A Mind for Numbers — Brain Gym

Section 01

Focused vs. Diffuse Mode

"The harder you push your brain to come up with something creative, the less creative your ideas will be. Relaxation is an important part of hard work." — Shaun Wassell, computer engineering student

Your brain has two thinking modes. Focused mode is tight, concentrated, analytical—like a flashlight with a narrow beam. Diffuse mode is relaxed, big-picture thinking that makes unexpected connections. Toggle between them to see how thoughts travel differently.

Focused

Diffuse

Focused Mode

In focused mode, bumpers are packed tight. Your thought bounces in a small area—great for familiar problems, but you might miss solutions elsewhere.

Section 02

Chunking

"Mathematics is amazingly compressible: you may struggle a long time, step by step, to work through the same process. But once you really understand it, there is often a tremendous mental compression." — William Thurston, Fields Medal winner

Chunking compresses many small ideas into one smoothly recalled unit. Click the pieces below to group them into chunks. Watch how separate fragments merge into powerful, compact knowledge.

Click related pieces to group them into chunks

Section 03

Working Memory Limits

"Your working memory holds only about four chunks of information. We tend to automatically group memory items into chunks, so it seems bigger than it actually is." — Barbara Oakley

Your working memory is like a juggler with only 4 slots. Test yours: watch the sequence, then type it back. How far can you go before the juggler drops a ball?

Ready?

Section 04

The Einstellung Effect

"An idea you already have in mind, or your simple initial thought, prevents a better idea or solution from being found." — Barbara Oakley

Einstellung (German for "mindset") is when your existing approach blocks you from seeing a better solution. Try this number puzzle: find pairs that sum to 10. The obvious pairs are easy—but can you find the hidden pair that requires stepping back?

Select two numbers that add up to 10. Find all pairs!

Section 05

The Pomodoro Technique

"The dread of doing a task uses up more time and energy than doing the task itself." — Rita Emmett, procrastination expert

Procrastination triggers real pain in anticipation—but the pain vanishes once you start. The Pomodoro technique: 25 minutes focused work → reward. Focus on process, not product. Try a mini Pomodoro below.

25:00

Focus on process, not product.

(Demo uses 1-minute cycles for quick testing)

Section 06

Illusions of Competence

"Merely glancing at a problem's solution and thinking you know how to do it is one of the most common illusions of competence in learning." — Barbara Oakley

Rereading feels productive but barely works. You think you know the material because it looks familiar—but can you actually recall it? Test yourself: read the fact, then see if you can pick the right answer without looking back.

Section 07

The Memory Palace

"We have outstanding visual and spatial memory systems. Memory tricks used by ancient and modern experts tap into these naturally supersized abilities." — Barbara Oakley

Your brain remembers places brilliantly. The memory palace technique: deposit vivid images along a familiar route. Click each room below to reveal the learning concept hidden inside.

Click rooms to reveal the learning concepts. Can you recall them all?

Section 08

Deliberate Practice

"Deficiencies of innate ability may be compensated for through persistent hard work and concentration. One might say that work substitutes for talent, or better yet that it creates talent." — Santiago Ramón y Cajal, Nobel Laureate

Experts don't just practice—they focus on their weakest points. A violinist drills the fumbled passage, not the easy one. Interleaving (mixing problem types) beats overlearning (repeating the same type). Build your chunked library, and Lady Luck will be on your side.

🧱→🏛️

The Brick Wall Metaphor

Learning is like building a brick wall. Each focused session lays bricks. Each rest period lets the mortar dry. Cram and you get a pile of rubble. Space it out and you build a cathedral.

🧱

Spaced Practice

Strong wall

💥

Cramming

Rubble pile

"The first principle is that you must not fool yourself—and you are the easiest person to fool." — Richard Feynman

The 10 Rules of Good Studying

1. Use recall — don't just reread
2. Test yourself — constantly
3. Chunk — compress ideas into units
4. Space repetition — a little every day
5. Interleave — mix problem types
6. Take breaks — let diffuse mode work
7. Use analogies — explain like you're 5
8. Focus — Pomodoro, no distractions
9. Eat your frogs first — hardest thing first
10. Mental contrast — visualize your goal