Democratizing Physics: Borrowing Techniques from Programming for Clear, Self-Documenting Equations

 J. Rogers, SE Ohio, 07 Mar 2025, 1543

Physics is often seen as an intimidating field, filled with complex equations and obscure symbols. But what if we could make physics more accessible, intuitive, and easier to understand? What if we could borrow techniques from the world of programming—where clarity and readability are paramount—to transform the way we write and communicate physics equations? This article explores how adopting self-documenting techniques from programming can democratize physics, making it more approachable for students, researchers, and enthusiasts alike.

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The Problem with Traditional Physics Notation

Traditional physics notation is often opaque and hard to parse. Consider the following example from Planck’s Law:

$$\mathrm{<span\; style="background-color:\; white;">B</span>}<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">,</span>\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">)</span><span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">2</span>}\mathrm{<span\; style="background-color:\; white;">h</span>}{\mathrm{<span\; style="background-color:\; white;">f</span>}}^{\mathrm{<span\; style="background-color:\; white;">3</span>}}}{{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}}<span\; style="background-color:\; white;">\cdot </span>\frac{\mathrm{<span\; style="background-color:\; white;">1</span>}}{{\mathrm{<span\; style="background-color:\; white;">e</span>}}^{\mathrm{<span\; style="background-color:\; white;">h</span>}\mathrm{<span\; style="background-color:\; white;">f</span>}\mathrm{<span\; style="background-color:\; white;">/</span>}<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">k</span>}\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">)</span>}<span\; style="background-color:\; white;">-</span>\mathrm{<span\; style="background-color:\; white;">1</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

At first glance, this equation is packed with symbols ($h$, $c$, $k$) that don’t immediately convey their meaning. To understand it, you need to know:

• $h$ is Planck’s constant,

• $c$ is the speed of light,

• $k$ is Boltzmann’s constant.

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• And you need to know that h/c^2 is just a hertz to frequency conversion, and that h/k is just an inverse temperature to frequency conversion.  This is a heavy conceptual load to add to the simple problem.

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This reliance on single-letter symbols and implicit meanings creates a barrier to understanding, especially for beginners. It’s like reading code with variables named x, y, and z—without comments or context, it’s hard to know what’s going on.

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Lessons from Programming: Self-Documenting Code

In programming, self-documenting code is a best practice. Instead of writing:

x = y * z

A good programmer would write:

total_cost = price_per_unit * quantity

The second version is immediately understandable because the variable names describe their purpose. This principle can be applied to physics equations to make them more intuitive and accessible.

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Applying Self-Documenting Techniques to Physics

Let’s take the example of Planck’s Law and rewrite it using self-documenting terms:

Traditional Planck’s Law:

$$\mathrm{<span\; style="background-color:\; white;">B</span>}<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">,</span>\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">)</span><span\; style="background-color:\; white;">=</span>\frac{\mathrm{<span\; style="background-color:\; white;">2</span>}\mathrm{<span\; style="background-color:\; white;">h</span>}{\mathrm{<span\; style="background-color:\; white;">f</span>}}^{\mathrm{<span\; style="background-color:\; white;">3</span>}}}{{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}}<span\; style="background-color:\; white;">\cdot </span>\frac{\mathrm{<span\; style="background-color:\; white;">1</span>}}{{\mathrm{<span\; style="background-color:\; white;">e</span>}}^{\mathrm{<span\; style="background-color:\; white;">h</span>}\mathrm{<span\; style="background-color:\; white;">f</span>}\mathrm{<span\; style="background-color:\; white;">/</span>}<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">k</span>}\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">)</span>}<span\; style="background-color:\; white;">-</span>\mathrm{<span\; style="background-color:\; white;">1</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Self-Documenting Planck’s Law:

$$\mathrm{<span\; style="background-color:\; white;">B</span>}<span\; style="background-color:\; white;">(</span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">,</span>\mathrm{<span\; style="background-color:\; white;">T</span>}<span\; style="background-color:\; white;">)</span><span\; style="background-color:\; white;">=</span>\frac{\text{<span style="background-color: white;">frequency\_energy</span>}}{\text{<span style="background-color: white;">frequency\_distribution\_factor</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Where:

• $\text{frequency\_energy}=2{\text{Hz}}_{\text{kg}}{f}^3$,

• $\text{frequency\_distribution\_factor}=e^{f\mathrm{/}(T{\text{K}}_{\text{Hz}})}-1$.

• Hzkg  = h/c^2
  
  

KHz  =  k/h 

Here’s why this works:

1. Clear Variable Names: Instead of $h$, $c$, and $k$, we use descriptive terms like ${\text{Hz}}_{\text{kg}}$ (frequency-to-mass conversion factor) and ${\text{K}}_{\text{Hz}}$ (temperature-to-frequency conversion factor).
   
   

2. Modular Structure: The equation is broken into logical components that reflect the underlying physics.
   
   

3. No Hidden Constants: The conversion factors ${\text{Hz}}_{\text{kg}}$ and ${\text{K}}_{\text{Hz}}$ explicitly show the unit transformations being performed.

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Benefits of Self-Documenting Physics

1. Enhanced Clarity

Self-documenting equations are easier to read and understand. For example:

• $\text{frequency\_energy}$

  
  

  frequency_energy clearly describes the energy density of blackbody radiation at a given frequency.

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• $\text{frequency\_distribution\_factor}$ describes the statistical distribution of photon energies at a given temperature.

2. Reduced Cognitive Load

By using descriptive terms, we reduce the mental effort required to parse equations. This is especially helpful for beginners who are still learning the meaning of traditional symbols.

3. Improved Communication

Self-documenting equations make it easier to communicate ideas across disciplines. For example, a programmer or engineer unfamiliar with physics notation can still understand the equation because the terms are descriptive.

4. Educational Value

This approach is a powerful teaching tool. It helps students focus on the physical meaning of the terms rather than getting bogged down by abstract symbols.

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Examples of Self-Documenting Physics

Example 1: Einstein’s Mass-Energy Equivalence

Traditional:

$$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">m</span>}{\mathrm{<span\; style="background-color:\; white;">c</span>}}^{\mathrm{<span\; style="background-color:\; white;">2</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Self-Documenting:

$$\mathrm{<span\; style="background-color:\; white;">E</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">m</span>}<span\; style="background-color:\; white;">\cdot </span>{\text{<span style="background-color: white;">kg</span>}}_{\mathrm{<span\; style="background-color:\; white;">E</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Where ${\text{kg}}_E=c^2$ is the mass-to-energy conversion factor.

Example 2: Frequency-Wavelength Relationship

Traditional:

$$\mathrm{<span\; style="background-color:\; white;">c</span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">f</span>}\mathrm{<span\; style="background-color:\; white;">\lambda </span>}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Self-Documenting:

$$\mathrm{<span\; style="background-color:\; white;">\lambda </span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">\cdot </span>{\text{<span style="background-color: white;">Hz</span>}}_{\text{<span style="background-color: white;">m</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

Where ${\text{Hz}}_{\text{m}}=\frac{1}{c}$ is the frequency-to-inverse-wavelength conversion factor.

$$\mathrm{<span\; style="background-color:\; white;"><br\; class="Apple-interchange-newline">\lambda </span>}<span\; style="background-color:\; white;">=</span>\mathrm{<span\; style="background-color:\; white;">f</span>}<span\; style="background-color:\; white;">\cdot </span>{\text{<span style="background-color: white;">Hz</span>}}_{\text{<span style="background-color: white;">m</span>}}\mathrm{<span\; style="background-color:\; white;">.</span>}$$

 

Where ${\text{Hz}}_{\text{m}}=\frac{1}{c}$ is the frequency-to-mass conversion factor.

kg_E = c^2  is the mass to energy conversion factor.

E_kg = 1/c^2 is the energy to mass conversion factor.

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Challenges and Considerations

While self-documenting physics has many benefits, there are some challenges:

1. Notation Length: Descriptive terms can make equations longer. However, this is a trade-off for clarity.
   
   

2. Adoption: Traditional notation is deeply ingrained in physics. Widespread adoption of self-documenting techniques would require a cultural shift.
   
   

3. Context Dependency: Some terms may still require context to fully understand. For example, $\text{frequency\_energy}$ assumes knowledge of blackbody radiation.

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Conclusion: Democratizing Physics

By borrowing techniques from programming, we can make physics more accessible, intuitive, and inclusive. Self-documenting equations reduce barriers to understanding, making physics easier to learn and communicate. This approach has the potential to democratize physics, opening it up to a wider audience and fostering greater collaboration across disciplines.

Imagine a world where physics equations are as clear and readable as well-written code. This is not just a dream—it’s a real possibility, and it starts with adopting self-documenting techniques in how we write and teach physics.

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Call to Action

If you’re a physicist, educator, or student, consider experimenting with self-documenting techniques in your work. Share your experiences and help build a community around clear, accessible physics. Together, we can make physics more approachable for everyone.