# Consequences of an altered square cube law

In an effort to make it possible for fantastically large organisms to exist I've altered the square cube law of my universe so that instead of something getting 8 times the mass when doubling size it instead only doubles its mass, three times the size three times the mass instead of 12, etc. So far this is the only alteration of physics I've made, with all others remaining the same.

While this might work to make creatures larger, I found myself wondering, what other effects or consequences for lifeforms would this altered square cube law have?

• My guess is that planets, suns and black holes cease to exist. The mass stops going up exponentially so you need to have something like 7x the circumference of the planet to get the same mass. But the lack of mass increase means that matter has a much better resistance to compression, meaning the total amount of matter required to even ignite a sun is now massively increased. That is ofcourse a nitpicky answer that side-steps the focus of your question, living beings. I would clarify that in your question before people head too far in the wrong direction. Oct 21 '21 at 10:40
• You are confusing physics with geometry. Physics may be different in a different universe. Unfortunately, geometry holds true in any self-consistent universe. Oct 21 '21 at 11:15
• How does this work self consistently? If eight 1 metre square cubes each 1kg in mass are stacked into a 2m by 2m by 2m cube does their combined mass suddenly drop to 2kg. Do cubes actually have to touch to get this "disappearing" mass? Oct 21 '21 at 21:35
• I feel like this needs an answer from @The-Square-Cube-Law
– Zags
Oct 21 '21 at 21:46
• Here is an exact equivalent scenario: What are the consequences of a universe where 2+2=5, 5-2=e-flat, and 2-5=green? Oct 22 '21 at 12:16

## 9 Answers

Wrong Question. There is a Different Solution.

The real question you have here is "how do I make extra large creatures feasible," and you're looking for a solution for this by tweaking the square cube law.

That's a problem: you can't.

It's a geometric rule that relates area to volume. You can't change that without doing some really weird stuff physics-wise, like warping space.

But if your problem is how to make large creatures more feasible, there is an answer.

Take the strength to weight ratios of an ant, a cat and an elephant. The ant is super light, but can carry many times its own weight. The cat is heavier, but due to its muscle strength vs its body weight, can still jump many times its body length. The elephant however, can't even jump. Not that it's not strong, but the strength scales with the cross sectional area of the muscles. And the weight increases by the total volume of the creature.

So the strength doesn't decrease as much as mass decreases going smaller, but it also doesn't increase as much as mass increases going larger. This is a simple geometric and biological fact of life.

What you want to do here, is tweak the scale. If you were to make normal humans have strength to weight ratios of smaller animals, it would mean that the upper weight(or in this case, volume) for animals is much higher overall. Normally if you were to get too large, the bones or the muscles would no longer be able to support the weight.

So finally, to get to the point, the thing you really need is to change is: the mass to volume ratio.

Change the Mass to Volume Ratio

Simply put, you can have larger more complex creatures behaving as if they were at the scale of much smaller creatures if the matter itself that they are made of is lighter, but functions in the same way otherwise: the same strength of muscles, but the weight of the body is lighter.

This would mean your larger creatures could get truly BIG. Their muscles and bones would be able to handle much more mass. Your humans would be able to do things that would seem superhuman from our perspective. They would be able to lift much larger objects, and jump further, fall farther, with no ill effect. In fact, if you had melee weapons in this universe, they might look oversized by our standards, in order to make up for the lost mass. And thus you reach the realm of Final Fantasy physics.

The effect this would have on planets and the landscapes, I'm not entirely sure, but perhaps mountains wouldn't be compressed as much and slopes could be more extreme before crumbling. Perhaps the atmosphere would reach higher. The planets would have to be larger than Earth to have the same force of gravity. It would make life easier for flying creatures as well.

So there you go, I hope this helps you with your problem. If anybody has major issues as to the feasibility of this solution, leave a comment!

• I doubt that this would produce a universe that looks much different from ours though. Everything would be bigger in an absolute sense, but everything would be equally bigger, so the 'giant humans' of that world would have the same subjective experiences as the 'humans' of our world. Oct 21 '21 at 22:09
• @Brilliand That stands to reason, but just because something could grow larger, doesn't mean it would. There are other factors such as being able to support as much body mass though nutrition and a minimum size needed for a human like brain. If food supply is a factor, the humans in this world could have evolved to be smaller, or about the same size as humans in our world. There are a lot of factors to consider, not the least of which is the author's artistic liscense to add or remove details necessary to the story. If the author wants the humans to be roughly the same size, then why not? Oct 22 '21 at 1:18
• I don't think you need to make EVERYTHING lighter. Maybe just making lighter but equally strong bones and muscles (or equally light but stronger). Maybe only for those giant creatures. Oct 22 '21 at 14:47
• Could this not just be solved with lower gravity and/or a higher atmospheric oxygen content? I feel that this question has a less hand-wavy solution than altering physics itself. Oct 22 '21 at 15:22
• You know I was all set to go with everyone else in the "It can't be done and here's why" crowd, and then I read this. Absolutely brilliant dodge. Neatly avoids the problems of impossible geometry, other-dimensional physic, alternative chemistry, and pseudo-biology. Kudos. Oct 24 '21 at 14:41

Square-cube law is a consequence of us living in a space with 3 spatial dimension, is not a whim made up by bored biologists.

when doubling size it instead only doubles its mass

You have created a 1 dimensional universe, where I doubt life can exist based on scientific criteria (you can't have an in and an out to start with).

if N < 3, gravitation of any kind becomes problematic, and the universe is probably too simple to contain observers. For example, when N < 3, nerves cannot cross without intersecting.

In general it looks like such a universe in unpredictable.

On purely fantasy criteria instead, Abbot skimmed through such a world in his masterpiece Flatland, when the protagonist visits Lineland.

• Comments are not for extended discussion; this conversation has been moved to chat.
– L.Dutch
Oct 24 '21 at 4:21

If by mass you mean gravitational (passive) mass, then what you suggest is kind of doable, if we postulate that in your universe, gravity is shielded by matter. That is, gravity is not something that fundamentally affects your geodesics, but it is a mundane interaction force mediated by relatively high mass particles, or something.

This means the "mass" (i.e. sensitivity to gravitation) grows with the square of linear length, which is still much better than in our universe. And let's assume that gravity from inside of huge astronomical bodies slowly "leaks out" until an equilibrium is reached, so that planets and stars work more or less as usual.

The differences are numerous - a sheet of matter might be enough to shield you from Earth gravity, flight (including interplanetary flight) will be much easier. Evolution will probably not even get to the wings, flying creatures will extend sheets of thick matter to shield them from gravity, and they will be tall and thin, to expose the smallest possible cross section to the planet.

(conical) Skyscrapes will be almost trivial, because they will be shielded from the most of the gravity.

Less incentive to develop wheels, when a sleigh is enough.

And many, many more examples.

• I love your line of thinking here, but I'd want to challenge your "sheet of matter" shielding--if a sheet of matter protects you from the gravity of the ground below it, why doesn't the earth's crust protect the atmosphere above it from the rest of earth's gravity? Wouldn't you end up with the atmosphere mostly escaping (and the oceans boiling off) because it's only feeling the gravity of the top few feet of earth below it...?
– Qami
Oct 21 '21 at 15:58
• @Qami it does, but since this alt-gravity is caused by an exchange of massive particles, those particles inside Earth build up until they start to seep through the crust, eventually (on geological timescales) an equilibrium is reached and the alt-Earth starts "gravitating normally", much like the photons from the inside of our Sun take thousands of years to get to the surface, because the photosphere is opaque. Or something. Oct 21 '21 at 18:37
• @RadovanGarabík Massive particles decay into less massive ones, though; they wouldn't build up. Not if they follow rules remotely similar to the existing force carriers. Oct 24 '21 at 0:20
• @Hearth in this context, even electrons are "massive" - and protons are pretty much stable, within errorbars comparable with the future age of our universe. Anyway, in this universe, even massive massive particles do not decay, because you know, it is a different universe :-) Oct 30 '21 at 12:13
• @RadovanGarabík electrons and protons don't decay only because there's nothing less massive for them to decay into, not while observing other conservation laws (of lepton number and baryon number, specifically). Oct 30 '21 at 12:56

You have a severe problem. As @RichardTingle asked:

How does this work self consistently? If eight 1 metre square cubes each 1kg in mass are stacked into a 2m by 2m by 2m cube does their combined mass suddenly drop to 2kg. Do cubed actually have to touch to get this "disappearing" mass?

To really show the problem, consider the reverse: take a cube that's 1 meter per side and weighs a kilo in total. Now divide that cube into 8 equal smaller cubes each 0.5 meters per side. In a normal universe, each smaller cube would mass 0.125 kg (1/8th of a kilo). In yours, however, they can't. They'd mass 0.5 kilograms each for a total mass of 4 kilograms. (Don't see how that works? If doubling the dimensions doubles the mass, a cube 0.5 meters per side going to a cube 1 meter per side that masses 1 kilo has to mass 0.5 kg to start.)

Now do it again. Divide each of those 0.5 meter sided cubes into 8. Each 0.25 meter cube has to mass 0.25 kilograms. But now there's 64 of them, each means the total mass has increased to 16 kilograms.

Now do it again. Divide each 0.25 meter cube into eight 0.125 meter cubes, each of which has to mass 0.125 kilograms. But now, there's 512 of them, and the total mass of all those cubes is 64 kilograms.

Starting to see a pattern? Cut them in half again, the total mass will be 256 kilograms. Cut them in half again, 1,024 kilograms. Cut in half again, 4,096 kilograms. In other words, if you half the size of something, the relative mass goes up by four times.

In such a world, I trust you wouldn't buy your children Lego: the individual bricks required to build a structure might require a box capable of holding several tonnes. And that pretty succinctly, I think, illustrates the problem.

• Of course, the bricks would be delivered already stacked together so that they weighed less. There is a deeper philosophical problem though - how close together do the blocks have to be before they count as a single object? Perhaps easier to think about if we ask about some fluid like water or air, how do you decide how many things it is in order to determine its mass? Oct 22 '21 at 1:34
• Oddly enough, what you're describing as a problem is, in fact, a wonderful explanation of how the OP's rules would need to accommodate his desires. Suddenly, in the OP's fictional world, the relationship between mass and gravity changes with volume! That's a pretty cool rule and not a problem at all (unless we're trying to build worlds that only conform to Real World physics). Oct 22 '21 at 4:37
• @JoinJBHonCodidact It is a problem because it creates paradoxes. Physics shouldn't care whether we consider a pile of sand to be one object or a trillion grains of sand to be a trillion objects; but if the mass of a pile of sand is not the mass of the grains of sand then your world's physics now depends on how you choose to frame the issue in words. The problem is not that it's inconsistent with real world physics, the problem is that it's logically inconsistent with itself. Oct 22 '21 at 14:19
• @kaya3 quantum mechanics has entered the chat Oct 22 '21 at 15:08
• @JoinJBHonCodidact By all means, if you want to write a story where the square-cube law doesn't apply, and you don't mind that your world is logically inconsistent, then write that story - but the question is tagged physics and asks what the other consequences of changing the square-cube law in this way would be, so the answer is that either you get a one-dimensional world where life is impossible, or logically inconsistent laws of physics. "There are no other consequences because the writer says so" would not answer the question as it's written. Oct 22 '21 at 17:31

While this might work to make creatures larger (...)

It doesn't, really.

The real Square Cube Law maintains density as you scale things up. Your altered Square Cube law means that everytime you double length or height, stuff becomes 12.5% as dense as it was before.

Now using the standard Colombian measure of Shakiras... One Shakira height is about 157 cm and one Shakira weight is 53 Kg.

If you got Shakira ballooned up to 16x her size, she would be 25.12 m tall (about the distance between baseball bases), but she would weight only 848 kg. She would go from 1g/cm3 to about 0.000025 g/cm3.

That is lighter than air and she would float like a Zeppelin. Likewise, all your Kaiju would be doomed to forever fly above the stratosphere. They would also be fragile as cotton candy.

• This question was made for you
– Zags
Oct 22 '21 at 17:21
• I think this was a big point people were missing, they got too focused on how the framing is nonsensical, and they didn't bring up practical issues with changing mass:size ratios like this. Its a world where people can lift elephants by themselves, and balloon Kaiju float through the air. Even if you handwave the mechanics of how it works, and ignore how it only changes mass and not say thermodynamics. It just doesn't accomplish what you want. Oct 22 '21 at 18:11

Frame challenge: Reverse Your Approach

Instead of messing with universal constants or geometric principles, change your standard for the people. If your "average person" is 3.5 feet tall (completely plausible) , then a 7 foot tall person (also completely plausible) is an absurdly huge giant.

If you really feel the need to have a physics-plausible universe, but want giant monsters and massive beasts, just make the people smaller.

You're developing a fantasy world where physics don't work like they do on Earth. Wonderful! That's literally what the Help Center says our Stack is for!

The square-cube law is nothing more than an expression of the relationship between the volume of an object and its surface area — and what I suspect is happening is people are getting stuck on your phrase "I've altered the square cube law" and what you say after that.

...something getting 8 times the mass when doubling size it instead only doubles its mass, three times the size three times the mass instead of 12, etc.

In other words, what you're really changing is the relationship between gravity (or something else) and the square-cubed law (SCL).

Cool!

Let's fool around with a few relationships:

Density vs. SCL: You could say that the density of any material in your universe decreases without the loss of any structural strength or other appropriate characteristic. So, as a creature gets bigger in your world, the heart of that creature does not need to become impossibly large or complex because the amount of blood being pumped and the distance the blood must travel benefit from the blood being a lower density without losing any of its value as blood. Curiously, this means that as creatures get larger, they get stronger! A large creature (having lower density muscles that haven't lost any of their strength per-cubic-meter) could jump higher than a small creature (normalized by mass) because there's more cubic-meters worth of muscles without the accompanying increase in weight.

Gravity vs. SCL: You could say that the consequence (force) of gravity in your universe decreases as mass increases. This doesn't mean things float away, only that the planet is more attracted to its denizens than its denizens are attracted to the planet! That could mean that all solar systems orbit around a barycenter because the sun isn't necessarily the largest gravity source in the solar system. (There could be a lot of fun with that...). I'd vote to call this one the "Weebles universe," because everything wobbles without falling down.

Energy vs. SCL: You could say the biological need for energy decreases with increasing mass. This one's a bit harder to swallow, but fun nonetheless. The problem is rationalizing how anything would be small. After all, Nature would favor larger creatures because they need less energy (per-cubic-meter) to do the voodoo they do than smaller creatures.

Conclusion

What's the consequence of changing the relationship of the square-cubed law with something in your universe? In your case, and generally speaking, it will mean that Nature favors larger things over smaller things.

And that's important, because here in the Real World, nature favors smaller things over larger things. It's difficult to imagine a world where elephants outnumber mosquitoes, because modifying the relationship of the square-cubed law with anything means that you're changing the balance of small-vs-large, but that could be a lot of fun!

How would a world pollinate flowers when the average bee is larger than the bloom? Answer: the flowers would be bigger, too.

What you won't have is people being just like Earth people experiencing mega-fauna that we wouldn't see on Earth because your people are also subject to the effects of those modified SCL relationships. But let's ignore that, because it isn't any fun.

What you really care about are the secondary consequences. Like the ability to jump higher when you're bigger or the ability to live longer because there's less energy dependence or how utterly cool the night time sky would look because everything's wobbling! Those are the interesting consequences of goofing around with the relationship between the square-cubed law and other things.

Now, if you want more details about what advantages and disadvantages could come from messing around with such a relationship, that would require another question that asks about just one relationship.

• Thank you for the extensive and rather useful answer as to the various effects mucking around with the relationships of things vs the square cube law would give rise to, but I've done some thinking with all of the answers here and have instead gone with an 'everything is lighter' universe. I may explore a different setting with the SC law vs other forces relationship alterations though, they are too interesting to not write around. Oct 22 '21 at 12:27
• @Lemming A better expression would be "gravity is weaker", which is as simple as changing the gravitational constant to some smaller value. Oct 22 '21 at 15:06
• I for one am glad to be rid of SQL. It is a bad design... why does the select clause precede the from clause? It makes it difficult for intelligent auto-complete systems. Why does the join clause use the "on" keyword, instead of "where"? MongoDB is web-scale. Oct 22 '21 at 15:29
• @JohnO :-) While I understand your sentiment, my use of "SQL" means "Square-Cube Law" not "Structured Query Language." I should have seen the confusion coming.... Oct 22 '21 at 17:17
• @JoinJBHonCodidact Shouldn't it be "SCL"? You seem to have gotten a Q from nowhere. Oct 24 '21 at 0:21

What if you let your story take place on a much smaller planet? Creatures would be able to get much bigger. The mass would be the same but they wouldn’t collapse under their weight. You could still have smaller creatures too, like we have ants.

Alternatively, rather than changing the square cube law, change how strong a force gravity is.

Increase the breaking strength of muscle fibers and increase the gas-in-liquid diffusion rates.

The limits on muscle strength are these two. If gasses diffused faster and if muscle fibers broke at a higher limit then creatures could be larger.

It would be tempting to increase muscle strength by strengthening the weak bonds; but that breaks everything. Rather, make slightly better biochemistry available. The actual chemical limits exceed what biochemistry can currently make, and there's no hard reason why biology can't use better materials. I can't come up with a reason why muscle fibers can't be half as string as spider silk, nor can I come up with a really good reason why there's no tungsten in our bones, but our biology can do neither.