One day, in the 3rd Century BC, King Hiero II of Syracuse, Sicily, summoned Archimedes—a young, Greek physicist and mathematician, donning a long, flowing, white beard—to verify that his new crown was made of pure gold, or that some silver had been fraudulently substituted by the goldsmith.
This would’ve been a simple task for Archimedes, but for the King’s one caveat: the crown must not be damaged, or else there would be serious repercussions.
For several weeks, Archimedes pondered upon possible solutions to the King’s crown problem, but he couldn’t crack the code, and time was running out.
One evening, as he was taking a bath, Archimedes noticed that the level of water in the tub would rise and overflow, as he lowered his body into it.
Putting two and two together, Archimedes figured out that the amount of water overflowing from the bathtub corresponded to how much of his body was immersed in the water.
Shortly afterwards, Archimedes conducted a quick experiment to verify the authenticity of crown: he tested whether the King’s crown would displace the same amount of water as a lump of pure gold of the same weight.
Surprisingly, the experiment revealed that the King’s crown displaced far more water than the lump of pure gold, proving that some silver had been mixed into it, and it was a counterfeit.
His insights from this experiment would later be formalized as Archimedes’ principle—a law of physics fundamental to fluid mechanics—and today, aside from inventing the word “Eureka!” Archimedes is regarded as the greatest mathematician of antiquity and one of the greatest of all time.
In particular, Archimedes’ principle contains useful analogies that could provide answers to an important question:
Why do we fail in life and work?
Archimedes in thought. Domenico Fetti [Public domain].
Archimedes’ Principle of Failure
For the sake of analogy, imagine that a ship is your life and the water the ship floats on is your environment i.e. the people, items and sounds in your surroundings.
In this case, a ship that sinks would represent failure, whilst a ship that floats would represent stability and success in life.
In On Floating Bodies, Archimedes explains why some ships float and others sink:
“Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.”
In other words, for a ship to float on water, it needs to displace a weight of water that equals that of itself.
If the ship displaces a weight of water less than that of itself, it will sink.
This is because the buoyant (or upthrust) force exerted by the water would be less than the downward force of the ship’s weight. 3
The weight of the ship must be less than or equal to the buoyant force, for the ship to stay afloat. If the weight of the ship is greater than the buoyant force, the ship will sink.
This law of physics, known as the Archimedes’ principle, can also be represented with this simple formula (which has been converted for the ship analogy example):
Buoyant Force = (Density of water minus Density of ship) multiplied by acceleration due to gravity and volume of displaced water. 4
In simple terms, density is the amount of stuff in a given amount of space.
The more stuff in an identical amount of space, the greater the density. And since liquids, like water, have a density, a ship with greater density than that of water will sink, and a ship with less will float.
Now, let’s toy around with the Archimedes’ principle to uncover the reasons for failure in life and work.
Success = (How well your environment supports good habits minus the number of goals you pursue) multiplied by your capacity to take action.
Based on this formula, there are three main causes of failure in life and work.
A simplified interpretation of the Archimedes Principle for everyday life.
#1. Poor environment
The things we can see, smell, taste, hear and touch in our environment, shape our behaviors in powerful ways we often can’t see.
For example, it’s much harder to stay focused and get important things done, if your mobile phone is within sight.
Conversely, a working environment free from visible clutter and distractions would significantly boost productivity and reduce stress.
As a rule of thumb, it’s much harder to stick to good habits over the long run, in a poorly designed environment.
The people, items and voices that surround you on a daily basis will ultimately dictate your odds of failure or success in life.
Solution: Just like water, different liquids have different densities. For example, salt water is more dense than fresh water, and since our body weight is less dense than that of water, it’s much easier for us to float in a salt lake like the Dead Sea, than in freshwater. 5
Likewise, we can design our environment to make it easier for us to stick to good habits over the long run.
The better designed our environment, the greater the likelihood that we’ll stay consistent with our goals and achieve them in the process.
#2. Lack of focus
Just like a ship that is too dense, we often pursue more goals than we can handle.
We get excited to start new goals, but after a little while, we lose focus and fail to finish what we start.
As a result of this, over a span of months or years, we have little to show for our efforts.
Solution: To prevent a ship from sinking, naval architects remove inessential contents from the body of the ship, leaving it with space and air instead. This way the density of the ship remains less than that of water, keeping it afloat.
In a similar fashion, the best way to avoid failure in life, is to ruthlessly eliminate the inessentials and focus on what matters most.
By eliminating the inessentials and shifting our focus only towards the essential, we create the time and energy necessary to finish what we start on a consistent basis.
#3. Low energy (not enough capacity to take action)
Capacity can be narrowed down to three things: time, energy and competency.
When we pursue a goal or task, without enough time, energy or competency to tackle it, we’re setting ourselves up for failure.
A classic example of this problem is low energy levels caused by lack of sleep. After a few nights of little to no sleep, our ability to think, learn, remember and problem solve, drastically reduces to levels of incompetency. 6
If a task requires more time and competency than you have available, consider either increasing the deadline till completion, eliminating the task completely or reducing the amount of the task you’d have to complete.
Keep Your Head Above Water
In the same way there are multiple factors that cause a ship to sink in the middle of the ocean, there are a combination of forces that cause failure in life and work.
Archimedes’ principle provides useful analogies that help us to unravel these hidden forces: a poorly designed environment, lack of focus and low energy levels.
It’s the interaction of these hidden forces that ultimately shape our life and destiny.
Mayo Oshin writes at MayoOshin.com, where he shares practical self-improvement ideas backed by proven science, philosophy, art and history. To get these ideas to beat procrastination and improve your focus, you can join his free weekly newsletter here.
- 1st Century BC Roman author and architect, Vitruvius records an account of the crown story in his book, “De Architectura, Book IX. However, it doesn’t appear in the writings of Archimedes.
- According to Greek historian, Plutarch, Archimedes was killed whilst the city of Syracuse was under siege by the Romans. Whilst solving for a solution to a mathematical problem, a Roman soldier commanded Archimedes to meet a Roman general, but Archimedes refused saying “Do not disturb my circles,” in reference to his mathematical drawings. The angered Roman soldier then slaughtered Archimedes with his sword.
- If you’ve ever tried to push a beach ball into a pool of water, you’ve experienced this buoyant force acting against your efforts.
- Please note that the explanation of the Archimedes principle in this piece is an oversimplification of the complex mechanics of the formula.
- In general, salt water weighs 2.5% more than the same volume of fresh water.
- Why We Sleep: The New Science of Sleep and Dreams, by Matthew Walker.
Originally published at mayooshin.com