## 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!

Anonymous said...

it seems to me, based on this, that the question is less of "can giants ride mammoths?"...and more of "do giants need to bother riding mammoths?"
:)

-anthony

Sigmund Nastrazzurro said...

Anthony: good one!

Petr said...

What a fun post! Even though i am aware of the square cube law, it's still mindblowing how much heftier beasts get as they grow larger!

Sigmund Nastrazzurro said...

Petr: I agree; I'm quite familiar with scaling effects by now, but seeing the giant next to a mammoth really makes a difference, doesn't it?

Petr said...

Yeah. Definitely. Really drives home the term giant though. you certainly wouldn't want this beefy boy to step on your big toe. :D

was said...

I study also issue of Giants
But more realistic look, instead of 3,6 meter, I went for 2,4 meter hight.
the grow factor is 1,35 what give body mass of 197 kg
But Femur Bone cross section is only increased by factor 1,58
(sqrt (1,35x2x2x2)=1,58 )
What give body mass of 126 kg. (1,58 x80 kg)
To match 197 kg the femur bone need increase factor 2,46
(197/126= 1.56 x 1,58 = 2,46 )
what give Femur bone of 4,39 cm ø, compare to 2,8cm ø of Human of 180 cm hight.

Other issue is Food
A Human of 2,4 meter hight need allot Food
around 3~4 time more as human of 180 cm size
(Based on Joule consumption of hard working human per day.)
The GoT Giants are around 1440kg there Food consumption must be "Gigantic"
Instead riding Mammuts they would eat them...

Sigmund Nastrazzurro said...

Miichel Van: Thank you. Your giants would be smnaller than the GoT ones, but for that reason more realistic. However, have you got their height right?
With a height factor of 1.35 as you wanted, the width and breadth factors become 1.57, so the weight factor becomes 1.35 x 1.57 x 1.57 = 3.33. With an original weight of 80 kg, you then get 266 kg for your giant of 1.35 times his original height.

You are certainly right to worry about their food consumption. A big rabbit is like a peanut, and a whole reindeer is probably a nice dinner. As for eating mammoths, well, that's probably an animal welfare issue...

was said...

I use this: 1.35x1,35x1,35 = 2,46 x 80 = 196, 83 Kilograms
next to that i look in Wiki about Tallest people and Bodymass
like Robert Wadlow who was 2.72 m high and weight 220 kg
and Gabriel Estavao Monjane how had hight 2,44 meter and weight 193 kg

Petr said...

@Michael - Yeah, but you are using anomalous individuals of one species as a basis for another. I don't think that is good enough to illustrate what proportions an actual giant would have.

Those people you mentioned also needed crutches to walk, because they weren't sufficiently well-proportioned for their height to support their weight unassisted, so I would side with Sigmund (Gert) here in that an actual giant would need to be much more robust to be viable, which means a higher overall mass, much thicker bones and probably an even steeper caloric intake than you expect.

I agree it's a fun experiment to think about though.

Sigmund Nastrazzurro said...

michael van: Aha, I see now. By using the same scaling factor for all three dimensions your resulting giants will have bones and musles that are, relatively speaking, weaker than for the unscaled 'prototype'. There is a doubnle effect there, because the adpated scaling factors do not yet take into consideration the added weight of the thiker limbs, which means that even the adapted bones are relatively weak.
I don't think you should worry much too about the difference between the doubly weak 196 kg 'minigiant'and his sturdier 266 kg cousin. That's still a reasonable mass. A male gorilla weighs up to 195 kg, and they are not very tall.
I think Petr is on the right track about the examples: many of these people suffered from too much growth hormone and had various health problems. You may wonder whether they had these problems just because their proportions were nòt scaled properly according to biological scaling laws. (I do not know how nature manages to get the proportions right when animals evolve a large size; trial and errror each time?.)

Petr said...
This comment has been removed by the author.
Petr said...

All this talk about giants has made me wonder about the proportions of probably the most beloved giant of paper and screen, Hagrid. In the films he's portrayed as being 260 cm tall, 1.48 times taller than the average male human.

I haven't adjusted the calculations for extra beefiness originally and got these results:

The average weight of a male human is 89 kg, and by taking that number and multiplying it by 1.48^3 (which is roughly 3.24), you get that Hagrid in the films weighed around 290 kg.

Now in the books he's described as being twice as tall as an average human, so that would make him around 3.5 meters tall, and you'd then have to multiply the average weight by 8 (2^3) which is a whopping 712 kilograms. Yikes.

I then started to wonder why my numbers were so much lower than yours and read the blog article again.

If I were to follow your example, then the formula for movie Hagrid would be 89*1.48*2.98*2.98, which would put him at 790 kg, and he honestly didn't look THAT fat in the film, so if I toned it down a bit but still made him gain weight faster than he gains height, the calculation would be 1.48*2*2, which is 527 kg, which is still a whole lot, but not nearly as outrageous.

If I were to do the same with the book hagrid, then I'd essentially get very similar results to what you have gotten for the GoT giants, 89*2*3*3 would put Hagrid at 1602 kg, which is almost concerning, and a more slender version of him would be something like 89*2*2.25.2.25, which is 901 kg or 89*2*2.5*2.5, which is 1113 kg.

On the other hand, that may not be entirely unrealistic for a man who could look eye to eye with an elephant. :D

Sorry for deleting the previous comment, i didn't want to double post.

Sigmund Nastrazzurro said...

Petr: It is an excellent idea to discuss Hagrid! I I would have thought of that myself I would perhaps have written another post. I read the books but do not remember anything specific about his weight, so I'll take your word for it. If he is indeed twice as high as a man, he could look the GoT giants in the eye. I must say that the films never convinced me that he was very large, whereas the makers of GoT did succeed in giving me that illusion.
Of course, there is a way to avoid the harsh results of our mathematics: magic. Perhaps magic causes properties such as bone strength to increase more with size than on our magic-deprived Earth...

Petr said...

Magic solves everything, as always, but where is the fun in that, right? :D

I don't know why I even thought about Hagrid, I just thought I'd check how he compares to the GoT giants and I thought it might be interesting to share the results here.

As for the differences between books and film adaptations, some things work on paper much better than they would in picture, and I think making Hagrid shorter in the films was a very conscious choice.

There had to have been an actual human wearing the costume and makinghim 3.5 meters tall in the films would most likely make him appear so frighteningly huge side by side with little kids, that it would become difficult to make Hagrid look gentle.

If the size difference were as stark as this, it would probably make it very difficult for Hagrid to interact with the students as well, especially the youngest ones. He wouldn't even be able to walk hand in hand with Harry, because Harry would have been too short for him, assuming Hagrid had more or less "normal" arm length in comparison with his body.

This is not something you necessarily catch on as a writer and no reader would think nothing of it, but these inconsistencies are something you need to deal with somehow when translating word into picture.

You don't need to think about this as a writer, but as a scriptwriter, you absolutely need think about such seemingly trivial things as how a 10-year old child would even be able to hold onto a giant's hand if that hand hovered naturally some 180 cm above the ground.

Hagrid would have to crouch constantly to hold his hand, and then you would never see him in full height anyway, or he would just need to carry Harry around when he'd deem it necessary to keep him close. Harry could probably fit into Hagrid's fanny pack (if he had one).

That picture of Harry being carried by Hagrid like a baby kangaroo is mildly amusing, but every time Hagrid and Harry walked hand in hand in the films, it was a magical moment, and had Hagrid been any taller in the films, those scenes wouldn't have been possible.

I think the filmmakers wanted to strike a ballance between Hagrid passing for a giant and Hagrid managing to look endearing on screen and being able to interact with the child actors comfortably. I don't even think the team behind the films wanted Hagrid to look as large as possible in the first place. He just needed to be taller than everyone else and that was it. And ultimately, I think that it was a good compromise. :)

Sorry for the rant.

Sigmund Nastrazzurro said...

Petr: those are good points, in particular the point about losing the emotional connection with a giant. I also wonder whether the filmmakers considered the maximal size that would make Hagrid large as well as believable. Perhaps the technical problems could not be solved well enough then. You would probably need a completely CGI giant to do justice to details such as hairs, the diameter of which should not increase with size. If you have a human actor to do the job, beyond a certain scale he will simply not look convincing.

Petr said...

Yeah, I guess that could be a part of the problem as well. Speaking of hair, I remember reading something about Monsters inc. and how difficult it was to render Sully. It seems we still have quite a ways to go in terms of creating realistic CGI characters, even though Pixar always seems to outdo themselves with every next film.

If I can jump franchise again, I was not particularly impressed with the way Tarkin and Leia looked in the new instalment of Star Wars, for example. Tarkin looked too twitchy and Leia looked like the had a head-shaped lantern on her neck instead of an actual face.

It seems photorealistic human faces are especially difficult to capture and reproduce completely in cgi even as an overlay over a real person's face, as opposed to environments, which I think we can do pretty well already, including things like moving debris, mud and water.