Dong barking, stochastic processes, and a recipe for getting crazy,
My dad and me are dog-sitting three dogs and cat-sitting just one cat at my older daughter’s place near NYC. Let us do a math bio modeling exercise. We set a unit DB (dog bark) for the amount of irritating barking one dog produces. What about three dogs? You guess, 3 DB? Alas, the function is highly non-linear.
Let as start with a naive model. Say, a dog starts barking randomly once in ten minutes. Then three dogs start barking three times in ten minutes. However, once one of them starts, the rest join. So we end up with 9 DB already.
Let me list just three of many very important non-linear factors that should be built into the model further:
1. Durations of barking. A dog stops after some time, which of course varies, but in average it is not too long. Three dogs bark much longer. When one of them is almost about to stop, she hears the others and starts it over with doubled enthusiasm. Roughly, multiply by three again.
2. When three dogs of different sizes are together, they are agitated and, instead of starting barking once in ten minutes at average, a dog starts in five. When two large dogs play, the small one is afraid to join them and barks at them permanently. Multiply by three again.
3. We also need to estimate how this barking affects a human brain. One dog barking at the same tone and rhythm is one thing. A chorus of three dog each with its pattern of barking is a killer. No numerical factor comes to my mind. I put two as a rough lower bound.
One can add that they start between 5AM and 7AM, so for a one like me who does not go to bed before 2AM not much sleep is left.
But anyway, three dogs at one place are a more powerful disturbing factor than at least 162 dogs taken alone.
The cat is not a big troublemaker. At least, she does not bark:) Of course, it is important to be attentive. For instance, make sure you do not forget to close the notebook: it is warm, the cat likes to sleep and walk on it, and who knows what emails she would send. Brushes and such should be hidden well for she thinks they are furry mice and such.
Here are the dogs with my dad. The cat selected not to participate.
