Why Ships Float and Companies Sink

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Have you ever wondered how a steel ship, a material heavier than water, can stay afloat?

In this post I want to tell you about a tool I've designed to represent and analyze our understanding of any topic, Personal Understanding Maps, which we'll apply here to answer the previous question, as a tutorial. If you're interested in exploring this learning and analysis tool further, you'll find all the details in my book "Everything I Can Imagine: The Algorithm of Understanding. Part I".

Understanding maps also work as a springboard to connect seemingly distant concepts. In this case, we'll apply our knowledge about ship buoyancy to analogically examine why some companies survive in the market while others "sink".

Why do ships float? An intuitive explanation

Here's a concise explanation of the phenomenon. Imagine two objects of the same size:

• A solid steel ball

• A hollow steel sphere of the same size

The hollow sphere will float because:

• It displaces the same amount of water as the solid ball

• It weighs much less thanks to the empty space inside

This same principle allows enormous steel ships to float in water: their large volume displaces enough water to generate an upward force greater than their own weight.

Why do ships float? Detailed analysis

The previous explanation, although intuitive, can create an illusion of understanding. These illusions are the same ones that cause a student, after having read and apparently understood an example, to go blank during an exam.

To more critically evaluate our understanding of steel ships' buoyancy, we'll create a Personal Understanding Map (PUM) applied to this case.

A PUM consists of several nodes that represent the objects we want to understand. In this case, we'll use two: the ship and the water.

Each node will connect to subnodes that describe the relevant properties of the object. These subnodes are linked to each other by arrows representing the logical implications of the flow of understanding. Above these arrows, we'll explicitly write the logical relationships in additional containers, as they are fundamental to our understanding and its critical evaluation.

Let's see how all this would take shape in our example. After a more detailed analysis of the buoyancy phenomenon, I personally arrive at the following key information, which will allow me to complete the information for the subnodes and logical containers:

1. Water has a higher density than air
   

2. The ship, although built with heavy materials like steel, has a hollow hull containing air
   

3. The total density of the ship is a weighted average between the density of air and steel, resulting in less than the density of water
   

4. Newton tells us that the weight of the ship P is expressed as P = m ⋅ g = ρ⋅g⋅V. Where:

   • ρ (rho) = net density of the ship

   • g = acceleration due to gravity

   • V = volume of the ship
     

5. Archimedes taught us that any body immersed in a fluid experiences an upward thrust equal to the weight of the displaced fluid. The Thrust E equals E = ρ⋅g⋅V. Where now:

   • ρ (rho) = density of the fluid

   • g = acceleration due to gravity

   • V = volume of displaced fluid
     

6. Since the density of the ship is less than that of water, the thrust it experiences is greater than its weight (E>P), and according to Newton, there is a net upward force. This is why the ship floats.
   

This list presented this way can be a bit dry. Let's bring it to life through visual representation!

A personal understanding map (PUM)

Let's visualize the previous analysis in the form of a personal understanding map. To do this, we'll use a color code that will help us evaluate our level of real comprehension.

The map relies on three colors:

• Red: what we don't yet fully understand

• Green: what we accept as basic axioms

• Blue: what is strictly understood, that is, relationally.

The key is in the connections: an element is considered "deeply understood" (blue) only when we can logically connect it with other elements we already understand (in green or blue) through a logical relationship that is understood (in green or blue).

Our goal is to maximize the blue in the map!, which means we truly understand the logical connections between the different concepts.

Applying this convention to our previous analysis of buoyancy, I've arrived at the following map.

A critical analysis of our understanding

The exercise of creating an understanding map clearly reveals the extent to which we have deepened our explanation, which is evidenced through the elements marked in green.

Precisely in view of this, our explanations still leave some questions unresolved:

1. Why does air have a lower density than water?

2. Why is the density of the ship a weighted average of steel and air?

3. Why is the weight of the ship expressed in that way? Where does Archimedes' expression of thrust come from? How is the net force calculated?

PUMs are also here to foster your critical thinking.

Explanation by analogy: why companies "sink"

One of the most fascinating characteristics of knowledge is how principles governing one phenomenon can illuminate our understanding of another completely different one. Let's look at a surprising example: the analogy between ship buoyancy and business survival.

When we talk about a company "sinking," this metaphor turns out to be more accurate than we might suspect. Just as a ship needs to maintain its buoyancy, a company requires other conditions to stay afloat in the market. Let's explore this comparison in detail.

Ship Component	Company Analog
Hull volume	Total operational capacity
Ship weight	Fixed costs
Water thrust	Income and liquidity
Water density	Market conditions
Waterline	Financial break-even point
Hull leaks	Short-term debt
Air inside	Operational efficiency
Hull design	Operational structure

The Fundamental Balance

A ship's waterline is analogous to a company's financial break-even point. Just as a ship needs to maintain its waterline to remain stable, a company must keep its income above its expenses to ensure its survival.

Capacity and Potential

A company's operational capacity, which includes its infrastructure, equipment, and human capital, is comparable to the volume of a ship's hull. This capacity determines the maximum potential of the organization, just as the hull volume determines the ship's water displacement capacity.

Efficiency and Survival

Now let's look at an interpretation of business efficiency illuminated under this analogy

Ship density	Operational efficiency
Measurement: Mass/Volume	Measurement: Operating Margin = (Income - Costs)/Income
High density = Less buoyancy	Low margin = Lower survival capacity
Low density = Greater buoyancy	High margin = Greater survival capacity

This comparison helps us understand why companies with high operational burden and low efficiency struggle to remain competitive, similar to a very dense ship that battles to stay afloat.

The "Sinking" Process

1. Phase 1: Just like a hull that begins to leak water, debts begin to accumulate gradually

2. Phase 2: The buoyancy of the ship decreases, just as the operating margin of the company reduces

3. Phase 3: The critical point comes when the thrust can no longer support the weight of the ship, or in business terms, when liabilities exceed assets, leading to technical bankruptcy

This nautical-business analogy is a perfect example of how mental models from one field can enrich our understanding in another.

Conclusion

Through this detailed analysis of ship buoyancy, we have explored how personal understanding maps can help us delve into complex concepts.

On the other hand, the analogy between the physics of buoyancy and business dynamics demonstrates how mental models from one field can enrich our understanding in another seemingly unrelated one. This ability to transfer knowledge between disciplines is fundamental for innovative thinking and creative problem-solving.

Personal understanding maps, with their color code and logical connections, provide us with a valuable tool to evaluate and deepen our true level of comprehension, avoiding the illusions of understanding that often limit us on our path toward the highest peaks of our intellectual destiny: understanding the universe.