I recently got a video on Whatsapp from a distant family member about how if a flea was the size of a human, it would be capable of jumping 300 meters into the air, and other ‘facts’ like this. It was crudely made, involving a serious voice combined with cartoonish animations, and at first I thought it was supposed to be funny. I promptly sent some laughing-face emojis and added a gif for good measure. You can imagine my surprise, then, when I got a call from my relative telling me how ‘horrible’ I was and how I ‘had no appreciation for nature.’ He then cut the call, refusing to hear any of my explanations. He hasn’t talked to me since then.
Looking back on it, I can understand his thought process. For whatever reason, school-level biology syllabi ignore the concept of size, so it makes sense to think that somehow scaling up a flea would allow it to retain its abilities. Indeed, I can locate only a single instance in my textbook where size is even mentioned: when comparing the mouse and the elephant, the authors (grudgingly) agreed that one was larger than the other. Despite this, it is elementary to see why an eagle cannot be shrunk to the size of a kingfisher, and why nothing will ever be jumping 300 meters in any direction, all of which is primarily due to the Square-Cube law.
The square-cube law is fairly simple: it says that if all the lengths of an object are multiplied by n, the surface area grows as n², while the volume as n³. This is an indispensable law whenever biology is concerned because some processes occur through the surface while others in the bulk. Let’s drop a mouse, a human, a sperm whale and a bowl of petunias from the top of a 1000-metre cliff to see what happens.
The whale splashes, spewing huge chunks of former whale everywhere. The human is broken, and very dead. The mouse, however, is just fine: a little bit shook, perhaps, but not injured in the slightest. These varying results are all because the mouse, being smaller, has a higher surface area to volume ratio, giving it more air resistance. It is virtually impossible to kill any living thing smaller than a rat by dropping it from a height. This is also the reason why spiders are capable of clinging to the ceiling without any effort.
Just like gravity is a formidable force for large creatures, there is a force which is deadly to small ones: surface tension. When any insect gets wet, it develops a film of water around its body which is several times its own weight, which eventually kills it. Water also has a high specific heat, which means that it takes a lot of energy to heat up and evaporate. Any small mammal like a mouse will die of hypothermia if it doesn’t dry fast enough after getting wet. It’s no wonder almost every bug has a proboscis that keeps it far away from its drink.
The falling-down thing wasn’t much fun, so instead, let’s enlarge a hamster to the size of an elephant and shrink an elephant until it’s hamster-sized.
The hamster feels uncomfortable for a bit, then unceremoniously explodes, while the elephant quickly succumbs to the cold of the atmosphere and dies. The reason for such a bloody end to the mouse is the same as the tragic one for the elephant: different metabolic rates. Since larger animals have lesser surface area per unit volume, they lose energy at a much slower pace than smaller ones. The smaller ones need to continuously pump oxygen-rich blood all over their body to stay warm, while the big ones can relax and go slowly. In the case of the giant hamster, it radiated too little energy and overheated, which caused its blood vessels to burst. The tiny elephant’s slow heart couldn’t keep up with the heat loss, freezing it to death.
This difference in metabolism is actually key in determining the lifespan of any given animal. The faster the metabolism, the shorter it will live, and vice versa. Here’s a plot between the heart rate (a good indicator of metabolic activity) and lifespan:
The prevailing reason given for this is aging: the more an organ is used, the more damage it accumulates until it stops functioning. The reason humans are an outlier is the advances made in medicine and the discovery of vaccines.
Another advantage size provides is sensory. Organs like eyes aren’t of much use below a certain size because light is detected using specialized cone cells present on the retina. For two objects to be perceived as distinct, the light reflected off of them should fall on different cells. One can’t just reduce the cell dimensions because there is a hard minimum on their size: the wavelength of visible light. Because of this, a mouse can barely distinguish things ten feet away from its eyes. Meanwhile, big creatures like whales and elephants don’t have eyes too much bigger than a human’s because they don’t need to. It also explains why houseflies have those nightmarishly large eyes in comparison to their faces.
The Square-Cube law also explains why larger animals are so much more complex than smaller ones. Take an earthworm: it breathes through its skin, has a smooth gut, no true heart, and few internal organs. This is because its size takes care of mostly everything: oxygen is automatically gained via diffusion, the energy from food is absorbed without too many complications due to the higher surface area per unit volume, and there is not much pumping required for blood to reach every part of its body. If a human were to try to breathe through their skin, they would almost immediately suffocate. This is because there simply isn’t enough surface for air to diffuse in from on the skin; specialized organs like lungs are needed to increase surface area. A similar process occurs in our guts: the intestines are all coiled up to increase the length of the food channel, allowing more epithelial cells to come in contact with the food, increasing digestive efficiency. And of course, without a heart there is no possible way blood would flow everywhere it is required in time.
This law is also crucial in matters of flight. Let’s take a hummingbird: capable of all sorts of beautiful acrobatics in midair, it is also the only bird capable of flying backwards. Its wings beat so incredibly fast they appear as a blur. If this same hummingbird were to be made to the size of an eagle, and if it were to somehow avoid the metabolic issues, it would be rendered unable to fly. This is because flight gets exponentially more difficult as you get bigger due to a combination of energy requirements and the limitations of the body. Flapping wings to fly is highly inefficient and requires a lot of power. Indeed even humans, with all our ingenuity, have just barely managed to create a plane that flaps its wings to stay aloft (these are known as ornithopters; and while there have been a few successful flights, they are largely unmanned or single-person ones). Only at small scales does this become efficient, mostly because the buoyancy of air comes into play too. Larger birds mainly ‘glide’, i.e. balance atop a stack of warm air with their wings outstretched. Even this becomes harder with increasing size, like almost everything else.
Let’s end this needlessly long treatise on size by examining the case which started it all: the flea. The main reason it is capable of jumping so high is because its size means that even air feels sort of like a very thin jelly. It also has specialized hind legs evolved solely for jumping, both of which contribute to its 1.2-meter jump. If it were made bigger, it would instantly collapse under its own weight, raining down pieces of flea everywhere. In fact, it appears that its muscles are actually less efficient than humans’; otherwise their upper limit would be 1.8 meters.
Everything has a ‘right’ size for itself, be it animals or people or Medium articles. For the last one, that value is 6–7 minutes, which is coincidentally precisely where we’ve reached.
Proofreaders: Mokshit N., Durga C., Ashani P.