Thinking in Physics
Move beyond rote formulas by learning to analyze the world using order-of-magnitude estimation, dimensional analysis, and scaling laws. Build the practical intuition physicists use to solve complex problems on the back of an envelope.
Like Duolingo, but for Thinking in Physics. Tomo turns the whole topic into a game you play five minutes a day, until it actually sticks.
A short one: 11 levels across 2 sections, about 22 minutes end to end, roughly 4 days at five minutes a day. It moves through Reasoning from Rough Numbers and Seeing Invariants and Scale. It assumes you already know the basics.
Free forever · No credit card · iPhone & Android
Key ideas in Thinking in Physics
- Rounding to the nearest power of ten gives rapid order-of-magnitude bounds without precision math.
- A standard bathtub volume is a fraction of a cubic meter, rounding to roughly 0.1 to 0.2 m³.
- Water has a density of 1,000 kg per m³, so 0.1 m³ yields roughly 100 to 200 kg.
- Breaking an unmeasurable bulk rate into human-scale steps isolates errors to simple factors.
- Multiplying volume per breath by breathing rate gives volumetric flow per minute.
- Multiplying volumetric flow per minute by total event duration gives overall fluid volume.
- Order-of-magnitude uncertainties scale multiplicatively on a logarithmic axis.
- The geometric mean sits at the exact midpoint in log space, balancing factors of over- and under-estimation.
- Independent errors in multi-factor physical estimates tend to cancel out in log space rather than compound.
- A healthy human can mechanically sustain roughly 100 watts of useful work over long periods.
- Water density (1,000 kg/m³) anchors volume-to-mass conversions across everyday liquids.
- Standard atmosphere (~100 kPa) anchors pressure and column-of-air force estimates.
- Terms added or subtracted in a physics formula must possess identical physical dimensions.
- Dimensionally mismatched terms remain invalid regardless of what numerical constants are inserted.
- Non-algebraic functions like exponentials and sines require strictly dimensionless inputs.
- Period has dimensions of time, while gravitational acceleration g has units of length per time squared.
You've tried the other tabs
Thirty open tabs. Four facts you actually kept.
You watched. You nodded. By Sunday it was gone.
One answer, then back to scrolling.
Eight weeks. You meant to finish. You didn't.
Tomo gives Thinking in Physics the Duolingo treatment: levels, streaks, and quick quizzes that test what you just learned. That game loop is what the tabs above never had, so it's the one you actually finish.
Here's what playing it feels like
A real question from this course. Take your best guess.
Why do physicists round tricky numbers to the nearest power of ten?
Get it right to open this lesson and 10 more in the app.
How to learn Thinking in Physics, step by step
Go in order. 11 short levels across 2 sections, about 22 minutes in all, five minutes a day.
- 1
Reasoning from Rough Numbers
- Back-of-the-envelope estimation
- Dimensional analysis as a discovery tool
- 2
Seeing Invariants and Scale
- The geometry of scale
- Conserved quantities over complex forces
2 sections · 4 units · 11 levels. Built to play, not to enroll.
Questions about Thinking in Physics
How do I learn Thinking in Physics?
Go in order: start with Reasoning from Rough Numbers, then Seeing Invariants and Scale. On Tomo that's 11 short levels, about 22 minutes in all, played five minutes a day. Start free and play the first level in under a minute.
Is there a Duolingo-style app for Thinking in Physics?
Yes. Tomo works like Duolingo: short daily lessons, streaks and quick quizzes. Thinking in Physics is one of its free courses, and you can type any other topic to get a course of your own.
Is the Thinking in Physics course free?
Yes. Thinking in Physics is playable on Tomo's free plan, which doesn't expire. No credit card, no waitlist. Download the app and start your first lesson.
How long does it take to learn Thinking in Physics?
11 levels across 2 sections, about 22 minutes of play in total. It's built for five minutes a day, so you finish it a little at a time instead of all at once.
Do I need any background to start Thinking in Physics?
No. It's pitched at an intermediate level, so it starts where you are and builds up. If you can tap a phone, you can start.
Tomo is in ChatGPT
Tomo is also a ChatGPT plugin: the same playable courses, built and played inside your chat.
Add Tomo to ChatGPT- What to ask
- “Make me a Tomo course on black holes.” “Turn this chat into a Tomo course.”
- What you get
- Quick questions with instant feedback, hearts and stars, ready to play in about a minute.
- Where it goes
- No sign-up to start. Connect your Tomo account and your streak carries on in the app.
You pick the voice
Thinking in Physics is taught in the Explain Like I'm 5 style: no big words. promise.. Want a different feel? In the app you can spin up the same topic in any of Tomo's teaching styles. Same facts, totally different vibe.
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Start Thinking in Physics today.
Download Tomo, search Thinking in Physics, and play your first lesson in under a minute.