Wednesday, April 15, 2009

Fun with Scale

So here's what I woke up thinking about. Ants and bees, among others, are high-functioning creatures, especially when viewed from the societal level. They possess specialization of function. Career paths, if you will. And yet, they are so small, relative to us and our over-sized world.

But why must we rate everything in comparison to ourselves? What makes us think that, if we ever discovered extra-terrestrial life, it would always exist at our scale? Much larger planets with much stronger gravity could create extremely large animals.* Our planet supported dinosaurs. How much larger could organisms grow on other worlds? How big would a creature have to be so that the relative size difference between and it and us was the same as between us and ants?

Wow, Jason. That's a perfectly useless question. Let's find out!

Ants, according to a random website I found, weigh on average three milligrams, or .003 grams. I, a premium specimen of human being, weigh 91 kilograms, or 91,000 grams. This makes me 30,333,333 times more massive than an ant. Applying that difference to ourselves and our alien interlopers, we find that our soon to be slavemasters would weigh in at a continent crushing 2,760,333,303,000 grams, or 6,085,493,240 pounds (by earth's gravity.)

Six billion pounds. To put that in terms we can process, the Empire State Building is estimated to weigh 365,000,000 kilograms, or 804,687,257 pounds. Our imaginary Meganism is almost eight times more massive than that. So how tall (or long) would it likely be?

Well, since multi-legged critters are measured head to butt, I lopped off our legs temporarily for a truer comparison. Ants are .006 meters long. With my legs removed I'm about .91 meters tall. This makes me 151 times longer than Mr. Ant. Our Meganism then would be roughly 137.5 meters (451 feet) long, or, with legs added back on for an erect walking species, about 275 meters (902 feet) tall. Again, for scale, the Empire State Building is 1,250 feet tall to the roof. So an erect Meganism would be roughly 3/4 the height of the Empire State Building, and eight times as heavy.

Are these numbers right? Who knows. Who cares. Even if I'm off by a full half, the Giganthors will crush us under their mansion-sized Reeboks. It is interesting how much faster weight grows compared with height or length. I'm sure the width, which we didn't look at, would have something to do with the disparity.

Aren't you glad you finished this?

*I'm not sure I'm right here. Would titanic creatures be more likely on a larger planet with stronger gravity or a smaller planet with weaker gravity? A stronger gravitational pull could might force the indigenous animals to evolve stronger and larger to bear the extra burden. But larger means heavier, and you'd expect evolution to favor lighter creatures on a planet with strong gravity. So maybe a weaker gravitional pull would evolve gigantic creatures, freeing them of the need to be extremely strong and giving more leeway to weight. Anyone know?

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