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?
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?)
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.
> 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) 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.
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.
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)
Note that if you disable JavaScript you can read this without the nag wall.
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?
Regarding 1, horses in particular are known to jump off two hind legs and land on their two forelegs, putting a lot more force on them than their stationary weight.
On 2, I believe that's the GP's point too — human leg bones (or horses') can obviously take a lot more than their standing/walking/running weight.
The practical limit for bipeds is probably ability to survive a fall to the ground. It's not super common, but enough people die simply from falling from standing.
On the other hand, people can learn to fall more safely (like in gymnastics and martial arts). Maybe some version of those skills could somehow become instinctual, as maybe the corresponding thing is in cats?
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.
They were larger but not as dense as mammals, we know had adaptations like less denser bones and different respiratory systems that allow for more efficiency and much more rapid growth into maturity. Modern birds show evidence of all these traits. When the Chicxulub extinction event happened it reset things so mammals got the upper hand on large sizes and eventully won out for the most part. Highly recommend The Rise and Fall of Dinosaurs, which I thought was going to be mostly stuff we learned as kids but was educational for me.
You are right that they had pneumatic bones and they were not as heavy as mammals with the same volume would have been.
Nonetheless, the biggest dinosaurs were several times heavier than the heaviest terrestrial mammals that have ever lived, which in turn were several times heavier than the biggest elephants of today.
So probably dinosaurs were close to the size limit that is imposed by the mechanical properties of vertebrate tissues like bones, tendons and muscles, while in the present terrestrial mammals the size is limited by the availability of food and by the humans who have always hunted preferentially the biggest animals they encountered, and not by the strength of their bones.
That seems to not be the reason from the latest data. Insect oxygen transfer basically doesn't scale cleanly with oxygen in the atmosphere like the original hypothesis thought.
What IS true though is that pterosaurs and later birds and bats came onto the scene, and that's just game over for giant dragonflies.
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.
https://en.wikipedia.org/wiki/On_Being_the_Right_Size
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.
> 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) 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.
Arguments around bone scaling ignores the impact forces of running. Scaling often means trading margins not just keeping all constraints the same.
True for Scientific American today, not true for Galileo.
“Dinosaur” wasn’t a thing we started knowing about until the early 1800s. Benjamin Franklin died not knowing Dinosaurs were a thing.
But Galileo would have certainly known about elephants though.
Right, that’s what I was implying. However, I looked again and the article does mention elephants and dinosaurs.
Hopefully no cheese eating space mold gets up there or we're done !
Note that if you disable JavaScript you can read this without the nag wall.
2. That would be assuming that human legs are sized at the max capacity they can carry, which is not true.
On 2, I believe that's the GP's point too — human leg bones (or horses') can obviously take a lot more than their standing/walking/running weight.
They can take more stress than standing, but the scaling law is still there.
If you scale linearly height/section the max stress won't scale linearly because the weight will scale cubically.
The practical limit for bipeds is probably ability to survive a fall to the ground. It's not super common, but enough people die simply from falling from standing.
Also we know in the past there were dargonflys with wingspans greater than 2 feet and centipedes that grew as long as a car.
Nonetheless, the biggest dinosaurs were several times heavier than the heaviest terrestrial mammals that have ever lived, which in turn were several times heavier than the biggest elephants of today.
So probably dinosaurs were close to the size limit that is imposed by the mechanical properties of vertebrate tissues like bones, tendons and muscles, while in the present terrestrial mammals the size is limited by the availability of food and by the humans who have always hunted preferentially the biggest animals they encountered, and not by the strength of their bones.
What IS true though is that pterosaurs and later birds and bats came onto the scene, and that's just game over for giant dragonflies.