Visualizing Concepts: Effective Figures & Diagrams

The Power of Visuals: From Information to Insight

Why do we draw diagrams? It's more than just an aesthetic choice. As cognitive scientists Herbert Simon and Jill Larkin famously showed, a good diagram can be computationally superior to a sentential description of the same information. By grouping related information and making relationships explicit through spatial arrangement, a diagram allows us to "read off" conclusions that would require significant effort to deduce from text. This is sometimes called a "free ride" in inference.

For an introduction to the diverse roles diagrams play in reasoning across science and mathematics, you can explore the Stanford Encyclopedia of Philosophy entry on the topic. It discusses how diagrams are not just aids, but can be part of a formal system of reasoning, a perspective highly relevant to fields like QFT where Feynman diagrams constitute a calculational framework.

With this foundational idea in mind, let's explore the key principles that make a figure effective.

Guiding Principles of Figure Design

Crafting a good figure is an exercise in guided communication. Your goal is to direct the reader's attention to the most important message, making it as easy as possible for them to understand your point.

Principle 1: Every Figure Tells a Story

A figure should not be a data dump. It should have a clear, singular message. Before you even start plotting, you should be able to articulate the figure's purpose in a single sentence. For example: "This plot shows that the energy gap closes at the critical point" or "This diagram illustrates the flow of quantum information in the teleportation protocol."

Every design choice—colors, line styles, annotations, layout—should serve to reinforce that central message. The following video provides an excellent discussion on this strategic approach.

Principle 2: Respect Cognitive Limits

Our brains are powerful but have well-known limitations. Effective design works with these limitations, not against them. A key constraint is the capacity of our working memory—we can only hold a small number of items in mind at once (typically 3-5 distinct concepts).

This cognitive constraint leads to two foundational design principles:

1. Graphical Parsimony: Keep it simple. Use the minimum number of symbols, colors, and elements necessary to convey your message. Every element on the figure should have a reason to be there. This is also known as minimalism or decluttering.
2. Chunking: Group related information into visual units. This allows the reader to perceive a complex set of elements as a single "chunk," reducing cognitive load. We naturally do this based on proximity, similarity (color, shape), and continuity, principles formalized in Gestalt psychology.

An excellent academic paper, "The Physics of Diagrams," provides a rigorous foundation for these ideas.

These principles tell us what to do (simplify, group). But how do we do it? The answer lies in the deliberate use of visual variables.

Principle 3: The Visual Toolkit

The French cartographer Jacques Bertin systematized the visual elements we can use to encode information. These are our fundamental tools:

• Position (x, y coordinates)
• Size (length, area, volume)
• Value (or brightness)
• Color (hue)
• Orientation
• Shape
• Texture

These variables are not created equal. Position is the most powerful for encoding quantitative data accurately. Color is excellent for categorical data but poor for quantitative data (is blue "more" than green?). Shape can distinguish many categories but has no inherent order. Understanding this hierarchy is key to making good design choices. "The Physics of Diagrams" paper provides a concise summary.

From Code to Publication: A Practical Workflow

As someone with strong skills in Python, Julia, and Typst/LaTeX, you are perfectly positioned to create high-quality, reproducible figures. The process is iterative and generally involves a few distinct stages.

Let's break down this workflow, focusing on the steps most relevant to a theorist.

Stage 1: Programmatic Generation (The 90% Solution)

Your starting point will almost always be a script (Python, Julia, Matlab, etc.). The default output of most plotting libraries like Matplotlib is functional for exploration but rarely suitable for publication.

The good news is that you can fix nearly all of these issues directly in your code. This is preferable as it keeps your figures fully reproducible. The video tutorial provides a step-by-step guide to transforming a default plot into a polished one. The key adjustments include:

1. Layout & Readability:

   • Vector Format: Always save your figures in a vector format (PDF, SVG, EPS). This ensures they are scalable without losing quality. Raster formats (PNG, JPG) will appear pixelated in print.
   • Font: Use a font that matches your manuscript (e.g., a serif font like Computer Modern for LaTeX) and ensure the font size is legible at the final size in the paper. A common mistake is to use a small font that becomes unreadable when the figure is shrunk to fit a column.
   • Figure Size & Aspect Ratio: Set the figure size and aspect ratio deliberately in your code to match the journal's column width (e.g., single-column, 1.5-column, or full-width). This prevents distortion.

2. Clarity & Aesthetics:

   • Colors: Choose colors deliberately. Avoid default "rainbow" colormaps, which are perceptually non-uniform. Use palettes from resources like ColorBrewer or colorcet for perceptually uniform and colorblind-safe options. Use color to highlight your story, not to decorate.
   • Line/Marker Styles: Adjust line widths and marker sizes for clarity. Lines should be thick enough to be seen, but not so thick they obscure data. Markers should be distinct.
   • Grids & Ticks: Use grids sparingly and make them light gray so they don't dominate the data. Ensure tick marks are sensible.

3. Composition:

   • Ordering (Z-order): Control which elements are drawn on top of others. Data points should typically be on top of fit lines or error bars.
   • Legend: Place the legend carefully so it doesn't obscure data. Often, placing it outside the plot area or directly annotating lines is cleaner.

The following video segments walk through these specific improvements. While the tool is Matplotlib, the concepts are universal.

Stage 2: Post-Processing in a Vector Editor (The Final 10%)

While you should aim to do as much as possible in code, sometimes you need manual control for final tweaks. This is where vector graphics editors like Inkscape (free and open-source) or Adobe Illustrator come in.

Common tasks in this stage include:

• Adding complex annotations, arrows, or labels that are difficult to position programmatically.
• Grouping multiple plots (panels) into a single multi-panel figure (e.g., Fig 1a, 1b, 1c).
• Making fine-grained adjustments to spacing and alignment.
• Converting to a format required by a journal or for use in a presentation.

Since you use Typst and LaTeX, you will be inserting PDF files. If you ever need to work with Microsoft Word, you'll need to export to SVG or EMF format to preserve vector quality.

Examples of Effective Diagrams in Physics

Let's look at two examples of complex, high-quality figures that embody these principles.

Conclusion

Designing a figure is an integral part of the research process, not an afterthought. It forces you to clarify your ideas and to think about how to best communicate them. In theoretical physics, where the concepts are abstract, a powerful diagram can be the key to unlocking a reader's understanding.

Here are the key takeaways from this lesson:

• Think Computationally: A good figure reduces the cognitive load on the reader by making information and relationships visually explicit.
• Tell a Story: Every figure must have a clear, central message. All design choices should support this narrative.
• Respect Cognitive Limits: Use the principles of parsimony (minimalism) and chunking to create clean, organized visuals.
• Master the Workflow: Use your coding skills to create reproducible, high-quality plots. Reserve vector editors for the final polishing and assembly.
• Be Deliberate: Make conscious choices about visual variables (color, shape, size), fonts, and layout. Do not rely on defaults.

In our next and final lesson of this module, we will shift from written communication to oral communication, exploring how to structure and deliver an effective seminar presentation on your theoretical work.