Saturday, 11 June 2016

The anatomy of giants in 'Game of Thrones': did they get it right?

Every now and then a giant shows up in the television series Game of Thrones. Obviously, GoT is not a nature documentary so there is no reason to be difficult and analyse it scientifically. After all, it has dragons that cannot fly but do. But as their eggs only hatch after having roasted in a funeral pyre there is magic involved, and that should do the trick. Still, every time a giant ambles across the screen, the science routines in my mind spring into action and start wondering about its anatomy.

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The giants do not just look tall but broad as well, and that makes sense. Their legs seem extremely broad and columnar, as wide as the feet. The feet do not even stick out much in front, unlike ours. The outer shape of the clothing suggests that the giant has feet like an elephant, with toes and a big elastic pad in the sole, all encased in a cylinder. But all those rags and furs hide the giant's shape so it is hard to tell. Perhaps the actor is standing on high heels or stilts to add some height, and the wide trouser legs are meant to hide that. The leg/foot assembly does look rather long.

So every time I see a giant I think: 'That looks convincing; I wonder whether they asked some biologist how to make a giant'. And then of course my attention is diverted away from that by someone being murdered unexpectedly in a gruesome manner; it's GoT, after all. In this series people die all the time, and with some recent story developments they might even do so more than once. Recently (series 6, episode 7) a giant stood still in one shot, together with some puny humans. His name is apparently 'Wun Weg Wun Dar Wun', in case you wonder, or 'Wun Wun' for short. I thought I should get that frame to have a closer look, after the killing would be over (temporarily, that is).

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So here is the shot in question. The giant appears twice as tall as the man on the left, who I suppose is normal height. I estimated that man's height to be 1.8 meters, so the giant would be 3.6 m. tall. Some internet searching revealed that the actor playing Wun Wun is over 2.1 m tall. What the producers  did was to use low camera angles to simulate his size. Here is a video of that, but be warned: Wun Wun is visible for only a few seconds.

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I copied the giant, and reduced his size to what should be about 2.1 meter, compared to the 1.8 m man. I stuck him in again to get a feeling of what the actor may have looked like without special effects. Here is the result of that, including doing away with the blue overcast. It does not look as if he is walking on stilts, so the cylindrical shape of his legs is probably there to suggest just that: big legs. He looks very broad; should he? What should the proportions of a 3.6 m tall giant be like?

To find out, please read the first and second post in this blog on why body size matters. In short this is what happens if you double the length, width and height of an object or animal: its mass and hence weight will not become twice the original amount, but eight times as much. But the strength of a bone is given by its cross section, and if you only double the radius of a bone, its cross section becomes four times as large. But the bone needs to be able to support eight times the weight. This means its radius has to increase disproportionally: if the weight increases eight-fold, then the cross section needs to increase by a factor eight too. The radius needs to increase by the square root of eight, which is 2.83 times. In case you are dazzled, it boils down to this: increasing bone length by a factor of 2 means that bone diameter has to increase by a factor 2.8.

Mind you, in real life that is probably not enough ('real life'?; what am I thinking here?). Muscle strength also depends on its cross section, and to keep the same relative strength means muscle cross section has to increase by a factor 2.8 as well, meaning more muscle mass. All these extra increases in bone and muscle will add mass, so the bones have to be even thicker and... You see where this is going. At some point there is no mass left for lungs, guts or brain (judging from Wun Wun's speech patterns, some savings were indeed made in the latter department). Say we use a factor 3.0 to accommodate for all that.

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Here is a nice schematic human anatomy image found on the internet. I cut it up in sections and increased the width of the sections appropriately. Well, mostly: I reasoned that the increase should certainly apply to the thickness of weight-bearing bones, such as legs and the vertebral column. I did the same for the arms as well, or the result would look silly. But in principle pelvic and thoracic width do not need an additional increase beyond the factor two we started with. I did increase them some more, if only to give thigh muscles some room.

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Here is the result of this simple attempt. Do not forget that he is twice the size of the man we started with. The resulting giant certainly looks large as well as stocky, and so he should. Note that I increased the feet a bit more, to allow all the thicker foot bones to lie next to one another, as they must. But I did not alter foot anatomy any more. Before we discuss that further, let's approximate the giant a bit more by using the body outline and adding a suggestion of clothing.

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Here it is. This is what a morphologically reasonably sound giant, twice the height of a normal man, might look like.

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And to get a feeling for size, here is the giant next to a normal-looking human on the left, half the size. The giant is not that different from Wun Wun, confirming my intuitive guess that the designers got it right. The hands look quite good. The actor must have been covered in very thick layers of padding to get the stocky look. It is not often I get to write that the television or film industry got their biomechanics right. Regular readers will know that there was little reason to be happy before; see the posts on Avatar and John Carter of Mars.

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The one remaining matter is whether the giant should have his feet examined: can he stand on human-type feet or must he have elephantine feet, as shown above? If a 1.8 meter m. tall man has a mass of 80 kg, then simply doubling the height, depth and width wil ensure that the mass becomes 8 times as much (80 x 2 x 2 x 2), so 640 kg. But remember that we chose to increase the depth and width by a factor 3, not 2, so the mass becomes 80 x 2 x 3 x3, or a colossal 1440 kg. Wow. Being bipedal, one leg will have to be able to withstand all that weight. Mind you, we already have taken that into account as far as bone strength is concerned. Still, it is a lot. But Wikipedia tells me that draft horses weigh up to 1000 kg and giraffes weigh up to 1930kg, and these animals do not have elephantine feet at all. While running just one of their legs may be on the ground at a point in time, with a lot of dynamic forces acting on the bone as well. So I do not think a 1440 kg humanoid needs elephantine feet, but that does not mean he cannot have them. All this brings up the topic of whether very large bipedal animals should have elephantine feet with embedded toes, or whether they should have free toes, sticking out. I am in favour of the latter, but that is something for another post, on toes.    

Unless the GoT designers tell us what Wun Wun's feet look like, we will never know.  Unless... unless of course we get to see a naked giant. GoT is not afraid of nudity and there have been calls for nudity to be more equally divided among male and female cast members. Perhaps that equality should include not just sexes but species, too. So let's have a naked giant; purely for scientific reasons, obviously. Actually, just the feet would be enough, thank you so much.    

Note (March 2018): I had made a mistake by stating the weight of the corrected giant as 640 kg, but that was without taking into account the additional increases in cross sectional area, as pointed out by a commenter.  

Note (September 2018): you may wish to have a look at a later post asking whether it is unethical to let giants ride on mammoths...    
    

12 comments:

panel said...

I'm very glad to see that you seem to have taken up blogging again more regularly. Although I want to see the book done as much as anyone else, these blog posts hold me over until then.

Anonymous said...

It's always a happy surprise to see a new entry in the blog! I hope the book is going well!

Anonymous said...

Really nice to see you blogging. If it helps at all with your calculations, the giants in GoT stand 12-14ft tall and they actually have a pic of an actor in a body suit for a giant show the possible outline of one without clothing

http://gameofthrones.wikia.com/wiki/File:Giant_costume_behind_the_scenes.png

Sigmund Nastrazzurro said...

Panel"my pleasure: posts wil reappear about every month I guess.

Anonymous: that outline of the giant's body is very interesting. Thank you. I wonder whether they chose to increase limb width more than length based on biomechanical reasons; that would be great.

GnorthernGnome said...

Realise I'm a little late to the party, but wanted to say awesome post (as ever). As per the "elephantine" feet, I wonder if the GoT designers factored in environmental selection at all here (or, indeed, if it would even better). My limited knowledge suggests that tundra adaptations generally trend towards more splayed, circular foot design, so perhaps that explains Wun Wun? That said, I really have no idea as to the actual biomechanics involved in walking on snow all the time...

Sigmund Nastrazzurro said...

GnorthernGnome: thank you. That is a very interesting idea. It would indeed make sense to have feet with a large surface area for an animal walking on snow. I doubt the design has to be circular, but if you add a wish to prevent heat loss, that a large circular foot makes perfect sense. We will probably never know whether or not this is what drove the designers...

Keavan Ѳ said...

Argh, I typed out a long comment on my phone about giant's feet, and accidentally deleted it. I guess I'll do it again.
After rereading this post, had some thoughts on giant’s feet.

A potentially important consideration is that draft horses and giraffes are digitigrade, humans and elephants are plantigrade.

Human feet are weird. People who regularly walk barefoot tend to walk partly on the balls of the feet, apparently to cushion footfalls. When we run, we also tend to run on the balls of our feet. It's been suggested, when considering primative hunting practices, and the rather impressive abilities (even compared to other animals) of human marathon runners, that humans evolved to be long distance runners and walkers.
Our feet, though plantigrade, are long, and functionally digitigrade while running, and evolved specifically to do so. When we walk and stand, our columnular legs direct the force of our weight directly into the ground, saving energy. While running, our long feet, and inclination to kick off of and land back down on our toes serves to increase our leverage, increase our stride length, and decrease injury and pain due to jarring.

Elephant feet are weird. They have very large, tall, fleshy pads on their heels, raisinf the bones of the heel up such that their skeletons look (to me) like those of digitigrade walkers. It seems to me that these fleshy pad might exist to cushion footfalls and reduce strain due to jarring footfalls, considering how that is an important consideration in us humans, at a fraction of their size.
Also, though elephants are capable of running, and quite quickly too, generally they do not.


Giant's would be, well, giant, and human-like.
It seems likely to me that, due to their increased mass, the jarring stresses and energy expenditure required to walk around on their toes may make elephantine heel pads more biomechanically viable than walking around on their heels, or halfway on the balls of their feet. As elephants and most other plantigrade animals aren't runners for the most part, and many digitigrade animals are, such a significant change to the structure of the feet might necessitate a change of lifestyle: namely that plantigrade giants probably didn't evolve to be good at running, which itself suggests further lifestyle differences.
The other solution might be to make giants properly digitigrade, like a horse or theropod, potentially preserving their proficiency in running, or even turning them into dedicated runners. Doubtless this change in leg design too, would have large ramifications that I simply haven’t considered.
Admittedly, it may be that a change to foot structure doesn’t actually require that their lifestyle be changed any more than it would have to in order to accommodate their large size, as that itself would have its own ramifications.

Alright, my long-winded, poorly phrased comment is finally over.

Sigmund Nastrazzurro said...

Keavan: I think elephants are at least semi-digitigrade. If you look at the skeleton only and forget about the 'support cushion' the makes up the sole, you will believe they are digitigrade as they do walk on the tips of their toes. But that does not mean they are in fact fast like most 'real' digitigrades'. In fact, if you only look atn the outside, you would think there is a really flat foot skeleton in there.

So what is underneath the feet of Got's giants? Perhaps giants are to-walkers, but with a very large cushion filling up the spacem resulting in elephantine feet. I do not think we wil ever see a barefoot GoT giant...

HoveringAboveMyself said...

I know the post is old but there is a mistake in the weight of your giant, 640kg would be correct if was just an isometrically scaled up human but you increased its width and depth by a factor of 3, meaning its 2x3x3= 18 times as heavy as a regular human or almost 1500kg.

Sigmund Nastrazzurro said...

HoveringAboveMyself: You are quite right! The 640 kg is indeed the weight of a 80 kg man for whom all three dimensions are doubled, so the weight becomes 80x2x2x2= 640 kg. I forgot that making the legs thicker by a factor 3 instead of 2 would make the weight 80x2x3x3 = 1440kg. How stupid of me...
I will change the text when I have the time, probably a week from now.

windigo44 said...

@Keavan: If you're suggesting that humans are essentially digitigrade when running then why do my jogging shoes always wear out first on the heels? My own running mechanics are likely less efficient than those of pro marathoners but typical of average plodders striving for basic fitness. I observe my footprints in light snow & every single one shows the complete sole of the shoe in plain detail, whether I am going up the hill or down.

The nature of a runner's footstrike depends greatly on foot speed & leg extension. Watch Usain Bolt in slo-mo & see that he runs exclusively on the balls of his feet for the entire 100 meters, with his knees high & the lower leg vertical (or even behind vertical) to the ground upon contact. But with distance runners & neighborhood joggers the knees are nowhere near as high during stride & the lower leg at footstrike is considerably forward of vertical, necessitating that the foot land upon the full sole (or in an almost instantaneous ball-heel dynamic), then push off on the ball/toes.

If we walk or jog for very long only on the balls of our feet then the plantar-flexing calf muscle group fatigues very quickly & cramps up.

Also I don't buy human giants with stubby, relatively inflexible, semi-digitigrade feet like those of elephants. (The enormous troll in the first Harry Potter movie had such feet but he was CG & not real.) Standing stationary would be infuriating & energy-costly as you would rock back & forth trying to maintain balance. Elephants don't worry about this as they are not bipedal. Tables are stable because they have four legs, not two. Also, walking bipedally on elephant feet would be like shuffling around in ski boots as you'd have virtually no ability to flex/extend the foot due its severely truncated length, requiring far greater work by the knee & hip joints in order to ambulate. No, our giants need their metatarsals parallel to the ground & with toes extended beyond that in order to push off with each step & get around. The long, narrow foot structure of humans combined with the considerable range of motion of the ankle joint resulted in efficient bipedality over the evolutionary eons. Giants need feet that work like that.

Also, giants as pure digitigrades like giraffes & draft horses are a no-go for the same reasons, & doubly so because their feet are hoofed. There are no hoofed bipeds in nature.

Now avian digitigrade leg structures, though, like those of ostriches & theropod dinosaurs (T-rex), might work pretty darn well for a 10-foot tall, half-ton humanoid - but only because of those long toes. Balance/flexibility is everything when you have only two legs.

windigo44 said...

@Sigmund: Your speculations re giant physiology/morphology are nicely reasoned. A 10-foot human as having evolved into a subrace exclusively by natural selection (in contrast to a single spontaneous Robert Wadlow-type pituitary anomaly) might present with a proportionally smaller head, sloping narrow shoulders, rounded torso, more robust hip girdle, & proportionally shorter but stockier legs = a much lower center of gravity, by necessity. This is how Kodiak bears look when standing upright at 9-10 feet tall, at Goliath height. Google "bears walking on two legs" & watch them striding on their hind legs over considerable distances. (In contrast, plantigrade great apes, though similarly alternately bipedal/quadrupedal, are not rovers but essentially stationary occupiers of tropical habitats in which food is abundant & immediately available year round.)

Since bears (& not apes) are plantigrade wanderers then, the speculation of evolved 10-foot humans as being morphologically similar might be reasonable. But walking for you as a bipedal giant would be a plodding chore & travel over a significant distance for food or habitat upgrade would be impractical & overly energy-expensive. As you would not be capably migratory in this configuration your adaptability would be severely limited, meaning your kind would likely die out with environmental change. Now, if you evolved instead as a functional biped/quadruped (i.e., biomechanically ursine) while maintaining or even increasing your massive size then you & your fellow giants might have a better shot at species survival, but if you want to keep ypur characteristically human brain size/capability as well, then your forelimbs must also retain several dexterous digits & an opposable thumb. If you're not going to keep your hand basically as is (& guarantee continuous cerebral mass), then you 'd better grow some luxuriant body hair as you won't be making fires, shelters, tools & clothes. And your brain will therefore shrink over generations & capacities for conceptual language & innovative/abstract thinking will diminish while you get furrier & more club-footed. Meaning you'll basically turn into naked-faced bears. Ha!

Note: this whole analysis changes drastically if our giants were to develop theropodan lower extremities to accommodate their bulk, stride efficiently, & leave their arms & hands free to do clever stuff. They'd stay smart but be decidedly less structurally humanoid, which might be enough to disqualify the notion.

Also, when fabricating feasible giant morphology an in-depth consideration of center of gravity implications is surely indispensable.