Crossing a Line

Guess what that yellow line is

 

When someone says to me, “You crossed a line!” (which you can only imagine how often that occurs in my life,) it generally means I have broken some social code or caused offense in a way that cannot be easily remedied. In this case, the line is a metaphoric line in the sand, and the sand is just as metaphoric as the line. In full disclosure, I did recently cross a line, but of a different sort.

There are many kinds of lines, metaphoric or actual. There are the aforementioned lines which bound social dictates. There are mathematical lines which stretch indefinitely in two directions. I suppose these are neither metaphoric, nor actual, but intellectual constructions, abstractions. You can’t really cross an abstraction, at least not concretely. There are picket lines, and those can be crossed! They aren’t truly lines, but groups of people with a metaphorical boundary, but we all know what it means to cross one. If you are wondering if that is what I crossed, no, I am not a scab.

But what about actual lines? There are a lot of these actual lines, though usually you can’t see them, and most of them are not really straight. They might seem locally straight, but they curve or bend. So here I need to expand my definition of a line to a one-dimensional curve in which corners and cusps are allowed, or to be mathematically precise, a shape which I can describe parametrically with only one real variable. (Many of you likely shudder at that last description, sorry, ignore it. You will know what I mean by a line.)

But even these actual lines I would separate into two categories: Lines that humans invented and lines that humans use to describe natural phenomena. This last category is, in my opinion, the coolest.

Let me explain what I mean. A month ago (and it feels like a lot longer ago than that,) Alrica and I visited Mount Sassafras Observation Tower. This is on the border of North Carolina and South Carolina. And we were able to stand with one foot in each state. Does it matter which state I am standing in? Well, I guess if Alrica had chosen that moment to murder me it might determine which set of state police had to solve the crime (Alrica is too smart to leave much evidence) and arrest the perpetrator. How would they decide that? Where the attack came from? Where the body fell? Where a larger proportion of the body fell?

My body (still alive) straddling the border

 

The border is one of these lines, the ones that humans invented. In fact, all borders are invented lines. We, as a people, have decided that this is where one set of property or governmental jurisdiction ends, and another begins. There is nothing in nature that describes a shift there, only in our minds. In a thousand years, those borders could be different. Think of the world a thousand years ago. Not too many borders have stayed the same.

Another example of these lines that are a product of our imagination is lines of longitude. Don’t misrepresent me. These are very useful lines and they make logical sense to encircle the Earth that way. But why is the Prime Meridian, the zero line, where it is? Because humans arbitrarily chose to put it there. Astronomers working out of an observatory in Greenwich, England set the line so it would go through their observatory. Had Muslim astronomers defined the zero line of longitude while math and science were flourishing in Arabia and Europe was in the Dark Ages, we might have Baghdad Mean Time.

At least the Prime Meridian is a semicircular arc! (I might say it was straight, but you and I both know that’s stretching the word straight.) If you want to see just how active the human imagination is, check out the International Date Line! Yeah, it is supposed to be the meridian directly opposite the Prime Meridian. But that would be so inconvenient for places that it cut through the middle of. It’s Friday at my house but Saturday at my workplace down the street. Do I have to go in today? To handle such inconvenience, we use our imagination once again. What the heck, don’t go round the bend getting bent out of shape if we bend over backwards to bend it like Beckham! (Though Beckham’s bending is of a very different bent than that of a meridian.)

What about lines of latitude? Some of these are more than just our imagination, they have astronomical reality.

Take, for example, the Arctic Circle (or the Antarctic Circle). The Earth revolves about an axis (another line which you can’t see but describes a real world phenomenon.) And the Earth orbits the sun in a plane we call the ecliptic. But our axis and the ecliptic are not perpendicular. The axis is tilted about 23.5° (from being perpendicular. It is tilted about 66.5° from being a line in the plane of the ecliptic.) The Arctic Circle is the line of latitude at 66.5° north (and the Antarctic Circle is at 66.5° south) corresponding to this tilt in the Earth’s axis. Beyond these circles, there will be some winter days without sun and some summer days where the sun never goes away. These two circles represent a physical reality.

The Tropics of Cancer and Capricorn do as well. These are the circles at 23.5° north (Cancer) and 23.5° south (Capricorn). They are the northernmost and southernmost latitudes where the sun could ever be directly overhead. And its all about that tilt!

There is a certain irony for me personally about these two circles. When we were in Namibia in December of 2015, we crossed the Tropic of Capricorn. I blogged about it then and you can check it out. You can even see pictures of my adorable children, much younger, at the Tropic of Capricorn with Alrica and me. But what’s the irony?

Even though I have lived most of my life in the northern hemisphere, I have stood upon the Tropic of Capricorn in the southern hemisphere, but never stood upon the Tropic of Cancer in my own home hemisphere. I’ve crossed it in airplanes and even on ships, but they don’t have signs you can stand next to midair or midwater. We were pretty close to it in Al Ain, UAE. But there is a limited list of when close counts, and I’ve never heard Tropic of Cancer included in that list.

Finally, there is the granddaddy of all the lines of latitude: the equator! (Granddaddy is also metaphoric. There is not biological descent among lines of latitude.) And that brings me to our recent trip to Mitad del Mundo! (Yes, it took me over 1,100 words to get to the story. But hopefully at least 315 of those words were interesting.)

Mitad del Mundo, which translates as Halfway Point of the World, is a destination of the equator, by the equator, and for the equator. (Apologies to Lincoln.) This is a real line (or circle really). It is the circle around the surface of the Earth that is equidistant to each pole. Here the days last twelve hours and the nights last twelve hours all year long.

Head in the Northern Hemisphere, Feet in the Southern Hemisphere

 

Friends, I have stood upon the equator! I have sat upon the equator! I have laid upon the equator! I have risked being pulled apart by Coriolis Effect forces to have part of me in one hemisphere and part of me in another. (That last sentence is only half true. I was in two hemispheres, but there is no risk of being torn apart by the Coriolis Effect.)

If you make it to Quito, I recommend this attraction highly. We came in the morning when it is a lot less busy. We visited the monument built on the equator. You get to go up in the elevator and walk around it, crossing hemispheres as you go. But there is a lot more there than just the monument and the line.

At one place, tables have been set up, each with a nail sticking up so that the nail is on the equator. You can try to balance an egg on the head of the nail. Alrica tried, no success. And it doesn’t make any sense to me why this would be easier or harder at the equator than anywhere else.

There are museums here, shops, and historical recreations. For example, there are houses, recreations of the houses that the indigenous people built before the Spanish came. All of the houses were built of local materials like mud, reed, and grasses. This portion was split into three parts. There was a house of the natives from the Amazon region. There were two houses of the natives from the mountains, one round house which showed techniques before the influence of the Spanish and one rectangular house that showed techniques after the influence of the Spanish. Finally, there was a house of the natives of the Pacific coast.

One of the museums was all about the expeditions that were sent to Ecuador to find the equator and measure the curvature of the Earth at it. The expeditions were French, but Ecuador was controlled by the Spanish at the time. Spain allowed France to send the scientists. Did you know that after Newton proposed Universal Gravitation, there was some disagreement about what that meant for the shape of the Earth?

Many of us are taught that the Earth is a sphere. It’s not, but, to be fair, it is close. Newton proposed that the Earth was an oblate spheroid, like an M&M. In an M&M, it is like a sphere got squashed pushing on its poles, so its equator bulged out and its poles got closer together. Well, Newton didn’t think the Earth was as squashed as an M&M (in fact, all reliable evidence indicates that Newton never once even ate an M&M), but he did say it was the same sort of shape, just not squashed so much. The radius at the equator, said Newton, is greater than the radius at the poles, but not by a huge amount.

There was another school of thought that said, no, the earth is a prolate spheroid, where you would pull on a sphere at the poles, more like an American football or a rugby ball. They believed that the earth’s radius at the poles was greater than its radius at the equator.

No one really knew for sure which was right. No one had ever made the appropriate measurements before. The French, believing this to be an important question, both scientifically, and due to its impact on mapmaking and worldwide commerce, decided to send out two expeditions. One would go to the North Pole, the other to the equator. Each was to measure the curvature of the earth at their destination to settle the question.

The expedition to the equator chose the province of Quito. They thought it would be very close to the equator (they were right) and would give them enough access to enough land that they could make the measurements needed to calculate the curvature of the earth. They built checkpoints over a huge area of land in the Andes mountains. They made measurements of the stars in Orion’s belt from these various checkpoints. Then mathematically, they measured the curvature of the Earth using their observations.

It turns out that Newton was right, the Earth is an oblate spheroid. The equator is further from the center of the Earth than the poles are. This is because the Earth spins. When the Earth was forming, that spin caused a bulge in the middle, a centrifugal force effect.

So if anyone out there is still holding onto a belief that the Earth is a prolate spheroid (or that it is flat), I’m sorry to tell you this: that’s not the case. If, in so challenging your belief, I have crossed a line, well, I think we’ve pretty well-established that I'm a line crosser.