Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predictability.” – Chaos, James Gleick
Chaos is about chaos theory, something I didn't know very much about when I started reading the book. I grabbed it after watching a series of Stanford lectures by Robert Sapolsky on YouTube where it was promoted as potentially life changing.
While my life remains pretty much the same, I did learn a lot from Chaos. It's a hard book to understand some of the time, but the parts I grokked were pretty fun.
Tiny differences in input could quickly become overwhelming differences in output—a phenomenon given the name “sensitive dependence on initial conditions.” – Chaos, James Gleick
Why are the weather forecasters always wrong? I'm being hyperbolic here - short term forecasting is pretty accurate. If I need to know whether it will rain in the next few hours, the forecast can definitely help me (depending how close I'm located to the weather station), but longer term forecasting never seems to be correct.
Chaos opens with this problem and uses it as an example of a dynamic system. In a dynamic system, as I understand it, the outcomes are very hard to predict. This is because there are a large amount of variables that lead to said outcomes. Weather has a lot of variables.
A butterfly can flap its wings in Peking, and in Central Park, you get rain instead of sunshine. – Chaos, James Gleick
The so-called butterfly effect is pretty misunderstood. I mostly blame Ashton Kutcher for this and possibly that one Simpsons episode. Really, the butterfly effect is an example of how weather contains innumerable amounts of variables. So much so that long-term forecasting may never become fully predictable.
Edward Lorenz did get us closer (sidenote: how come so many intelligent people have the last name Lorenz?) by using computer-aided modeling. designed in 1963, the Lorenz weather model is a great example of deterministic chaos. Without getting too deep into the maths, there is this thing call the Lorenz attractor. From what I understand, which is only a small bit, you set a particle in motion and it can trace a figure-8 type path that never repeats itself. When looked at from a certain angle, the result looks a bit like butterfly wings. They are quite pretty to look at actually. Another very attractive bit of chaos are fractals.
An observer trying to estimate the length of England’s coastline from a satellite will make a smaller guess than an observer trying to walk its coves and beaches, who will make a smaller guess in turn than a snail negotiating every pebble. - Chaos, James Gleick
Isn't that beautiful?! It's a fractal from the Mandelbrot set. What is really neat about fractals is when you zoom in, they seem to go on infinitely. Here's a fractal explorer to experience this trippy effect.
The math is honestly well beyond me, but it wasn't beyond Benoit Mandelbrot. Mandelbrot studied Julia Sets at Harvard and the result are these truly gorgeous representations. It's like you're staring math in the face.
Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science. – Benoit Mandelbrot
I can understand the idea that as you zoom in, or out, on an object the topography of that object changes. How one is able to transform that to mathematics is, well, genius.
So, Nat’ralists observe, a Flea/Hath smaller Fleas that on him prey,/And these have smaller Fleas to bite ’em,/ And so proceed ad infinitum. – Jonathan Swift
Most people imagine the canonical dripping faucet as relentlessly periodic, but it is not necessarily so, as a moment of experimentation reveals. “It’s a simple example of a system that goes from predictable behavior to unpredictable behavior,” Shaw said. “If you turn it up a little bit, you can see a regime where the pitter-patter is irregular. As it turns out, it’s not a predictable pattern beyond a short time. So even something as simple as a faucet can generate a pattern that is eternally creative.” – Chaos, James Gleick
I was deep into Chaos when I really started to understand, for the first time, what it was all about. Robert Cahalan tries to predict the non-deterministic system that is a leaky faucet. Faucets seem like they drip in a rhythmic way, but that is our brain finding a pattern out of chaos. A faucet drip is not predictable and is a great example of the underlying chaos found in our world.
Instead of sitting, watching a faucet drip and marking off the permutations in some way, Cahalan built a computer model of a faucet. I found the resulting paper online and can't make heads or tails of it, but basically he was able to map the dynamics of a dripping faucet by reducing the drip down to some discrete variables.
That's what I now understand as chaos theory. It is a reduction of non-deterministic systems into formula that have adjustable variables and allow some level of predictions over the chaos.
There is a lot of math in Chaos. And a lot of physics. The book actually inspired me to try and learn a bit more about math because my comprehension ends at a2 + b2 = c2. I'm picking it up slowly, but I feel like I've been exposed to a whole new way of viewing the world. The natural world is full of golden ratios and fractals and chaos.
This was a tough one to write! Chaos was a challenging read and it was hard for me to extract what I learned in a way that was comprehensible. I actually had to give my brain a breather after this book and read something lighter.
I'm at 24 books read so far in 2021. This is more than I read in all of 2020!
Currently reading: The Body by Bill Bryson - Bryson is always a joy to read. I'm about halfway through this and have learned a lot of neat factoids about the human body.