Yocto- to Yotta-

Years ago, when I was a young American engineering student, I was taught to believe that the metric system is some kinda filthy hippie Euro-commie anti-freedom plot. Sorta like water fluoridation, the JFK assassination, and Crocs.

One thing I always liked about the metric system (or technically SI, the Système International d'Unités) was its usage of prefixes to scale its base units up or down. The addition of a simple prefix can scale the base meter down to a millimeter or up to a kilometer.

I spell it as meter rather than metre because… well… America.

But prefixes have their limits, which is why God invented scientific notation. (Ok, scientific notation was probably developed by a person, but Google wouldn’t give me a name.) So what are the limits of the metric prefixes?

The smallest accepted metric prefix is yocto-, which is a scaling by 10-24. A yoctometer is a pretty small distance. It’s nine orders of magnitude smaller than a proton, and unless you’re a particle physicist, you probably don’t consider a proton to be huge.

On the other hand, a yoctometer is still a hundred billion times larger than the Planck length, the scale where a theory of quantum gravity becomes necessary. The SI system would need four more prefixes to get down to this scale.

And yes, “SI system” is as redundant as “PIN number” and “ATM machine”.

At the opposite end of the scale is the yotta- prefix, which is a scaling by 1024. Forget stars, galaxies, and galaxy clusters: a yottameter is about the radius of an entire supercluster of galaxies. That’s a whole yotta meters.

I apologize for that lame pun.

On the other hand, (how many other hands do I have, anyway?) the universe is very, very, very, very, very big. How big? Possibly infinite. I can’t think of anything bigger than that.

How about a distance that’s pretty big, but not infinite? If (among other assumptions) the universe is infinite, then by traveling far enough, you would eventually come upon a region of space identical to our own observable universe. This is similar to the Poincaré recurrence theorem, but for space rather than time.

So how far would you need to travel? 10^10^115 meters. There’s no metric prefix remotely close to this number: it dwarfs the number of grains of sands in all the beaches, and all the atoms in the entire observable universe. You won’t get there anytime soon.

And there you have it. Yocto and yotta: two prefixes that allow the humble meter to remain relevant from scales smaller than subatomic particles, to scales larger than galactic superclusters.


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