What do you think about the giant in The BFG? I haven’t seen the movie, but it is a great opportunity to talk about giants and scale.
Let me start with two people. They have the exact same shape, but one is a giant and one is normally sized. Here is my picture:
This is just some random giant, not too big (it would be harder to see the size). But notice that the giant is both taller and has thicker legs. If you calculated the ratio of leg thickness to height for both people, you would get the same value.
This is not the correct way for real giants. Here is a sketch of an elephant and a deer (the elephant is like a giant deer–just roll with it).
Although the deer doesn’t have a trunk like the elephant, they both have four legs. But look at the legs. Is the elephant just a bigger version of the deer? Nope. The elephant has thicker legs, that’s for sure–but the ratio of leg thickness to height for the elephant is much larger than the ratio for the deer. These two animals aren’t just the same shape but different sizes. Why?
Let’s look at a cylindrical animal. Here are two of these animals. The left one (call it A) has a height h and a radius of R. The right one (call it B) has a height of 2h and it has the same shape so that its radius is 2R.
Now for some physics. What is the weight of animal A? If I assume it has some average density, then its weight will be proportional to its volume. So, the volumes of the two animals will be:
Doubling the height of the cylindrical animal (and keeping the same shape) increases the volume by a factor of eight. Now what about the pressure in the legs? Yes, these “animals” have only one “leg,” but I will proceed anyway. The pressure on these legs is the weight of the animal divided by the cross sectional area of the leg. I don’t really care about the pressure, so let me just calculate the ratio of volume to cross sectional area for both animals.
Doubling the height of the animal doubles the pressure in the legs (leg). That is the problem. You can’t keep increasing the height of an animal and thus increasing the pressure in the leg. Eventually, something is going to break. How can you reduce the pressure in the leg? You could increase its width. That’s how biology solves a problem like this.
Go back to the elephant and the deer. The elephant is much taller, but it also has much thicker legs. It’s not just like a deer that’s bigger. Oh, you don’t like that comparison because it uses two different animals. OK, what about a small dog and a big dog? What about a small deer vs. a large deer? You can almost tell that a deer is small just by looking at a picture of it without any scale because of the thinner legs. How about another extreme example. Look at the legs of an ant. They have very thin legs compared to their body height.
The lesson here is that big things aren’t the same as small things. That might seem obvious, but it’s clearly not. Look at the giant in any movie (including The BFG). These giants look just like normal humans except they are bigger. If their biology is similar to human biology, they should look quite different. They would have much thicker legs in order to support their ginormous weight. But why aren’t they portrayed this way in movies? There are two reasons. First, giants aren’t real–well, not giants the size of BFG. Second, the movie is just that–a movie. It’s a story, not a documentary on science and giants.
I must admit, I love this story of the scale of things. I tend to retell it from time to time. If you want to see other examples of how things change with different scales, I have plenty of posts for you. And if you want a homework assignment, try drawing a giant with “realistic” legs.