Please get Tom Cruise first, please get Tom Cruise first, please get ...
In War of the Worlds, giant alien robots emerge out of the ground and begin vaporizing large numbers of actors. There’s a lot to like in those scenes, but there are three things I could not stand.
Like those three legs they walked around on. Not their fragile-appearing spindly-ness, but their actual three-ness.
There should be more legs. Around six of them, in particular.
“Look,” you might reply, “it’s an alien ship, and who knows what kinds of principles they’ve uncovered.”
Of course, that’s possible. But another way to look at it is that we Earthlings come in a large variety of body and limb plans, and yet we don’t find the three-limb design anywhere. Perhaps that’s a good argument that aliens wouldn’t build a ship with three legs.
What do we Earthlings do for limb design?
We tend to follow a law, one that may cut across all animal phyla, a law I first published in the Journal of Theoretical Biology in 2001 [ http://www.changizi.com/limb.zip ], and elaborated upon in my first book The Brain from 25,000 Feet [ see final section in http://www.changizi.com/ChangiziBrain25000Chapter1.pdf ].
This “limb law” relates an animal’s number of limbs to the length of those limbs (relative to the body’s size).
When an animal’s limbs are very long relative to its body size, I argued that the optimal reaching-out solution (that uses the least amount of “wire,” or limb material) is to have about six limbs. (This applies to animals with limbs that are approximately radially directed around a perimeter. For animals whose limbs directions are uniformly spread over a spherical surface, the expected number of limbs in this case would be about 12.)
As the animal’s limbs shorten relative to body size, the expected number of limbs rises, with tremendous numbers of limbs when the limbs are very short. (By the way, a snake is consistent with infinitely many infinitely-short limbs – i.e., no limbs.)
More generally, the law predicts that an animal’s number of limbs is inversely proportional to relative limb length. And, more specifically, the law predicts a particular proportionality constant, so that “six” is the solution in the case of really long limbs.
Letting L be the limb length and R the radius of the animal’s body, then k = L / (L + R) is the relative limb length, or “limb ratio”.
The number of limbs, N, is expected to vary approximately as
N ≈ 2π/k ≈6.28 k-1
The figure below (from my first book) shows how the number of limbs in fact relates to limb ratio, for 190 species across seven animal phyla (Annelida, Arthropoda, Cnidaria, Echinodermata, Mollusca, Vertebrata, and Tardigrada).
The predicted trend is shown with the solid line, consistent with the N ≈ 6.28k-1 equation we saw just above.
The actual trend is shown with the dotted line, leading to an empirical equation of N ≈6.24k-1.17 … or very close to the prediction.
To get a better impression of the Limb Law that Earthlings appear to follow, check out this little dynamic visual program by Eric Bolz, allowing you to vary limb length and watch how the number of limbs varies: http://www.changizi.com/limb.html . The right vertical axis allows you to modulate the limb ratio and watch the number of limbs change. The bottom axis allows you to make longer or shorter creatures. The left vertical axis just allows you to resize the creature on the page.
The alien ships from War of the Worlds should have – given their long limb length and assuming they should be treated as approximately pointing around a perimeter – around six limbs. Not three.
That’s why they look so silly. They’re outside of the sweet spot in design space for limbs.
In my next piece, I’ll discuss how this limb idea tells us why we have 10 fingers, and perhaps, therefore, why we have a base-10 number system.
This first appeared on May 10, 2010, as a feature at Science 2.0
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Mark Changizi is Professor of Human Cognition at 2AI, and the author of The Vision Revolution (Benbella Books) and the upcoming book Harnessed (Benbella Books).
I agree, three legs is not a good number for any sensible creature, but it wasn’t the makers of the film who specified that the fighting machines should have three legs, it was HG Wells himself.
In the 1950s version, it was virtually impossible for the special effects technology of the time to represent them convincingly enough, so, for the most part, they were ‘invisible’. They were visible briefly (outlined by a vague animation that looked like green sparks) as the protagonist, Doctor Clayton Forrester, pointed them out and described them as being composed of an ‘electromagnetic flux’.
There were a few things about the film that fans of the original book were disappointed with. the story was totally different, it was out of its time (late 19th century), and it was set in America (I assume because it would have failed at the box office if it were set in England). In fact, the only thing that linked it to the HG Wells story is the fighting machines, the cylinder type craft that landed like huge meteorites and the fact that the came from Mars.
The Martian aliens themselves were also different. In the book they were leathery octopus-like creatures with large disc-like eyes, but the 1950s film depicted them (very briefly) as one eyed, gangly bipeds with three fingered hands.
The Tom Cruise version also deviated from the original story in the same way as the 1950s version did, but at least the fighting machines conformed much more closely the the ones described in the book. So, I should imagine, the number of legs wasn’t an option.
One more thing to note: In the book there were also smaller, squat, six legged spider-like machines that were much faster than the fighters. These were used to hunt humans for food.
[...] 2, 2010 by changizi In How Many Limbs Should Humans Have? I described my Limb Law, an empirical law I discovered which relates how long an animal’s limbs [...]
I am curious though, that while it is true that longer limbs would necessitate more limbs to body mass, I am curious as to some of the anomalies in nature, such as a dachshund, or the daddy long legs, or perhaps the appendages to a crane or giraffe, where the body is squat and all limbs are disproportionately long including the neck and legs?
My limb theory applies to animals that can be modeled as having limbs poking out around them along a plane. Mammals mostly have “ventrally projected” (downward pointing) limbs, and so my own model doesn’t apply to them. A fuller account can be found in this link, namely the third section of this chapter from my first book: http://changizi.com/ChangiziBrain25000Chapter1.pdf Best -Mark
Fundamental logic flaw: The machines in the movie were machines
You are comparing them to living creatures
I don’t see many animals with wheels and yet they seem to work well as machines.
And then think about segway technology.
But they are machines that are (arguably) within the design space animals are in — they are a “limbed” machine, and so a comparison to a planet-filled menagerie of limbed animals seems appropriate.
wow. you really want to double down on that faulty logic, huh?
No, they are not in the same design space. One requires reproduction through genes, one does not. A being dependent on genes will inevitably evolve systems to deal with loss, hence an eight-legged spider can lose one leg and survive, whereas a 3-legged spider cannot. A machine will have a better model next year and is expendable.
Also the most efficient WOW machine needs to have the fewest number of legs for its mission. A tripod is the most stable man-made structure (or presumably alien made). the machine needs to step over obstacles and fewer legs assists this mobility pattern. Each of its legs is a potential point of attack, so minimizing them makes sense strategically.
I could go on, but you might want to admit that your bias limited your imagination.
Interesting hypothesis about the difference between machines and animals, but it is unclear why those alien limbed machines wouldn’t want to deal with limb loss (it would seem to acutely help the aliens sitting inside during their attack), and it is not clear that limb-loss helps explain why animals have as many limbs as they do. Also, your tripod idea is the nice beginnings to a reverse-engineering hypothesis for the alien-ship design, but I’d be skeptical it could be worked through. And one reason for skepticism is that there are millions of limbed animals here on Earth (and they conform very well to my “limb law”), and yet none appear to have three legs like these alien ships, nor do they deviate so significantly from the limb law that applies well across more than seven animal phyla.
That said, surely I have limits on my imagination, and there may well be alternative non-Earthly habitats and selection pressures that could, in principle, lead to a three-long-limbs design. Or, maybe there is something about the sheer size of the limbed machines that, due to size scaling issues, puts them in a qualitatively new design regime. (Although, larger size tends to lead to thicker, sturdier, legs, not more spindly ones.)
A machine doesn’t need to deal with limb loss because they don’t need to reproduce. They are expendable machines. Three legs could be the most efficient design. Also a disabled machine that lost one leg could walk home on gyroscopically balanced two legs
A machine is most efficient when it does not have any unneeded weight. Extra legs beyond what is needed make the machine more vulnerable. Can you really not imagine a futuristic synthetic material strong enough for a 1/30 slenderness ratio? It is still thicker than a daddy-long-legs spider’s legs. Also, they taper toward the bottom, just like actual real-world structural elements (see: table legs). And they seem to be very flexible.
Its much more interesting to imagine how an intelligent movie designer could have come up with his ideas than to criticize them for not fitting into your preconceived biases.
Also, you didn’t address why wheeled man-made vehicles do not work like carbon based life forms.
Machines need not reproduce, but they need to work robustly when kicking arse on an alien planet — robustness is high in the minds of engineers making war-making machines.
On wheels, human vehicles are much more plausibly in an entirely different design space. Those *limbed* alien robot machine things are much less obviously so, given that they have…limbs.
As for “more interesting to imagine how an intelligent movie designer could have come up with his ideas than to criticize them for not fitting into your preconceived biases,” I’d say both can be fun. I’m not criticizing them so much as having fun with it, and using it as a hook to talk about the design principles governing life as we know it from the data we do have (not mere “bias”).
Thanks much, -Mark
Interesting discussion. There’s one real-world analog to it that’s readily available to test your arguments: the Mars Curiosity rover is a machine designed to operate on another world that, in Changizi’s terms, came from ‘within the design space’ of human beings. It also has design constraints for survivability and robustness, just like the Martian fighting machines presumably would. Yet the Rover appears to have only two limbs for getting around (with three wheeled ‘fingers’ per limb), plus another limb for “reaching out” (or is that best defined as an ‘antenna’?) At first blush, the Rover doesn’t seem to follow the limb law at all. I’d go with jj on explaining why: it is a machine, not an evolved organism.
In fact, this raises an interesting problem with the “limb law” in general. Limbs aren’t there just to “reach out”–they’re also for locomotion. In evolved organisms, it is perhaps not efficient to think of separating these functions. But in engineered vehicles, that constraint may not be as relevant.
Maybe. But…the other explanation could be simply that we’re not very good yet at creating limbed machines that can move about.