Scale

Understanding relative sizes is mind-boggling. Here are two internet resources to help you understand how maddeningly large the ‘known’ universe is compared to us, and how maddeningly large we are compared to the planck constant (for example). The first is a video from the late 1970s. The second is a neat flash website from this year. Finally, I’ll quote a short article by Jim Holt from the now defunct magazine Lingua Franca, about how large we are compared to the biggest and smallest thing in the universe, and how far along we are compared to the shortest and longest known lengths of time.

Scale of the Universe (click on image to go to the website)

Some highlights from that website (from largest to smallest):
– Sloan Great Wall – the largest known object in the universe
– The Great Attractor – something MASSIVE that’s pulling our galaxy into it
– Andromeda Galaxy – our twin, which we’ll smash into in a few billion years
– VY Canis Majoris – largest known sun
– Angel Falls – largest waterfall in the world (in Venezuela)
– Porcine circovirus – smallest virus
– Neutrino

Finally, here’s the Lingua Franca article by Jim Holt:

Is life absurd? Many people believe so, and the reasons they give often have to do with space and time. Compared with the vast universe, we are but infinitesimal specks, they say, and the human life span constitutes the merest blip on the cosmic timescale.

Others fail to see how our spatiotemporal dimensions alone could make life absurd. The philosopher Thomas Nagel, for one, has argued that if life is absurd given our present size and longevity, it would be no less absurd if we lived for millions of years or if we were big enough to fill the cosmos.

The issue of life’s absurdity is moot, I suppose, but there is an interesting question lurking in the background: Which, from the point of view of the universe, is more contemptible–our minuteness or our brevity? Cosmically speaking, do we last a long time for our size or a short time? Or, put the other way, are we big or small for our life span?

The best way to go about answering this question is to look for a fundamental unit of space and of time that would render the two dimensions comparable. Here is where contemporary physics comes in handy. In trying to blend the theories that describe the very large (Einstein’s general relativity) and the very small (quantum mechanics), physicists have found that neither space nor time is continuous on the tiniest scales. Each appears to be made up of discrete units–geometric atoms, as it were. The shortest length that has any meaning is the Planck length, which is about 10-35 meters. The shortest possible tick of an imaginary clock (sometimes called a “chronon”) is the Planck time, about 10-43 seconds. (This is the time it takes light to cross a distance equal to the Planck length.)

image Now, suppose we construct two cosmic scales, one for size and one for longevity. The size scale will extend from the smallest possible size, the Planck length, to the largest possible size, the radius of the observable universe. The longevity scale will extend from the briefest possible life span, the Planck time, to the longest possible life span, the age of the universe.

Where do we rank on these two scales? On the cosmic size scale, humans, at a meter or two in length, are more or less in the middle. Roughly speaking, the observable universe dwarfs us the way we dwarf the Planck length. On the longevity scale, by contrast, we are very close to the top. The number of Planck times that make up a human lifetime is very, very much more than the number of human lifetimes that make up the age of the universe. “People talk about the ephemeral nature of existence,” the physicist Roger Penrose has commented, “but [on such a scale] it can be seen that we are not ephemeral at all–we live more or less as long as the Universe itself!”

Certainly, then, we humans have little reason to feel angst about our temporal finitude. Sub specie aeternitatis, we endure for an awfully long time. But our extreme puniness certainly gives us cause for cosmic embarrassment.

Or does it? In Voltaire’s philosophical tale Micromégas, a giant from the star Sirius visits the planet Earth, where, with the aid of a magnifying instrument, he eventually detects a ship full of humans in the Baltic Sea. He is at first amazed to discover that these “invisible insects,” created in the “abyss of the infinitely small,” seem to possess souls. Then he wonders whether their diminutiveness might not indeed be a mark of superiority. “O intelligent atoms,” he addresses them, “you must doubtless enjoy very pure pleasures on your globe, for having so little body and seeming to be all spirit, you must pass your lives in love and in thought, which is the true life of spirits.” In response, the microscopic humans begin spouting philosophical inanities from Aristotle, Descartes, and Aquinas, at which the giant is overcome with Homeric laughter.

Would we humans be less absurd if we were bigger? Probably not, but we would surely be less sound. Consider a sixty-foot-tall man. (The example comes from the biologist J.B.S. Haldane’s beautiful 1927 essay, “On Being the Right Size.”) This giant man would be not only ten times as high as an ordinary human but also ten times as wide and thick. His total weight would therefore be a thousand times greater. Unfortunately, the cross section of his bones would only be greater by a factor of a hundred, so every square inch of his bone structure would have to support ten times the weight borne by a square inch of human bone. But the human thighbone breaks under about ten times the human weight. Consequently, when the sixty-foot man takes a step, he breaks a thigh.

If we humans are, from the cosmic perspective, absurdly tiny for our life span, perhaps we can derive some consolation from our impressive complexity of form. That is what John Donne did in his Devotions Upon Emergent Occasions. “Man consists of more pieces, more parts, than the world,” he observed. “And if those pieces were extended and stretched out in man as they are in the world, man would be the giant and the world the dwarf.”

Advertisements

About dontdontoperate

28 year old originally from Barrie, Ontario, Canada. H.B.Sc. from UofT with a major in chemistry and a double minor in philosophy and math. M.Sc. from UofT in physiology and neuroscience. Finished my Ph.D. in biomedical engineering at McMaster in the fall of 2013.
This entry was posted in Mathematics, Philosophy, Science and tagged , , , , , , , , , , , , , . Bookmark the permalink.

One Response to Scale

  1. Kristina says:

    Nice call on the Eames video Alex! 🙂 Personally, I prefer the proposal film for Powers of Ten(http://www.youtube.com/watch?v=mmHa-meEOkE). It’s too bad they got rid of the original idea of the clock on the side of the screen, it was a great extra detail.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s