Physics works remarkably well for helping us predict the way things will unfold. It tells us that apples fall down from trees, but not up. Water flows down waterfalls, but not up them. Balls roll down hills, but not up them.
All of these situations are an example of a simple, universal principle: physical systems move in the direction that minimizes their potential energy. For Example, suppose we have a valley:
That black line represents the edges of the valley — and also the potential energy of a ball we place in anywhere in the valley. If the ball is at the left or right edges, it has lots of potential energy. The ball will move in a direction that minimizes its potential energy:
No matter where we place it in this valley, the ball will eventually roll down towards the bottom of the valley. It may roll past the bottom, but eventually friction will cause the ball to come to rest, and the only stable place for it to rest is at the bottom of that valley:
Almost every physical system you can think of follows this principle. There are counter-examples to all of these situations: sometimes, people pick apples off of the ground. Sometimes, people move water against the direction of gravity. Sometimes, people climb mountains.
But people are physical objects, too — right?
What is it about people — as physical objects — that sometimes causes them to go to the top of mountains, when an object like a ball, or a rock, or a leaf would be extremely unlikely to find its way up to the top of a mountain?
Salmon swim upstream, but rocks never do. Why is that? What’s physically different about the salmon that causes it to move in such a way that it seems to defy the basic pattern of physics — that systems move along energy gradients, to reduce their total energy?
Why is this physical configuration so unlikely to occur:
Whereas this one seems much more common?
Remember, people are physical systems, too. There should be a physical reason we can say “This is why people are much more likely to end up on top of hills, than round balls.”
I pondered this question for a long time. I came up with an answer a while ago, and finally thought about the answer enough to make it simple enough that I could express it in writing.
I think there’s something special about people — and other living things — something special, from a physics perspective, which allows them to move in ways that seem counter to the ordinary way physical objects move.
What makes people special from a physics perspective is that they reflect their environments. Let’s look at the simplest physical system I can think of, which has the same property:
The above drawing represents a motorized cart with a pendulum in the middle. The pendulum is connected to the motor in an interesting way: If the cart starts to roll down the hill, the swinging of the pendulum will activate the motors in a direction that rolls the cart back up the hill:
The neat thing about this system is that the cart will work its way towards the top of the hill, no matter where it starts:
Does this system follow the same principle of all physical objects? Does it minimize its total energy?
Yes, it does. Remember — the cart is driven by a battery, so as the cart moves, the energy of the battery is depleted.
The pendulum — in gray — also follows the same principle. If cart starts to move, the pendulum will initially look like this:
The heavy mass at the bottom of the pendulum has inertia; the cart starts to move, but the pendulum initially stays in place, until the cart starts to pull it. The pendulum is not at its lowest equilibrium position — and so it starts moving towards its equilibrium position, with the ball hanging straight down:
Remember, the cart is wired up so that the motor begins to engage the very moment the pendulum becomes off-center.
That pendulum is the key to this whole operation. Notice that when the cart is centered atop the peak, the pendulum is at a stable, low energy configuration. When the cart moves, the angle the pendulum makes relative to the cart increases. If we graph the cart’s gravitational energy, as a function of its position, we get this:
If we graph “the angle that the pendulum makes with the vertical”, as a function of the cart’s position, we get this:
That pendulum, in essence, reflects the cart’s position on the hill. The reflection itself is still a physical system — which means the reflection also moves to minimize its potential energy. The pendulum swings in the direction that trips the switch to make the cart roll back up the hill.
Now, imagine if we treat the angle the pendulum makes as an internal form of potential energy — it’s how badly the cart “wants” to go to the top of the hill:
As the cart gets closer to the top of the hill, the “internal potential energy” of the cart goes down. The lowest energy configuration for the pendulum is to have it centered evenly in the cart, and the only way to make that work is for the cart to be perched on top of the hill.
In other words — the cart “wanting” to be on top of the hill is a function of the way the cart is designed. That pendulum is like a very, very simple mind, which — coupled with the switches and battery in the cart — gives the cart one single “goal”: to be on top of that mountain.
We can imagine our climber, the purple person above — she set out to climb that hill because she wanted to. Just as the pendulum’s angle with the cart reflects the cart’s position on the hill, Her physiology contains a stable reflection of her location in her environment. Her wanting to go on top of the mountain means that her mental potential energy is lowest when she knows she’s standing on top of that mountain.
Why does it matter? Why is it relevant? For one, it lets you start to see that human beings are just as much a part of nature and reality as waterfalls, planets and stars — but also trees and fish and birds.
Yes, we have hopes and dreams and desires — which is to say, our physiology reflects the structure of reality, and sometimes our internal energy gradients causes us to move in ways that may seem unnatural for a rock or a pile of leaves to move. Having fingers doesn’t make us any different from the many other parts of nature that have fingers. Why should having dreams set us apart?
In other words, our ability to hope and dream and wish and want — those aren’t so different from our ability to grasp things with our hands. Those hopes and dreams are physical acts — they take place in a physical system (our brain) that follows physical rules — and so we don’t need to make it into some elaborate moral game, or judgement-laden speech about proper dreams and values and hopes.
We can learn to hope and dream better, just the same way we can learn to use our fingers and hands better. If you grab things too hard with your hand, you’re only going to waste energy and hurt your fingers. Why wouldn’t your mind work the same way?
Second — and far more practically — it suggests that when you want to motivate yourself, you ought to focus on what you want, rather than what you should do.
For example, say you’re in bed and you know you need to wake up. You could try to force yourself to get out of bed; ‘muster up the willpower’, so to speak. But what is that really accomplishing? You’re just expending limited energy being upset at yourself for not doing what you “should” do. Your internal potential energy is at minimum, and you’re looking up, saying “damn, I don’t want to do that.”
Instead, try thinking about why you should get out of bed. Because you want to make a good impression at people on work. Because you want to get your work done! Maybe it’s because you want to eat breakfast. When you give yourself reasons to act, your body will act on its own.
Remember, you can’t change much of the external world without a lot of work. But changing the shape of your internal world is largely up to you.
When I was in boy scouts, we learned that when you were sawing a piece of wood, you should ‘let the saw do the work’. You might feel an instinct to push down on the saw, hard, to cut into the thick wood. This is just wasted energy — it’s better to move the saw back and forth more times, and let the teeth of the saw do the cutting.
I think our minds work the same way — they’re remarkable at getting us to where we’d like to be. When we use them the wrong way, we just waste energy and get nowhere. When we focus on what we want — rather than on the bad things that have happened to us, or the problems with the world — our minds find us a way to get to what we want.
When we focus on our problems, or the world’s problems — we’re shaping the potential energy surface in our brains so that we just stay put. It doesn’t mean there aren’t problems in the world — it just means that fixating on the problems, rather than solutions, won’t get us closer to the solutions.
Physical systems are predictable, when you have enough information. They follow rules and patterns. I had a hard time understanding people for the longest time, because I couldn’t relate their behavior to the most intuitive system I know — physics. Answering this question was essential to me being able to integrate my understanding of science with the rest of my every day life. I hope it helps you.