Cows are dipoles

A recent study of Google Earth images revealed a preferential spatial alignment for grazing and resting cattle. In a survey of over 8000 cows in about 300 pastures, the study found conclusive evidence of a significant deviation from random orientation with preference for a magnetic North-South direction. They were able to use global differences in positions to rule out the effects of wind and sun, and show a statistical correlation which favored magnetic north over geographic north as a predictor of cattle pointing direction. In other words, cows are dipoles. But they’re not the only ones. Deer show an even stronger alignment with the magnetic poles. Look at this diagram from the original paper:

A is cattle, B is roe deer, C is red deer.

That’s a great looking distribution in the middle. I wish they’d clean it up and fit to it. I expect to see a follow-up study calculating the effective magnetic dipole moment of the cow.

The theory. If you’ve ever played with two bar magnets you know there is an orientation to the magnetic attraction between them. Indeed, the magnetic field is a vector field and dipoles tend to line up along its field lines. The needle of a compass for example is a magnetic dipole. If allowed to spin freely, it will point toward magnetic north/south. A dipole in a magnetic field feels a torque which is proportional to the strength of the field and the magnetic moment of the dipole.

T is the torque, u is the magnetic moment, B is the external magnetic field (of the earth, in this case).

This torque will tend to spin it in the direction of the magnetic field line. Viewed another way, the energy of a dipole in an external magnetic field is:

The natural inclination of a system is to move from a higher energy state to a lower energy state. The lowest energy in this case is represented by the case where u and B are aligned (theta = 0), therefore their dot product is maximized, and the energy is most negative.

Now, cows are lazy, and they undergo some kind of random motion, so naturally there will be a width to the distribution of the probability that a cow will be pointing in a given direction. Now, if this random motion is associated purely with thermal energy, the pointing probability could be calculated exactly. My guess is that it’s more complicated than that. If I come up with a good way to model it, I’ll probably publish the follow-up paper.

An interesting side note is that many animals have already been well-documented to have internal magnetic sensors. Birds and salmon have been known to use magnetic field lines to navigate their migration. Apparently, even rodents possess some kind of internal magnetic compass. What they need it for is beyond me. Interestingly, some studies suggest humans who sleep oriented East-West experience shorter REM sleep periods than humans who sleep oriented North-South. REM sleep is apparently important for memory, alertness, creativity, and every other good thing our brain does. There’s something, after all, to be said for feng-shuing your room.

From randomness, order. (personal blog update)

My life has been evolving slowly to become more and more structured and less and less what I feel like I really ought to be doing. In addition I’ve experienced a noticeable decrease in REM sleep lately as my days and nights have really filled themselves up. This is only adding to my sense of confusion.

Mondays and Fridays I teach at the UC. Mondays are discussion sections and Fridays are labs. I’ve been doing this for 3 weeks now and it hasn’t gotten any easier carrying 50 lab notebooks across Science Hill.

Tuesdays and Thursdays I tutor middle and high school students in Aptos. This last Thursday one of my duties was to help a 7th grader finish his auto-biographical slideshow presentation. His accomplishments included being the last to be cut from the basketball team and almost making the honor roll in the 5th grade. His goals were one day be richer than Bill Gates.

Wednesdays I head up to Stanford to report on the meager progress I’ve made that week in my research. This wednesday I bring up the issue of funding for probably the last time.

Yesterday I helped bartend at a frat party. Someone stole a handle of vodka and a $1.50 jug of safeway brand orange juice. A vinyl record was pilfered from the DJs. Party was eventually broken up by the police around 11:30. Pretty classy stuff. I’ve been thinking about getting a job in sustainable energy and bartending on the side.

In other news I bought a used 2000 Volkswaggen Passat with a V6 engine and a moon roof. I’m going to use it to learn how to drive stick. Also, I’ll probably use it to get around.

And move.

I don’t know where I’m going to move to come spring but I will move somewhere.


9 thoughts on “Cows are dipoles

  1. Chris says:

    Now I remember where I heard about this “cows are dipoles” study! It was brought up when we were playing with those magnetic balls:

    Can you imagine a giant icosahedron made of cows?

    Also, interesting point about the “thermal energy” of the cows. You could probably estimate the reduced distribution function F(\theta) using Maxwell-Boltzmann:

    f(v,\theta) \propto \exp[-E/kT]


    E = (1/2)mv^2 – \mu B \cos\theta

    and T is some “temperature” associated with the cow population. I wonder what a typical temperature for a collection of grazing cows would be. Their velocities are so low, but their mass is so large..

    Anyway then you just want

    F(\theta) = \int_{-\infty}^{+\infty} f(v,\theta) dv

    or something.

    I guess I’m ignoring rotational degrees of freedom… and I guess the “spherical cow” joke/approximation doesn’t apply if they’re dipoles. But, like, whatever. Phucket, halibut.

  2. Anonymous says:

    move? again? you’re crazy.

  3. Anonymous says:

    Hey Lulu, how do you think of Stanford for the time you’re there? I’m applying this year to Stanford and MIT. and I probably know more about MIT than any other schools since I’ve been following the blogs. 😛 How would you compare Stanford to MIT?

  4. I wanted to try sleeping north-south but it’s topologically impossible to move my bed as such without ruining my feng-shui.

  5. Speaker-to-Animals says:

    This article was really interesting, right up to the whole section “From randomness, order,” which was completely irrelevant to the rest of the article. I’m guessing the vast majority of us were no more interested in it than the details of what you had for breakfast; why include it?

    • Lulu says:

      Hi, this is my personal blog, where I practice science writing and creative writing and keep a small writing portfolio. Thanks for your interest, I didn’t think anyone except my friends (and me) would be reading this.

  6. Anon says:

    Is it true that the Passat’s moon roof can only be used at night? I read this on a blog somewhere.

    Also is it true that Federico is a Boss? I also read this on an Internet blog. And that Woolf is becoming more and more like him every day. Please advise.

  7. CW says:

    Rarely ever does damnation imply temptation.

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