1.3 Principle of Least Effort

“Nature does nothing uselessly” –  Aristotle, Politics

The Principle of Least Effort, or Principle of Least Action, might be one of the simplest, yet most fundamental principles that rule our universe. From our earliest observations on nature as a whole, as noted by Aristotle, with his observations on Telos and Eudaimonia, to later formalisations with Newton, Euler and Lagrange.

Its applications are so widespread, it can be seen in the most basic building blocks of physics, as well as in the most abstract and high level theories on the human mind. It is fundamental, yet in its essence it is simple.

Things will always move along the path of least effort.

Sometimes it is called Ockham’s Razor, sometimes it comes in motivational phrases like the one from Bill Gates, but they all stress the same point that everything tends to perform the least amount of actions to travel along its path. Though they might use differing metrics to measure action, like simplicity of explanation, they all, in essence, amount to the same thing: Energy. 

From psychic energy used to think of explanations, to the energy of a falling apple, the action always ends up amounting to the energy spent on the task. In physics, this action is defined with the letter L after Joseph-Louis Lagrange, who formalized it as such:

Which means the amount of action something can perform is the amount of Energy it currently is using minus the amount of energy left in it, or the potential energy it has.

One of the most important meals of the day is breakfast. It is the building block on which you will build your day. It provides the sugar your body needs to perform its basic needs as well as your morning routine up until lunch. Your morning potential is dependent on this meal. If you tend to go to the gym in the morning, the amount of energy you can spend on other stuff before lunch is the amount you got with your breakfast minus the amount you spent at the gym.

After a proper workout, though, one doesn’t have much energy left, so the list of things you can properly do in the morning, without a quick snack break, is not long. They usually amount to low energy things, mostly things you are familiar with, and have already internalised, like driving to work. But even that task is more nuanced than you imagine. 

To properly drive to work, a path must be chosen, a proper car playlist to pump you up to work, and so on. To do so, you have two similar choices: let your phone decide all of that for you, while you just vibe on the wheel, or spend a bit more brainpower and remember your usual path, playlist and so on. Most people won’t even think about the choice, they’ll just hook up the phone to the aux and go. This, neigh automatic response to conserve the amount of actions left in the reserves is the path of least effort. 

The amount of energy you will use before leaving the garage can be, on one hand the sum of the psychic energy spent remembering what playlist and path you usually take to work, dreading the traffic jams it might or might not have, the mood of your manager if you end up late… or on the other, the energy spent  just hooking up the phone on the aux. In mathematical terms, the energy of the former can be expressed as:

While the latter:

The latter is reduced to one action, and, as a consequence, being faster and demanding less energy, therefore automatised by your brain. 

To further transpose this notion to a more formal math, we can call this quarter of the day, between breakfast and work, q, meaning q is comprised of the set of situations:

q = {washing the dishes, changing into gym clothes, saying hi to the gym attendant, flirting with the gym baddie, getting a cold shoulder from the gym baddie, …, getting into the car, …}

So, since, the portion of q where you are sitting on your car, ready to go to work, is seen through a local reference frame, where all you can see is the car console, and your phone, we can call it a derivative of q, or dq. 

If we are to determine the effort you put on each action, can further determine the average amount of push through you excerpt during the day as the average amount of energy you spend on each situation:

But, locally, the amount of effort you have to use to push through each action is very different. If we consider the speed with which you conclude one specific situation as 

Then we can see if the actions taken in that specific situation were effortless and speedy, or slow and cumbersome, by seeing locally how hard you are pushing through that moment. To do so, we can see how much you are slowing down to execute each action :

dp = dL/dq’

Meaning if the dE correspondent to the dq of the car situation is E with phone, then L will have a very small change globally, going through it will be a breeze. If you put any thought at all into leaving the garage, it was a single quick thought, so not much of a push through it was needed. 

If dE is corresponding with E without the phone, then L, globally will change significantly, so you will have to mentally push harder to not lose your morning momentum, and, consequently, slowing you down, and taking away energy from you. Your head is running a thousand miles per minute, thoughts rushing through, but you still haven’t executed the main action to progress with your day: Leave the garage.

A really zen and confident fellow usually pushes through life like it is a breeze. A gym baddie rejected him? Eh, there are plenty more. His boss is fuming? Eh, why bother, he ain’t his mum. His mum is fuming? Well, it’s his mum, she’s always fuming, just turn up those tunes. He does what he needs to to get by. No more, no less. He puts no thought on what he can’t control, and puts the same amount of mental effort on what he can, making all of that come very naturally to him.

On the other hand, the average Karen’s internal world is a mess. She stresses about everything. A portrait is crooked? That’s the collapse of her social reputation. That odd fellow across the street looked at her once? God be good, the West is collapsing! Someone said thank you to the bus driver? Oh, boy, hold on to your seats, Jesus is coming again, the ground is opening up and the apocalypse is coming! She puts more than enough thought on everything. She is always pushing through something, her mind in a cycle between no thoughts at all, and an explosion of anxiety. The only thing that compares to the speed with which she can go from 0 to shouting at a manager, is her desire for high calorie treats.

The Zen Dude, in that car situation would sit down, and hook the phone up with the same ease that he walked up to the gym baddie. This means that at that time, the push he was doing to get out of the garage was equal to push he exerted throughout his morning: 

Or in other words:

Karen, though, is all over the place. She can do the dishes alright. She can walk to the gym effortlessly, but when it comes to actually working out she has to do a mental checklist the size of the Geneva Convention, let alone leaving the garage. This means her dF, though seemingly on par with the Zen Dude, when it comes to her push through each action, it is more varied than a package of skittles.