Skeptophilia (skep-to-fil-i-a) (n.) - the love of logical thought, skepticism, and thinking critically. Being an exploration of the applications of skeptical thinking to the world at large, with periodic excursions into linguistics, music, politics, cryptozoology, and why people keep seeing the face of Jesus on grilled cheese sandwiches.

Monday, August 5, 2024

A matter of scale

In Douglas Adams's brilliant book, The Hitchhiker's Guide to the Galaxy, a pair of alien races, the Vl'Hurg and the G'gugvuntt, spent millennia fighting each other mercilessly until they intercept a message from Earth that they misinterpret as being a threat.  They forthwith decide to set aside their grievances with each other, and team up for an attack on our planet in retaliation:
Eventually of course, after their Galaxy had been decimated over a few thousand years, it was realized that the whole thing had been a ghastly mistake, and so the two opposing battle fleets settled their few remaining differences in order to launch a joint attack on our own Galaxy...

For thousands more years the mighty ships tore across the empty wastes of space and finally dived screaming on to the first planet they came across -- which happened to be the Earth -- where due to a terrible miscalculation of scale the entire battle fleet was accidentally swallowed by a small dog.

I was reminded of the Vl'Hurg and G'gugvuntt while reading the (much more serious) book The View from the Center of the Universe, by physicist Joel Primack and author and polymath Nancy Abrams.  In it, they look at our current understanding of the basics of physics and cosmology, and how it intertwines with metaphysics and philosophy, in search of a new "foundational myth" that will help us to understand our place in the universe.

What brought up Adams's fictional tiny space warriors was one of the most interesting things in the Primack/Abrams book, which is the importance of scale.  There are about sixty orders of magnitude (powers of ten) between the smallest thing we can talk meaningfully about (the Planck length) and the largest (the size of the known universe), and we ourselves fall just about in the middle.  This is no coincidence, the authors say; much smaller life forms are unlikely to have to have the complexity to develop intelligence, and much larger ones would be limited by a variety of physical factors such as the problem that if you increase length in a linear fashion, mass increases as a cube.  (Double the length, the mass goes up by a factor of eight, for example.)  Galileo knew about this, and used it to explain why the shape of the leg bones of mice and elephants are different.  Give an animal the size of an elephant the relative leg diameter of a mouse, and it couldn't support its own weight.  (This is why you shouldn't get scared by all of the bad science fiction movies from the fifties with names like The Cockroach That Ate Newark.  The proportions of an insect wouldn't work if it were a meter long, much less twenty or thirty.)

Pic from the 1954 horror flick Them!

Put simply: scale matters.  Where it gets really interesting, though, is when you look at the fundamental forces of nature.  We don't have a quantum theory of gravity yet, but that hasn't held back technology from using the principles of quantum physics; on the scale of the very small, gravity is insignificant and can be effectively ignored in most circumstances.  Once again, we ourselves are right around the size where gravity starts to get really critical.  Drop an ant off a skyscraper, and it will be none the worse for wear.  A human, though?

And the bigger the object, the more important gravity becomes, and (relatively speaking) the less important the other forces are.  On Earth, mountains can only get so high before the forces of erosion start pulling them down, breaking the cohesive electromagnetic bonds within the rocks and halting further rise.  In environments with lower gravity, though, mountains can get a great deal bigger.  Olympus Mons, the largest volcano on Mars, is almost 22 kilometers high -- 2.5 times taller than Mount Everest.  The larger the object, the more intense the fight against gravity becomes.  The smoothest known objects in the universe are neutron stars, which have such immense gravity their topographic relief over the entire surface is on the order of a tenth of a millimeter.

Going the other direction, the relative magnitudes of the other forces increase.  A human scaled down to the size of a dust speck would be overwhelmed by electromagnetic forces -- for example, static electricity.  Consider how dust clings to your television screen.  These forces become much less important on a larger scale... whatever Gary Larson's The Far Side would have you believe:

Smaller still, and forces like the strong and weak nuclear forces -- the one that allows the particles in atomic nuclei to stick together, and the one that causes some forms of radioactive decay, respectively -- take over.  Trying to use brains that evolved to understand things on our scale (what we term "common sense") simply doesn't work on the scale of the very small or very large.

And a particularly fascinating bit, and something I'd never really considered, is how scale affects the properties of things.  Some properties are emergent; they result from the behavior and interactions of the parts.  A simple example is that water has three common forms, right?  Solid (ice), liquid, and gaseous (water vapor).  Those distinctions become completely meaningless on the scale of individual molecules.  One or two water molecules are not solid, liquid, or gaseous; those terms only acquire meaning on a much larger scale.

This is why it's so interesting to try to imagine what things would be like if you (to use Primack's and Abrams's metaphor) turned the zoom lens one way and then the other.  I first ran into this idea in high school, when we watched the mind-blowing short video Powers of Ten, which was filmed in 1968 (then touched up in 1977) but still impresses:


Anyhow, those are my thoughts about the concept of scale.  An explanation of why the Earth doesn't have to worry about either Vl'Hurgs and G'gugvuntts, enormous bugs, or static cling making your child stick to the ceiling.  A relief, really, because there's enough else to lose sleep over.  And given how quickly our common sense fails on unfamiliar scales, it's a good thing we have science to explain what's happening -- not to mention fueling our imaginations about what those scales might be like.

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