Debunking the Myth: Why Complex Ideas Can't Always Be Explained Simply

The Fallacy of Oversimplification

In the realm of knowledge and understanding, there's a pervasive myth that has gained traction over the years: "If you can't explain it to a 5-year-old, you don't understand it." This statement, often misattributed to Einstein, has become a mantra for those who believe in the power of simplification. However, this claim is not only false but potentially harmful to the pursuit of knowledge and understanding. Let's delve into why this concept is flawed and what we can learn about the nature of explanation and understanding.

The Origin of the Myth

Firstly, it's crucial to address the misattribution. Einstein never said this phrase. In fact, his actions suggest he believed quite the opposite. When Scientific American held a competition in the 1920s to explain relativity in 5,000 words to a general audience, Einstein chose not to participate. This decision implies that he recognized the complexity of his theory and the challenges in simplifying it without losing its essence.

The Complexity of Simplicity

What we perceive as simple is often based on our familiarity with the terms and concepts, not on their inherent simplicity. Take, for example, the concept of logarithms. To understand logarithms, one needs to grasp multiplication and exponentiation, which in turn require a solid understanding of addition. Each of these mathematical operations requires months of practice and repetition to master. It's only after this extensive process that we consider these concepts "simple."

The Disconnect Between Understanding and Explanation

There's often a significant gap between deeply understanding a subject and being able to explain it effectively. This is particularly evident in academic settings, where professors are often hired based on their research capabilities rather than their teaching skills. Being a great explainer and a great understander are distinct skill sets that don't always overlap.

The Arbitrary Nature of the "5-Year-Old" Benchmark

Why set the bar at explaining concepts to a 5-year-old specifically? Why not a 15-year-old or a 25-year-old? The arbitrary nature of this benchmark highlights its impracticality. Some concepts simply cannot be grasped without years of foundational knowledge and cognitive development.

The Trilemma of Explanation

When it comes to explaining complex ideas, we face a trilemma. We can achieve two of the following three qualities, but never all three simultaneously:

1. Succinctness
2. Simplicity
3. Accuracy

Let's explore this concept using an example from advanced mathematics.

Example: Explaining a Classifying Space

Succinct and Accurate, but Not Simple: A classifying space (BG) for a group G is a topological space such that its principal G bundles, over any other space X, are classified by maps from X to BG considered up to homotopy.

Simple and Succinct, but Not Accurate: A classifying space shows all possible ways some object or group can be organized or arranged.

Simple and Accurate, but Not Succinct: This would require an extensive explanation, similar to what you might find in a comprehensive textbook on algebraic topology.

This trilemma demonstrates that we can't have it all when it comes to explanations. We must choose which aspects to prioritize based on our audience and goals.

The Limitations of Simplification

When we attempt to explain complex ideas in overly simplified terms, we often end up with explanations that are so vague or inaccurate that they become almost meaningless. This is particularly true when dealing with abstract concepts in fields like mathematics, physics, or philosophy.

For instance, trying to explain the concept of "emptiness" in Buddhist philosophy to a 5-year-old would likely result in an explanation that's so stripped down it no longer captures the essence of the idea. The process of simplification doesn't always distill a concept to its core; sometimes, it fundamentally alters it.

The Value of Complexity

While simplification has its place, there's also immense value in embracing complexity. Some concepts are inherently complex and require a certain level of background knowledge and cognitive development to grasp fully. Recognizing this fact can lead to a more honest and productive approach to learning and understanding.

Non-Analytical Concepts

In mathematics, there exist non-analytical functions - concepts that can't be broken down into simpler parts without losing their essence. This mathematical reality serves as a metaphor for many complex ideas in various fields. Not everything can be reduced to simpler components without fundamentally changing what it is.

The Reality of "Simplified" Explanations

Often, what we see as simplified explanations are actually quite different from what they claim to be. Let's examine a popular format: explaining concepts at different levels of complexity.

Case Study: Explaining Infinity

In a video featuring Professor Emily Riehl explaining infinity at "five levels," we see several issues:

1. The youngest audience member is 9, not 5.
2. Different concepts related to infinity are explained at each level, rather than the same concept being simplified.
3. The explanations range from basic ideas about unboundedness to complex mathematical concepts like the axiom of choice and the continuum hypothesis.

This example illustrates that truly explaining complex mathematical concepts to young children is often not feasible. Instead, what we get are different, related concepts explained to different age groups.

The Dangers of Oversimplification

Overly simplified explanations can lead to misconceptions and a false sense of understanding. For example, explaining reproduction to a child by saying "the stork brings babies" might be simple, but it's entirely inaccurate and potentially harmful in the long run.

Even when we try to simplify while maintaining some level of accuracy, we often end up with explanations that raise more questions than they answer. This is because complex ideas often rely on a network of interconnected concepts that can't be easily separated or simplified.

The Hunger for Complexity

Contrary to popular belief, there's often a significant appetite for technical, rigorous explanations among educated audiences. Many people don't want watered-down explanations; they want explanations they can handle, which are often more complex than what's typically offered in popular science.

This channel, for instance, has found success with highly technical interviews and discussions. People are capable of engaging with complex ideas, and there's a real desire for content that doesn't shy away from technicalities.

The Learning Process and Unconscious Questions

When we struggle to understand an explanation, it's often because we have unconscious questions that aren't being addressed. These unasked questions can create a feeling that something is left unexplained, even if we can't articulate what that something is.

For example, when explaining General Relativity using the analogy of a bowling ball on a mattress, several unconscious questions might arise:

• Why is the object constrained to the mattress?
• Why does it have to move at all?
• Why can't it just stay still?

These questions, while not explicitly stated, can create a sense of incomplete understanding.

The Challenge of Learning

Learning complex subjects is inherently challenging, and that's okay. Often, our difficulties in understanding stem from what we don't know we don't know - our ignorance about our ignorance.

When learning without a teacher, we often have to repeatedly revisit concepts and examples, sometimes becoming more confused before we have a breakthrough. This process of grappling with confusion is a natural and necessary part of learning.

The Physical Aspect of Learning

There's a physical, neurological component to learning and knowledge acquisition. Just as you can't expect to lift heavy weights without training, you can't expect to understand complex concepts without mental preparation and practice.

However, there is value in exposing yourself to concepts that are currently beyond your understanding. As John von Neumann said, "You don't understand mathematics, you just get used to it." While this is somewhat tongue-in-cheek, it contains a kernel of truth. Familiarity with complex terms and ideas can reduce the intimidation factor, allowing you to grasp the spirit of concepts even if you don't fully understand all the details yet.

Levels of Understanding

We can think of understanding in three levels:

1. Grasping the gist of a concept
2. Understanding with rigor
3. Being able to smoothly transition between the gist and the rigorous understanding, and even invent new concepts

The third level comes with deep familiarity and extensive practice with the concepts.

Embracing the Learning Journey

When engaging with complex ideas, it's important to remember that the goal isn't always complete understanding on the first encounter. Sometimes, the point is just to "get wet" - to expose yourself to new ideas and become more comfortable with complex terminology and concepts.

Don't feel discouraged if you don't understand everything immediately. Learning is a process, and it's okay to feel overwhelmed at times. The important thing is to keep engaging with challenging ideas and to recognize that understanding often comes gradually, with repeated exposure and practice.

Conclusion

The idea that all concepts should be explainable to a 5-year-old is a myth that oversimplifies the nature of knowledge and understanding. Complex ideas often require complex explanations, and that's not a failing of the explainer or the learner - it's a reality of the subject matter.

Instead of demanding simplicity at every turn, we should embrace complexity and recognize the value of rigorous, detailed explanations. We should also acknowledge the challenges inherent in learning difficult subjects and be patient with ourselves as we navigate the learning process.

By moving beyond the "explain it to a 5-year-old" mentality, we open ourselves up to a richer, more nuanced understanding of the world around us. We allow ourselves to engage with ideas in their full complexity, recognizing that sometimes, the journey to understanding is just as valuable as the destination.

Article created from: https://www.youtube.com/watch?v=eASBzSNB8ts