Posts Tagged ‘Earth’

Fucking Geomagnetism, How Does That Work?

October 14, 2010

Here’s a tidbit from the lore of physics history. It’s from Einstein.

A wonder of such nature I experienced as a child of 4 or 5 years, when my father showed me a compass… I can still remember – or at least believe I can remember – that this experience made a deep and lasting impression upon me. Something deeply hidden had to be behind things.

Einstein’s scientific work led us directly to a deeper understanding of magnets (among other things). Specifically, his seminal paper on special relativity is about electromagnetism.

With the later addition of quantum mechanics, we now pretty much understand magnets. We know how they work, meaning that we know what the rules are for magnets, and roughly how to go from those basic rules to making levitating trains.

I learned some of those rules in college. The fundamentals don’t require relativity or quantum mechanics and are not abstruse. They’re just things like this: you run current through a wire. It deflects a compass needle. You set up another wire next to the first, with current running the same way. The wires attract each other. You make the currents run the opposite way. The wires repel. This is all fairly simple. It really works, and it’s been known for 200 years.

Shortly after Facebook introduced its “Questions” app, someone asked, “Fucking magnets, how do they work?”. Innocently, I thought it was someone who wanted an answer, but not a very serious one, so I replied,

Some magnets hate each other because their electrons are spinning the wrong way, and this makes them very, very angry. They repel. On the other hand if you turn one around the electrons are spinning the opposite way and then they get along fine and attract.

Which is wrong for a few reasons. One is the anthropomorphizing; another is treating quantum mechanical “spin” as colloquial “spinning”, third is that it doesn’t really explain much, and fourth is that the person wasn’t asking a question, but quoting an internet meme I didn’t know about.

After I learned about the meme and the band, Insane Clown Posse, which created it, I didn’t think much more of it. Then yesterday, Sean at Cosmic Variance compared “Miracles” to a famous Whitman poem.

Whitman says, “When I heard the learn’d astronomer; … How soon, unaccountable, I became tired and sick;”. ICP says, “And I don’t wanna talk to a scientist / Y’all motherfuckers lying, and getting me pissed.” Juxtaposed, the sentiments sound similar (and even form a slant rhyme), but there’s a major difference of intention. Whitman is speaking about disillusionment with scientific thinking – the familiar sentiment that mathematical or scientific explanations kill the beauty of what they describe. ICP’s objection is not directly to science, but to scientists themselves, as a group. Whitman’s objection is essentially intellectual, ICP’s essentially cultural.

Whitman was much less likely to object to Y’All Motherfucker Scientists because science wasn’t yet a firm American establishment in 1855. There was certainly a culture of science, but there were not that many scientists, and Science, as a group of people representing a certain general worldview, was not prominent.

Today there is a huge culture of science, and most of the reaction I’ve read to “Miracles” is defensive; people identify with that culture and view “Miracles” as an affront to what they believe and value. They want to get in a room with ICP and tell them that, for example, their attitude is perverse, it’s hypocritical to impugn science while taking advantage of the benefits of scientific research, and there’s a perfectly good explanation for magnets that only adds to their wonder and beauty.

I’ve allowed this essay to wander slightly off course. I’d like to bring it back to compasses. I’m not a scientist but I do like to party with them. I remember one time I had just met a bunch of geology grad students, and I wanted to know how compasses work, so I asked them.

The problem here is that the more I learned about electricity and magnetism, the less sense the Earth’s magnetic field made to me. As a kid, I knew the basic story about where it comes from, exemplified by an article on the popular website How Stuff Works:

The “big bar magnet buried in the core” analogy works to explain why the Earth has a magnetic field, but obviously that is not what is really happening. So what is really happening?

No one knows for sure, but there is a working theory currently making the rounds. As seen on the above, the Earth’s core is thought to consist largely of molten iron (red). But at the very core, the pressure is so great that this superhot iron crystallizes into a solid. Convection caused by heat radiating from the core, along with the rotation of the Earth, causes the liquid iron to move in a rotational pattern. It is believed that these rotational forces in the liquid iron layer lead to weak magnetic forces around the axis of spin.

It kind of makes sense. Why does Earth have a magnetic field? Because there’s convection of molten iron in it. Why does convection of iron create a magnetic field? Because iron is magnet stuff. You know, like, when you want to make an electromagnet you need some iron, or you can trace out the field lines of a bar magnet with iron filings. It’s just… um.. iron! magnets! boom!

This is pretty much the answer I’ve gotten most times when I ask someone about Earth’s magnetic field. But it’s a pretty bad candidate for the next “rainbows are made by refracting and reflecting light in spherical raindrops” (which is pretty accurate). What I learned from physics was that if you make things hotter, they’ll lose their magnetic properties (magnetized iron has aligned domains, and hence lower entropy). The molten iron is obviously very hot and not very magnetic. And even so, just moving normal iron around doesn’t create a magnet anyway. If I take an iron crowbar and start waving it around like a madman, it doesn’t give me the powers of Magneto. It does attract things like police officers with tasers, but not by magnetism.

A few times, earlier on when the topic of geomagnetism came up, I got the feeling that no one was willing to acknowledge that the Cartoon Guide to Geomagnetism made no sense. I further felt like no one was acknowledging it because no one realized it. They had bought into Science hook line and sinker, forgetting about science, which holds that you should keep good track of how little you actually know about things.

My conversation with the geology grad students at that party went better than previous conversations. They were better informed, and more willing to admit that it’s a hella-complicated problem involving magnetohydrodynamics, and basically said it wasn’t their specialty and they didn’t know. That was more satisfying to me.

It’s not satisfying enough though, so reading Sean’s essay and being reminded of the fucking mysterious magnets, my internal compass brought me back to wondering about geomagnetism. I’ve spent the last day or so looking for a decent explanation of the origin of the Earth’s magnetic field. Here is the simplest, most direct answer I found in that time that meets the criterion of not sounding like an uncomfortable circumlocution, a lie, or the insane rambling of a misinformed member of the science posse.

Am. J. Phys. 69 5 , May 2001

That actually makes sense to me. I know what those equations mean, and I know where they come from (pretty much. Nobody’s perfect). I know basically what numerically solving means, too. It means that it’s all very complicated and you shouldn’t wrack your brain trying to understand it, because you won’t.

When I hear ignoramuses profess a love of ignorance, it’s probably either insincere or incorrigible. But when I hear scientists or science appreciators declaiming that science can only ever make our picture grander, only makes the night sky more beautiful, and then also hear the same people expounding scientific doctrines they don’t understand, I can only believe that their avowal of the beauty of science is, like their stories about how things work, a regurgitated ideology.

I don’t feel childish wonder when confronted with mysteries. I don’t feel naive awe. I don’t feel sophisticated, informed appreciation. I feel an intense desire to understand better – to be a little less stupid about the thing.

I’d like there to be a better story about compasses. I realize I don’t understand them well enough to write a good story. It might not even be possible to write a really good story. But I think I at least understand it a little better than I did before.

So maybe I will write a story. I want there to be a story that’s bad, but at least a little less bad than the one I heard over and over. Based on what I read so far, the knowledge about this phenomenon is impressive, though incomplete. But experience tells me that what’s been discovered is not broadly known.

There are a lot of basic things about geomagnetism I don’t understand, like why the convection currents should be planet-sized, or why solutions should exist that persist for thousands of years with very little change, or why the strength of the field is a Gauss to order of magnitude. I’m not even sure why the field aligns roughly with the axis of rotation. If there were a totally new geomagnetic theory ten years from now, I probably wouldn’t have too hard a time letting go of the old one. I want to learn the stuff I’m missing and fill in as much as I can. There are thousands of things I want to learn, though, and there won’t be time for them all. So for now, even though it’s incomplete and inaccurate and confusing and sloppy, here’s a story.

The Earth’s magnetic field is generated by the complex interplay of the motion of molten metal in its interior, the motion of electric charges through that metal, and the dynamic electromagnetic fields that affect those motions. The inside of the Earth is hot, melting the metals that constitute it. The very center core is solid due to the high pressure there, despite its intense heat. The solid core and the temperature gradient from the deep interior of Earth to its crust combine to create hydrodynamic forces that push on the molten metals. It turns out that metals respond by moving in huge, continent-to-planet scale loops. The metals are too hot to be magnetized, but they do have electrical conductivity. That means that if we did, for some reason, have a dynamic magnetic field in the Earth, it would induce electromagnetic current in these metals. Once the metals have electromagnetic current, the posited magnetic field exerts forces on them, influencing their motion. Further, since the metals are carrying current while being pushed around by heat gradients and things, they go on to create their own complicated magnetic fields. The magnetic fields they generate then feed back to change the forces on the currents, etc. In this way the originally hypothetical dynamic magnetic field becomes a plausible alternative, needing only a small seed field to grow into some approximately-steady-state field like the one we observe. The result is a huge, complicated mess. Because of that, it could conceivably do absolutely wild things, like completely change directions every few score millenia, or get stronger or weaker, or wind and curl in strange loops, or even go out.


Random Spots on Earth

July 25, 2009

Don’t know where to take your next vacation?

Here’s some python code to generate a bunch of random locations on Earth. Copy and paste into python, run, then copy and paste a location into Wolfram Alpha or Google Maps. Google Maps has pictures, but is slower. Wolfram Alpha will tell you the country, and then you can click on a link to Google Maps (the link is just called “satellite image”) if it’s someplace interesting. Or, try guessing where the location is before you plug it in.

WordPress doesn’t allow javascript, so I can’t easily generate the locations for you or embed the Wolfram Alpha search bar. Too bad.

About generating random locations:
The longitude is easy, since you just pick a random number between -180 and 180 degrees.

Latitude is not so straightforward. If you draw a thin band (one mile wide, say) around the line of latitude at 60 degrees North, that band is only half as large as one around the equator, since it’s a shorter way around the globe up at 60 degrees. The size of the band at a certain latitude, relative to one at the equator, is the cosine of the latitude.

To get a random location on Earth (all locations being equally likely) we choose a random number from zero to one, and say that this is the percentage of land that lies south of our chosen location. The percentage of land south of a line of latitude \theta is
\frac{1}{2}\int_{-90}^\theta \cos\theta' d\theta' = \frac{1}{2} (1 + \sin\theta).

That’s equal to some random number r, so we need to solve for \theta.
\theta = \arcsin(2r-1).

The code accomplishes the same thing in a slightly more convoluted way, because I originally solved it thinking of the north pole as zero radians (as we do in math) rather than 90 degrees (as we do in geography). Okay, here’s the code

import random
import math

for i in range(1,100):
        long = random.random()*360 - 180
        lat = math.acos(1-2*random.random())*180/3.14159-90
            ew = "E"
            long = -long
            ns = "N"
            ns = "S"
            lat = -lat

        print "%.2f %s , %.2f %s" % (long,ew,lat,ns)