A Company Safety Discussion overheard at Time Safari, Inc: Safaries to Any Year in the Past:

“All right,” Travis continued, “say we accidentally kill one mouse here. That means all the future families of this one particular mouse are destroyed, right?”

“Right” “

And all the families of the families of the families of that one mouse! With a stamp of your foot, you annihilate first one, then a dozen, then a thousand, a million, a billion possible mice!” “

So they’re dead,” said Eckels. “So what?”

So what?” Travis snorted quietly. “Well, what about the foxes that’ll need those mice to survive? For want of ten mice, a fox dies. For want of ten foxes a lion starves. For want of a lion, all manner of insects, vultures, infinite billions of life forms are thrown into chaos and destruction. Eventually it all boils down to this: fifty­nine million years later, a caveman, one of a dozen on the entire world, goes hunting wild boar or saber­toothed tiger for food. But you, friend, have stepped on all the tigers in that region. By stepping on one single mouse. So the caveman starves. And the caveman, please note, is not just any expendable man, no! He is an entire future nation. From his loins would have sprung ten sons. From their loins one hundred sons, and thus onward to a civilization. Destroy this one man, and you destroy a race, a people, an entire history of life. It is comparable to slaying some of Adam’s grandchildren. The stomp of your foot, on one mouse, could start an earthquake, the effects of which could shake our earth and destinies down through Time, to their very foundations. With the death of that one caveman, a billion others yet unborn are throttled in the womb. Perhaps Rome never rises on its seven hills. Perhaps Europe is forever a dark forest, and only Asia waxes healthy and teeming. Step on a mouse and you crush the Pyramids. Step on a mouse and you leave your print, like a Grand Canyon, across Eternity. Queen Elizabeth might never be born, Washington might not cross the Delaware, there might never be a United States at all. So be careful. Stay on the Path. Never step off!”


From the Short Science Fiction Story: A Sound of Thunder by Ray Bradbury


Chaotic dynamical systems:

“In the mathematical field of dynamic systems, an attractor is a set of numerial values toward which a system tends to evolve, for a wide variety of starting conditions of the system.

Describing the attractors of chaotic dynamical systems had been one of the achievements of chaos theory.” Attractor – Wikipedia, October 19, 2019.

Chaos Theory: Chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected. While most traditional science deals with supposedly predictable phenomena like gravity, electricity, or chemical reactions, Chaos Theory deals with nonlinear things that are effectively impossible to predict or control, like turbulence, weather, the stock market, our brain states, and so on.

These phenomena are often described by fractal mathematics, which captures the infinite complexity of nature. Many natural objects exhibit fractal properties, including landscapes, clouds, trees, organs, rivers etc, and many of the systems in which we live exhibit complex, chaotic behavior.

Recognizing the chaotic, fractal nature of our world can give us new insight, power, and wisdom. For example, by understanding the complex, chaotic dynamics of the atmosphere, a balloon pilot can “steer” a balloon to a desired location. By understanding that our ecosystems, our social systems, and our economic systems are interconnected, we can hope to avoid actions which may end up being detrimental to our long-term well-being.”  The Fractal Foundation