## Saturday, 4 August 2018

### Is it cruel for giants to ride mammoths in Game of Thrones?

In season 4, episode 9, of Game of thrones (GoT) there are several scenes of tame mammoths: in one, a mammoth is being ridden by a GoT giant, much as a man would ride a horse.

 Click to enlarge; still from GoT; colours changed for clarity
When I saw that scene anew, my mind immediately came up, uninvited and unasked for, with the question whether a mammoth could in fact carry a giant. Is that a silly question? Of course it is, but this entire blog is to a large extent about serious answers to silly questions, so there you are.

Unfortunately, an internet search for questions such as 'How many giants can you fit on a mammoth?'  did not provide anything useful. That was disappointing, but perhaps publishing this post will change that sad state of affairs. Forced to come up with an answer myself, I divided the problem in parts. The first asks 'What is the mass and weight of a GoT giant?', and the second concerns an educated guess at the load-carrying capacity of a mammoth.

What are the mass and weight of a GoT giant?
I had already answered that question in a post built on well-known animal scaling laws, but a later image made me think that the giants were well over twice as tall as a man, so I looked at the question again.

The basic principle is simple: if you scale an animal up with a factor x, its weight will by multiplied by the third power of x, but the cross section of its bones is only multiplied by the square of x, not enough to deal with the increased mass. Bones of large animals must be relatively thicker than of small ones. In that post, I scaled the height of a 1.8 m man weighing 80 kg up by a factor 2, but the width and breadth had to be multiplied not by 2 but by 2.8, which I rounded up to 3.0. The giant's weight became 80 x 2 x 3 x 3 = 1440 kg.

 Click to enlarge; still from GoT; colours changed for clarity

In the new scene, shown above, the giant certainly seemed more than twice as high as the men around him, but foreshortening made it difficult to be certain. But if you understand perspective a bit you know that you can use vanishing points to put things into, well, perspective. The troops are standing in fairly orderly lines, allowing some lines to vanishing pints and a horizon to be drawn. Vertical lines indicate the height of the giant and a man. Once a man and the giant could be placed on the same set of lines to a vanishing point, the job is nearly done. The height of the man is given by the line AB. Using the perspective lines AB can be projected as A'B' onto the height line of the giant. All that is needed then is to estimate how much taller the giant's is than A'B'. That was about 2.8 times, so if we take a 1.75 m tall man the giant becomes an incredible 4.9 m tall. The range of 2.0 to 2.8 times a man is very large; either my estimates are off, or giants are very variable, or the makers of GoT were not too consistent with their special effects. I suspect the latter; the image at the top suggests that the giant is fairly small relative to the mammoth. Let's pretend otherwise.

 Click to enlarge; copyright Gert van Dijk

Does that affect the giant's mass to a relevant degree? Yes, very much so. The graph above shows the mass of a giant for a range of scaling factors, from 1 to 2.8. Note that the scaling factor of 1 represents the original man at 80 kg. In these estimates the height of the giant is 1.75 m multiplied by the scaling factor, and the factors for width and breadth are adapted as explained before, but without rounding up (for the mathematically inclined, their factor is the height scale factor to the power of 1.5). For a giant twice the height, we get a value of 1280 kg (less than the earlier 1440 kg because I did not round up). A factor of 2.8 results in a staggering mass of 4917 kg. That is a lot of giant...

But my estimate may have been off, so let's also consider height scale factors of 2.0 and 2.4, resulting in masses of 1280 and 2654 kg. Gravity in GoT is probably the same as on Earth, as people move just as they do on Earth, so we step from mass to weight as we do on Earth (meaning without thinking about it).

 Click to enlarge; left part: Gert van Dijk; right half: Mauricio Antón

I assume that GoT mammoths are the same size as Earth's woolly mammoths, because I could not find a scene that had mammoths standing conveniently still next to a group of people. Scenes of mammoths with people around them in GoT do not suggest that the mammoths were larger than elephants. I took an excellent scale drawings of extinct elephants, done by the illustrator Mauricio Anton, and put the modified giants next to them. The image was copied from this book. Mr Anton often poses animals next to another, with a background of squared giving the scale. That works very well so I copied the idea, with gratitude, and made a similar image for giants to the same scale as Antón's picture of elephants. Mind you, the left elephant is your prototypical mammth.

The giants are very, very large, aren't they? They can actually look over a mammoth. It makes you wonder whether they could in fact push them over if they wanted to...

How much weight can a mammoth carry?
The only way I could think of to answer this question was to see how much weight living elephants can carry. African elephants are not very cooperative in this regard, but there are data on Asian elephants. Apparently some people are worried that putting tourists on elephant's back harms the elephants, and I found a detailed defence by a company doing just that, saying that their elephants, with a weight range of 2081 to 5000 kg, carry tourists and gear that together make up 4.9 to 13.0% of their body weight. They also state that elephants can carry up to 25% of their weight without discomfort, but that percentage is based on studies in horses. If you look up the article on 'pack animals' in Wikipedia, you will find numbers for camels, yaks, llamas, mule, horses and reindeer. If you try to compare those with typical weights of these animals, you end up with values of about 20-30% of the animal's weight. My guess is that the percentage should be lower for larger animals, because the safety margin might be smaller, seeing how their own skeletons already make up more and more of their mass as their size increases. So it is probably wise to restrict the load on a mammoth to a maximum of 20 or perhaps 25% of their body mass.

Actually, most species of mammoth were only about as large as a modern Asian elephant, and the maximum weight of those is around 5000 kg. Several sources state that the woolly mammoth was about the size of an African elephant, so male 'woollies' must have weighed up to 6000 kg.

Putting two and two together
So we have a 6000 kg big male woolly elephant, and we make it carry 20-25% of its weight, or 1200-1500 kg. Come to think of it, it may be wise to ask the mammoth to do that rather than 'make' it do so. A discontent mammoth might cause all kinds of unpleasantness. Our giants with height scaling factors of 2.0, 2.4 and 2.8 weighed 1280, 2654 and 4917 kg respectively. Obviously, only very small giants should be allowed to ride mammoths ('small giants'??). Putting a really large giant on a mammoth would definitely constitute cruelty to mammoths. This must not be allowed to continue!

Mind you, with only one season left for GoT, and with the state of general carnage we have seen so far, all giants may by now have been recruited as soldiers in the army of the dead. Without mincing words, they are all zombified; it's sad, actually. Mammoths may all be zombified too, to the very last calf, which I personally find even sadder.

But the good news is that zombified mammoths probably are beyond suffering, so animal welfare concerns probably do not extend to dead mammoths. That's a relief!