The Physics of Movie Monsters: The Cube Square Law

[silazcarbryck]

Would the square strength vs Cube weight not present a problem for a dinosuar No WAIT NO! I still haven't finished watching it yet. LOL! This guy can read my thoughts...

[xtcarnage15586]

but what if they have different proportions?

[shippem]

what about proportionality in increased size

[jackhuskey]

I recall a discussion with some friends about the squared/cubed law being applied to heat dissipation (skin, squared) vs heat production (internal volume/cubed) would result in mammalian monsters basicly cooking in thier own heat. Never covered insects & reptiles.

[nevermore1000]

An interesting thought is that this works in reverse as well. If humans were somehow to be shrunk down to the size of insects, we would be musclebound supermen endowed with preternatural strength, considering our small size.

[SpreadingtheMuse]

@nevermore1000

There's a whole batch of superheroes based on that. Marvel's Wasp, YellowJacket, and Ant Man to name a few all have "regular" strength, but shrunk down to bug size it makes them superpowered.

[SteveSabbai]

...i find your videos very entertaining and very informative but i have a question...so the cube square law only applies to land animals? what about animals in water environments?...since water supports most of their weight then all those stories about giant sea monsters are real?...

[SpreadingtheMuse]

@SteveSabbai

Water animals can get bigger than land ones due to the decreased weight (the largest mammals are all whales for example) but I think cube square would still apply, just at a larger starting point. Whales have never passed a certain size, so maybe they cant. At some point the water cannot support the extra weight.

[albedoshader]

@SteveSabbai: All physical laws apply everywhere. Water causes buoyancy which makes bigger animals possible because in water animals have a density that is more similar to the surrounding.

On land the density of air (our surrounding medium) is far lower than the average density of our bodies.

Another fact is that bigger land animals have a heat problem. The surface/volume ratio gets smaller for bigger animals. That's a problem because these animals have to protect themseles from overheating.

[albedoshader]

@albedoshader: The same reason makes small animals like mice lose their heat very rapidly. Their surface is large compared to their volume. Because of the permanent strong heat loss they also have a higher food consumption per body weight ratio than bigger animals.

[AceofDlamonds]

a 30 foot typical man would be, wtf? 10 tons? lolz!

[SpreadingtheMuse]

@AceofDlamonds

Sure. 30 ft tall is what, 5 times more height? But weight is 3 dimensions. So its 5 x5x5, all times a weight of say, 200 lbs.

200x5x5x5 =

1000

5000

25000 lbs = 12.5 tons. Pretty good guess ;)

[AceofDlamonds]

@SpreadingtheMuse

aah i see, we were referring to a 6 foot man? then yea, 200 lbs is about average, i was going for average.

but damn this little variation scaled up makes a difference of more than 2 tons in a theoretical giant human lol.

[isawman1]

@AceofDlamonds You dont give a credible explanation as to why dinosaurs could reach the size they did.If an 80 ton Brachiosaur is ten times bigger than an 8 ton Elephant it would be 100 times stronger but 1000 times as heavy right?

[SpreadingtheMuse]

@isawman1

This was the hardest concept to get across admittedly. Its about whats normal. A dinosaur is a 1000 times heavier, yes, but what makes it possible is that it was BUILT FOR THAT. It was specifically designed from DNA up to be heavy. Bigger bones, wider bones, bigger muscles, etc. But you take the Ant. Ants were built to be little and weigh nothing. They've got skinny legs, skinny muscles. Now pump him up to 1000 lbs. Skinny legs, of whatever length or size cant hold 1000 lbs

[isawman1]

@SpreadingtheMuse But that really does not explain the size paradox?An Ant may be small but it has great strength owing to its small size"Gravity is not against it"on the other hand an Elephant is large and strong,but scale to scale is really quite weak, able to lift probably 25% of its body weight,"gravity is against it",Now if as seems likely the large Sauropods occupied the same eco place as the Elephant,why would they grow ten times larger unless the enviroment was radically different.

[SpreadingtheMuse]

@isawman1

What makes some animals grow large and other small is another question, Mother Nature's Decision. What we're talking about here is talking an animal with a shape meant for being lite, and pressing the "Times 10" button and seeing that lite shapes cant hold heavy weight.

Then again, I think the air was thicker 100 mil years ago, allowing for higher oxygen intake, therefore bigger size perhaps.

[isawman1]

@SpreadingtheMuse Greater oxygen content and much denser water content,perhaps slightly less than water,which might make land animals more buoyant?

[AceofDlamonds]

@isawman1

did you even listen....Brachiosaurus and Loxodonta africana are TWO DIFFERENT ANIMALS....it would make sense to say an elephant 10 times bigger would not survive.....not saying one animal built one way would not surivive because it's much bigger than another different animal.

In other words...Dinosaurs have small ambiguities, if you will, that allow them to be as big as they were....the theoretical limit for terrestrial tetrapods is estimated to be about 140 tons? I think.

[isawman1]

@AceofDlamonds I would say large ambiguties to say the least!!,An african Elephant can be penned in by a shallow moat owing to its size which makes leaping,jumping and falling highly dangerous,it even has to strain to get up from a laying position,Your telling me that a land animal that has roughly 225 times the strength of an Elephant but is 3375 times as heavy is possible under currant Earth conditions?Sorry there is a limt to small or large ambiguities.

[AceofDlamonds]

@isawman1

no moron....a Brachiosaurus is NOT an elephant...hence, the same "equation" so to speak for the elephants size cannot be used on the Brachiosaur!!!!! the ambiguities may be something like differences in bone composition, metabolism, feeding habits, and even the environment at the time.

That's like saying because Megistotherium existed, and today's dogs(Canis lupus familiaris) don't get giant.....the SC Law must be invalid.

[isawman1]

@AceofDlamonds My point was based on a radically different envroment !!!! None of your other suggestions wash.

[AceofDlamonds]

@isawman1

actually things like metabolism and body composition matter as well...

For instance........If you've ever read "A biomechanical constraint on body mass in terrestrial mammalian predators" (Sorkin 2008). which I highly doubt you have...it deals with environmental and evolutionary pressures that practically set the weight limit for terrestrial mammalian predators, or carnivores, for that matter, to just over 1 ton.

you were saying?

[isawman1]

@AceofDlamonds YES I know there is constraint on land animals today,what I am saying is the enviroment has radically changed since the time of giants.

[AceofDlamonds]

@isawman1

actually, you are wrong, metabolism and body composition play roles as well.

If you've ever read, "A biomechanical constraint on body mass in terrestrial mammalian predators" (Sorkin 2008), which I doubt you've read, you can see the environmental and evolutionary pressures that limit terrestrial mammalian predators, let alone CARNIVORES, to just over 1 ton.

So you were saying??

[AceofDlamonds]

@isawman1

and yet.....we KNOW that the largest tyrannosauroids and spinosaurids can reach near or exceed about 10 tons

the largest predators to ever walk the earth.

[isawman1]

@AceofDlamonds Yes I know that too.

[SupremeCommander360]

If I'm correct it's true that you can drop a small insect from any height and it won't die?

[SpreadingtheMuse]

@SupremeCommander360

More or less. Since it has little to no weight, the force of it hitting the ground is minuscule.

[justinneversleep]

then what about dinosaurs

[AceofDlamonds]

@justinneversleep

it has something to do with the structure and posture....but more importantly...bone density i think....

[Apwrath13dMusic]

you must teach me your ways

[ApolloWasReal]

Very nice work!

[bat353]

what movies have the giant ants and grasshoper oh and the 3oft giant lol oh and thats not how u find the weight of something

[SpreadingtheMuse]

@bat353

Not the weight, mass. Density is based on volume which is based on 3 dimensions.

The giant ants were from a movie called "THEM" and the grasshoppers were from "Beginning of the End."

[bat353]

@SpreadingtheMuse what about the giant spider

[zebadee277]

@SpreadingtheMuse indeed, as also in some cases an athleat or martal artist can have a higher muscalur densaty than the avaredge person so the size is the same but there mass and weight is higher.. my brothe is a fat bloke and has probably got the same diamater arms as Arny but i know whos gonna punch harder

[SpreadingtheMuse]

@bat353

I forget where the spider came from. Might have been "Atomic Spider" or something.

[ThatsMrFrank]

which explains why a lower gravity planet could have larger monsters.......

[aarontaylor94]

killer bunnies 8O dragons :D

what crack have you been smoking killer bunnies ridiculous

[GeneralCalculus]

@aarontaylor94 Have you not seen movie Monty python and the Holy Grail! KILLL INFIDEL! Sorry I was joking. In Monty Python and Holy Grail is rabbit that cuts heads of men with one jump.

[MithraisAugustus]

But what if we're attacked by evil alien space invaders throwing King Ghidorah at us and WE NEED GODZILLA? WHAT THEN?!

[RicardoAugustoLifeCo]

In retrospect i think you should give to mother nature from those paralel universes where this monsters came from a chance, if our own mother nature could help the evolution to give existence to dinosaurs why not a similar evolutionary race could not bring gargantuos monsters to live ? Maybe our own mother nature didn't do it, maybe our own mad scientist shouldn't do it, but, i some corner of the universe something or someone else did it and in that case give to us more ammo and popcorn please.

[dantheman1507]

true , because mass is density times volume.

But if the MONSTER has another density or, molecular structure... can't it survive?

[SpreadingtheMuse]

Yes. A different, or more DENSE, muscular or molecular structure would have a higher tolerance for gravity, and be able to grow larger.

But that merely defines their version of "normal." Their "normal" might be larger than ours, but then cube square would take effect at their higher tolerance.

[dantheman1507]

funny thing about ants though, it is known that they can lift about 15 time their own mass, and move with the load to... how come they aren't double the size, I don't thing that would've been a problem... or the ants I'm talking about are those of smaller species?

[SpreadingtheMuse]

Ants: 15 times zero is ZERO. Thats why they can lift it. ;)

But we're not talking about regular ants, we're talking about 10 foot long ones. So think about the skinny spindly legs of an ant. How thick would those legs be on a ten foot ant? Wouldnt they still be skinny and spindly compared to the rest of it? Could skinny legs really hold up a ten foot long ant?

[dantheman1507]

well of course not :)

[Skaramine]

This hit me in high-school. We're safe from ants the size of stretch limos.

Eight inch long mosquitos, five pound yellowjackets, and a nest of 5000 ants the mass of a Norwegian rat not only have prehistoric precedent, but would totally ruin someone's day.

Cripes, there are two-foot centipedes with sufficient poison to make a human sick. That's one centipede at a time, so thank goodness arachnids don't swarm.

'Course, you did mention the evil insect swarms.

[LORDKEROTH]

can you do a video on FTL travel please? thank you!

[NodDisciple1]

I love your vids, but any idea how rl giants in nature (such as those uber-huge dinosaurs) were able to hold up thier weight? :(

[thirdclass2006]

He covered that already; dinosaurs evolved to be big. They weren't accidents like so many sci-fi monsters.

[NodDisciple1]

Sowwy, I couldn't delete that one for some reason. X(

[isawman1]

@thirdclass2006 He didn't cover how Dinosaurs could grow that big in a currant Earth climate.

[NodDisciple1]

Thanks for making such an educational video. I wish Hollywood/Tokyo would take a tip from nature and actually bother to mention "Hollow bones/exoskeletons" and "super-dense muscles" to make giant monsters more realistic. X(

[nekovelo]

I'm quite ignorant of physics, so how does all this fit into areas of different levels of gravity? (Assuming the equations you use here are not universal) Because alot of sci-fi is set in areas of different g :)

[SpreadingtheMuse]

Cube square is independent of gravity, as its purely a mathematical concept. That only means that different planets with different gravities will have their own "max" size for native animals.

But a 80 foot tall giant ape, impossible on our planet as the weight grows faster than muscle, MIGHT survive if it was transported to a low gravity planet where it wouldnt weigh as much.

[qahharus]

That Dinosaur in King Kong is called a Venatosaurus Rex or simply V-Rex. Oh yeah and thanks for the info, I learned a lot about monsters now.

[SpreadingtheMuse]

Is that a real dinosaur or something Peter Jackson just made up?

[sci0nparag0n]

He made them up. They are the supposed Skull Island descendants of T rex.

[PSshadow92]

It's one Peter Jackson made up, but they were the result of the Tyrannosaurus' continued evolution on the isolated island. They were bigger because most of the food sources on the island were so large, they would have killed a T-rex. Besides, there were real carnivorous dinosaurs that were twice the size of T-rex.

[EnigmaHood]

Not twice the size, but there were larger carnivorous dinosaurs. The largest meat eater on land was the Spinosaurus. In the ocean, the new Predator X was probably the largest.

[SpreadingtheMuse]

If there was a land-dwelling carnivore twice as large as the T-Rex, I havent heard of it. I know that the Spinosaur was bigger, but only a LITTLE bigger. You can stand next to the largest T Rex skeleton in existence in both Chicago and Montana and see its head is no larger than an average coffee table.

[CloanLabs]

Thank you for your reply comment, Bernard. I'll watch the vid you cited tomorrow when I can get audio. As it was, I wrote you a long reply to your channel wall, but it got lost because of my longwindedness. I hate when that happens. Mostly I just wanted to say that I intend to write you a longer letter later with questions and request for a little on some physics questions I've had working on my upcoming sci-fi anime show. But I got too cute in my long reply and the computer ate it. Happens.

[CloanLabs]

My god, Bernard, you just totally rock! I hope you'll make some more of this series soon. You'd be surprised how much time us young sci-fi filmmakers spend lying in bed at night worrying what actual physicists like yourselves would SCREAM once they get wind of the cheat we've just thought up because it sounds cool and we got kicked out of physics class. And besides, we're supposed to be doing animation, not equations. WE SO NEED YOU!

[SpreadingtheMuse]

Watch the "Physics of Energy, Waves, and Sound" to hear my personal commentary on taking science accuracy too far. I'm in favor of a good thrill movie, my only complaint is that the filmmakers give up too easily and take the easy way out (see my Independence Day rant on my Gravity movie).

[BoomBoomSticks]

Lol my physics teacher taught me this law, though instead of monsters we used the "cow is a sphere" analogy.

[11Jamie11]

A 30-foot giant??

Oh, NO.

[theunraveler]

i'm not near any paleontology museum ...

[theunraveler]

wat about the brontosaurus and t-rex? i'm pretty sure they are monsters in their own right

[SpreadingtheMuse]

And they had big fat legs WAY out of proportion to human sized limbs. King Kongs main problem is that his muscles arent thick enough to support all that weight. But go look at how thick a T Rex leg was.

[kinggodzilla87]

lol what about Godzilla

[EnigmaHood]

He would have to have some pretty thick legs!

[Humancyclone7]

that was really good, i never knew that, you're the only person who makes learning and education enjoyable

[dmt290889]

Dino power! So basically it is ok for us to make a new monster big but with really light bones, but just not ok for us to get any old animal and drop it in a vat of radiation.

So dragons could be made realistically so long as some old man does'nt glue bat wings to a rat and enlarge it with a martian reygun heh.

[SpreadingtheMuse]

Dragons could exist so long as the skeleton was specifically designed to hold up the 50,000 lbs it would take. Dinos were built for that, insects were not. Dinos have legs that were THICK. Insects have legs that were skinny. Skinny legs can hold up a .01 lb ant, not a 10000 lb one. If the ants legs were really REALLY thick, then maybe...

[dmt290889]

Needing thick legs would probably kill any chance they have at flight because they would basically be a flying T-rex or something so if western dragons have no chance then i would like to know how those snake like chinese dragons fly xD

[EnigmaHood]

The dragon can fly as long as its wings are large enough, and its muscles strong enough. Wing area is key. After all, we do have large planes that can fly just fine.

[syrayian]

So do Giant Mechs and other non living things have the follow the same rules?

[SpreadingtheMuse]

Mechs are OK, as they can be as strong as the motors are, which we can make as big as we like (so long as the technology is available).

This rule here applies to muscles, which are more or less the same strength, not like electronics which can be beefed up with amplifiers and stuff.

[EnigmaHood]

But the problem with giant mechs is... they can fall down lol. And when they do, the damage would be considerable considering their weight. The mech would have to have some kind of invincible armor, and good reflexes/agility.

[SpreadingtheMuse]

Playing the ole Robotech back in the early 90's, the preferred tactic was to just blow away ONE leg and let the sucker fall.

Cheaters. ;)

[EnigmaHood]

Don't you mean Battletech? Robotech was the anime which took segments of a couple of Japanese animes, notably Macross. Battletech was the pen and paper tabletop game, which later gave rise to the computer games, MechWarrior, and MechWarrior 2.

[SpreadingtheMuse]

Something with "tech" in the title. Some 1992 computer game, back when 8 MB of ram was a lot. ;)

[EnigmaHood]

Ok it was probably MechWarrior 2 then. It was released in 1995 though. Or it could have been MechWarrior 1 which was released in 1989, but it wasn't nearly as popular. Both games are based on the Battletech tabletop game, and are considered videogame adaptions of it.

[samopollo]

So if WE were made really small, would we be practically invincible? because if you look at insects their all really spindly but we're not so we'd be like, Uber strong and be able to jump really high etc. (i think)

[SpreadingtheMuse]

Now we're talking. ;)

Insects have those skinny spindly legs and can lift 50 times their weight. So if WE were in fact shrunk down to their size, since the cross-section area of our muscles is so much proportionally bigger, we'd be able to lift 500 times our weight, maybe more.

[LesHut]

I have an idea for a new super-hero. He's called "Perspectiveman", and he derives his power from the idea that if he's closer to the camera for example, he not only looks bigger, but he can interact with the world as if he "is" bigger. Hmm, or maybe he could be called Movieman, or 2Dman!

[LesHut]

This is a terrific video to see. I'm 55 years old now, and have always had a great interest in physics. Its always bothered me when someone (supposedly learned) on some "nature" show, mentions that if humans had the "strength" of ants, they would be able to lift automobiles for example. Or if we had the strength of a grasshopper, we'd be able to jump over a 50 story building. They always leave out the part that we'd ALSO have to have the insects SIZE in order for us to DO those wonderous things.

[SpreadingtheMuse]

Yes, why can an ant lift 50 times its weight? Because 50 times nothing = NOTHING!

But I still like giant apes. ;)

[strengthandhappiness]

Dear Mr. Bernard Finnigan

This movie was truly facinating. I am one who is keen in the physics department and I find this theory quite proportionally accurate. The movie clips are also tremendously entertaining. You are quite an individual. I wish you much success and hope to see more movies from you. I think I may go back to college to try to further my science education. Movies like this, might I say, truly inspire the human spirit! After watching this I know you, Mr. Finnican, are a genius!!

[ShadesOfKnight]

"Can nine times the strength possibly hold up 27 times the weight?"

Hm.  Well, considering that humans are, on average hundreds of times larger than ants... we manage somehow to hold up our weight, though according to this fellow we shouldn't be able to...

Something tells me that this fellow's "honest physics" is only half-understood and only about a quarter (half, squared) applied.

[SpreadingtheMuse]

"we manage somehow to hold up our weight, though according to this fellow we shouldn't be able to..."

You blanked out on most of what I said obviously.

Humans arent "9 times" anything. We're size 1, with a body specifically designed for size 1. Triple our size, and we're not size 1 anymore, and a body built for size 1 cannot suddenly support 27 times the weight as if nothing had happened.

What part of "gargantuan monster" didnt you understand?

[ShadesOfKnight]

The part where you ignore that the very term "gargantuan" is itself relative. Relative to us, movie monsters are gargantuan. Relative to ants, WE are. That's my point. If the math works as you say, then it will work regardless of the scale or relative nature. So, since we are hundreds (if not thousands) of times larger than ants... should we not be tens of millions of times stronger? And yet, they are the stronger species, able to lift far more than their size indicates possible.

[SpreadingtheMuse]

" the math works as you say"

You are misinterpreting what I am applying the math to. Cube/square does not apply to anything NORMAL. Thats the context of "garguatuan," ABNORMAL.

Everything has a normal size. But if that size is changed, then the math comes out. An ant 10 times as big gets 100x the strength but 1000x the mass. How long can the spindly skinny legs of an ant support that discrepancy?

Our legs are BIG, almost 1/2 our mass, MEANT to support heavy objects. An ants are not.

[Dorjan24]

You are right, YOU are ignoring the "relative"ness of your own arguement.

How much smaller is an ant to a human?

Do the maths of a human of that size and I bet we'll be as if not stronger (i'm too lazy to work it out :lol:)

[TheBinaryNomad]

@shadesofnight

We ARE millions of times stronger than an ant. The average human can easily throw a baseball 50 feet. Do you know any ants that can do that?

[PSshadow92]

PHAGOCYTE!!

[Velikan121]

Nice clip but you make life harder for us macrophiles.

[datubaman]

What about muscle density?

[SpreadingtheMuse]

Thats a whole other problem thats way out of the league of this video. But by and large, animals that live on the same planet, breath the same air, and eat the same food ought to have similar densities. Even dinosaurs floated after all.

[saltygrasshopper]

This seems to make the assumption that given the same area all types of muscular fiber exerts the same force despite differences in creatures. Is that a safe assumption? Is my left butt cheek just as powerful as the finger on a T-Rex's forelimb?

[SpreadingtheMuse]

Thats the assumption I was under. Even if particular muscle fibers would create greater strength, it would not be on the order of 2-3 times. Sooner or later, no matter how strong, cube square would catch up.

My local musuem used to have an exhibit to demonstrate the strength of a Trex limb. Whereas they would beat us in arm-wrestling, it was only because their arm was thicker.

[SwordlordRoy]

The Giant Grasshoppers from the "Beginning of the End"...I guess science was the beginning of the end for them...

But still, not every day one sees something with classics such as "The Beginning of the End" and "Them", Awesome job!

[SpreadingtheMuse]

I never knew about "Beginning of the End" until Netflix recommended it. I went looking for "THEM" specifically and was hoping to find other giant bug gems along the way. I almost rented a giant scorpion movie, but figured that the point had been made. ;)

Gotta love the 70's kong though. Its delicious.

[SwordlordRoy]

Yea, "The Beginning of the End" is one of the lesser classics...heck, I didn't even know of it until I saw the "Mystery Science Theater 300" version...

[FearlessSon]

Excellent!  Another awesome video.

Now if only the Japanese would take this law into account when designing fictional robots...

[Vire70]

Robots aren't really subject to the same principles.

Besides, this theory is pretty flawed anyway.

[SpreadingtheMuse]

Thems fighting words.

The mathematics is pretty straight forward, and its common biological knowledge that no creature ever gets bigger than its own muscles can allow.

[Valen123456]

welcome back ... bringing your unique brand of humour to addressing the age old mistakes we make in fiction ... good job