Interactive Paradoxes

A small collection of math and probability paradoxes you can actually play with instead of just reading about. Each one gets its own page with a short explanation and a visualization you can poke at, drag, click through, or run over and over until the counterintuitive result stops feeling like a trick and starts feeling obvious.

The idea behind the project: most of these paradoxes are easy to state but can still be difficult to grasp. For many people, watching the numbers move in front of you tends to work a lot better. So every paradox here gets an interactive piece built around whatever visualization the research on that specific topic suggests will make it click fastest for the widest range of people.

Live site

gregroe.com/interactive-paradox

What's in here

The paradoxes are organized into six groups, each built around a different flavor of "how does that even make sense."

Belief Revision & Coincidence

Exploring how human intuition fails to grasp the implications of massive scales and vast opportunities.

• The Law of Truly Large Numbers
• Littlewood's Law Calculator

Clustering Illusions

How genuine randomness produces clumps, gaps, and streaks, and why we so often read them as meaningful or as "not random."

• The Clustering Illusion
• Human-made Randomness
• Random Streaks
• This Couldn't Just Be Coincidence!

The Egocentric Blind Spot

Paradoxes that trick us by making us focus on our personal perspective rather than the entire network.

• The Birthday Paradox
• The Friendship Paradox

Hidden Structures in Chaos

Investigating statistical laws that govern seemingly random or chaotic datasets.

• Benford's Law (The First-Digit Anomaly)
• The Inspection Paradox (Bus Stop Bias)
• Simpson's Paradox
• The Prosecutor's Fallacy (Base-Rate Neglect)

Information & Conditional Probability

How new information from a knowledgeable source should change the odds you assign to what you already picked.

• The Monty Hall Problem

Psychological Effects

Not mathematical paradoxes, but cognitive and memory biases that distort how we judge track records and evidence.

• The Jeane Dixon Effect

Sources

Every paradox's math and visualization design is backed by actual research rather than guesswork, and it's all logged in docs/references.md — papers, articles, and videos consulted, organized by paradox, along with a note on why each one mattered.

Tech stack

Built with Astro for static site generation, styled with Tailwind CSS, and interactive bits are plain JavaScript (no framework, no charting library dependency beyond what a specific exhibit needs).

Running it locally

You'll need Node.js 22.12 or newer.

npm install
npm run dev

That starts a local dev server, usually at http://localhost:4321. A few other commands worth knowing:

npm run build      # builds the static site into dist/
npm run preview    # serves the built site locally so you can sanity-check the build

Adding a new paradox

The site pulls its sidebar, landing page, and page headers from a single list in src/data/paradoxes.js, so adding one is mostly three steps:

1. Add an entry for it to the right group in src/data/paradoxes.js (or start a new group).
2. Create src/pages/<slug>.astro, using an existing page as a starting point.
3. Create src/scripts/paradoxes/<slug>.js for its interactive logic, and import it from that page.

Before building the visualization itself, it's worth a quick look at what the research says is the clearest way to show that particular kind of paradox to people who've never seen it before, then adding whatever you find to docs/references.md.

License

MIT — see LICENSE.