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.
> Clearly then if one wishes to maintain in a great giant the same proportion of limb as that found in an ordinary man he must either find a harder and stronger material for making the bones, or he must admit a diminution of strength in comparison with men of medium stature; for if his height be increased inordinately he will fall and be crushed under his own weight.
> While Galileo’s argument explains the nonexistence of human giants ...
The blog completely misreads what Galileo wrote. Galileo did not write that human giants did not exist, as the blog asserts. Galileo wrote how they could have existed, which could not have happened simply by scaled body structures.
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?
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’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.
> 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.
Yeah exactly. There’s an implicit assumption here that everything scales together in perfect proportion. This is a large and limiting and unnecessary assumption that undermines the argument somewhat. Maybe giant humans could exist with stockier legs…
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?)
> do the artificial structures humans use, like house frames or bridges' trusses recover strength:weight ratio?
There is some improvement from computer design. We have better tools to know the margins that allow us to remove as much material as possible, things like that. So we can tweak existing designs to make them more efficient, like adjusting the section of beams to make them as strong but with a few percent less materials.
But the major improvements come from using different materials and new techniques, side-stepping the scaling issue.
For example, we could not scale old arch bridge designs very far. Getting steel beams let us build truss bridges, but even these cannot be that long in a single span. Suspended bridges were a step forward, with the improvement coming not from better beams, but from removing them altogether. Then, cable-stayed bridges solved some issues with older suspension designs and we can now have very large spans. Every time, scaling up is enabled by a change in strategy.
> 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?
Looking at things like elephants and dinosaurs, there certainly would be a way to have bones strong enough to support a 10m high human-like thing. Now, whether we would recognise that thing as human, I don’t know. Every time the problem was solved, there were significant compromises. I am not sure a giraffe’s vascular system could sustain a human’s brain. Elephants are not particularly agile. Whales cannot get out of the water.
Actual bone does incorporate some things we would consider "architectural" or "engineering" techniques to do more with less, not least of which they are composite materials and not mere rocks. They remodel the structure dynamically to respond to stresses as well.
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.
It's answered in the article. The argument is not that giant creatures can't exist, but that they cannot exist as a simple scaled-up version of the otherwise identical smaller version.
i can’t read the article to see what the specifics are, but assuming it’s essentially the square-cube law it doesn’t mean giant creatures can’t exist, it’s that small creatures can’t scale to be giants while being unchanged.
again i’m guessing, but if the conclusion is something like “if giant humans existed, X, Y and Z wouldn’t work”. then a “giant humans” would have to be something decidedly non-human.
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.
As I mentioned elsewhere, eg. femur can take at least 30x body weight, and we've got two to carry us. If a giant is 10x the size, and femur is just scaled linearly, even with 10x the relative weight, it can still take 3x giant's body weight. So perhaps no jumping on one leg anymore, but walking or light jogging should be fine.
But, their bones could also have larger cross-section and a giant could be stockier yet still appear "human like".
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 air sacs 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.
For those interested, I think many of these issues are discussed (but not in the particular way we are) in the trilogy of books starting with the Rise and Fall of Dinosaurs, continuing with The Story of Birds and the Rise and Reign of Mammals.
« Highly recommend The Rise and Fall of Dinosaurs » (by Steve Brusatte)
This book fails to mention both Gideon Mantell (1790–1852) and Richard Owen (1804–92). It's through them that dinosaurs entered our modern, scientific world.
I don’t have good recollection of names of early scientists he notes but I think he discusses many of them if not in this work but also in either The Story of Birds or The Rise and Reign of Mammals. I read all three in quick succession so it’s mildly blurred in my brain. It’s pop science so I’m not expecting comprehensive overview but the most up to date science as of date of publication.
Giant bugs are a totally different design though - don't they basically have a big exoskeleton made of different stuff than bone ? That's more like how we design a modern tank or airplane
It's also possible that for larger creatures a less dense and more flexible skeleton material (in general) might be ideal. Especially for animals that are not warm blooded (larger volume to mass ratio might resist temperature changes better?)
One theory about large sauropods is that they were aquatic animals that propelled themselves like hippopotamuses, using their feet against the bed of the lake/river. Just as whales can get very large, so could buoyant sauropods.
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.
Vertebrates have 2 essential advantages over insects, at big enough sizes.
An efficient circulatory system and myelinated nerves.
At small sizes, the circulatory and respiratory systems of insects work better (less friction for blood in the absence of capillaries and less friction for the air that circulates as a gas through the body), but at big sizes those of vertebrates work better, due to efficient pumping.
The myelinated nerves have the same speed for propagating nervous signals as non-myelinated nerves that are much thicker, so thick that an insect could not have many such nerves. At small sizes this does not matter, but at big sizes if the nerves are not fast enough the reaction times of an animal can become too slow, e.g. the head might need a big fraction of a second until noticing that something bites the tail.
The combined results are that an insect as big as a typical vertebrate would react mostly sluggishly and it would be able of only very short bursts of intense activity, before becoming tired. This would put it at a serious disadvantage.
What do you mean? The Earth does not "grow" and is not really bigger now than at any point in the past (since the creation of the Moon). On the contrary, it is losing mass through the escape of light atoms escaping, but even that is absolutely tiny.
Also, the Earth is absolutely not a living organism.
What he means is probably the idea of Earth Expansion. See Ott Christoph Hilgenberg, a disciple of Alfred Wegener, and more recently (but still a couple decades ago) Australian geologist Samuel Warren Carey. Here's a 1982 video featuring him on the topic of “Planet Earth: A Question of Expansion”:
It is growth and not simply expansion. All planets grow and are living organisms. This was common knowledge for the ancients. Carl Sagan made a similar remark once
I once learned that the ancient Greeks had already figured out all of Dawkins talking points on atheism. It wasn't a very popular message at the time and largely forgotten but it is nice to know that we stand on the shoulders of giants.
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.
> Clearly then if one wishes to maintain in a great giant the same proportion of limb as that found in an ordinary man he must either find a harder and stronger material for making the bones, or he must admit a diminution of strength in comparison with men of medium stature; for if his height be increased inordinately he will fall and be crushed under his own weight.
> While Galileo’s argument explains the nonexistence of human giants ...
The blog completely misreads what Galileo wrote. Galileo did not write that human giants did not exist, as the blog asserts. Galileo wrote how they could have existed, which could not have happened simply by scaled body structures.
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?
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.
J. B. S. Haldane discussed this in his essay On Being the Right Size:
https://en.wikipedia.org/wiki/On_Being_the_Right_Size
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.
You can also read Galileo's argument without Scientific American filtering: https://archive.org/details/dialoguesconcern00galiuoft/page/...
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> 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.
Yea, we’ve scaled wooden buildings to 25 stories.
Arguments around bone scaling ignores the impact forces of running. Scaling often means trading margins not just keeping all constraints the same.
Yeah exactly. There’s an implicit assumption here that everything scales together in perfect proportion. This is a large and limiting and unnecessary assumption that undermines the argument somewhat. Maybe giant humans could exist with stockier legs…
> dinosaurs
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.
> True for Scientific American today
Right, that’s what I was implying. However, I looked again and the article does mention elephants and dinosaurs.
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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?)
> do the artificial structures humans use, like house frames or bridges' trusses recover strength:weight ratio?
There is some improvement from computer design. We have better tools to know the margins that allow us to remove as much material as possible, things like that. So we can tweak existing designs to make them more efficient, like adjusting the section of beams to make them as strong but with a few percent less materials.
But the major improvements come from using different materials and new techniques, side-stepping the scaling issue.
For example, we could not scale old arch bridge designs very far. Getting steel beams let us build truss bridges, but even these cannot be that long in a single span. Suspended bridges were a step forward, with the improvement coming not from better beams, but from removing them altogether. Then, cable-stayed bridges solved some issues with older suspension designs and we can now have very large spans. Every time, scaling up is enabled by a change in strategy.
> 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?
Looking at things like elephants and dinosaurs, there certainly would be a way to have bones strong enough to support a 10m high human-like thing. Now, whether we would recognise that thing as human, I don’t know. Every time the problem was solved, there were significant compromises. I am not sure a giraffe’s vascular system could sustain a human’s brain. Elephants are not particularly agile. Whales cannot get out of the water.
Actual bone does incorporate some things we would consider "architectural" or "engineering" techniques to do more with less, not least of which they are composite materials and not mere rocks. They remodel the structure dynamically to respond to stresses as well.
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.
What about dinosaurs? not sure he's explanation makes sense given we have proven that giant dinosaurs where roaming on earth for ages.
It's answered in the article. The argument is not that giant creatures can't exist, but that they cannot exist as a simple scaled-up version of the otherwise identical smaller version.
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i can’t read the article to see what the specifics are, but assuming it’s essentially the square-cube law it doesn’t mean giant creatures can’t exist, it’s that small creatures can’t scale to be giants while being unchanged.
again i’m guessing, but if the conclusion is something like “if giant humans existed, X, Y and Z wouldn’t work”. then a “giant humans” would have to be something decidedly non-human.
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?
1. They stand on 4 limbs, rather than 2.
2. That would be assuming that human legs are sized at the max capacity they can carry, which is not true.
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.
Agree re 1, but point 2 still stands.
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.
As I mentioned elsewhere, eg. femur can take at least 30x body weight, and we've got two to carry us. If a giant is 10x the size, and femur is just scaled linearly, even with 10x the relative weight, it can still take 3x giant's body weight. So perhaps no jumping on one leg anymore, but walking or light jogging should be fine.
But, their bones could also have larger cross-section and a giant could be stockier yet still appear "human like".
How big is big?
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 guess if there were resources that were much more available to these agile tall people that might happen.
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 air sacs 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.
For those interested, I think many of these issues are discussed (but not in the particular way we are) in the trilogy of books starting with the Rise and Fall of Dinosaurs, continuing with The Story of Birds and the Rise and Reign of Mammals.
« Highly recommend The Rise and Fall of Dinosaurs » (by Steve Brusatte)
This book fails to mention both Gideon Mantell (1790–1852) and Richard Owen (1804–92). It's through them that dinosaurs entered our modern, scientific world.
I don’t have good recollection of names of early scientists he notes but I think he discusses many of them if not in this work but also in either The Story of Birds or The Rise and Reign of Mammals. I read all three in quick succession so it’s mildly blurred in my brain. It’s pop science so I’m not expecting comprehensive overview but the most up to date science as of date of publication.
Giant bugs are a totally different design though - don't they basically have a big exoskeleton made of different stuff than bone ? That's more like how we design a modern tank or airplane
It's also possible that for larger creatures a less dense and more flexible skeleton material (in general) might be ideal. Especially for animals that are not warm blooded (larger volume to mass ratio might resist temperature changes better?)
One theory about large sauropods is that they were aquatic animals that propelled themselves like hippopotamuses, using their feet against the bed of the lake/river. Just as whales can get very large, so could buoyant sauropods.
The atmosphere is believed to be more oxygen rich back then, in order for those dragonflies to exist.
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.
Vertebrates have 2 essential advantages over insects, at big enough sizes.
An efficient circulatory system and myelinated nerves.
At small sizes, the circulatory and respiratory systems of insects work better (less friction for blood in the absence of capillaries and less friction for the air that circulates as a gas through the body), but at big sizes those of vertebrates work better, due to efficient pumping.
The myelinated nerves have the same speed for propagating nervous signals as non-myelinated nerves that are much thicker, so thick that an insect could not have many such nerves. At small sizes this does not matter, but at big sizes if the nerves are not fast enough the reaction times of an animal can become too slow, e.g. the head might need a big fraction of a second until noticing that something bites the tail.
The combined results are that an insect as big as a typical vertebrate would react mostly sluggishly and it would be able of only very short bursts of intense activity, before becoming tired. This would put it at a serious disadvantage.
Giant sauropods are basically big balloons, so that's a nice little hack around the issue. https://www.youtube.com/watch?v=WuMHfWSyoGI
Important to keep in mind that the earth was smaller back then with lower gravity. The earth grows like all other living organisms.
What do you mean? The Earth does not "grow" and is not really bigger now than at any point in the past (since the creation of the Moon). On the contrary, it is losing mass through the escape of light atoms escaping, but even that is absolutely tiny.
Also, the Earth is absolutely not a living organism.
What he means is probably the idea of Earth Expansion. See Ott Christoph Hilgenberg, a disciple of Alfred Wegener, and more recently (but still a couple decades ago) Australian geologist Samuel Warren Carey. Here's a 1982 video featuring him on the topic of “Planet Earth: A Question of Expansion”:
https://youtu.be/Othb0xsvZb4 – 26 minutes
This view is kinda ostracized in geology and considered heresy.
It is growth and not simply expansion. All planets grow and are living organisms. This was common knowledge for the ancients. Carl Sagan made a similar remark once
https://m.youtube.com/watch?v=7kL7qDeI05U
The earth is both gaining mass and losing mass at the same time
We are losing gases and energy (hydrogen, helium, radioactive decay)
Concurrently, we are aggregating cosmic dust, micrometeorites, meteoroids, and the occasional larger body
Overall a tiny loss
Right, I know that. But that’s not the point.
So does the moon though so it all evens out. Bigger gravity of earth pulls you down and bigger moon stretches you out.
Hopefully no cheese eating space mold gets up there or we're done !
Yes all planets grow and are living organisms. This was common knowledge for the ancients
I once learned that the ancient Greeks had already figured out all of Dawkins talking points on atheism. It wasn't a very popular message at the time and largely forgotten but it is nice to know that we stand on the shoulders of giants.
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