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Steven Strogatz on chaos theory, game theory, and why math isn’t boring

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Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#41

Post by mannykannot »

posterboy wrote: post #24
mannykannot wrote: post #20

Earlier quoted context omitted.

I first came across an alternative view in Godel, Escher, Bach, where Hofstadter was writing about Euclid's parallel postulate and the development of non-euclidean geometry. The latter could have been accepted sooner, he suggests, if people were not hung up on the idea that geometry was about physical space, rather than a derivation from axioms. Ironically, it turned out later that physical space is not euclidean.

I believe our ideas are formed in our brain, that is part of the physical word. So I think the schism you presented would be void.

Does this get us into the question of whether anything mathematical exists before anyone (or anysomething) first thought of it, and exists even when no-one is currently thinking of it? If you answer yes, then mathematics has an existence independent of thought. If you answer no, then that conditional existence presumably extends to physics as well, especially if Max Tegmark is right about math being the reality of physics. In that case, then it seems to follow that the universe only exists when it is being thought about, a conclusion that appears to have a bootstrap problem...

I think I can avoid the whole issue by observing that I can imagine things that do not physically exist, and they are not made to physically exist by dint of a conceptual representation of them physically existing in my brain.

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#42

Post by Ar-Curunir »

goldenkek wrote: post #2

Mathematics is the study of objective truth in a universe that has certain rules. How could knowing the universe in all its glory be boring? Wish they taught this rather than calculation at school. It's very uninspiring to not realize this and do math. In fact, natural numbers are the basis for almost all of mathematics. And natural numbers are a manifestation of counting. Information theoretically, to count, one nee…

This is pseudoscientific crap. Mathematics does not concern itself with physical reality.

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#43

Post by TeMPOraL »

posterboy wrote: post #36
TeMPOraL wrote: post #17

Earlier quoted context omitted.

> Do you know what the uni~ i universe means? It means only (one-ly). How could there be multiple? That's just non-sense. Do you know what "atom" in "atom" means? "Indivisible". But somehow we've been dividing them for power for quite some time. Arguments from etymology are invalid, because words are not obliged to be backwards compatible.

> Arguments from etymology are invalid, because words are not obliged to be backwards compatible. That's how you end up with loads of confusing homonyms, which the parent almost admited to. I mean, sure an etymologic argument can be insufficient or even wrong.

My point is, words are only labels - pointers to concepts. You can't prove facts about objects from just their labels, nor do the labels have causal power over reality. Universe being derived from "uni" doesn't force the concept of universe to be a singleton.

Proliferation of homonyms is another topic altogether; it is an issue, but it's about creating barriers to communication.

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#44

Post by gravypod »

charlieflowers wrote: post #40
j2kun wrote: post #32

Earlier quoted context omitted.

In anticipating a book like this, would you ideally want to learn the math context and notation (provided one goal of the book is to teach that), or skip that entirely in favor of the underlying ideas (as in your example with Newton's Method). Also, would you be interested in being paid to read a chapter or two and provide feedback?

Not the GP, but I'd want to learn both the ideas and the notation. That way, more math would become accessible to me. Just don't let the notation get in the way of reaching clarity on the ideas.

Yes exactly. It seems that no matter what you know math majors don't care. You need to walk the walk and talk the talk.

If you read through my comment history you will find me arguing with many mathematicians who think that math is just inherently harder and I must not understand it because I'm not smart enough. I think that the concepts and basic building blocks seem simple when explained outside the context of the current notation used.

You can see a perfectly prime example of this here: https://news.ycombinator.com/item?id=12991581

Read through my comments to see how I feel.

I'd also like to be clear. I'm not saying math is easy, I'm just saying that it can't be impossible for my peasant brain to not be smart enough to understand the concepts of what's going on. I mean it's not Greek.... well... it currently is but it doesn't need to be!

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#45

Post by marai2 »

calhoun137 wrote: post #16

Proffesor Strogatz wrote a book called Ninlinear Dynamics and Chaos which is the best intro book on non linear diff eq I have ever come across. I highly recomenend it: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications...

And I'd like to recommend Prof. Strogatz's book "The Joy of X" as a wonderful sampling of a number of basic math topics. It's very easily digestible. https://www.amazon.com/Joy-Guided-Tour-Math-Infinity/dp/0544...

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#46

Post by weerd »

calhoun137 wrote: post #16

Proffesor Strogatz wrote a book called Ninlinear Dynamics and Chaos which is the best intro book on non linear diff eq I have ever come across. I highly recomenend it: https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications...

A great book! It's very readable and more of an applied math book written with engineers and scientists in mind.

Starting out with the basics of state-space representations, it moves from 1D to 2D to 3D dynamics. The last section deals with the popular topics of chaos theory and fractals. But not from a simple pop-math perspective that you'll find in the math section of the book store. It's the real deal, except presented in a way that can be understood by non-mathematicians.

Strogatz is also coauthor of the paper that introduced small world networks. I really admire him for being so brilliant and at the same time capable of getting these topics across to everybody. I also recommend his book Sync.

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#47

Post by GuiA »

ivansavz wrote: post #28
GuiA wrote: post #6

Earlier quoted context omitted.

I feel the same way as you. But I don't know that my younger self had the maturity to see the deeper beauty. It was only starting college that I had the necessary complexity of thought (combined with wonderful professors). It takes a while to develop a taste refined enough to perceive these things. In the meantime, rote memorizing your multiplication tables and polynomial expansions might be a necessary evil to have…

> In the meantime, rote memorizing your multiplication tables and polynomial expansions might be a necessary evil... I disagree on both ideological and technical terms. Won't students lose the "flow" as soon as they start memorizing? It seems like an anti-intellectual activity to memorize data or particular steps (e.g. (a+b)^2 = a^2 + 2ab + b^2). I think the further we stay from memorization the better the learner's…

I've been doing math for the past 15+ years as well, and the nature of my education (French system) forced me to learn a number of things by rote. I'm very glad I now have these automatisms built in my brain and basic things come instinctively to me.

> Won't students lose the "flow" as soon as they start memorizing?

The core of my argument is that memorization will help them better find and stay in the flow in the first place, over the long term.

People wouldn't argue that having to learn your scales, chords, etc. gets in the way of creative piano playing, for instance; how and why is math different?

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#48

Post by mathperson »

posterboy wrote: post #10
goldenkek wrote: post #2

Mathematics is the study of objective truth in a universe that has certain rules. How could knowing the universe in all its glory be boring? Wish they taught this rather than calculation at school. It's very uninspiring to not realize this and do math. In fact, natural numbers are the basis for almost all of mathematics. And natural numbers are a manifestation of counting. Information theoretically, to count, one nee…

>Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe. But space and time are natural, ie. you mention a physical interpretation. And a paradox one at that, because you are explaining counting (numbers) by counting (dimensions). > Want to study the universe at the most raw level? I'd rather offer that mathematics is about formalization of what you know, w…

if you think mathematics relies on intuition..you haven't done much mathematics unfortunately. the field is deeply paradoxical once you get into it deeply

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#49

Post by chestervonwinch »

goldenkek wrote: post #4
stpapa wrote: post #3

The reason I posted this article was that this is the second mathematician I've come across in two days to talk about the elegance and beauty of mathematics. I wish I had seen some of this beauty from a younger age. It goes to show how much the right teacher, especially early on, can have a profound impact on your life.

I agree. Most of mathematics is taught as calculations without motivation. If it was taught as the study of systems, and a toolbelt to understand the universe, more people would be passionate about it. All we can do is show the light to others.

> If it was taught as ... a toolbelt to understand the universe ...

While true, I think that this is still a bit abstract. Rather than "a toolbelt to understand the universe", I would say "a toolbelt to formally characterize problems in order to analyze and solve them".

Let me add in addition that in order to learn to use the fun tools in the toolbelt, one must first grasp the basic ones. This (in my limited experience teaching lower level math courses) is another obstacle in teaching math: (continuing with the tool analogy) it would be quite boring to spend 3 months studying screwdrivers, another 3 months on wrenches, etc. without applying these tools to any "fun" problems.

Re: Steven Strogatz on chaos theory, game theory, and why math isn’t boring

#50

Post by monk_e_boy »

lordnacho wrote: post #14
ColinWright wrote: post #7

So here's the dilemma. People who see the beauty and elegance of mathematics are always going to go into something that exercises that, and will never go into teaching. Why would anyone who is seriously good at lots of math go into teaching? Especially in the USA, UK, or other countries where teaching has such a low status. In many cases teachers are genuinely despised. Why would anyone good at math ever go into teac…

Because one way to appreciate beauty is to show others. One of my math teachers in school had no kids, lived frugally. He could have retired a long time before I ran into him. Instead, he gave me extra classes and put me on the math team. He spent lots of his own time to show me the interesting bits while also making sure I wouldn't get anything less than the top mark on the exams. You're right though. It's not enoug…

No teacher has time to do that. The workload is insane. Work from 7:30 to 3:30 in school. Then after school stuff with some kids for an hour, then staff meetings and a cup of tea (maybe a shit if you've got time). Commute home. 6pm cook and eat dinner. Bath kids, put to bed. 8pm plan lessons for next day, try to find some beauty in maths that works for the A* kids and the F kids and is in the curriculum.

Yeah. That's not happening often. Schools are broken.

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