- ...chaos theory turned out to be mind-numbingly boring. Before this, my major exposure to chaos theory was Jeff Goldblum’s character in Jurrasic Park, who kept arguing that, “nature finds a way.” Guess what? That’s not chaos theory.
From my readings, there seem to be two ways to discuss chaos theory. The first is the idea that many small changes in conditions can have huge consequences. It’s the butterfly effect. But instead of throwing up our hands and saying that means it’s impossible to measure things like weather, the field of chaos is dedicated to trying to understand how we can use this understanding to understand the world around us, and make better predictions about it in the future. I get it. I wish one of the books could have made it more interesting.
The second idea is fricking Mandelbrots. If I never see one of those diagrams again, it’ll be too soon.
I enjoyed the two James Gleick "sciency books for non-science types" quite a bit; Chaos in particular inspired me to write my own Mandelbrot set generator in QBasic. I didn't care so much for a different book by Ian Stewart, who wrote the "definitely for the math and science types" book on chaos theory.
Dr. Carroll seems to have only picked up on the first of what seem to me seven very interesting aspects of chaos theory:
2.1 Sensitivity to initial conditions 2.2 Topological mixing
2.3 Density of periodic orbits
2.4 Strange attractors
2.5 Minimum complexity of a chaotic system
2.6 Jerk systems
2.7 Exactly-solvable chaotic systems
Even Jurassic Park the book had more chaos theory than the butterfly effect.
But Dr. Carroll is prolific and it sounds like he has been unusually busy. Too bad we will miss out on music appreciation, but linguistics and knitting should be good.
#learnnewthings schedule:
January 2016 – Water and growth in California
February – Wine
March – Game theory
April – Cryptography
May – Art history
June – The history of railroads in the U.S.
July – Oceanography
August – Football (strategy and theory)
September – Chaos theory
November – Linguistics
Check out bifurcation theory and diagrams. Here's a diagram I made yesterday showing x_n+1 = a*sin(pi*x_n), with alpha ("a") on the x-axis and x_n on the y-axis. The system becomes truly chaotic around a=0.89.
What do the different colors lines mean? I'm only vaguely familiar with bifurcation diagrams.
Well, that's what author gets for taking a highly mathematical topic and wanting to be cursorily acquainted with it in a month. That's not unlike taking an interest in control theory and being annoyed about lack of RC cars (although there are some cool drones)! Having said that, especially when keeping in mind the cryptography segment from April, it's perhaps not something that's covered all that well. There is certainly a higher barrier to entry when comparing basic ciphers and physics that most people know mainly from movies. So to not end on the sour tone: I am still in need of a topic of discussion to declare for my semester project for ODE course. If anyone is interested, I could do it about jerk systems and share.mind-numbingly boring
That's just what I am confused about. I think a month and five books should be more than enough to gain an appreciation for such a broad and accessible subject (for differential equations it might be another story -- I was pretty well lost after a month of class). The dismissal of The Information as merely "sciency" but not sufficiently academic is understandable, but not "boring." It was a bestseller and won several awards and honors, and is full of great stories on a variety of subjects.
Regarding thing being 'sciency', perhaps you would like the following situation that happened to me. About four years ago I went to my father, ex-researcher theoretical physicist in field of superconductivity and statistical physics, to get some clarification on all that string theory hubbub. Here's how that went (changes due to my memory and translation may occur): Father: I honestly can't explain it to you. Aside of it being quite far from my speciality, I don't think it's accessible to you? Me: Why? Father: First of all, you lack about three or four years of university-level mathematical and conceptual preparation. Second of all, there's not just one string theory but a term for at least four theories that I'm only vaguely aware about. Thirdly, it's an extension of what's called Quantum Field Theory that itself is an extension of quantum mechanics. Me: And I need to understand all of that just to get the gist? Father: Understand? You would need to master them! Honestly, I would feel a certain level of contempt toward a string theorist who would not be able to solve QFT problem that I could. Me: But what about concepts? What are these strings? Father: Abstractions. Like atoms. Look, the only thing I can tell you myself is this: there is some structure that physicists called string. Depending on how it 'vibrates', moves or whatever else it does in ST it is responsible for properties of lower level abstractions. Gluons, leptons, bozons, neutrinos and whatever you have there. Remember these particles are also abstract and you probably have only a vague understanding of them, because I'll assume that you had at least heard me talk about some of them. Only string theory is, presumably, valid even in relativistic sense. Please don't ask me about that one, I already feel like a parrot, mindlessly repeating to you what I heard or happened to read about. I felt a bit deflated, but I need to say that he was right. Road to Reality by Roger Penrose (I cannot give enough praise to that book!) is a book that he gave me a few weeks later, "because if I want to learn about it, I'll better hit the books and do the work myself". It's a book to which I'm returning constantly, each time going a chapter or two further. It allowed me to appreciate many abstract concepts and connections. I got some insane mathematical preparation in the meantime and can quite competently read even certain graduate level texts. Few months ago I went on YouTube and watched some 'string theory documentaries'. It was just… baffling. It managed to bore my dormmate (biology major, just started senior year along with second year of chemistry major) got bored out of his skull. I felt almost insulted at the level. It didn't say anything about string theory, just pretty much the same things that my father told me… only in the span of hour or more. There was nothing about WTF that even is, halfway seemed to give up and just began showing more and more animations of vibrating strings, ribbons and membranes in the back of clearly trying physicists who were assigned something impossible: condense something that takes over a decade of prep into few minutes worth of ELI5. It felt like they were repeating the same thing over and over without adding anything. I would imagine that something similar occurs around chaos theory. If you lack the hard science and maths prep, you can easily end up feeling like you are simply amassing trivia. And if you have that prep (or even still acquiring it, like I am now)… it's actually an intriguing quirk, but I can't really see myself passionate about it. Seems like it's a bit too famous while not being easy to appreciate without some serious work. And you don't want to study calculus for years to get a pop-sci book, right? You want to read a book without maths that explains what basically emerges as a result of doing some serious mathematics. ;)