by O Bod
Of All Places
Sometimes it's the Journey
Chapter 10: Recap
I step outside, and feel my heart surging as I observe a huge full moon just over the horizon. I know already why the moon looks so big when it is near the horizon, but it's still a sight to behold.
I glance at my cell-phone, which doubles as a pocket-watch (do pocket-watches still exist, or have they, too, gone the way of the record-player? Or are both making a retro-comeback?) It shows 5 o'clock. Huh, isn't the full moon supposed to rise at 6 pm? Maybe it's because of Daylight Savings Time. No, that moves the clock forward by an hour, so it would make a full-moon moonrise at 7, not 5. But anyway, it's not Daylight Savings Time anymore, we changed our clocks last week. Then how could the full moon rise at 5?
This troubles me greatly, and I ponder it for several minutes. I finally come up with several possible solutions to this mystery. One - last week, when they moved back to Standard Time, I may have moved my cell-phone clock back an hour after (or before) it moved itself back an hour, so now it's really 6 o'clock, as it should be - so my phone is wrong. Or maybe this place is not exactly in the middle of its time-zone, so it's more like 5:30 pm ... - again, human error (humans invented the time-zones, after-all ...) Or maybe my eyes are deceiving me, and the moon is just shy of full, and will be full tomorrow (when it rises about 6 pm). Once again - human error. Could it be anything else?
I read somewhere that Einstein is reputed to have said something on the order of (excuse the vagueness here, but I also read somewhere that you need special permission to quote Einstein, so I'm paraphrasing): If a natural phenomenon is observed to contradict the Theory of Relativity, then God must have made a mistake, for the theory is correct. Oh, and Einstein was also known for is humility. So, what if the full moon did actually rise at 5 pm? I'm no Einstein, so it must be the theory that needs some adjustments (or fudging - back to the drawing board...)
I feel I am on the verge of something great, for I have made a remarkable discovery. And like all great discoveries (or some of them anyway), it kind of happened by accident.
Where do I begin? Some things in nature come in threes. They are bonded together in such a way that if we know the value of two of them, we can derive the third. Can't think of any examples right now... Come to think of it, Einstein's famous equation, E=mc squared. Newton's 3rd law fits the bill: F=ma, or from high-school physics we had V=a*t (Velocity equals Acceleration times Time). Then there was X=V0t + half-a-t-squared... never mind.
Anyway, say there's no acceleration, just a car moving at a constant speed V. If you know the speed of the car, and the time it's been moving, you can easily figure out the distance it covered. Or, conversely, if you know the distance and the time, the speed is quickly derived by dividing the distance by the time (for example, if you covered 100 kilometers in an hour, then your average speed is 100 kilometers-per-hour). Give me any 2 of those 3 values (distance, time, speed) and I'll tell you the 3rd one. Like a magic trick (I should take this on the road ...).
Same with, say, mass, volume and density - isn't that what Archimedes found? Nature is rife with such examples. Sometimes there are more than 3 variables (though I can't think of any right now), but I think the better-known cases are the ones with 3. I wonder if there's a name for that. How about 'triad'. Let's look it up ...
This dictionary here says that 'triad' is defined as 'A Chinese organized crime organization'. Wait, that can't be right ... oh, here's another definition: 'a group of three, especially of three closely related persons or things' - I like that one.
I suppose it could also be less than 3, e.g. tell me your age and I'll tell you the year you were born, or vice-versa. Would that be a 'duad'? That doesn't sound as nice, so let's stick with the triad. So where does the moon fit in? Variable number 1: The moon's rising time. Variable number 2: The moon's shape Variable number 3: Its position in the sky. Variable number 4: The current time.
That's 4 variables, but didn't we establish that numbers 1 and 2 are equivalent (they are a duad) - a full moon rises at 6 pm. Tell me its rising time or shape, and I'll tell you the other one. So we're left with a triad: The moon's shape, its position in the sky, and the current time. If it's 6 pm, and the moon is full, then I'd look for it just rising on the Eastern horizon. Conversely ...
Anyway, I think I may have stumbled upon something really useful here: I can tell the time by looking at the moon's shape and height! I wonder if anybody before me ever figured that out? How do I present it to the world?
I slowly climb the steep winding road. The buildings I pass mostly contain shops (shoes, bakery, postcards) and small eateries, but there are also residential houses and bed-and-breakfast hotels. I stop next to a coffee shop to catch my breath, and see a familiar face sitting at an outdoor table, sipping something hot while reading a local newspaper.
Concentrating for a moment, the name 'Eli' springs to mind, but I can't recall where I know him from. Maybe he was just the kind of guy who looks familiar. You just had to say "hello" to him.
No, more than hello. "Hi, how have you been?!" I call out to him, and Eli greets me back accordingly. Grade school? Scouts? University? I try to bide my time, keep asking him questions until I figure it out. "So, what are you up to these days?" I venture.
"Any field in particular? Where?"
"Math, of course. Here in Visby."
"Oh, yes. You were always good at math." It's coming back now.
We are at a coffee shop about halfway up the hill, looking down at the little harbor. In the distance I can see the twice-daily ferry from the mainland approaching. It appears to be sitting squarely on the horizon now.
"How far would you guess the horizon is these days, Eli?"
"That depends on your height, of course. From here I'd say about 15 kilometers, maybe 20."
A waiter comes over.
"Coffee?" Eli offers.
Eli turns and speaks a few words in Swedish. A short exchange follows, and then the waiter inhales between clenched teeth and walks off.
"What was that all about? The inhaling?"
"Oh that? That's like saying 'well alright then, nothing else to say'. It's cool."
"Tell me, Eli, have you noticed any changes in the horizon?"
"What do you mean?"
"Do you think it may be shrinking?"
"The distance to the horizon is easy enough to figure out, if you remember your Pythagoras from high-school days. You do, I assume?"
"You mean a-squared plus b-squared equals c-squared?"
"Yes, were 'c' is the hypotenuse."
"You know, in a right triangle, you have your 2 sides that make the right angle, and then the hypotenuse that connects them and completes the triangle. So the sum of the square of the length of two sides equals the square of the length of the hypotenuse."
"So here you also have a right triangle: One side is the radius of the earth, another side is the line from the observer to the horizon, which makes a right angle at that point with the radius because it is tangent to the circle of the earth, and the hypotenuse is the distance of the observer to the center of the earth, which is the radius plus the height of the observer over the surface of the earth. Right now I'd say we are about 25 meters above sea level."
"So the distance to the horizon depends on the radius of the earth and your height?"
"Well, assuming the radius is constant, then only the height of the observer. That's a nice exercise. Let's see, do you know the radius of the earth?"
"I know its circumference: 40,000 kilometers."
"Good enough, so to get the radius you divide that by 2 pi, about 6.28, and we get, say, 6300 kilometers."
"That was fast. As I said, you were always good at math."
"Well, pi is almost the same as the square root of 10."
I didn't know what that had to it with it, and how that helped him in his speedy calculation.
Eli rambles on: "Anyway, give me a sec", and he closes his eyes for maybe a minute, every so often mumbling phrases like 'those cancel out' and 'h squared is negligible'. Finally he announces "Approximately 3-point-5 kilometers times the square root of 'h' in meters."
"If you're one meter above sea level, say you're standing in the water at the beach knee-deep, then you see the horizon 3.5 kilometers away, but if you're 100 meters above sea level, and the square root of that is 10, then it's 3.5 times 10, so 35 kilometers away."
After a moment to take this in, I continue: "So it can't be getting nearer?"
"It looks nearer."
"How could it be getting nearer? If we were looking at it from a lesser height then it would look nearer. Or if the earth was getting smaller then it would also be closer."
"How about if we were moving closer to the horizon?"
"Hmmm, I don't think so. As you move along the surface of the sphere, the earth, the horizon would move away from you."
"So it's either moving down the mountain, or the earth is shrinking."
"Well, the earth isn't shrinking." Eli thinks a second, and then adds: "Maybe you witnessed some optical illusion."
"How can that affect the distance to the horizon?"
"Maybe one day you saw a small boat on the horizon, and the next day you saw a bigger boat, so you may have thought that it was nearer."
"Or maybe the earth is shrinking."
"I think we'd notice that!"
"Well, for one thing, distances would get shorter, so you'd get places faster".
"What if time was also shrinking?"
Eli thinks about that, too. "That would work for speed, but not everything is linear with time. Acceleration, for instance, would behave differently. You'd notice that if you dropped something, because gravity causes falling objects to accelerate."
"What if mass would also shrink by the same amount?"
Eli chuckles. "You can't just scale everything down and expect it to work. If you half each of an object's dimensions then you get one eighth of its volume, hence one eighth its mass."
Then he abruptly changes the subject: "C'mon, I'll show you around the island".
We walk north for a while, until we are next to an old wall. "The old town was walled in," Eli explains. "There are lots of old churches here. This one is 14th century," he says, and we finally pause to rest.
"Were there Vikings here?" I inquire.
"Oh, yes, Gottland is big on Vikings. That and the rock formations on the beaches at the other side of the island."
From our perch above the church we have an excellent view of the old city below and the rest of the town to the left. The little harbor looks nice - probably lined with tourist gift shops and places to eat, like most marinas I've visited. A couple of small fishing boats are out. People used to think that the boats should care not to venture too close to the horizon, or they'd risk falling off.
A Lesson in Humility
"I figured out something, too", I say. "Kind of developed a new idea".
"What's that?" Eli asks, "but be warned I'll probably shoot it down and you'll feel depressed for a while, but you'll get over it. It's good for you, really, a lesson in humility, or in humiliation, anyway."
He has a smirk on his face, but I plow on and tell him how one can tell the time by the sun and the moon, the moon phases and rising time, and how you don't really need a watch or clock anymore.
"I can even express it in a scientific way," I summarize: "The current time equals 6AM, plus the-number-of-days-since-the-new-moon times 50 minutes, plus the elapsed-time-since-the-moon-rose-today. And in the summer-time you add at the end an hour for daylight-savings-time. And I'm getting pretty good at estimating the-number-of-days-since-the-new-moon and its height in the sky."
Eli seems more bemused now than ever. "I don't know which expression is more apt", he begins, "'Popping your bubble' or 'Raining on your parade', because I'm pretty sure I heard or read about that somewhere, or if not then it's pretty obvious anyway. Not to mention all the flaws."
"Go on," I urge.
"Where to start? For one, you're going to want to catch the ferry back to the mainland at some point, so you need to know the exact time. And, as far as your 'moon clock' - it can't be new anyway. My guess is that the earliest humans had that figured out even before they could express that in words. Many thousands of years ago. What do you think Cavemen did in the evenings, before they invented TV, or even the light bulb? They looked at the sky, that's what they did. Not much you can discover that hasn't been discovered millennia ago. Then there's the complexity of your method, not to mention the accuracy. If that's all we had, then somebody would invent the watch."
I think he's being a bit unfair, that it can be fairly accurate. If I knew the date according to a lunar calendar, say the Muslim or Jewish one, then I'd know exactly how many days passed since the new moon. And one can readily estimate how many hours passed since moonrise: If it's at its apex, then 6 hours have passed. If it's halfway there, then 3 hours. And to divide the remaining arc into 3 equal parts is elementary...
Nero returned home from his travels deflated.
'A fine Miss Rumphius I've been,' he thought, as he settled into his parents' attic.
he caught a glimpse of the sea behind the trees from his window and
Making the world a better place would have to wait.