Puzzle

On bus 105, Anna sits 3 rows in front and 2 seats to the left of Brian. Chris also sits 3 rows in front and 2 seats to the left of Brian on bus 105. How can this be?

Solutions

Anna sits in the seat mentioned in the morning and Chris sits in that same seat in the evening.
Bus 105 is a double-decker. Anna sits directly above Chris.

What are dimensions?

Have you ever heard a carpenter talking about the dimensions of a piece of wood? Any idea about what s/he meant? One answer to the carpenter's question might be "2 by 4".

The carpenter was asking about the measurements of the wood when s/he asked about its dimensions. When we talk about living in the third dimension, we have a related idea in mind. Suppose you are telling a friend where to plant a tree behind your school. What do you need to tell your friend?

Well, first you need to tell her the distance from your school. Then you need to tell her how deep to dig the hole. Of course, if you'd told me you'd dug the hole already, then I wouldn't have asked such a silly question! You could just wait until she tripped over the hole after wandering around all afternoon! Seriously, the location of the hole is fixed by three perpendicular distances: the distance east, the distance north, and the distance down.

These three distances give the "measures" of the hole in relation to your school. Each measurement is called a dimension. We talk about three dimensions since the location of the hole, like anything in our physical world, is determined according to three measurements.

How did that puzzle relate to dimensions?

Many people think of time as another dimension. Location in time does specify another "measure" or dimension. But, just as there was a second answer to the puzzle, there is at least one other way to think about other dimensions. We can add another physical measurement to the three measurements of our space.

What if we lived in a world with only two dimensions? Let's visit Flatland.