The term butterfly effect may refer to more than a 2004 film starring Ashton Kutcher. What’s the saying again? A butterfly flaps its wings and a tornado touches down in Texas? How could that even happen? Let’s think for a moment about butterflies. While I’m reasonably sure that even the mightiest of earthly butterflies outside of fiction couldn’t generate disastrous wind storms with a single motion, further investigation into the processing of natural laws could make the idea a little less far-fetched.
The average monarch butterfly has a wingspan of about 10 centimeters and weighs close to half a gram. If butterflies had perfectly square wings, then the approximate total surface area would be 10,000 square millimeters or 0.01 square meters, roughly two iPhone screens put side by side … I’m not trying to insult anyone’s intelligence.
Butterflies exist on earth, and they fly. In order to achieve this, they need to overcome this pesky thing called gravity. Sir Isaac Newton observed gravity’s action on falling bodies, and through some fancy math, discovered that our planet’s gravity causes falling bodies to accelerate at a constant rate. In order to cause acceleration, gravity exerts force. It just so happens that the force acting on the butterfly is about half a millinewton. In simple terms, the earth pulls on this hypothetical butterfly just about as much as it pulls on a paper clip.
In order to achieve flight, the butterfly would need to exert a force greater than the 0.0005 newtons of downward gravitational force acting on it. Insects in general are pretty spry and zippy; for simplicity’s sake, I’ll say that the flap of a butterfly’s wings exerts .001 newtons (1 millinewton) of upward force, twice the force keeping it down. Conservation of energy would lead us to believe that any of the subsequent molecules of air in the hypothetical volume of the butterfly’s wingbeat are being hit with about 1 millinewton of force.
The International Union of Pure and Applied Chemistry’s standard measure of temperature and pressure gives dry air — the air our butterfly is flying through — a density of about 1.3 kilograms per cubic meter. Meaning that for every flap of the wings, if our butterfly’s 0.001 square meter wings travel 4 centimeters (0.04 meters), we’d have a total volume of 0.0004 cubic meters of air being displaced, or .5101 grams of air being hit.
Recap number one: every time the butterfly flaps its wings, it is moving half a gram of air, about the same as the butterfly weighs. The information is irrelevant, but it’s a cool coincidence.
Assuming the atmospheric air being hit is largely oxygen and nitrogen gas, we can use Avogadro’s number (6.02*1023) to calculate that our little butterfly is hitting 240,885,660,000,000,000,000 (240 quintillion, 885 quadrillion 660 trillion) molecules of air with about 1 millinewton of force. There is a lot of other complex math involved that I am probably forgetting to include, but the things I don’t understand are literally Greek to me.
Recap number two: we have this monstrous insect transferring enough force to cause a plurality of molecules to accelerate by a value of some other unwieldy number. But to put things in perspective, every time a butterfly flaps its wings, it moves a small jar’s worth of air — still a big stretch from throwing any houses out of Kansas.
So now let’s move to the tornado. How do tornadoes work? In simple terms, when warm air passes underneath cold air, the warmer air tries to rise, but can’t pass through the dense, cold air. The air swirls horizontally until enough force builds up that the different bodies of air have to move past one another, and the entire rapid wind current comes spiraling to the ground.
Conceptually, we are now left thinking about two things that at first glance are wildly different. One is a weather-pattern-sized mass of destructive air, and the other is small enough to fit into a jam jar. It’s easy to imagine one small butterfly causing this small jar’s worth of air to move. From there it wouldn’t be hard to imagine that jar of air going out and pushing other “jars” worth of air. Before too long, this butterfly has made a very large number of air molecules move just a little bit faster.
This miniscule speed increase doesn’t happen all on its own either. The additive forces from billions or trillions of other literal and metaphorical butterflies all come together in a very specific, yet random, interconnected way. The funny thing about time, is that on earth at least, it happens for everything simultaneously; on a long enough timeline, everything affects everything else.
Recap number three: butterfly flaps its wings, moves a little bit of air, which in turn moves a lot of air very slowly. The small butterfly has contributed to the monumental force of a tornado.
And while no single butterfly may ever be the sole progenitor of an entire tornado, the miniscule shift in initial conditions caused by that one flap of a butterfly’s wings could have an untold cascading effect on future events.
Ultimately, be it with regard to particle physics, or something complex like interpersonal interactions, no moving matter exists as an isolated system. Our universe is made out of a vast web of connections both visible and invisible, known and unknown. In a long enough timeline, even the smallest change in initial conditions can yield a quantifiable different outcome.
ALAN LIN likes to think about butterflies’ effects on weather and can be reached at science@theaggie.org.
I’d like to thank our copy desk for their attention to detail in formatting exponents during their edits.