Square-Cube Law and fantasy physics

[Greywander]

I assume most of you are familiar with the Square-Cube Law, but just in case, it's basically the fact that as you make things bigger they tend to get heavier faster than they get stronger. If you double the size of a thing, it's going to be about 8 times heavier, but only about 4 times stronger. The weight increase is pretty easy to demonstrate using cubes; a 2x2x2 array of cubes has twice the length, width, and height of a single cube, and requires 8 cubes total. Strength is a bit trickier, but the basic idea is that making a bone longer doesn't make it stronger, only making it thicker, thus only two dimensions contribute to strength.

The Square-Cube Law ends up wreaking havoc on a lot of fiction, usually involving very big things, whether that's giant robots or huge dragons. Basically, eventually something will get so big that it gets crushed under its own weight. This is actually a problem that D&D handily sidesteps by simply not counting a creature's own weight towards its encumbrance. It's assuming that carrying your own weight is second nature to you and doesn't slow you down at all. And that actually works pretty well to avoid this issue. However, it does still leave the problem of a creature not being able to lift another member of its own species. But is that a bug, or is it perhaps a feature?

Generally if you want to "solve" the Square-Cube Law, you have to make big things either lighter or stronger. The cube example above is pretty trivial, and you'll have a hard time justifying why 8 cubes somehow weighs less than 8 times as much as a single cube. So then the solution seems to be to make big things stronger. And this can actually work if we imagine that certain mythical creatures possess supernatural strength. This is even true to a degree in the reverse direction: chitin is great for small insects, but at larger sizes it simply isn't strong enough to support them. Just like chitin is swapped out for other, stronger materials, we can imagine that something like a dragon might have bones composed of something stronger than normal bones. This can then be represented as a multiplier to that creature's carrying capacity, as with the Powerful Build trait seen on some creatures in D&D 5e.

However, that runs afoul of one of the other major ways large sizes are used in fiction. Specifically, I'm talking about having something that's just a normal thing, but bigger, that uses exactly the same physics as if it were normal-sized. One place in particular that you'd expect to see this is with giants. A giant, wearing giant's armor, and wielding a giant's sword, is expected to look basically identical to a human in human armor wielding a human sword. Same proportions, just bigger. But because weight is increasing much faster than strength, the proportions should actually be totally different. The larger a creature is, the smaller the weapons it will wield proportional to its own body size. A giant twice the size of a human is only four times as strong, and thus a giant's sword would be much larger, but not twice as large.

However, if we want the physics to work exactly the same as at the smaller scale, then what we'd actually expect is something like a giant twice the size of a human to be both twice as heavy and twice as strong, so that everything scales linearly at the same rate. This is how we maintain the same physics proportional to size. But that just brings us back to the example of cubes. The idea that 8 cubes somehow only weighs twice as much as a single cube is beyond ridiculous. What it would have to mean is that a giant is much less dense than a human, and once you get big enough density would decrease to the point that giants would float in air.

I feel like there's some kind of "alternative physics" going on here, I just can't put my finger on where to draw the line between real-world calculations and fantasy physics. Like, it doesn't matter what kind of laws of physics you're running, 8 cubes is still going to weigh 8 times as much as one cube. You could say, "Just don't worry about it," but I kind of have to when I need to determine the carrying capacity of a monster or the weight of a giant-sized weapon.

[Lord Raziere]

Your thinking is backwards.

DnD nor any fiction doesn't need to "solve" any question of physics with anything. Because the square cube law isn't a thing that just exists and can be forced onto the universe to suddenly make a dragon be crushed under itself. You don't have some weird metaphysical power to point at a giant and say "you don't exist because square cube law". thats not how science works. thats not the process of figuring out how the world functions.

the process is: "oh look I see dragons fly around and giants move just fine in this world" and compare it to a world where square cube law exists, where they wouldn't. Therefore they are a world where square-cube law doesn't apply and no scholar/scientist/wizard/whatever within that world would even come to the conclusion such a law even exists in that world.

your starting with a rule and expecting the universe to follow that rule in your observation of the universe rather observing the universe and making sure a detail is consistent so you can deduce that a certain rule exists BECAUSE of what the observations point to. as far as science or physics is concerned, thats a non-starter no matter what the world.

you do a second mistake where you assume an OOC mechanical rule about DnD is something that exists within the universe when it can't be assumed that any or all rules of DnD exist within what DnD is modeling. you can't assume an rpg mechanics universe in universe. you can't assume an out of universe mechanical thing is observable in universe, and you can't conflate a universe with the rpg rules it runs on, because no matter how complete, a ttrpg ruleset can't and doesn't model everything.

[Greywander]

I think you're missing the point. I have a giant that is twice the size of a human. How heavy is the giant? How big is the giant's weapon? How heavy is the giant's weapon? How much weight can the giant carry?

The point is, how do I answer those questions?

I wasn't starting off of the assumption that the Square-Cube Law applied to D&D or any other fantasy setting, I just wanted to explain what the issue was first before looking at some ways of handling things different and how those fail to capture all aspects of how very big things are often portrayed in fiction. The reason I bring up the example of the cubes again and again is because it's such a basic, elementary demonstration that something twice as big should be 8 times as heavy, no matter what physics your universe is running on.

If we want strength and weight to scale at the same rate, then we could just make a giant twice the size of a human be 8 times as strong, but then I feel like strength ramps up way too fast. It seems like we'd want to instead make the weight scale up more slowly, but I don't know how you'd do that in a way that makes sense, given the cube example.

I dunno, maybe I should just accept that a giant's greatsword would have the same proportions as a shortsword. That just looks weird, though. I guess the crux of the issue is that one part of my brain thinks the giant should have identical physics to the human, while the other part of my brain can't ignore the cube example and that the physics must necessarily be very different. And I guess I'm trying to find a way to reconcile these, a way for the giant to have the same physics as a human without violating the example given by the cubes.

[Mechalich]

It's important not to be too strict about the square-cube law. Biological systems are complex and are not going to react to the law in idealized mathematical ways. For example, the largest land mammal ever (probably Paleoloxodon namadicus) might have capped out at ~20 tons, but the largest land animal ever was a giant sauropod of at least 80 tons, and quite possibly considerably more. The reasons sauropods were able to get much bigger than elephants or rhinos don't appear to have involved anything like overall bone & muscle strength, but appear to have more to do with differences in lung structure and reproductive method.

So you absolutely can have gigantic creatures in fantasy, especially if you get creative with the biology and allow for things like superstrong but ultralight bones made out of some kind of highly advanced material, more efficient oxygen-carrying molecules than hemoglobin, and high-capacity muscle fiber proteins, and various other improvements that evolution has not provided but that could be part of designed organisms.

The big problem with the square-cube law is when fantasy authors attempt to directly scale up some existing organism without otherwise altering its biology. This is most commonly an issue with organisms that have the word 'giant' in the beginning of their names, especially giant insects and humanoids. These present obvious problems, ones that D&D is not entirely unaware of. For example, the 2e supplement Thri-Kreen of Athas recognized that a vaguely-mantid animal the size of a pony was physically impossible and generated a completely alternate internal physiology for the thri-kreen (and by extension most of Athas' considerable menagerie of gigantic arthropods). This can be extended out to most giant arthropods in fantasy, with the assumption that they look like insects on the outside but look very different on the inside. Humanoid giants are probably the trickiest, especially the really big ones. A bipedal primate roughly the size of Gigantopithecus is probably possible, with some adaptations to the pelvis and spine, but that only gets to the low end of the hill giant range.

Edit: with regard to the sort of weapons giants might wield, it's worth noting that the limitations of quasi-medieval metallurgy are likely to matter more than weight. Making a chunk of steel large enough and strong enough to actually be wielded by a being that size (or even just by an actual gorilla, which has much, much greater upper body strength than a human) would be extremely difficult. Giants should fight with spears and polearms, and their ability to wield those kind of weapons at that size is far less straining on the square-cube law.

[Lord Raziere]

I think you're missing the point. I have a giant that is twice the size of a human. How heavy is the giant? How big is the giant's weapon? How heavy is the giant's weapon? How much weight can the giant carry?

The point is, how do I answer those questions?

thats the neat part, you don't.

If your in a ttrpg the only rules that matter are the mechanical abstractions. these abstractions are there you don't HAVE to calculate it out with real physics yourself or answer the questions because there are abstracted easier answers done for yoiu. its a convenient time saving measure like that, because if we had to do that for every single creature in existence, this would take forever.

[NichG]

I think you're missing the point. I have a giant that is twice the size of a human. How heavy is the giant? How big is the giant's weapon? How heavy is the giant's weapon? How much weight can the giant carry?

The point is, how do I answer those questions?

I wasn't starting off of the assumption that the Square-Cube Law applied to D&D or any other fantasy setting, I just wanted to explain what the issue was first before looking at some ways of handling things different and how those fail to capture all aspects of how very big things are often portrayed in fiction. The reason I bring up the example of the cubes again and again is because it's such a basic, elementary demonstration that something twice as big should be 8 times as heavy, no matter what physics your universe is running on.

If we want strength and weight to scale at the same rate, then we could just make a giant twice the size of a human be 8 times as strong, but then I feel like strength ramps up way too fast. It seems like we'd want to instead make the weight scale up more slowly, but I don't know how you'd do that in a way that makes sense, given the cube example.

I dunno, maybe I should just accept that a giant's greatsword would have the same proportions as a shortsword. That just looks weird, though. I guess the crux of the issue is that one part of my brain thinks the giant should have identical physics to the human, while the other part of my brain can't ignore the cube example and that the physics must necessarily be very different. And I guess I'm trying to find a way to reconcile these, a way for the giant to have the same physics as a human without violating the example given by the cubes.

I mean, I think the answer that makes sense is that the giant is in fact 8 times as strong, when strength is expressed in terms of bulk modulus and yield modulus. That doesn't mean that the giant's strength score is 8 times higher, nor that the damage it deals with a strike is 8 times higher. For one thing, 'damage' need not have any sort of linear relationship with e.g. pressure or force exerted. In something like D&D where damage is linear in Strength score but carrying capacity is exponential, this is certainly the case - and that logarithmic relationship is extremely forgiving of whatever scaling law you want to have Strength obey. Or, it might just mean that more of the giant's strength is in the static properties of their body rather than in the balance of tensions between muscles. Which supports the 'big, strong, and slow' sort of fiction (whereas for real things that size, the 'slow' impression is usually more about distance than large things actually being slower - large things in reality tend to be faster by the numbers).

There are a bunch of other weird things you could do. For example, you could decide that the magic in dragons, giants, etc acts to weaken gravity on and around it linearly with size. So the giant is only 4 times as strong as a human but experiences 1/2 the gravitational acceleration, so it doesn't need anything funky for its body to not collapse. Also meaning that the giant can lift a proportional 2-handed sword, but it won't be swinging it proportionally as quickly as a human would swing a 2-hander because its magic is lightening the sword but not reducing its inertial mass. Also this would have a convenient bit of fiction where aerial hijinks actually become easier around dragons and giants - you can jump up the side of a giant if you judge the extent of its field correctly, in a way fundamentally unlike how you'd e.g. try to jump up the wall of a castle.

Or you could say that the magic empowering the giant or dragon means that the rate of passage of time is literally different within its body. Mass scales as density * L^3, pressure is density * L^2/T^2. So when you double L, mass goes by 8 but pressure goes by 4, which is the problem. Unless you also simultaneously scale T by 1/sqrt(2), in which case they go in proportion. So essentially, in the time the normal human's body experiences 1 second of time the giant's body has only experienced 0.7 seconds. In practice this probably would correspond to strength scaling as the cube of size rather than the square, but depending on what happens when momentum fluxes cross that boundary of different rates of time passage will determine what specific sorts of feats of strength you'd be seeing. One reading of it could be something like 'the giant is only in phase with reality for 7/10 of every second' such that the ability to stop a giant in motion has the full 8x difficulty, but the ability of a giant to actually accelerate its own body would only be 4x. So while in principle the giant could deliver 8x on external objects due to Newton, because its ability to accelerate external objects is contingent on it also accelerating itself, the difficulty of moving its own body always bottlenecks that.

Anyhow, you have lots of options. The deeper question is, are any of these options enabling other interesting things if you explore them and their knock-on consequences?

[Greywander]

Yeah, I think giant humanoids are the main thing I'm struggling with wrapping my head around right now. Not counting a creature's own weight against their encumbrance is a pretty good solution for at least allowing giant creatures to exist. The problem is the relative proportions. Once you reach a certain size, a giant will no longer be able to lift their fellow, even though humans don't have much trouble lifting one another (okay, a person is pretty heavy, but most adult can at least carry another person if they have the right hold, e.g. slung across a shoulder). If giant weapons have the same proportions as human weapons, eventually those will also get too heavy that they become unwieldy.

Basically, I seem to be faced with a variety of different options, none of which seems acceptable:

• Giant weapons eventually get so heavy that even the giant can't wield them. This is just silly, just don't make the weapons that big then.
• Giant weapons are proportionally smaller so they don't become too heavy. This just looks silly, furthermore it doesn't fit the common fantasy tropes where giant weapons are usually bigger proportional to their body size (e.g. one-handed greatswords).
• Giants get 8 times stronger each time you double their size. I guess this works, but it gets janky when the giant interacts with smaller creatures, making them monstrously strong by comparison.
• A giant twice the size is less than 8 times as heavy. Okay, but how does that work given the example with the cubes?

I think what's frustrating is that I know there has to be an answer out there somewhere. This isn't a new thing, giants have been around in folklore since forever. I'm pretty sure the ancient Greeks were well versed in the rate at which a thing's weight increased as it got bigger, so how did they explain things like giants? Or is the answer that they just fight unarmed because a properly sized weapon would be too heavy?

thats the neat part, you don't.

If this was true, I wouldn't be here asking the question.

Like, technically the developers of D&D didn't need to provide rules for combat. They didn't need to, but they did anyway. Because people who play D&D want combat rules. And I want rules for giant weapons and armor. Technically, you don't need any rules for anything. The things we do write down rules for are generally the things we consider to be important and worth codifying.

If your in a ttrpg the only rules that matter are the mechanical abstractions. these abstractions are there you don't HAVE to calculate it out with real physics yourself or answer the questions because there are abstracted easier answers done for yoiu. its a convenient time saving measure like that, because if we had to do that for every single creature in existence, this would take forever.

I still need to let the large or tiny player know how much their equipment, which is properly sized for them, weighs.

I suppose another option is to move to a different form of encumbrance tracking that doesn't rely on weight. Giant characters have twice as many "slots", and giant items take up twice as many "slots", and the exact sizes and weights are left vague. I think the encumbrance system could use some serious improvement, but I'm not convinced I'd want to stop tracking weight entirely.

Perhaps this is much ado about nothing, though. Playing a smaller race necessarily means having a reduced carrying capacity, but perhaps the trade-off is having proportionally lighter equipment. So even though your carrying capacity is lower, you can actually more easily carry all your armor, weapons, tent, bedroll, and such without overencumbering yourself. On the other side, a larger race has a higher carrying capacity, but their weapons and armor eats up a greater proportion of that capacity. If you're playing a character who doesn't wear heavy armor or use big weapons, then the larger race can carry more mundane gear like ropes and torches and such that don't care about your size. So maybe that trade-off is a feature, not a bug, making the loss of carrying capacity on smaller races more palpable and the increased carrying capacity on larger races less overpowered.

[Mechalich]

A giant twice the size is less than 8 times as heavy. Okay, but how does that work given the example with the cubes?

Non-uniform density. A living being isn't a solid block of slightly-denser-than-water material. Volume can increase without significantly increasing mass by utilizing low-density material. Sauropods (and birds) have a system of air sacs within their bodies that helped to support them in this way. Giants could, theoretically, have lots of spongy bone that's mostly air comprising a significant portion of their physical structure. Or maybe they pad out their bodies with lots of low density fatty tissue.

I think what's frustrating is that I know there has to be an answer out there somewhere. This isn't a new thing, giants have been around in folklore since forever. I'm pretty sure the ancient Greeks were well versed in the rate at which a thing's weight increased as it got bigger, so how did they explain things like giants? Or is the answer that they just fight unarmed because a properly sized weapon would be too heavy?

There's significant evidence that Greek myths of giants (which included many of their mythic heroes, who were presumed to be literally larger than life), are derived from the discovered of fossil elephant and rhinoceros bones. If you stand up an elephant skeleton as if it were a humanoid you basically have a giant, this will require some modifications to the bones, but elephants can and do rear up on their hindlegs, so it's not like they can't support themselves temporarily using just two limbs.

Greeks, notably, fought primarily with spears. An oversized spear is perfectly plausible for a giant to carry. Wood has no problem scaling up to make a thicker, longer spear shaft, and oversized spearheads are only a modest contributor to overall weight. It's things like gigantic swords, axes, and hammers that have problems, especially given that those weapons are often already portrayed massively oversized in fantasy art (so that you're talking about scaling up something that is already unreasonably huge and heavy).

[King of Nowhere]

Your thinking is backwards.

DnD nor any fiction doesn't need to "solve" any question of physics with anything. Because the square cube law isn't a thing that just exists

errr... sorry, wrong.
the square cube law is not a law of physics. it is a law of mathematics. you can totally rewrite the laws of physics in your universe, but the square cube still applies.

I think you're missing the point. I have a giant that is twice the size of a human. How heavy is the giant? How big is the giant's weapon? How heavy is the giant's weapon? How much weight can the giant carry?

The point is, how do I answer those questions?

I guess the crux of the issue is that one part of my brain thinks the giant should have identical physics to the human, while the other part of my brain can't ignore the cube example and that the physics must necessarily be very different. .

My easy, convenient answer: magic.

Dragons absorb the background magic and use it to reshape realitiy so that they can move around easly without being crushed by their own weight. Giants too. It also works in antimagic, because an antimagic field is simply a spell that suppresses other spells, but there's still magic in the area.
So basically the giant has identical physics to the human, scaled up, and uses magic to make up for the impossibility of it.
It gets even better: level adjustment. As humans level up, their soul learns to also use background magic, which they use to gain supernatural capabilities - like dismissing multiple impalements as flesh wounds or punching through stone walls. Giants and dragons can also do this, but it's a lot harder for them - because they are already using up magic from the environment, and there's a limited amount of it. So they have a harder time leveling up.
Finally, you'll notice that the strongest dragon, the strongest humanoid, the strongest monster, the strongest golem, they are all more or less there in terms of actual power. and that's no coincidence; they are all using magic to get so strong, and they are all limited by the amount of background magic they can get.

Background magic allowing for breaking of physics can explain so many things.


As for the sword, a giant's sword is still small enough that it won't break the square cube law. you can make a giant-sized sword and it still works.
Of course, it breaks more easily. but then, every sword breaks if wielded by someone with enough force to punch through stone walls, and used to punch through dragonhide or golems. To which, my answer is that they are using magic swords. If a 20th level fighter used a mundane sword, it would break at the first swing. it's just a little piece of fluff, because when did last happen that a 20th level fighter didn't have a magic weapon?

[Lord Raziere]

errr... sorry, wrong.
the square cube law is not a law of physics. it is a law of mathematics. you can totally rewrite the laws of physics in your universe, but the square cube still applies.

who says?

Its fantasy. 1+1 need not equal 2. mathematics is still based on the real world as observed and thus still describes our own world, because it is created to describe that world. If math in a world where someone made the square cube law, applied to a block of matter and said that the cube cannot be lifted by any human no matter how strong and a confirmed human lift it, the math is wrong. mathematics have been made for phlogiston and ether as well, that never meant they were correct.

[Khedrac]

For example, the largest mammal ever (probably Paleoloxodon namadicus) might have capped out at ~20 tons, but the largest land animal ever was a giant sauropod of at least 80 tons, and quite possibly considerably more. The reasons sauropods were able to get much bigger than elephants or rhinos don't appear to have involved anything like overall bone & muscle strength, but appear to have more to do with differences in lung structure and reproductive method.

Err, the largest vertebrate ever is the blue whale which is also a mammal. Do you mean the largest land mammal?

[Vahnavoi]

Trying to explain everything in terms of material sciences misses the point that there's realms beyond material that you can rely on.

The giant, the dragon, the massively oversized spiders? They aren't flesh and bone. What they look like is a result of a human's mind struggling to represent some greater entity in terms the human is familiar with. The giant looks like a human, acts like a human, is affected by gravity like a human despite the physical paradox of it, because that's what the human observer can comprehend. If one attempted to make physical measurements of the observer and observed, one would get multiple, complementary yet paradoxical sets of results. From the giant's perspective, the giants are the humans, weighing as much as humans do, obeying normal laws of physics, with the humans being tiny insects.

It would be easy to make it so that such creatures are only met where subjective and objective, the dreaming and the waking worlds, overlap. Outside such spaces, the monsters are not directly encountered at all, only observed by effects they have on the world. You know a giant is around because the ground trembles and the trees shake, a dragon is around when sun shines all too bright from the sky and the forests catch fire, giant spiders are around when all the birds vanish and you start finding webs everywhere. So on and so forth.

[Anymage]

who says?

Its fantasy. 1+1 need not equal 2. mathematics is still based on the real world as observed and thus still describes our own world, because it is created to describe that world. If math in a world where someone made the square cube law, applied to a block of matter and said that the cube cannot be lifted by any human no matter how strong and a confirmed human lift it, the math is wrong. mathematics have been made for phlogiston and ether as well, that never meant they were correct.

It's possible to conceive of a world where dividing a square into half along each edge does not result in four squares or a world where pi is equal to exactly 3, but those worlds would necessarily look so wildly different from our own to be difficult to game in. Basic math is one of those things you don't muck with unless you want to set your campaign in the far realm.

Making giant beasties work does require a liberal application of "it's magic", but fantasy worlds having magic be an inherent part of how the world works is entirely on brand so that makes sense. To Greywander's specific question, it's very easy to say that increases to the strength score add a linear amount to attack and damage rolls but a nonlinear amount to carrying capacity. 5e has linear encumbrance rules because they're largely vestigial (which happened because players by and large found the effort of tracking encumbrance to be more hassle than it was worth), but 3.5 has a nonlinear relationship between Str score and carrying capacity on top of having modifiers for size and build. From a very cursory look at a couple of giants in 3.5 they're actually better equipped to carry another giant than a human commoner is equipped to carry another human commoner.

Additionally, appreciably large giants do not need equipment that is straight upscales of human gear. A larger person wearing a bulletproof vest might require more material to fashion their vest, but they don't need the kevlar or ballistic plates to be thicker. An edged weapon similarly cares mostly about the edge and is okay being as thin as possible so long as it isn't rendered structurally unsound. Gear can afford to be thinner, which means it isn't just a simple cubic function. Add in fantastic materials, mythic craftsmen, and just a touch of pure "yup, it's magic" and you should get numbers that are easier to stomach if you want to be more strictly simulationist about it.

[theNater]

I'm pretty sure the ancient Greeks were well versed in the rate at which a thing's weight increased as it got bigger, so how did they explain things like giants?

I would guess they mostly used vagueness. "The giant was as tall as a house, carrying a spear the size of a tree" is understandable by virtually everyone, gets the point across, and lets people fill in details in whatever way makes sense to them.

They were also familiar with the concept of magical items, so if somebody insisted a giant that size can't possibly heft a spear that size, they could always say "well, the giant was wearing a fancy sash. Perhaps it made the giant stronger."

The way you can use this in your own situations is to refrain from calculating the details. Don't calculate how much weight the giant can carry; decide how much weight the giant is carrying. When the giant tries to lift something large, you can decide in the moment whether the attempt succeeds based on what feels good and works for the story. And if your players catch you in a contradiction, where the giant can lift a heavier thing but not a lighter thing, you can just say the giant's strength waxes and wanes with the moon, or ebbs and flows with the tide, or whatever.

[Quertus]

The reason I bring up the example of the cubes again and again is because it's such a basic, elementary demonstration that something twice as big should be 8 times as heavy, no matter what physics your universe is running on.

And that’s your problem right there: you’ve made an assumption that is, simply put, false.

For example, my worlds physics is “this is a computer simulation. Everything is exactly as heavy as the database says it is. If I ‘break down’ a cube, I get 7 half-sized cubes, or 9, or however many the code says I get.”.

Or my world physics is, “this is all a dream. I can lift mountains if the Dreamer dreams that I do.”.

I mean, I generally agree that most people who would mess with such basic concepts (or math) should be banned from world building until they learn to understand the consequences of such foolish action, but, even so, it isn’t a given that a world must behave by square-cube law.

Throw out your preconceptions, your misconceptions, look at what really is, and then you will be ready to be a scientist.

Otoh, learn to think things through given a concept / physics, and then you will be ready for world building.

So, how can giants work? Different materials, different physics, magic. Maybe two pies don’t weigh twice as much as one pie in this world. Maybe what you know and intuit about bone strength and square-cube laws is nonsense. Maybe giants eat (and, unlike most other creatures, can digest) crystallized time, to allow their proportions to work. Maybe they can subconsciously manipulate gravity. Maybe maybe maybe.

Pick something that works… and do the world building to make the rest of the world work given those physics. Even if that means “weight? What’s that? How much I can carry? Oh, you mean ‘item slots’.”

Physics as we know it exists to the extent you make it exist; it isn’t an inherent property of any imaginable world.

[OldTrees1]

The Square-Cube law in RPGs is fixed by the Cube-Cube law or the Square-Square law.

For example a Giant might weight 8x as much and be 8x as strong (due to fantasy muscles scaling off of volume instead of IRL muscles scaling off of cross-sectional surface area) but since much of that strength is used to move their increased weight, the net gain they can exert is merely +4 Str.

So why would fantasy muscles work by the Cube-Cube law? Actually why don't IRL muscles work by the Cube-Cube law. I know they don't but the mechanism I know of (sub sections of the muscle volume contracting) would scale by volume. Obviously IRL is more complicated and something nerfs that down to the Square-Cube law, but it means the explanation works for me for fantasy.

However I also tend to have bigger creatures use lighter weapons. A Giant might use a club rather than a greatsword.


So what works for me is saying the square-cube law applies to equipment but the cube-cube law applies to biology (with some modifications like Dragons mixing flying & gliding rather than being hummingbirds).

[PhoenixPhyre]

Giants (and other megafauna) have bigger issues as well. For one thing, what do they eat? And how much caloric energy does it take to keep one mobile? In a "physics-based" world, a family of giants must be like a plague of animal-guzzling locusts. Dragons have similar, if not greater issues.

But I solve them the same way as I do the square-cube issues. As someone else said--background magic. In particular, for dragons it's their hoard. They are tied into the world's elemental energies by their hoard, which may or may not be physical objects. This link both feeds them and gives the Authority over the winds, letting them fly, and over the earth, giving them strength to move and act despite that not working "normally". A dragon's muscles are powered by the intrinsic powers of the world.[1] It's why dragons get so pissy when you steal from them--you're literally stealing their source of vital energy and ability to move. A dragon without its hoard either gathers a new one fast or starves to death. This is part of the transition to adulthood--before that, as young dragons, they still need "real" food to supplement their lack of significant hoard. But that can't take you very far.

Giants, on the other hand, aren't natural. They're jazuu (goliaths in D&D terms) who have been rewritten by ancient runic magic. Those that survive and master the transformation become somewhere on the hierarchy, gaining Authority over various aspects via the runes implanted in them. Hill Giants, whose Authority is over labor, use crude weapons and brute strength. And their strength is whatever it needs to be for the task at hand, drawing strength from the bones of the earth. Frost and fire giants, whose Authority is over War and Making, respectively, use more complex items. And since the higher giants also carry the same Authority as the lesser ones, their strength remains. A fire giant's (improbably large) greatsword doesn't fall apart because the giant's Authority (by which it was crafted) denies that possibility. Cloud and Storm giants have Authority over people, and the hypothetical Titan has Authority over all things. This same runic transformation ties the giant into the flow of aether throughout the world, feeding them. Giants do eat, as do adult dragons, but mostly only for taste.

[1] Gravity is not a warping of space-time. It's a natural component of umbral-earth-aspected aether (of which much solid matter is composed). The planet is heavily composed of this aether, as are most objects. And they attract each other in proportion to the dominance of UE aether. Which means you can make something float not by buoyance caused by displacing fluids, but by altering the aetheric composition or wrapping yourself in a bubble of luminous air, UE's counterpart. Similarly, muscles don't work by bundles of cellular fibers contracting against each other. It's an interplay of physical aether and will power. For most people, this all balances out to "something similar to what we see around us, if you don't pry beyond the surface much. Applying the techniques of modern math and chemistry and physics will just leave you seriously confused, because none of it makes any sense. Apply the concepts of 12th(ish) century alchemy and you'll be a lot closer.

[Quertus]

Actually why don't IRL muscles work by the Cube-Cube law. I know they don't but the mechanism I know of (sub sections of the muscle volume contracting) would scale by volume.

This is the world building counterpart to my roleplaying stance: if you can imagine it working a particular way without seeming incoherent to you, then it’s fine. That… didn’t come out right.

That is, “why don’t things work by cube-cube law?” is a perfectly reasonable thought process, so it’s fine to build a world that works that way (so long as the world building is consistent). And it’s possible to roleplay a character who comes from a cube-cube law world, they just have a few different expectations from… not even from irl, but from the most informed/aware members of irl. (Also different from “why not cube-cube irl” just because of our experiences).

Oh, crazy question: what if… everything worked just like irl, except: matter / atoms were smaller. Thus, a “giant” is actually smaller than a human irl, and so perfectly supported by the physics? Would anyone have problem with giants then?

(Does that makes sense? I have no idea. But I can imagine that physics could exist where that would work, even if they don’t actually match how “small atoms” would work irl.)

[Mechalich]

Giants (and other megafauna) have bigger issues as well. For one thing, what do they eat? And how much caloric energy does it take to keep one mobile? In a "physics-based" world, a family of giants must be like a plague of animal-guzzling locusts. Dragons have similar, if not greater issues.

Assuming Giants are primarily vegetarian, they don't have any greater impact than other megafauna. In fact, they aren't even described as being particularly heavy. 3.5e weights range from 500 kg for Hill Giants to 5500 kg for Storm Giants. That's a range from roughly 'Bison' to 'Bull Elephant.' Storm Giants are a bit ridiculous, but many of the other giants are much more manageable, massing around the same as Giraffes. A Giant tribe that has the same impact as a herd of elephants is not a big deal (especially if their digestive system is more efficient than the rather lousy one elephants have). If giants are pastoralist - which they are sometimes described as - that's a little harder, since it means massive herds of super-sized goats (also not unreasonable, oversized fossil caprines are known) ranging over wide areas, but giants can presumably cover large territories as shepherds.

Dragons are harder, because they are usually presumed to be carnivores and because flight is energetically intensive. However, dragons are also usually presumed to be exothermic as adults, taking advantage of gigantothermy to maintain a higher body temperature, which significantly reduces caloric needs. Fantasy also often postulates that dragons sleep a lot, husbanding their energy for relatively short periods of intensive activity. In general the metabolic needs of dragons are manageable if there are large megafauna targets for their predation (when Game of Thrones had Drogon constantly raiding local livestock they were on the right track) and they do not engage in a lot of long-term sustained flight. The bigger issue with dragons, in fantasy, is that they are drawn as unreasonably robustly framed with far too small of a wing surface.

[Morphic tide]

So why would fantasy muscles work by the Cube-Cube law? Actually why don't IRL muscles work by the Cube-Cube law. I know they don't but the mechanism I know of (sub sections of the muscle volume contracting) would scale by volume. Obviously IRL is more complicated and something nerfs that down to the Square-Cube law, but it means the explanation works for me for fantasy.

The "main" contributors are the "ceiling" of the musculature's own tensile strength which is exactly a "chain's weakest link" concern, as well demonstrated by how commonplace the ability to cause structural damage to oneself by muscle contraction, the need to stabilize which occupies most of what's "above" and "below" the "plane" considered as applying the force, and the logistics of activating the muscles between resources to do so and the nervous system's ability to activate them governed directly by surface-area to volume.

If we are to stick to specific mechanisms obeying geometric laws, I think the best answer is to use field effects instead of discrete contact, as penetrative inverse-square scaling is still superior to surface area to volume or cross-sectional area to volume as constraints. Repulsive fields in leu of tensile strength lining up, attractive fields in leu of discrete contractile elements, and diffusive fields in the vein of quantum tunneling instead of surface area transfer.

Don't think there's any useful way to do that with actual physics at the scale of life as we know it (exotic matter systems at the nanometer scale are a different story), but it's a structure for a magic answer, and the interplaying field effects will be very obtuse in their equilibrium points so in-universe understanding will take a VERY long time.

[Telok]

The actual issue (I think) isn't so much the physics or biology of it, but an issue of a "versimilitude & stats" conflict. We accept as given a 20' tall humanoid called "giant" that functions basically as a really big human. It has gear given by game stats, but the gear is missing game stats.

We can "magic does everything" the narrative of it away but that still leaves missing stats stuff like the weight & size of the gear and how PCs interact with it. If we follow any square cubed setup we can hit an issue where the giants can't function because gear weight vs strength stat says they can't lift their pants off the floor. If we go with even linear increases like a 3 ft. & 3 lb. weapon scaling up to a 18 ft. & 18 lb. we start having issues with game stats because PCs can easily use items of that size & weight (ref: RL pikes, yes they're heavier but the PCs involved are also often beyond max human normal strength) and we're apparently afraid of fighters doing giant sized damage with the giant sized weapons and the giant level strength given by the game.

Personally I just fix by ditching D&D for a game with functional size scaling and let the PCs do the big damage if they can use the weapon. D&D would probably work fine to just fiddle with carry limit scaling, make giants stronger, and use 1d12+20 instead of something like 4d10+6 for damage for a 3x size sword.

[Jay R]

In the introduction to the game I'm currently running, I included the following:

It is not true that this world is run by the laws of modern physics except when somebody casts a spell. It has different physical laws. You have no idea if there are galaxies; the sun clearly and obviously orbits the earth, there are 9 or 10 known planets, which are bright lights in the sky that move relative to the stars. They are the moon, Mercury, Venus, the sun, Mars, Ceres, Jupiter, Saturn, and one or two more that I will name if I ever need them.

The earth is not a planet; it is the unmoving center of the universe. There are (as far as you know) no electrons, neutrons, protons, plate tectonics, relativistic speeds, radioactivity, or 92 natural elements. [Of course, nobody on our earth knew of those things in medieval times, either, so who knows?]

Cold is an active force, not merely the lack of warmth. Electricity does not flow from highest to lowest potential (or wizards could not aim lightning bolts). There is no cube-square law (or there would be no giants, and dragons couldn’t fly). Gravity is not universal (or flight and levitation spells wouldn’t work). Some creation spells violate conservation of mass, and many attack spells violate the three laws of thermodynamics.

Cute stunts involving clever use of the laws of thermodynamics simply won’t work. Note that cute stunts involving the gross effects thereof very likely will work. Roll a stone down a mountain, and you could cause an avalanche. That’s entropy in action. But in a world with teleportation, levitation, and fireball spells, Newton’s three laws of motion do not apply, and energy and momentum are not conserved. Accordingly, modern scientific meta-knowledge will do you more harm than good. On the other hand, knowledge of Aristotle, Ptolemy, medieval alchemy, or medieval and classical legends might be useful occasionally.

[Emphasis added.]

My purpose in writing that was to keep players from trying to think in modern scientific terms, and instead try to think in medieval and mystical terms. [I started gaming at an elite engineering schools. Those guys will try anything to break the game with science.]

My answer to anybody who asks me how much the giant's sword weighs is, "He's swinging it at you. Are you going to estimate its weight, or duck?"

Or possibly,
Player: How much does the giant's sword weigh?
DM: Probably less than all the gold pieces currently in your backpack. Do you really want to start tracking weight?

Answering these kinds of questions doesn't improve the game, and might hurt it. Therefore the best way to handle such a question is not to ask it in the first place.

[Greywander]

This is the world building counterpart to my roleplaying stance: if you can imagine it working a particular way without seeming incoherent to you, then it’s fine. That… didn’t come out right.

That is, “why don’t things work by cube-cube law?” is a perfectly reasonable thought process, so it’s fine to build a world that works that way (so long as the world building is consistent).

I think this is sort of the other side of the point I was making by bringing up the example with the cubes over and over again. It's so trivial to show that weight should scale cubically with size that it simply wouldn't make sense for it not to, even with fantasy physics. Therefore, something like a Square-Square Law just doesn't work. Cube-Cube Law is at least somewhat plausible.

I would be curious to see someone do a deep dive into the implications of using a Cube-Cube Law, both just for some specific creatures (e.g. giants), but also for all creatures including humans and normal animals. What sort of changes would this add to the world? What else would be different as a result? And so on.

The actual issue (I think) isn't so much the physics or biology of it, but an issue of a "versimilitude & stats" conflict. We accept as given a 20' tall humanoid called "giant" that functions basically as a really big human. It has gear given by game stats, but the gear is missing game stats.

We can "magic does everything" the narrative of it away but that still leaves missing stats stuff like the weight & size of the gear and how PCs interact with it. If we follow any square cubed setup we can hit an issue where the giants can't function because gear weight vs strength stat says they can't lift their pants off the floor.

I think this sums it up pretty nicely.

In the end, I think the "solution" is something I referred to in the OP: follow the Square-Cube Law as a general rule, and then in select cases give certain creatures a multiplier to carrying capacity. This doesn't necessarily need to bring them up to cube-cube scaling, but we can think of that as an upper bound. For smaller giants, no buff should be needed as most giant weapons should still be light enough for them. Only larger giants would need a buff, and even then the buff could be a lot less than cube-cube scaling.

This does remind me of a question I posed in another thread but never really got a satisfactory answer for: how does the weight of gear scale according to size? We can imagine, for example, that armor might not change thickness at different sizes, and thus would only scale in two dimensions. Or maybe it would change thickness. But somehow armor provides the same AC bonus against attacks, regardless of both the size of the armor and also the size of the attack? It's kind of a big fat question mark, isn't it?

[Quertus]

Or possibly,
Player: How much does the giant's sword weigh?
DM: Probably less than all the gold pieces currently in your backpack. Do you really want to start tracking weight?

Answering these kinds of questions doesn't improve the game, and might hurt it. Therefore the best way to handle such a question is not to ask it in the first place.

If I’m playing a Gravity Mage, the answer will almost certainly be “yes”, unless the entire game is played at “handwavium” level of abstraction.

That is, certain concepts might lend themselves to desires to “deep dive” (or even “shallow dive”) into more concrete numbers. And these concepts might be as simple as a race, or how shallow the draft on a boat is.

I say this from the PoV of having played with people whose intuition for such things was so horrible as to wreck suspension of disbelief for the entire table. “Wanting numbers and physics” was kinda a survival instinct around them.

I think this is sort of the other side of the point I was making by bringing up the example with the cubes over and over again. It's so trivial to show that weight should scale cubically with size that it simply wouldn't make sense for it not to, even with fantasy physics. Therefore, something like a Square-Square Law just doesn't work. Cube-Cube Law is at least somewhat plausible.

I would be curious to see someone do a deep dive into the implications of using a Cube-Cube Law, both just for some specific creatures (e.g. giants), but also for all creatures including humans and normal animals. What sort of changes would this add to the world? What else would be different as a result? And so on.

The thing is, by itself, cube-cube law doesn’t invalidate anything. That is, all it says is (effectively) “anything that can exist, can exist at any size”. So, giants? Giant bees? Little green men? Micro-whales you wear as earrings? Yup, all fine.

It may be odd that dragonflies exist, when micro dragons would fill the same ecological niche[*], but better, but the setting being suboptimal is not the same as the setting being incoherent.

[*] of “eat everything” (and look pretty doing so), at least for 3e values of dragons.

[Mechalich]

This does remind me of a question I posed in another thread but never really got a satisfactory answer for: how does the weight of gear scale according to size? We can imagine, for example, that armor might not change thickness at different sizes, and thus would only scale in two dimensions. Or maybe it would change thickness. But somehow armor provides the same AC bonus against attacks, regardless of both the size of the armor and also the size of the attack? It's kind of a big fat question mark, isn't it?

In general armor would not change thickness as it increased in size, which is something we can see even in humans. If you armor up a 4'11" 105 lb. person and a 6'5" 300 lb. person the armor is still going to be roughly the same thickness, they'll just be less of it overall. However, at giant scale it gets a little funny, especially with plate metal armor. A lamellar coat can be made essentially infinitely big at the same thickness, but huge metal plates made need greater thickness in order to hold together as their surface area increases. The same thing is true of blades, the only reason a giant would want a sword thicker than that of a human, as opposed to merely longer, is to sustain the structural integrity of the weapon (though admittedly giants with larger hands will need larger grip areas).

[Greywander]

Or possibly,
Player: How much does the giant's sword weigh?
DM: Probably less than all the gold pieces currently in your backpack. Do you really want to start tracking weight?

Answering these kinds of questions doesn't improve the game, and might hurt it. Therefore the best way to handle such a question is not to ask it in the first place.

It's strange how many people just assume that everyone has the same values as them. "Pshaw, inventory tracking, am I right? Who would ever want to do that?"

Meanwhile, I created a character sheet that automatically tracks coin weight, and even tells you how many pouches you need to carry all your coins. I have an option to drop your pack, which deducts the weight of your pack from your encumbrance, but not the weight of anything on your person. I freaking love tracking that kind of minutia.

Honestly, I'd be more likely to get upset that no one else, not even the DM, was tracking coin weight. I mean, yes, I'll acknowledge that I might be a little weird in this respect, but it really undermines the point you're trying to make when you use tracking coin weight as an example of something so ridiculous no one would do it, when talking to someone who actually tracks coin weight.

It's kind of like if someone were to ask about treatments for a rare disease, and then get a bunch of dudebros responding with, "Just don't worry about it, dude, nobody gets that disease man." The fact that the person is asking in the first place should probably be an indication that they, or someone they care about, actually does have that rare disease, and just being told "not to worry about it" is not a helpful answer to them.

[Notafish]

Would having a different value for gravity in the fantasy world (or the planes of different beings' origins) open up the range of options for body types?

[olskool]

I would think too much about the Square-Cube law. Science is still fighting over its validity as it pertains to our own World. They KNOW this law can be calculated mathematically, but they also KNOW that 80-Ton dinosaurs... which violated the law... existed. Science also KNOWS (genetically from DNA testing) that there was NOTHING special about the dinosaurs themselves other than their size. We also KNOW (from fossils) that 10ft long Centipeeds existed before dinosaurs even though the largest insect today would be just over a foot in length. What we DON'T KNOW is HOW these things could exist. They violate our understanding of the laws of nature... so something's wrong with the Square-Cube Law's implementation.

[Telok]

I would think too much about the Square-Cube law. Science is still fighting over its validity as it pertains to our own World. They KNOW this law can be calculated mathematically, but they also KNOW that 80-Ton dinosaurs... which violated the law... existed. Science also KNOWS (genetically from DNA testing) that there was NOTHING special about the dinosaurs themselves other than their size. We also KNOW (from fossils) that 10ft long Centipeeds existed before dinosaurs even though the largest insect today would be just over a foot in length. What we DON'T KNOW is HOW these things could exist. They violate our understanding of the laws of nature... so something's wrong with the Square-Cube Law's implementation.

Speaking of giants among us, someone recently found a centimeter long bacteria.

That said, for a fic world a combination of lower gravity and higher air density & oxygen content could cover a bit. Help with the fire breathers too.

But mostly I tend to think of "magic", if and only if its some unified force type thing in the setting, as just another type of energy. It interacts with physical stuff and other energy fields, it has predictable outputs for specific sets of inputs (otherwise its 100% wild magic random tables for all magic forever), and... well it basically acts like a different energy that responds to sapience instead of just gross material manipulation. So yeah, chemistry & physics & thermodynamics & gravity still work under that. You just have an additional way to add, remove, or transform energy to whats going on under normal physics type stuff. Flight? Use magic to change the direction of the acceleration that gravity provides.

'Course I don't personally do my settings & magic that way too much. I prefer actual different magic techniques with different rules & at least some level of less than perfect predictability.

[Lemmy]

Dinosaurs absolutely DO NOT violate the square-cube law... Neither do giant arthropods from the past. That's a common misunderstanding of what the square-cube law actually means.

But in any case, my personal take is that in worlds with magic, aether is a real thing... And creatures exist simultaneously in the physical world and in a world filled with aether. The reason giants and dragons can exist is the same reason blue whales don't have their organs crushed by their own weight. Buoyancy... Except instead of water, it's aether that (partially) sustains the weight of giant creatures and objects, making them easier to lift, move and carry than they would be in the real world.