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[GoblinCookie]

Any increase to the size of the object will increase the force applied to it by gravity. Increasing the thickness will cause the ratio between mass (and the associated force) and cross-sectional area (and therefore, the strain as well) to remain constant, while increasing the height will increase it. You build a tower high enough, and eventually the stress will become too high and the whole thing will collapse. There is not a lot to misunderstand here.

No, if the width and length of the building continue to increase disproportionately to the increase in height then the building can theoretically get taller forever.  However since the increase in the supporting dimensions scale is not linear but exponential the total amount of material needed keeps increasing more and more to the eventual effect that basically the whole earth could not afford to make the building any taller.  Therefore Square-Cube Law does not ever stop the building from getting taller, it merely makes it too expensive to make it any taller than it is by having the required amount of materials perpetually multiply. 

Let us look at this scientifically; if you were right, then the largest buildings in the world would have to be made of marble and titanium; instead what we see is that they are made out of the same steel and concrete as ordinery tower blocks. We also see that elephants are made of the same flesh and bone as mice and not some kind of super flesh and bone.  Yes, using stronger materials allows you to make a creature or building taller without increasing it's supporting dimensions disproportionately but I am assuming that larger creatures as in real-life are not made of stronger materials than smaller creatures.

The cross-sectional area you speak of is simply what I am calling the supporting dimensions and nothing else; that is the two dimensions other than it's height.  However small the creature is, the supporting dimensions always be holding up the whole weight of the creature; since that also includes their own weight what this means is that their material *must* always each provide 50+% extra carrying capacity on top of the weight that the materials add to the system.  If this is not the case, then the creature will collapse under it's own weight regardless of how small it happens to be. 

Since all supporting dimensions carry 50+% of the weight of the third dimension, 2*4*4 is the formula that would physically allow you to basically scale something humanoid up forever.  I think a creature with more than two legs on the other hand would instead use 2*2*6, the latter being it's width, the former being it's length and the middle being it's height (what is supported).  The problem is not that the creature cannot be scaled up, but that the cost of perpetually increasing the supporting dimensions disproportionately to every increase in it's height ever multiplies to the point that there is no way to get enough nutrients and energy from the enviroment in order to sustain it. 

[miauw62]

I know that the square cube law is universal, but I'm just saying that you can't literally apply it to this scenario and say "according to this UNBREAKABLE MATHEMATICAL LAW, a human of volume x will have height y"

Also, you don't know how long the dragon would be, because non of this follows strict mathematical laws. We don't know how big a crocodile needs to be to be thirty feet long. A simplistic mathematical model can't simulate that, so any results you get are basically meaningless.

[cochramd]

No, if the width and length of the building continue to increase disproportionately to the increase in height then the building can theoretically get taller forever.

Perhaps if the building is a cone or pyramid, and one that can have the angles of its sides adjusted at that, something certainly not implied by "2x4x4". At this point, I'm 99.9% percent sure that you're merely feigning complete and utter stupidity just to see how frustrated you can get anyone who tries to help you.

[GoblinCookie]

I know that the square cube law is universal, but I'm just saying that you can't literally apply it to this scenario and say "according to this UNBREAKABLE MATHEMATICAL LAW, a human of volume x will have height y"

Also, you don't know how long the dragon would be, because non of this follows strict mathematical laws. We don't know how big a crocodile needs to be to be thirty feet long. A simplistic mathematical model can't simulate that, so any results you get are basically meaningless.

Provided the crocodile and the dragon have the same body-plan and materials, the same physical requirements in height vs supporting dimensions needed to make a 30ft crocodile will also make a 30ft dragon.  You are right in one sense however, if the body plan is not essentially the same between the larger creature and the smaller creature then you cannot determine how big in dimensions the creature. 

However the body plan of a giant and a human are fundamentally the same.  This means that if we can make a 12ft human, we have basically got a giant, so whatever mathematical formulas allow a human to be scaled up also allow us to determine how big a 12ft giant is.  We know a giant is basically a 12ft human, just as we know a dragon is basically a 30ft crocodile.

Perhaps if the building is a cone or pyramid, and one that can have the angles of its sides adjusted at that, something certainly not implied by "2x4x4". At this point, I'm 99.9% percent sure that you're merely feigning complete and utter stupidity just to see how frustrated you can get anyone who tries to help you.

No, I am entirely here to come up with a formula to scale creatures up and down without the larger creatures realistically collapsing under their own weight.  I am not interested in arguing, I want a formula and I think I have the formula now; people saying that formula will not work need to come up with a better formula.

A humanoid is shaped roughly like a cone, it is quite feasibly possible to make the humanoid more cone-like than it already is as the creature gets bigger.  Most animals tend towards 'square-cube-law friendly' shapes that can be scaled up and could also be easily be made more extreme as well. 

[cochramd]

I know that the square cube law is universal, but I'm just saying that you can't literally apply it to this scenario and say "according to this UNBREAKABLE MATHEMATICAL LAW, a human of volume x will have height y"

Also, you don't know how long the dragon would be, because non of this follows strict mathematical laws. We don't know how big a crocodile needs to be to be thirty feet long. A simplistic mathematical model can't simulate that, so any results you get are basically meaningless.

Actually, we've found skulls of crocodiles in that size range, and have been able to estimate their mass (and thus presumably their volume too) by comparing them to various extant species:

Spoiler (click to show/hide)

Note that the one at the top is about 1.8 times longer than the one on the bottom, but only about 1.47 times as tall. Also note that since crocodilians spend most of their life in the water and are short, the square-cube law gives them less grief than for being enormous than it would
a tall and/or land-based creature. Personally, I would only use a crocodile as an approximation of a dragon if it were a sea dragon, otherwise I'd use dinosaurs or monitor lizards. [INSERT WITTY LINE ABOUT KOMODO DRAGONS HERE]

However the body plan of a giant and a human are fundamentally the same.  This means that if we can make a 12ft human, we have basically got a giant, so whatever mathematical formulas allow a human to be scaled up also allow us to determine how big a 12ft giant is.  We know a giant is basically a 12ft human, just as we know a dragon is basically a 30ft crocodile.

No, no, no. The entire point of this conversation is that they a human and a giant DO NOT share the same body plan any more than a mouse and an elephant do.

No, I am entirely here to come up with a formula to scale creatures up and down without the larger creatures realistically collapsing under their own weight.  I am not interested in arguing, I want a formula and I think I have the formula now; people saying that formula will not work need to come up with a better formula.

No one here is going to give you a better formula because no one here possesses the relevant education. Go to university and get a degree in biomechanics, specializing in allometry. Between yourself, your professors and your fellow students you should be able to figure it out. If you need something RIGHT THIS SECOND, what you should do is find the best approximation of what you want that already exists in DF, then multiply its base volume by (desired height/average height of base creature)^3. Provided that (desired height/average height of base creature) isn't that much larger than 1, then it is safe to assume that the increase in size wouldn't realistically cause it to collapse under its own weight. Your 12 foot human, for instance, would be calculated to have a volume of 518400 based on a 10 foot sasquatch.

A humanoid is shaped roughly like a cone

Not healthy ones.

Spoiler (click to show/hide)

[GoblinCookie]

Actually, we've found skulls of crocodiles in that size range, and have been able to estimate their mass (and thus presumably their volume too) by comparing them to various extant species:

Spoiler (click to show/hide)

Note that the one at the top is about 1.8 times longer than the one on the bottom, but only about 1.47 times as tall. Also note that since crocodilians spend most of their life in the water and are short, the square-cube law gives them less grief than for being enormous than it would
a tall and/or land-based creature. Personally, I would only use a crocodile as an approximation of a dragon if it were a sea dragon, otherwise I'd use dinosaurs or monitor lizards. [INSERT WITTY LINE ABOUT KOMODO DRAGONS HERE]

Crocodiles do not spend their whole time in the water, it does not matter how little time they spend on the land the square-cube law is still going to hurt them; more so because they have less practice bearing up their own weight to strengthen their bones than a creature that spends most it's time on the land.  The key thing that you have not factored in however, is that crocodiles are quadrapeds and so increase in 2*2*6 rather than 2*4*4, the same thing applies to dragons.  As they get longer they get taller in proportion, which requires another dimension to support the extra load so quadrapeds always get thicker as they get longer. 

No, no, no. The entire point of this conversation is that they a human and a giant DO NOT share the same body plan any more than a mouse and an elephant do.

The two share basically similar bodyplans, but the proportions of that plan are different.  The skeletal structure of a mouse and an elephant are, aside from the skull pretty similar; the main distinction being how thick the elephant bones are compared to the mouse's bones. 

No one here is going to give you a better formula because no one here possesses the relevant education. Go to university and get a degree in biomechanics, specializing in allometry. Between yourself, your professors and your fellow students you should be able to figure it out. If you need something RIGHT THIS SECOND, what you should do is find the best approximation of what you want that already exists in DF, then multiply its base volume by (desired height/average height of base creature)^3. Provided that (desired height/average height of base creature) isn't that much larger than 1, then it is safe to assume that the increase in size wouldn't realistically cause it to collapse under its own weight. Your 12 foot human, for instance, would be calculated to have a volume of 518400 based on a 10 foot sasquatch.

In which case our buisness is sadly concluded, I have my formula of 2*4*4 to be applied to the human in order to produce a 12 foot giant.  I am only interested in those who can come up with a better formula, not those who have so little faith in their own intellectual abilities that they cannot come up with a formula without having Professor X handing down the knowledge from above. 

Scaling up a sasquatch, a creature which is already quite likely straining under it's own considerable stress already by another 2 feet is not likely to make sense unless we reduced the creatures agility by a pretty large margin.  It is also impossible to know how much excess carrying capacity a creature that big actually would have left without knowing how much it has scaled up from a human being as no explicit depictions of sasquatches exist in the game. 

Not healthy ones.

Spoiler (click to show/hide)

I said basically not absolutely.

[cochramd]

Shitposting.

Incredible. It's like I'm on 4chan, except everyone's got a name and I can't be banned for telling you that you've been reported.

I said basically not absolutely.

Keep moving those goalposts, anon. Next thing you'll be telling me that a cube is basically a sphere.

[Salmeuk]

Firstly, I am confused as to why GoblinCookie posted the OP. He seems to infer a whole lot from a rather arbitrary number set up by Toady. Arguably interesting concepts were brought up but nothing much was really said with specificity. DF is hardly a perfect world right now and a lot of things are like the number used to determine size - placeholders or decidedly arbitrary because anything more specific is too much work / time.

I am then particularly confused as to why cochramd decided to take the bait and commence argumentation over basic physical concepts with a patently misguided OP. Just let the thread live or die, nothing here to gain or teach or win. Reeks of miscommunication and e-wanger.

[GoblinCookie]

Firstly, I am confused as to why GoblinCookie posted the OP. He seems to infer a whole lot from a rather arbitrary number set up by Toady. Arguably interesting concepts were brought up but nothing much was really said with specificity. DF is hardly a perfect world right now and a lot of things are like the number used to determine size - placeholders or decidedly arbitrary because anything more specific is too much work / time.

I am then particularly confused as to why cochramd decided to take the bait and commence argumentation over basic physical concepts with a patently misguided OP. Just let the thread live or die, nothing here to gain or teach or win. Reeks of miscommunication and e-wanger.

No, I cannot infer anything simply from the numbers, that is the problem; DF is going to be 'incomplete' and 'imperfect' for the next 20yrs probably so get used to it.  The thread exists because I want to know how big a giant that was say 12ft high would be, it so happens that as far as I am concerned I have come up with a workable formula for doing so, this thread then is a success from my POV whatever happens now to it, I got what I wanted.

A 18ft giant is 7,560,000 according to my formula.  The DF giant is 9,000,000 and so my formula is giving me similar results to the values for the creatures in the game, suggesting that something similar was being done by Toady One in calculating the sizes in the first place.

[exdeath]

One way to find the size of stuff would be to use use walking speed.

if you assume walking speed of a human is realistic on DF, you can use it and compare with real life walking speed to find what the size of tiles.

I did that once, but dont remember the results.
Actually after checking the results, people on another board compared the results with alot of stuff, like the distance he can fall without dying, how high someone can jump and etc... and the results were totally unrealistic, actually the df is super complex but still a game so being unrealistic is not a extreme problem, the thing it was very very unrealistic in a way a assume is not toady intentions.


One extremely important thing to df determine tile size and multitile stuff, to have a more specific thing to work with when creating the game.

[GoblinCookie]

One way to find the size of stuff would be to use use walking speed.

if you assume walking speed of a human is realistic on DF, you can use it and compare with real life walking speed to find what the size of tiles.

I did that once, but dont remember the results.
Actually after checking the results, people on another board compared the results with alot of stuff, like the distance he can fall without dying, how high someone can jump and etc... and the results were totally unrealistic, actually the df is super complex but still a game so being unrealistic is not a extreme problem, the thing it was very very unrealistic in a way a assume is not toady intentions.


One extremely important thing to df determine tile size and multitile stuff, to have a more specific thing to work with when creating the game.

That would not work.  Creatures do not move any faster or slower simply for being bigger or smaller, if they did everything would be getting perpetually bigger since the bigger they are the more food they can catch and eat.  The problem that bigness poses is precisely that it does not make the creature faster and indeed can even make the creature slower.  The fastest creatures in existance are the cheetah and the gazelle and not the elephant for that reason.

The longer your legs are compared to the rest of your body the faster you can walk.  This is what makes the square-cube-law also annoy quadrapeds, in order to keep on getting bigger they have to increase the length of their legs to keep up with the increase in their length or they get slower.  Snakes on the other hand can continue to get longer without getting taller, this is because they do not depend for their speed on the length of their legs.

[vjmdhzgr]

One way to find the size of stuff would be to use use walking speed.

if you assume walking speed of a human is realistic on DF, you can use it and compare with real life walking speed to find what the size of tiles.

I did that once, but dont remember the results.
Actually after checking the results, people on another board compared the results with alot of stuff, like the distance he can fall without dying, how high someone can jump and etc... and the results were totally unrealistic, actually the df is super complex but still a game so being unrealistic is not a extreme problem, the thing it was very very unrealistic in a way a assume is not toady intentions.


One extremely important thing to df determine tile size and multitile stuff, to have a more specific thing to work with when creating the game.

That would not work.  Creatures do not move any faster or slower simply for being bigger or smaller, if they did everything would be getting perpetually bigger since the bigger they are the more food they can catch and eat.  The problem that bigness poses is precisely that it does not make the creature faster and indeed can even make the creature slower.  The fastest creatures in existance are the cheetah and the gazelle and not the elephant for that reason.

The longer your legs are compared to the rest of your body the faster you can walk.  This is what makes the square-cube-law also annoy quadrapeds, in order to keep on getting bigger they have to increase the length of their legs to keep up with the increase in their length or they get slower.  Snakes on the other hand can continue to get longer without getting taller, this is because they do not depend for their speed on the length of their legs.

They were talking about finding the size of tiles, not creatures.

[Button]

This is Dwarf Fortress. Critters that couldn't possibly exist, exist. And that's OK.

Take rocs, for example. IRL, birds can't fly above a weight of 40 lbs or so, because either their wing muscles get too heavy for their leg muscles to support, or their leg muscles are too heavy for their wing muscles to lift. (Pterosaurs overcame this limit by walking/launching using their wings, which meant their flight muscles could do double duty, but that's not consistent with the avian body plan.)

But giant birds are cool, so we have giant birds.

If you wonder how the creatures work, and other science facts, just repeat to yourself: "it's just a game. I should really just relax."

[JoRo]

The OP is kind of hard to parse, but the "size" number is cubic centimeters.  The average human body volume, as per google, is 66.4 liters, or 66,400 cm3, which Toady rounded up to 70000.  A giant that's twice as tall but with the same proportions would be multiplied by 2 along the depth, width, and height, so 70,000*2*2*2 or 560,000.

[puke]

A humanoid is shaped roughly like a cone

Not healthy ones.

Spoiler (click to show/hide)

While I agree with your statement, the picture you supplied is not in fact a human, sir.  It is an octopus.