### Scientific Thinking

Each year, people spend millions of collective hours learning the rules to Sudoku. But to what end? After solving a few Sudoku puzzles, all we can say for sure is that you've learned how to play Sudoku.

In Scientific Thinking, the rules are scientific principles that you're going to put together to make predictions about the real world. Our bet is that by the end of the first chapter, you're going to know a good deal more about physics.

How's it going to work? Let's take a quick tour.

# Science Rules

Our first stop is mechanical gearings. A lot of good science gets done without any deep principles. Sometimes all you need are intrinsic things like how two objects touch or what shape they have. This puzzle is one of those cases, and you can probably solve it with your intuition.

The small gear has $10$ teeth and the big gear has $50$ teeth. When the small gear rolls around the big gear, how many times will the arrow return to its initial orientation (pointing upward)?

# Science Rules

The next stop on our tour is heat transfer. Prepare to meet your first rule:

Rule: all objects release heat in all directions.

Emperor penguins live in Antarctica and form large huddles (with up to thousands of penguins) to stay warm. Penguins on the outside are very cold, but they constantly shuffle so that each penguin spends a tiny fraction of their time on the outer edge.

When a penguin is on the outer edge, are they any warmer than if they were standing alone?

# Science Rules

You've probably heard of Newton's laws, they explain the motion of most ordinary objects.

One of Newton's great insights (known in any other circumstance as Newton's Third Law™) is our next rule:

Rule: for every push, there is an equal push in the opposite direction — if you push a box to the right, you'll receive an equal and opposite push from the box to the left.

See if you can use this to figure out our next puzzle:

The fire hydrant above receives water from the ground at high speeds and redirects it towards the right. At some point, the rusty bolts that hold it into the ground all break and the hydrant comes free.

In what direction does the fire hydrant move?

# Science Rules

Our last rule on the tour is a little bit deeper. It isn't so much a scientific principle as it is a principle about scientific principles.

Rule: no matter how we choose to look at a physical process, the outcome has to be the same — if a car collides with us from the right at $\SI{5}{\meter / \second}$, the outcome is the same as if we collide with the car from the right at $\SI{5}{\meter / \second}$.

Sometimes, all you need is a little change in perspective to turn a hard problem into an easier problem that you know how to solve.

See if you can do that here:

A train is barreling down the tracks at $\SI{200}{\kilo\meter/hr}$ toward a bouncy ball that sits on a stand. After the ball and the train collide, how fast will the ball be moving?

Hint: what happens when a ball bounces off the ground?

# Science Rules

Now you should have a better idea of the approach we're taking — learning by doing.

In this tour, we kicked the tires on a few rules. If you missed some problems, don't worry about it. In the course, we'll spend more time with each idea, getting our bearings with some lighter puzzles so that we can step up to the truly beguiling.

But don't take our word for it — see for yourself. One set of ideas we'll explore, in the Light chapter, are from the study of electricity and magnetism. In the next exploration, you'll start to unravel these concepts in a house of mirrors.

# Science Rules

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