alt Hacker News388 years ago, Galileo worked out why human giants can't exist
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TV Tropes calls it the Square-Cube Law, and cites Galileo in the real life examples section:
https://tvtropes.org/pmwiki/pmwiki.php/Main/SquareCubeLaw
It's the reason why giant robots probably couldn't be as agile or powerful as in something like Transformers or Gundam, and why kaiju like King Kong or Godzilla couldn't exist in the real world.
I'm not sure about this... for pure shear or tension load the strength scales by the square of the diameter, so increasing beam "linear size" by 10 gives only 100x strength, but our beam-bones would usually fail in bending, not in shear, where the strength scales by a factor of 10,000x (stress = (bending Moment x beam radius) / (Area Moment of Inertia of beam cross section), where the Area moment of inertia is a function of cross section diameter^4) And don't we already know that giant dinosaurs existed?
> for if his height be increased inordinately he will fall and be crushed under his own weight
> scaled-up wooden houses would not support their own roofs
Hmmm this argument fails to mention giraffes, elephants or dinosaurs. (Edit: ooops it does mention elephants and dinosaurs) But clearly, land animals with bones can be quite a bit larger than humans. Similarly the houses comment ignores that large multi-story wooden buildings that support their own roofs exist, and already existed in Galileo’s time.
There might be reasons today’s evolution of human anatomy can’t get any larger than 9 feet tall, but this argument about physics and bones and square vs cube growth rates is pretty unconvincing. The argument skips right past the idea of “giants” that are only 1.5x or 2x or 3x taller, rather than 10x or 100x taller. Sure animals cannot be “inordinately” bigger, but that does not explain why they can’t be twice as big.
About the argument that a beam's strength:weight ratio worsens as it grows: do the artificial structures humans use, like house frames or bridges' trusses, recover strength:weight ratio? Would a theoretical giant with a skeletal structure like a bridge or a house's frame be better off than one with a human-like skeleton of the same material? (And, related to another comment here, guessing the actual structure of bone produces some improvement relative to something solid?)
What about dinosaurs? not sure he's explanation makes sense given we have proven that giant dinosaurs where roaming on earth for ages.
I’d heard this before, but it’s a fun reminder of how, in a sense, the laws of physics depend on what size you are. (Or rather, which laws have the most impact depends on the size of objects in question)
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J. B. S. Haldane discussed this in his essay On Being the Right Size:
I remember as a kid reading Lucifer's Hammer novel by Larry Nivel and J Pournelle, where at some point they discuss the theory that Earth was in a very different orbit and under different gravitational conditions that allowed giant dinosaurs to exist. It didn't make much sense to me at the time, but the description of muscle and bone cross-section as the core factor in their performance stayed with me.
This seems like a flawed argument. By the logic in this article, wouldn't horses or cows, which weigh multiple times what a human does, have to have stocky rather than slender legs?
Important to keep in mind that the earth was smaller back then with lower gravity. The earth grows like all other living organisms.
I don't know how convinced I am. First there were dinosaurs in the past, the brachiosaurus was 4 x as big as an elephant and there are probably yet undiscovered dinosaurs that were even bigger given discovery of partial fossils like the Sauroposeidon.
Also we know in the past there were dargonflys with wingspans greater than 2 feet and centipedes that grew as long as a car.
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In general, the argument holds some water, but it ignores the fact that human bones can take a lot more than their own weight today — depending, obviously, on how they are stressed (they can probably take maximum force along their lengthwise axis, but depends on the bone too — femur is said to take 30x the body weight, and we've got 2). Also, their structures — just like bending an edge on thin metal sheet — can significantly increase their carrying strength without changing the weight.
I'd also note that it does not take a lot for someone to be a "giant". When average height was 1.6m, someone 2.2m tall was certainly a "giant" (they are even today, but it means they'd frequently be asked if they are playing basketball :)).
But even if they were 4m tall, they'd certainly be called a giant and certainly regular human bones could handle weight up to say 450 kg. Heck, someone brought up horses and cows, and horses certainly jump off two hind legs and land on two front ones, putting a lot more than 600kg of their standing weight on them.
So in short, Scientific American is right to bring up the fact that someone like Galileo would put his genius to folk topics back in the day, we do have a bit more to lean on today to come up with even stronger conclusions — so they'd better highlight how his thinking compares to what was known back in the day.