I’ve been re-reading a book I’ve had for many years Chaos: Making a New Science
Anecdote1: Insolvable Equations – Mathematicians didn’t take to Chaos because it dealt with equations that can’t be solved. My education included a heavy dose of mathematics and I can confirm, as the book suggests, that everything I was taught was ultimately about solving equations. The thing is that equations that can be solved represent a very small part of the field of mathematics – most of it is made up of equations that cannot be solved. That’s where the magic of Chaos was hidden.
Anecdote2: It’s Just Mathematics – Meanwhile physicists didn’t really take an interest in it because it had no real-world applications – it was “just mathematics”. It took a dedicated mathematician to create and experiment for 2 years with a 1 millimeter sized capsule as a testing apparatus to unknowingly provide a real-world example of chaos at work. So, the field of chaos was dormant for many years until eventually some scientists and mathematicians begun stumbling on to strange discoveries … and eventually on to each other.
Anecdote3: Exploring instead of Solving – The mathematics of Chaos is founded on processing equations rather then solving them. Any equation, no matter how complex or unsolvable can be plugged with numbers to see what happens (sometimes using fairly basic math skills). In Chaos such a process of calculation is executed over and over until beautiful images appear carrying illusive and inspiring messages.
Anecdote4: Simplicity describes Infinity – A wondrous quality of these images-of-chaos is that they can be described and precisely defined with very little information (less then half a page’s worth of text) – yet when they are processed they lead to patterns of infinite complexity. Following is one such image image created from one of the most famous mathematic mechanisms called the Mandelbrot Set (<- checkout this link for more cool images or search google images) named after another dedicated mathematician that was ignored for many years:
But what prompted me to write this post was the following quote from the book:
… used a brilliant chain of new mathematics to prove that every floating molecule does indeed hang on a filigree that binds it to all the rest, a delicate web springing from tiny outcroppings on the main set … The mathematicians proved that any segment – no matter where and no matter how small – would, when blown up by the computer microscope, reveal new molecules, each resembling the main set and yet not quite the same. Every new molecule would be surrounded by it’s own spirals and flame-like projections, and those inevitably, would reveal molecules tinier still, always similar, never identical, fulfilling some mandate of infinite variety, a miracle of miniaturization in which every new details was sure to be a universe of its own, diverse and entire.
Doesn’t that sound like mathematicians dancing around Brahman?