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9 January 2013

Sorry Obama, there’s no correct answer on the horse-sized duck question

It's the perennial internet question. What would you rather fight: a horse-sized duck, or one-hundred duck-sized horses? So we took it seriously. Maybe too seriously. Warning: biology ahead.

By Alex Hern

Boris was asked it. Obama was asked it. My old student union president was asked it. What would you rather fight: a horse-sized duck, or one-hundred duck-sized horses?

Thanks to Buzzfeed‘s Michael Hastings, we now know that Obama’s team seriously considered the answer. In fact, it was only because they didn’t spot the question in time –during the president’s Q&A on Reddit– that he wasn’t given the chance to respond in public.

Hastings reports the Obama camp’s deliberations:

“Ducks are not exactly teeny-tiny—so 100 duck-sized horses (as opposed to duckling-sized horses), while smaller than a miniature pony, are still probably clocking in somewhere around ten pounds each,” one Obama official argued. “That’s a lot to kick/throw/battle.”

Who would choose to fight a duck the size of a horse? The beak. The wingspan. The ability to defend and attack in the air, on land, and in the water. “Also, lacking a weapon of some kind, how exactly do you defeat it? Wrestling it to the ground seems unlikely. Can you break its legs? Snap a wing?” the official continued. “Yet, it’s just one opponent—you can focus all your energy, attention, and strength on outsmarting it. Maybe it tires easily. Hard to know.”

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Now, I like the unnamed official’s moxie. Overthinking this sort of thing is exactly the right response. But they haven’t overthought it enough.

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The first thing that anyone taking this question seriously – which is obviously everyone – needs to consider is a key point of GCSE biology. As the height of something increases, the volume of it goes up by, roughly, the cube of the increase. So a 1cm high mouse may have a volume of 1cm3, but increase that height to 100cm and the volume will rise to 1000000cm3. Similarly, the surface area of an animal increases at the square of the height.

Height, surface area, and volume all interplay in rather important, and finely tuned, ways. For example: breathing works by gases diffusing across the surface area of your lungs. But as an animal gets bigger, the amount of tissue which needs oxygen for respiration increases in proportion with the volume. So if you increase the size of an animal by ten times, but don’t fundamentally change its shape, it could suffocate.

That works even for animals which don’t breathe. Insects are small enough that there is enough surface area for gaseous exchange just on their exoskeleton, so they don’t need lungs. But blow an insect up to the size of, say, Mothra:

And it suffocates.

Godzilla would suffocate too, of course. Godzilla vs Mothra: The Scientifically Accurate Cut is a very short film.

Same with flight. Wing power increases with the surface area of wings, but weight increases with the volume of the animal. That’s why an albatross has wings multiple times longer than its body, while a bumblebee can fly with those tiny lacy things (bumblebees flying at all is a whole ‘nother topic, of course. Scientists never really said they couldn’t, they just said that a bumblebee with rigid wings couldn’t. Luckily for bumblebees they don’t have rigid wings).

Back to horses and ducks.

Scale a duck up to the size of a horse and it would not be able to fly. In fact, it would probably not even be able to walk. Depending on the breed of duck and the size of horse, it might not even be able to breathe. There’s also the problem that the hollow bones of a duck, which make it light enough to be able to take off, don’t scale very well. Without a significant change in structure, they would get weaker as they grew thicker, rendering them even less capable of supporting the increased weight of the animal.

At the opposite side, the horse-sized ducks, faced with a massively increased surface area, would have great trouble staying warm. Their body, adapted for a size at which a far greater proportion of their weight was contained a good distance from their surface, does not have to conserve heat in the same way as a smaller animal. Their metabolism would not be able to cope, and, after a short period of incredible hunger, they would die.

At this stage, though, it’s looking like advantage to the duck-sized horses. Their death, while as inevitable as the horse-sized duck’s, might be able to be postponed by long enough to do some damage to the president. To defeat the duck, all he’d have to do is make sure it didn’t fall on him.

But there’s more.

“Duck” and “horse” are not scientific terms. All ducks are of the family Anatidae, which also includes swans and geese. Irritatingly, there is not a specific taxon for ducks and ducks alone; they are intermingled with other members of their family, and for the most part we must look at common names.

“Horse” is a common name, not only for the species Equus ferus – the domesticated horse – but also for the family Equidae, which also includes donkeys and zebras.

Why does this matter? Well, there aren’t too many Equidae left knocking around the place anymore. Three types of wild ass, three types of zebra, and wild horses. But there used to be a lot more. Including this little guy:

(It had more skin at the time.)

Mesohippus, a genus of Equidae, lived less than 40 million years ago, and was around 60cm tall. That’s significantly closer to the size of ducks, no matter which ones we pick, and suggests that, while it would still have some major physiological issues from being shrunk down, there’d be a relatively healthy survival rate of duck sized horses.

Conversely, even if we cheat and assume that “duck” refers to all Anatidae – clearly not the case – the biggest there is is the American trumpeter swan. Now, swans are some scary bloody Anatidae. But they are still significantly smaller than horses. And even the biggest ducks are smaller than swans. And all of the problems with being scaled up would still apply to them: they would be unable to fly, would be lucky to walk, and might just suffocate to death immediately.

A hundred “duck-sized horses” (a Mesohippus shrunk down to stand 30cm high) would, then, have a significant advantage over a “horse-sized duck” (a Trumpeter swan inflated to around 1.5m). If president Obama needs me, the CIA (I assume) have my number.