Skin Deep

I’m always impressed with the ingenuity scientists display when coming up with names for natural phenomena.  When introduced to the public, abstract mathematical concepts are presented with extremely evocative, almost emotional names that manage to cut to the heart of the math: black hole, big bang, the special theory of relativity.

Okay, so not always.  But enough of the time that it’s impressive — a way to directly connect science to intuition.  One of my favorite examples is a phenomena in electromagnetism called the skin effect, which describes how alternating current is carried in wires.  The skin effect is particularly interesting to me because it’s also a pretty direct analogy for a lot of the interactions I have with casual acquaintances.  I don’t think it’s often that the fields of social science and, well, science science intersect so perfectly — not only on a nomenclature and imagery level, but in the behaviors they describe.  I’ll start, as always, with physics.

The skin effect occurs all around us.  (It is notably distinct from the article in this month’s Cosmo with the same title.)  When electric wires carry alternating current — i.e. the stuff that comes out of the wall and/or one half of a legendary Australian rock band — most of the current never actually penetrates all the way through to the center of the wire, instead skirting along on the surface, creating a kind of electric sheath or skin along the wire.  This is a big break from the orthodoxy of how electromagnetism is usually taught in school, where it’s a common analogy to think of electricity racing along wires like water flowing though pipes.  While true for direct current (DC), this breaks down with AC — you’ll never see a water pipe with a hollow center and water rushing along the edges.

The difference mostly comes from the key distinction between AC and DC current, and is what makes AC so devilish to work with without an assload of math behind it.  Alternating current is called “alternating” because it switches back and forth, constantly, from positive voltages to negative voltages.  It rolls in and out of your wall like the tides at the beach, pushing electrons in and then dragging them back out to sea.  This inexorable changing of the electronic tides creates magnetic fields that similarly expand and collapse as the voltage changes, but these magnetic fields are always strongest in the center of the wire.  If you want to go back to the water analogy, magnetism here acts like a rock in the stream, pushing the flow of electrons around it and forcing the electricity to hug the banks of the stream, so that the vast majority of the current is carried along the outer skin of the wire.

I’ve always thought that the beauty of electricity and magnetism are their complexity: changing currents cause changing magnetic fields, changing magnetic fields cause changing currents, and the process constantly ebbs and flows in harmony, a symphony of the invisible as fields burst into life then dissipate into void, over and over and over again.

But that has nothing to do with friendship — and, in fact, I think if you start spouting that stuff at parties you may find yourself with a lot fewer friends by the end of the night.  So back to the main point here: the AC current carried in a wire — whether a transmission cable along the side of the road or the extension cord in your garage — only penetrates a fraction of the way into the wire.  This is called skin depth, designated δ.  Formally, skin depth is the depth into a conductor where the current carried falls to 1/e, or about 37%, of its value at the surface.  For AC frequencies in the realm of everyday experience — think the 60Hz that goes into your iPhone charger — skin depth is a function only of the material the wire is made from and the frequency of the current:

skin depth

Here ρ is the resistivity of the wire, f is the frequency of the current flowing through it, and the μs are something called magnetic permeability, which is a measure of how susceptible a material is to magnetic fields.  Something like iron, which can be made into a magnet, has a very high permeability; the permeability for wood or glass is very low.

For a current coming out of the wall and into copper wire, the skin depth is:

Screen Shot 2016-03-13 at 3.01.15 PM

For your phone charger, this means nothing — the wire is way smaller than 17mm in diameter.  But imagine the transmission lines used to send electricity from the power plant to your house: those cables that hang from wooden poles along the side of the road are much bigger, and that means when it comes to electricity they’re essentially hollow.  All of the power is running along the skin, never reaching the heart of the cable.

As the frequency of the current, f, gets bigger and bigger, the skin depth shrinks — as the electricity switches back and forth from positive to negative voltages faster and faster, the current penetrates into the wire less and less.  AC current switching at 150,000Hz penetrates into copper wire just 170 microns, or about the diameter of a human hair.  It will never see the copper’s core.

This is where my social circle enters the equation.  I have — and I assume you have, too — a lot of what I call skin effect friends.  (Though admittedly, I’m probably the only one of us who calls them that.)  These are the people that I’ve met casually and who circle the nucleus of my close friends in fast but erratic orbits.  They show up across the room at parties; I see them walking down the street in San Francisco.  Maybe I remember their names, maybe I don’t.  I usually don’t have their phone numbers or know their email addresses.  But every time we see each other, these skin effect friends and me, we say hello, because the world is a big and scary and sometimes lonely place, and finding a familiar face in an unexpected setting is a beautiful thing.

Yet when I talk to these people, I never actually have a conversation with them.  We only ever hit the topics that are skin-deep: how are you, where’re you living, how’s work these days.  And it seems that the more frequently I see them, the shallower the topics become, just like current skirting around the outside of a wire.  We never get to the heart of anything.

This isn’t a critique or a complaint — I can’t be best friends with everyone, and I’m misanthropic enough to not want to try.  I enjoy having a wide circle of acquaintances, and I enjoy these skin-deep conversations because they show me the surface of worlds I don’t inhabit.  I wish I could dive into those worlds, wish I could be deeply connected to everyone I’ve ever met, but just like a wire, there’s only so much current I can carry before I catch on fire / have a total psychotic breakdown.  So if you’re reading this and thinking to yourself wait a minute that bastard is talking about me, it’s not a bad thing.  Next time we run into each other, let’s grab a beer.  We’ll talk about sports.

And even though I like all these skin effect friends, they also make me acknowledge that those friends I have where our conversations do penetrate — those friends where, even if we don’t see each other very frequently, we can pick up right where we left off, or those friends who I feel like I really connect with — are something remarkable, almost physics-defying.  It’s DC friendship.

There’s a lot of discussion about a possible unified field theory in physics, but I’m happy stopping at a unified theory of physics and friendship.  Einstein, eat your heart out.