Butterflies and mathematical models

“Dr. Kayoticus,” the curmudgeon slurred, “You have perhaps heard of the so-called butterfly effect?”

“Of course, Philterawl, as you well know, I have made many published advances in that field of study. Why do you ask?”

“Yes, yes – a hurricane in Bermuda due to a little flapping moth in Paraguay! Well, I have been talking with old Netty over drinkies and billiards about his biologics and his insects and his obsession with Darwin and all that. He is convinced that your whole butterflying making a big blow is bunk.”

“What’s bunk, old man? The butterfly effect? Does he think that I consider one of his little Lepidoptera as a giant wind turbine? Doesn’t the poor man understand a model? I have proved that, because of cumulative effects in an inherently chaotic, non-linear process, a little change might magnify – in a layman’s sense, mind you – the minor disturbance in some distant point and produce effects of many orders of magnitude greater at another point.”

“Oh, I understand the basics, I suppose. Still, he was claiming that if butterflies could cause hurricanes at the flap of a diaphanous wing, then there would be more hurricanes that I could count. And so, well … look here, old man – do you seriously think that butterflies could survive in a world of millions of hurricanes, just happening with each fluttery take-off from a tea rose bush?”

“What in heaven’s sake are you talking about, Philterawl?”

“Well, I mean, Netty might have a point. In a world of flapping butterflies making hurricanes willy-nilly, there wouldn’t be any possibility for butterflies to have evolved into butterflies – what with all the storms and chaos and such from their infernal flapping. Where would they land to have a go at laying eggs, or whatever bugs do?”

“Not all butterflies cause hurricanes! Just some could. Obviously you and Netty do not understand the point of the exercise. Butterflies are not making hurricanes willy-nilly – the point is that they could, and in the precisely right circumstances, cause a devastating effect far beyond their little expenditure of energy.”

“So butterflies don’t cause hurricanes?”

“No, no, man – don’t you understand? – they could! As I, and others, have shown in many, many models.”

“So some butterflies do cause hurricanes? I would like to have a specimen of the type that swamped New Orleans. I could give it to my sister Elizabeth for her birthday – she collects the vermin, you know.”

“Are you drunk again, Philertawl? Good God, man! I said that they could – it’s a mathematical model, for god’s sake! I’m not saying that we have evidence of the fact.”

“Well then, has a butterfly ever caused a hurricane?”

“Heavens!, man how do I know?”

“Then what’s the butterfly effect again?”