [the idea of] infinity”, proposed a thought experiment that deals with the paradox of The Grand Hotel with an infinite number of rooms. Suppose all the rooms were occupied, will the hotel still be able to accept one more guest?  This is how Hilbert solved it, “Suppose a new guest arrives and wishes to be accommodated in the hotel. We can (simultaneously) move the guest currently in room 1 to room 2, the guest currently in room 2 to room 3, and so on, moving every guest from his current room n to room n+1. After this, room 1 is empty and the new guest can be moved into that room. By repeating this procedure, it is possible to make room for any finite number of new guests”.

We remember the silly argument kids do when trying to one up another: “whatever number you can think of my number is one over that”… which is essentially how youngsters deal with what is infinite; n + 1 +1 + … to forever, is one version of infinity – no matter how large a number one can think of, it will only be a small part of infinity.

In other words the human mind has a way to deal with the idea of the insanely large without having to confront what the concept of how huge exactly is infinity.  Or, are we just fooling ourselves? Well, we must know that there is no point in trying to make sense of what could very well be beyond any of our limited natural or physical senses.  Just as we cannot discern what our limited sense of smell cannot detect, although our friendly blood hound does not only smell a hamburger, it can actually breakdown everything that’s in it and even track it down if the meat were in a bun wrapped in a foil and then dragged from one location to another; a day later.

So, if we cannot tell how infinitely large anything is, how do we know what everything is that’s in between?  Wait, we haven’t dealt with how small is small, yet.  It is actually very interesting because small is something we can hold up close; study intently on a work table or under a microscope.  Well, it is just as challenging as finding out about how large the universe is.

When first our ancestors thought a grain of sand, then a speck of dust, was the smallest particle there was, an early Greek philosopher, Leucippus of Miletus and his student Democritus of Abdera in the 5th century B.C. came up with the idea that all matter was made up of indivisible particles called atoms (atomos was Greek for indivisible). A little later after about 2,300 years since, more enlightened folks discovered that the indivisible atom was composed of a nucleus, with one or more electrons circling it. Then much later on, even cleverer individuals realized that much of what is in an atom was empty space.  This calls for another analogy. If the nucleus were the size of a basketball, the electron was the size of a ping-pong ball, orbiting it at a distance at roof top level of the Houston Astrodome in Texas. The implication is that no matter how solid an object is it has lots of empty spaces in it.  That is good in a very big way, because that’s how X-rays make it through our body to reveal a fractured bone or a decayed tooth, and a host of other unseen issues within. Defective welding joints in steel structures, etc. are detected in a similar manner, thus preventing disastrous failures that in some cases save lives.

Presently, the electron is now a huge particle because it is still made up of even smaller stuff.  But first, let me mention that around us, from somewhere in outer space, are “ghostly” particles called neutrinos.  The sun makes lots of them, exploding stars from billions of miles away expel them, and they come showering down on us from all directions, passing our entire bodies from head to toes, or from our toes through our heads, without interacting with a single atom of any part of any organ. Actually, neutrinos will hit China, go through from there and come out the opposite side in a straight line, without stopping, go through your body, and out it goes towards outer space. And in one square centimeter of your body, 65 billion of them pass through every second. Throughout your life a trillion trillions of them will have passed through your body. (I’ve always wanted to say, “a trillion trillions”, just to one-up the late astronomer Carl Sagan, who made famous the phrase, “billions and billions” in his famed TV show, “Cosmos”). However, all trillion trillions of them, if compacted, would be the size of an average mole. That is how small they are.  But there are particles smaller than them.

How in the world do scientists find these smaller than small stuff?  Here is an analogy they love to use. To find out what cars are made of, two superfast racing cars are accelerated to their maximum speed from opposite directions of the race track for a head on collision (let’s assume they were driven remotely, so we don’t have to worry about the drivers). All that will be left are smithereens of car parts. From the parts one may conclude what the cars were made of.  So, physicists do the same thing with accelerating heavy particle beams from opposite sides of the Large Hadron Collider until some of them collide head on. High speed cameras capture the smithereens that result from the collisions.  Cameras had to be used because the smithereens will decay quickly (as in microseconds) into some other stable stuff.  From the pictures they can tell what makes up the basic component of matter.  They do indeed have a short glossary of what they are: six quarks and bosons, etc.  Now, is a quark made up of something even more basic or smaller?  We don’t know that.  Will we actually find out someday that matter is after all made up of even more “ghostly” particles and we’ll ultimately call them “spirit” particles?

So, we can potentially have infinitely small stuff and infinitely huge stuff, so that everything that is in between could still be beyond our limited comprehension.  And we must still deal with what is infinitely forever versus the infinitely short period of time.  Max Planck some time ago thought of very short units of time.  So short that there are more Planck units of time in one second than there are seconds in the entire age of the universe that today is estimated at 13.7 billion years.

Your head has not exploded since you did make it to this point. Well, I hope you now have a slightly modified view of what is small, medium and large.