The smallest and the largest

In 1968, designers Charles and Ray Eames released a short film called “Powers of Ten.”  Here it is:

Here’s a tribute to the film that appeared as xkcd #271:

There’s something I occasionally wonder about.  People sometimes say that hearing about the scale of the universe at its largest makes them feel small and unimportant.  On that scale, the earth figures as a minuscule portion of a solar system that is itself a minuscule portion of a galaxy that is in turn a minuscule portion of one of countless clusters of galaxies in the universe.  When I hear that remark, I think about the scale of the universe at its smallest.  Tiny as our world is in comparison with the deepest reaches of the sky, how large do we bulk in comparison with the smallest units of the submicroscopic world?

This flash animation from Cary and Michael Huang, released a couple of days ago as a followup to a similar project they put out in 2010, takes us from the Planck length, which is evidently the smallest size a thing can be, up to what theorists currently suspect is the total size of the universe, which extends at least 7000 times as far as we will ever be able to see.  The latest theories hold that the total size of the universe might be about 1.6 times 10 to the 27th power meters.  That theory may be as mistaken as all the previous theories about the same thing have been, but it’s the best we have going at the moment.   So, if that theory is correct and you were to lay humans end to end, the number of them you would need to stretch from one end of the universe to the other would be 28 digits long.  The Huang brothers note in their animation that the total height of all living humans is much shorter than that, of course; in fact, if we were all to lie down end to end we would only reach about 1o million kilometers, only about 1/15 of the way from the earth to the sun.  Even if all 100,000,000,000 humans who ever lived were to be reincarnated and join us, we would still reach less than 15 billion kilometers, which would barely get us from one side of the Solar System’s Kuiper Belt to the other.

So, compared to the largest scale of structure in the universe, we are indeed quite small.  But let’s take a moment and look at the smallest scale of things in the universe.  The Eameses stopped their exploration at the level of the proton.  In 1968, there wasn’t much point in trying to delve deeper.  Since then, science has made advances.  The Planck length is 1.6 times ten to the minus 35th power meters; so, if you laid the shortest possible objects end to end, the number of them it would take to stretch from one end of your body to the other would be 36 digits long. A 36 digit number is of course bigger than a 28 digit number, vastly bigger.  So our size is much closer to that of the entire universe than it is to that of an object that exists on the scale of the Planck length.  The 2010 version of the Huangs’ flash animation illustrated this dramatically, with a human symbol standing well to the right of the center of the zoom bar. If contemplating the scope of the universe as a whole makes us feel small and insignificant, does contemplation of the Planck length make us feel large and mighty?

Perhaps it does.  If it doesn’t, I can think of two possible reasons.  First, it might be that the feature of astronomy that gives people the feeling of smallness and weakness is not the size of the structures astronomers study, but the fact that those people don’t understand what astronomers are talking about and don’t feel confident in their ability to figure it out.  That sense of smallness is not likely to be relieved when the conversation turns from light-years and dark energy to yoctometers and the quantum foam.

Second, it might be the legacy of monotheism.  When we visualize the universe on the largest scale, we imagine ourselves to be standing outside it, taking it in at a glance.  To minds formed under the influence of a belief in an all-powerful, all-knowing, ever-present Creator God, such a visualization is clearly an imitation of God.  In such an imagination, it shows an awesome power to zoom in and find individual humans, to number the hairs on their heads (between 50,000 and 200,000, according to the Huang brothers) and keep an eye on the sparrow.  On the other hand, to look up from the level of the Planck length may not suggest much to such a mind.  It’s true that medieval theologians like Albertus Magnus and Thomas Aquinas developed ideas about angels as one-dimensional beings who had the power to assume visible form as the situation required; to those titans of Scholasticism, the idea of two-dimensional strings vibrating at the smallest levels of scale in the universe and forming the basis of the physical world might have been extremely interesting.  Still, to the extent that people think about angels today, it’s in terms that neither Albertus nor Thomas would have recognized as rational, or even as Christian.  Aside from a few eccentric philosophers like Massimo Cacciari and the late Mortimer Adler who maintain an interest in the Scholastic conception of angels, the only people who bring them up nowadays seem to be those who believe that the souls of holy people become angels.  For the Scholastics, this would have been rank heresy.  They believed that angels represented an order of creation separate from humans, who may operate within time and space on occasion, but who are not generally subject to the passage of time or extended in three-dimensional space.  Humans, they held, were destined either to be resurrected in perfected bodies, as Jesus had been, or to be cast into Hell.  In either case, we would continue to be three-dimensional beings of something about a meter and a half in height.  I can’t see what motive believers in the Hollywood-derived conception of the afterlife would have for attaching any special significance to a view of the universe that looks up from the smallest scale, and indeed they do not seem to be excited about the submicroscopic world.

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