Scientists often use the strangest examples to explain to us ordinary mortals how some natural phenomenon works. One of the most interesting examples is the so-called “hairy dog theorem”, which helps us understand how wind and tornado systems develop on the planet, using a hairy dog as an analogy. Curious? Come in and read!
It must not be an easy task for a scientist to try to explain how the world works to someone not versed in science. Without using complex mathematical formulas or terribly boring theorems, it is almost impossible to demonstrate why certain things happen. But some specialists are extremely imaginative, and they always find some analogy that allows them to illustrate a phenomenon without us needing to study physics and math for five or six years beforehand. One of the funniest examples we have found is the so-called “hairy dog theorem”. Let’s see what it’s about.
Imagine you have a dog. Not just any dog, but one of those with long hair covering its little body. Surely, since you are a very clean and tidy person, you try to keep the animal as clean and neat as possible. You probably bathe it almost daily, and spend long hours combing its hair. These activities seem completely far from science, but a scientist is always able to see one step further and find an interesting application for anything.
Suppose we take the dog, tie it up properly (we don’t want it to bite us during the experiment), close its nostrils, ear canals, eyes, and any other (ahem) hole we find. When we finish, we’ll have something quite similar to a ball of hair more or less smooth (and quite nervous). If we were seasoned scientists, we would see that from a geometric point of view we have turned a beautiful pet into the topological equivalent of a sphere. When a scientist says “topological equivalent”, they mean something like: if the dog were made of putty or rubber, we could deform it into a sphere without cutting, piercing, or dividing it.
With that clear, let’s return to our hairy friend. If we take a comb and try to comb it, we’ll see that no matter how hard we try, we can never get all the hair to lie flat without leaving at least one “whirlpool”. No matter how many times we try or how nervous the dog gets, it is impossible to “comb” a sphere without places where whirlpools appear. You can untie the dog and unblock its orifices now. It might want to breathe.
Well, we have just made a truly momentous scientific discovery almost without realizing it. If instead of a dog you have a planet, and instead of hair you have an atmosphere, you can see that there will always be a cyclone or a tornado somewhere on the planet. Indeed, and unless there is absolutely no wind disturbing the atmosphere anywhere (which is practically impossible), the wind system will create collisions in some places, often many, that give rise to whirlpools.
These whirlpools may be more or less intense depending on how strong the winds that cause them are, but they will be there. Obviously, there are other factors involved in the creation of tornadoes or cyclones, but they are quite complicated and much less entertaining. As you can see, even a simple dog can be useful for understanding science, it’s just a matter of imagination..
