The best Chaos Theory books: Reddit reviews

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As someone who has studied dynamical systems for years, I'm pleased to see so many redditors getting interested in them through the double pendulum system. If you're a student and want to learn more, take a course in dynamical systems. If you're not a student, consider reading this book, which is my favorite math book of all time, and I'm far from alone in that sentiment.

Just posting in the top comment in case people want more.

3Blue1Brown on fractals. It's almost like you can understand them.

Also Chaos by James Gleick is a great listen on audio book.

For those interested in a popular overview of the topic, I recommend Chaos: Making a New Science by James Gleick. It does a pretty good job of popular explanations of the theory, and talks about a lot of key people in the field.

I've never read that book so I don't know the level you're at, but IMO the best undergrad book on the subject is:

Nonlinear Dynamics and Chaos by Steven Strogatz

That may be similar to what you've already read though, but it goes through the basics pretty well.

Nice! I'm still on the basics with chaos: making a new science

And https://www.amazon.com/Chaos-Fractals-Introduction-David-Feldman/dp/0199566445

For those interested in more details of some of the modern mathematics/science as it relates to philosophy I highly recommend Chaos by James Gleick.

It will depend on your level and the area. The best beginner book IMO is Nonlinear Dynamics and Chaos by Strogatz

Everyone's bad at reasoning about chance, here's a funny book with many great example. That book even uses the exact example of people - including doctors - rarely being able to correctly calculate the odds someone's sick given a problem like yours there. Hell: a lot of people can't even answer correctly: "If I flip a coin three times what are the odds it'll come up the same way all three times?". Prolific and well respected mathematician Paul Erdos struggled to intuitively understand the Monty Hall problem even though he conceded the mathematical proof was there.

If you're able to learn the answer, figure out how it works and start applying that sort of thinking to new problems you'll be fine. Next to nobody is able to just know the right way to approach probability problems without training.

I wonder if a lot of movies would be viewed very differently if everyone watched the movie, weighed it in their own mind, before seeing any discourse about it? For instance, I feel sometimes the same type of things in a movie is at times viewed positively (e.g. an homage to the way the genre was done before) vs negatively (e.g. unrealistic and corny) just based on whether or not the public opinion is "this movie is good" or "this movie is bad."

As an example- everyone pretty much hates the fridge scene in Indiana Jones 4. And all the criticisms of it are true. It is very unrealistic. And it is corny. But also, I'm not sure it isn't very similar to scenes in beloved movies like it.

There was an interesting study I read about in the book The Drunkard's Walk where 10 competent, but unknown songs, were chosen, and volunteers listened to them, and gave them a thumbs up or thumbs down rating. It was done in two ways- way 1 every participant got to see the rankings from the people who went before, and way 2 everyone listened to the songs and just ranked them. In way 1, songs ran away with many thumbs up or thumbs down, where in way 2, some songs came out as rated better than others, but they stayed much closer to the middle.

I found it. It's from the book, The Drunkard's Walk. It's a 269-game series. Here's a link to the book. It's one of the best books I've ever read. Definitely a big recommend, especially to fellow stats nerds.

Have read a few by leonard mlodinow. Started with The Drunkards Walk which was good, then read subliminal and Feynmans Rainbow. I would recommend them in that order. Drunkards walk

I can’t speak to what you need to get all the way to current literature, but given your background (and lack of any nonlinear dynamics course) I highly recommend:

Nonlinear Dynamics and Chaos - Steven Strogatz

In addition to being a well regarded text its also really well written and fun — very suitable for self-study. And I believe you can find solutions for most of the problems online (and theres a separate solution’s manual) so you can work problems.

Just tell them you hear voices and they’ll let you in (even if you don’t actually hear voices, they will not sniff out your “obvious” sanity as backed up by an actual study I read about once—once they think of you as being mentally ill, that perception will color every observation they make of you from then on. I too lazy to go looking for the book to give a proper reference, but iirc the book’s title was The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow. It was near 70% of the pages opened where he talked about it. Here’s the link

The Feynman Lectures on Physics, boxed set: The New Millennium Edition
$129.04

https://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/0465023827/ref=sr_1_1?crid=1AEZX8482CT7L&keywords=feynman+lectures+on+physics&qid=1638326397&sprefix=feynman+%2Caps%2C237&sr=8-1

Not textbooks, but to help you develop a really good framework for statistical thinking and to get your feet wet in different subdisciplines, first try reading Mlodinow's The Drunkard's Walk & then Spiegelhalter's The Art of Statistics. Both books are very readable (targeted at non-technical audiences).

I just bought it, I'll give it a read! I recommend Chaos - The Making of a New Science by James Gleick, I'm currently only half way through it at the moment but it provides a phenomenal introduction to the discovery of chaos, why it's important, and where it can be found. I've found this book pairs conspicuously well with the torus and I fully believe the two are interlinked, as a sort of yin / yang scenario.

Chaos: Making a New Science https://www.amazon.com/dp/0143113453/ref=cm_sw_r_apan_glt_fabc_0BJXQX3XG8ZG1TWJP4W4

This is just straight up wrong. It's a coinflip on what is going to be popular and there are tons of confounding variables. This book goes into detail about it.

I was reading a math book from 2008, and it cited Trump as an example of negative return on investment. If you invested 10,000 with him, in 10 years you would have turned your investment into 600.

He was pegged as a failure YEARS before he opened his mouth politically, and was an example to be used in a math book.

For reference: https://www.amazon.com/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175

James Glick https://www.amazon.com/Chaos-Making-Science-James-Gleick/dp/0143113453 is a great book to start to understand just how frickin odd this is. And weather tracking is of course the worst we know. Yet.

In general you don't solve most nonlinear ODEs. You analyze them to look for information about the solution space as well as use numerical solvers such as Dormand Price. That way you can create solution trajectories.

For equations higher than first order, you convert them to a nonlinear system of equations by the following:

y_1 = y', y_n = y^(n)

then analyze the first order system.

If you really want to learn about nonlinear ODEs, the best primer is Nonlinear dynamics and Chaos by Steven Strogatz is a great book to get you started on the awesomeness of nonlinear ODEs

Dynamical systems theory is a subset of the study of differential equations.

If you want to understand dynamics, you need to analyze the differential equations involved. My suggestion is to look into bifurcation theory and ODE methods since they can be extended to the study of PDEs. Dynamical systems isn't so much about solving the specific partial differential equations as it is about using them to understand the behavior of said system.

If you want an actual primer to the subject, the Strogatz book Nonlinear Dynamics and Chaos. Link is a very good way to begin understanding it.

But there isn't a good way to get a decent understanding of dynamical systems without dealing with differential equations because the study of dynamics is the study of differential equations.

> Thats coming from people who have no clue how the game is played.

In order to consistently beat the market you have to consistently be a step ahead of everyone trying to take advantage of you. Do you think that can work on the long term?

There are no traders that can consistently beat the market. For the very simple reason that all their peers are busy trying to outsmart them 24/7.

> The difference between the two? Risk management. Manage your position in a way that increases your statistical odds of success.

You can't use statistics on variables that aren't random. Markets aren't random, they're chaotic. They're bound to experience black swans, where suddenly your stop loss orders won't do anything because liquidity has evaporated from under your feet. And guess why? Because everyone had the same idea, everyone is running for the safety exits at the same time.

> If you were correct, the market would not have a 10% upside bias year over year. It would trade sideways

That's irrelevant. My point is that if the market is consistently up 10% year over year, nobody can consistently yield 12%.

I hope that helps.

Recommended reading :

• On chaos: https://www.amazon.com/Chaos-Making-Science-James-Gleick/dp/0143113453
• On investing: https://www.amazon.com/Little-Book-Common-Sense-Investing/dp/1119404509/ref=sr_1_1?dchild=1&qid=1607157897&s=books&sr=1-1
• On risk management: All of Taleb

I felt kind of the same way until I took a dynamical systems class. Sometimes you just need to find that area that you actually enjoy. I really didn't get the abstract part as easily, but applications peaked my interest just by virtue of being able to see the results of what all the abstract stuff could do.

Have you decided where you want to focus yet and where you want to lean into?

I had a weird path in school, so I ended up taking physics at the same time as I was doing complex analysis, and I remember immediately seeing the applications of what we were doing when we entered electromagnetism in physics. Its one of the main reasons I chose to stay on the math road rather than changing over to CS.

My suggestion is to branch out a bit and find some stuff you really like in math. Personally I found group/ring/field theory super boring, but analysis was really interesting. You should try to find a niche that sparks your interest or makes you interested in what you could do with math.

For some suggestions on interesting applied math topics (IMO of course) are numerical analysis and dynamical systems. Dynamics absolutely blew my mind so much that it solidified my decision to go to grad school and learn more about it.

Edit: if you want to see a really interesting book on all of the applications for diffeq, check out nonlinear dynamics and chaos by Strogatz

If anyone is interested in Chaos mathematics, I bought "Chaos" by James Gleick on a whim at Half-Price Books because the cover was cool (it was this cover, not the first one I linked).

It is very readable and gives good examples. I'm really dumb, but I read about 60-70% without giving up, which is pretty good for me. Recommended!

That’s definitely sufficient.

Anything can be taken to more complicated levels, but some diff-eq is the only prerequisite.

Like others have said, Strogatz’s Nonlinear Dynamics and Chaos is an exceptional book and accessible from there.

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I would also recommend Nonlinear Dynamics and Chaos by Steven Strogatz. He does a great job of introducing the subject without diving too deep into the mathematical weeds

One, I'm not attacking anyone and particularly not the youngsters. I'm trying to speed their progress. I provided plenty of directions on what they should be reading. Go up to my initial comment here. I didn't dismiss Graham completely; instead I suggested people read Zhang first for some proper framework. In particular, his approach is compatible with efficient markets so the premiums are there to be earned by everyone. (More broadly I like to live with an abundance mindset. It's not always zero sum, mi amigo, especially since we are not talking about alpha here.)

You present yourself as a thinking man and professional, but sometimes I wonder if you have a reading comprehension problem or alternatively your reading ability is fine but you are so resistant to the viewpoints of others that you fail to understand them properly before you lash out. I'm no psychologist so I will leave that to your therapist.

Second, go knock yourself out with his lectures (https://www.amazon.com/Feynman-Lectures-Physics-boxed-set/dp/0465023827/) . Not a real test since you are smarter than the average /r/investing bear but give it an honest effort and report back in a month.

Well... A lot of areas, actually. The main branch of mathematics that studies CA is called Complex/Dynamic systems, it focuses on the idea of interactions between certain systems and that's what gives us a framework around "rules of CA", I recommend the resources of the Sant Fe Institute along with this book there are some other math areas important to the subject, the key one is just discrete math, so you can get along the idea of recurrence, but it seems like you have some good programming background so you've probably taken a course on the subject already.

Read The Durnkard's Walk if you ever have time. Randomness plays a much larger part in our lives than previously thought.