### 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 sophisticated principles.

Sometimes all you need are intrinsic relationships like how two objects touch or what kind of shapes 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. Penguins on the inside are surrounded by other penguins giving off heat, which they absorb, keeping them warm.

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

# Science Rules

You've probably heard of Newton's laws, which 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...

# Science Rules

The fire hydrant below receives water from the ground at high speeds and redirects it toward 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 concerns the way that light moves:

Rule: Light takes the path between two points that takes the least time.

Typically, this means that light travels in a straight line, as a straight line is the shortest distance between two points. However, this can change when the speed of light isn't constant — for example, light travels faster through air than through water.

You've lost a ball at the bottom of a pond, and shine your flashlight into the pond to try to find where it sank. Which path will light take to reach the ball?

# 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 perplexing.

But don't take our word for it — see for yourself. In the Light chapter, you can explore more laws that govern electricity and magnetism and how they illuminate our world. The next quiz offers a preview into these rules, and you can start unravelling these concepts in a house of mirrors.

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