I’ve spent a good bit of time tutoring people in the last few years, mainly in physics. Pretty much every student who takes physics comes across problems about projectile motion eventually, and pretty much everyone struggles at least a little. Here's how it usually goes. The guy I've been working with will come to me with a problem. Something like a rock or baseball, or ewok, that gets picked up and chucked into the air by a catapult, an arm, or a stormtrooper. Then eight seconds after the ewok is tossed into the air at just such a speed, the Death Star explodes. But if the Death Star blows up first, then the stormtrooper will be stunned and the ewok has time to sneak away. Also if the ewok is falling too fast when it hits the ground it will pop. The ewok only survives if it hits the ground in more than eight seconds and if it's going less than 12 m/s.
Usually people get annoyed at this part. "How in the world am I supposed to know how fast the ewok fell, and how long it was in the air?"
That's when I get to tell him the good news. "This is a projectile motion problem" I say. "What does that mean?"
"It means I can use this equation" he says as he flips through a notebook filled with equations, diagrams, and sketches of pokémon, "Here it is."
"Great, now what does this equation tell us?"
"It tells us that physics is stupid." I'm tempted to start a speech about symmetry, elegance, and the marvels of reliable physical laws, but I restrain myself.
"Well, that's not what I was thinking. What else does it tell us?" He moves his head to the side to see if the secrets of the equation will become visible if viewed from a slightly different angle.
"It tells us... that the time, speed and position are all related."
"Yeah, which times, speeds, and positions?"
"Well, there's a term for the initial time and another for the final."
"So the final speed depends on the initial speed?"
"No" he says quickly, glances at my face, then the page and then "yes" he answers slowly.
“Alright, if we know everything about the way the ewok is thrown into the air, what can we figure out about the way it lands.”
“I don’t know. I guess we could figure out something, but I’m not sure what.”
“Here’s the nice thing about projectiles. If we know everything about the ewok when it is thrown into the air, we can figure out everything about the ewok when it lands.”
”How is that possible? Anything could happen to the ewok in the air that might change the way it lands.”
”That’s true, but if everything happens normally, we can predict what will happen very precisely.”
Physicists like projectiles because they are predictable. They assume that gravity will be the only thing affecting a projectile once it has been launched, so they know exactly where an object will land after it has left the ground. Not only do they know where it will land, they also know where it will be and how fast it will be going. A single projectile follows a single trajectory. It doesn’t deviate. If it starts out the same way, it will follow the same exact path, every single time.
Vocabulary.com says that a “trajectory is the path of an object through space, or the path of life that a person chooses.” Isn’t that interesting? We use the same word for a predetermined path of a rock from a catapult, as a person’s choices about their job, car, family and home. What does this mean? Birth is just like being shot out of a cannon? We get fired out at high velocity, then we fall into a nice little net at the end if all the calculations are right? If this is the case, all we have to do is smile and try to make the audience think we aren’t scared to death as we fly, float, and fall through our careering existence. This metaphor has been engrained for so long, that it made it into the dictionary. It happens to be very convenient for me, because it makes the similarity easier to point out in a blog post, but at the same time it’s sort of shocking. It’s a little bit dehumanizing. And it’s kind of sad. Our lives are like trajectories in some ways. They can be predictable, and the past and present do help us to predict our own futures, but thankfully, that isn’t the whole story.
When a high school student chooses a college, that decision does affect her future. There are consequences beyond the first four years. She will have different skills, different career options, a different friend group, and different ideas about the way the world runs. However, these outcomes will be highly unpredictable. You might think that finishing college will put you on a path to making more money in the long run, and statistically, this isn’t unreasonable, but there are a lot of exceptions. Bill Gates would have made less money if he had finished college for example.
Projectile motion may be predictable, but not all physical systems are. Chaotic systems are situations where the outcome is pretty impossible to predict. Even if we know a lot about the present and the past. Think about weather. We are always surprised by weather. We have centuries of data to look at and we have great maps to show us the current state of things. Meteorologists are right a lot of the time. But I’ve worn a jacket on a day with a 80 degree high, and I’ve looked at a 0% precipitation forecast before encountering a downpour, our best predictions are not reliable in complicated, chaotic situations.
I was talking to a friend a couple months ago and he said to me something like, “I know I’ve made mistakes, but I’ve decided never to make those mistakes again, because I know God has a plan for me, and every time I make a mistake, I’m giving up part of that plan.” This jumped out at me, because I’ve thought this before, and I’ve heard lots of people say it. It’s like saying, “when I was born, I had the potential to have the political impact of Abraham Lincoln, the revival impact of Billy Graham and the social impact of MLK Jr., but ever since I’ve been slowly trading away all these opportunities and now all the “good plan material” God has to work with for my life is just enough to become a cardboard box assembly worker (no offence intended to box assemblers), and then if I make any more mistakes, I’ll probably have to become a panhandling hobo.”
Here’s a fact: your decisions today impact your life tomorrow.
Here’s another one: if you’re tone deaf, you aren’t going to be an opera singer.
One more: If you have a sex addiction you’re gonna have a really tough time as a pastor.
However, if you were betrayed by your family, sold as a slave in a foreign country, worked hard until you had earned some respect, were unjustly accused of a crime and then imprisoned, you wouldn’t expect that in a few years you would have a position of high authority, save a country, and restore good relationships with your family members.
That’s what happened to Joseph. No one at the time would have predicted those things. Along the way, anyone reasonable would have easily predicted that he would be worked to death and die lonely, forgotten, and unvalued. The paths we take affect our lives in unpredictable ways. I think we need a new metaphor.
In physics, we refer use the word chaotic to describe systems that are unpredictable. There is an element of chaos in life, but it hasn’t dominated my experience. I like the idea of narratives because they have rational connections between events, but they also have shocking twists. Of course, they are intended to imitate human experience, so the similarities shouldn’t be surprising.
In the end, life is a journey. There’s no other way around it. We make some decisions, but the paths we walk on leave just a few available options. Sometimes things get dark, but sometimes light is most meaningful in small servings. In a journey, you pick a destination. You might select a course, but in a good journey, the first path you choose never works out so well. You end up going places you hadn’t wanted to go and finding strength you hadn’t needed before.