Tuesday, March 13, 2012

Square Cube Law

Have you heard of it? If you haven’t, I wouldn’t be surprised. I hadn’t heard of it until it was mentioned in Atomic Robo (and if you haven’t heard of that you must start reading more awesome comics).

Basically, it says giant ants can’t exist because their bodies would never be able to support them. Considering that ants are already poised to take over the world with their little, tiny bodies, I think the fact that they can’t get any bigger is a big load off our minds. Anyway, the reason the creators of Them! were thankfully wrong is because as something gets bigger, it’s volume increases exponentially. Something that’s two times bigger has eight times as much volume.

To illustrate, I’m afraid I’ll have to use math:
The volume (V) of a cube is the length of one side (L) multiplied to the third power, so L­3. If L equals 4, V equals 64. If L equals 20 (5 times an L of 4) then V equals 8000 (125, or 53, times a V of 64). This works for any formula volume, whether sphere, cone or anything else.

The same applies to anything. If an ant is made bigger by, say, gamma radiation, whatever its size is increased by (2, 5, or whatever number), the volume is the cube of that (8, 125, or whatever3). But the ant has its original body structure, because what is this? Some kind of magic radiation? And that body structure cannot sustain the increase in volume. It would be crushed by its own weight.

This same principle applies to any building, animal or ship your characters will use, so keep it in mind before creating any gigantic titans battling over the ruins of New York City. Or dinosaurs.


  1. Yay! Math! As a fantasy author it's good to be reminded of this because, even though I'm a math teacher, I tend to forget these kinds of technicalities when putting on my writer cap!

  2. The problem with that is that we already know that insects once existed that were much larger than this theory says they could have been. It's like saying that according to math bumblebees shouldn't be able to fly. And they shouldn't. But they do. And so do helicopters which also shouldn't work. But they do.

    1. Except the whole bumblebee thing has been disproven (or proven...not sure which word is correct here). I can't remember where I read it. Something about those mathematics not taking into account aerodynamics or the theory not taking into account how the bumblebee actually uses its wings.

      (I should find where I read it and just quote, but I'm too lazy to do that just now.)

    2. well actually, you are wrong, although the theory does say that the large insects that existed During the Carboniferous and Permian periods should not have existed, it has been illustrated that stuctures as complex as these cannot be large without structural change.
      for example, the modern day insects do not breath so much as respirate throu simple diffusion through cell walls all along their bodies. this works due to two factors, the size of the insect relative to the size of the o2 atoms, and the percentage of o2 in the air. if the insects were to be enlarged, they would need to develop a relatively complex respiratory system consisting of a pair o f lungs and anything else needed to pump oxygen round their body. something that would work in the favor of your argument, is the fact that the insects in the past would have had around 36% o2 to breath as opposed to the 21% of our modern insects.
      as for helicopters, if they shouldn't work in theory, which by the way they do, they would never have been made. and the theory has had plenty of time and world class minds to be proved wrong, with the first blueprints for early helicopters have origionated from as early as 400BC

      hop i don't sound like too much of a d!ck head 'cus i'm really not, just bored lol.

  3. Or you can assume that the body structure becomes simultaneously reinforced with the increase in volume (and, hence, weight) OR that the increase in weight and volume is accompanied by an ability to alter the prevailing gravitational field, thus reducing weight.

    PLEASE, PLEASE, PLEASE, don't let Newtonian physics limit our literary imaginations....Einstein didn't :)

  4. Yes, I did know this (but forgot it;)).

  5. Math admittedly gives me headaches!

    Size of the ant doesn't really matter when they're, oh... fireants and have started taking to biting you all over, of course.


Please validate me.