
Steven Strogatz on chaos theory, game theory, and why math isn’t boring - stpapa
http://www.businessinsider.com/steven-strogatz-interview-on-math-education-2016-6
======
j2kun
Shameless promotion: I'm writing a book in which I introduce mathematics for
programmers specifically. If you found yourself here you may be interested.
[https://jeremykun.com/2016/04/25/book-mailing-
list](https://jeremykun.com/2016/04/25/book-mailing-list)

~~~
gravypod
I'd be willing to spend a good 40 bucks on something like this (that may not
seem like a lot but 40$ to a college student _is_ a lot). Something that has a
twinkle of a promise in teaching a programmer math is something I need in my
life.

I just don't "get" what is being told to me when it's in the context of math-
notation. As a result I do horrible in math classes in college. The only thing
that was taught with a CS-Style notation was approximating using Newton's
method. After I saw that it made sense, it was just a recursive method that
zeroed in on that location.

Very little aside from that in my calc 1 class made sense. Probably limits,
but that's it really. It didn't click as well.

I'd like to get to the point where I understand math concepts as well as I do
most of the CS but I just think that's impossible at this point. It seems to
be very "this is our garden, you stay in yours".

~~~
j2kun
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?

~~~
charlieflowers
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.

~~~
gravypod
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](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!

~~~
jacobolus
The concepts are not individually hard, but they build on each-other
(sometimes unnecessarily, but sometimes very helpfully). If you care about
understanding the tools you should take the few years of study it takes to
learn the notation to a level of fluency, or you won’t be able to read the
vast literature written in that notation.

It’s like if you’re interested in 19th century piano music, but all your
experience with reading music is in the form of guitar tablature, then you’re
going to have a tough time with your study. You could conceivably find top-
down videos of someone playing some of the music you care about, or convince
someone to translate some parts of it into guitar tablature. But it would be a
better use of your time to just learn to read standard music notation.

------
calhoun137
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...](https://www.amazon.com/Nonlinear-Dynamics-Chaos-Applications-
Nonlinearity/dp/0738204536)

~~~
marai2
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...](https://www.amazon.com/Joy-Guided-Tour-Math-
Infinity/dp/0544105850)

------
stpapa
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.

~~~
goldenkek
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.

~~~
cttet
Actually if you dig in the calculation techniques taught in primary
school(Like multidigit addition/multiplication/ division), you would find some
of them are actually quite clever ideas (O(log n) algorithms), but what almost
all school do is to ask the student execute the algorithm like a computer, not
how to come up with ideas like those...

------
ColinWright
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 teaching? No money, no status, no
respect, no flexibility, no control, crushing hours, crushing workload ... why
would _anyone_ do that?!?

No wonder students are never exposed to the real beauty and elegance of
mathematics.

~~~
tgb
Steven Strogratz _is_ a teacher. He's also a popular math writer (he had a NYT
column for a while).

~~~
j7ake
Agreed. He also mentors many PhD students, which is where a lot of the magic
happens in terms of training.

------
goldenkek
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 needs two dimensions (or degrees of freedom.) Space for storage of
the number. And time to increment the storage medium, again and again, at
different points. You could use two dimensions of space instead, and you'd
just draw two orthogonal lines..and say the area inside the rectangle is the
product.

So if counting is fundamentally related to the relationship between two
dimensions, then so is addition since addition is repeated/recursive counting.
And multiplication is repeated/recursive addition.

Once you realize this, physics seems less fundamental than mathematics, when
it comes to understanding the universe.

Multiplication and addition are related in the way that f(x) and repeat(f(x),
y) are related. They distribute over eachother and have certain properties.

See:
[https://en.wikipedia.org/wiki/Ring_(mathematics)](https://en.wikipedia.org/wiki/Ring_\(mathematics\))

So..the primes, the chaotic relationship between the modularity of addition
over multiplication and the modularity of multiplication over addition, is due
to the relationship between our universe's dimensions.

Want to study the universe at the most raw level? Mathematics. Want to study
it a little higher? Physics. Want to study it at a higher level..maybe closer
to the phaneron? Biology/neurochemistry.

[https://en.wikipedia.org/wiki/Phaneron](https://en.wikipedia.org/wiki/Phaneron)

Want to study it at the thinking level? Zen buddhism.

Choose your pick. The causal chain of human to universe doesn't discriminate.
The whole chain could be the "real" reality. Pick your choice. It's all
beautiful. It's all mystifying and enigmatic. Just do it.

~~~
zeroer
Yea, mathematics is more fundamental than physics, in the sense that it would
be possible for different universes to exist with different physics, but it's
not clear at all that universes could exist with different mathematics. What
would that even mean? You may like Max Tegmark's idea that the universe _is_
math: [https://arxiv.org/abs/0704.0646](https://arxiv.org/abs/0704.0646)

But it's nonsense that the natural numbers require two dimensions. Time
appears nowhere in the Zermelo–Fraenkel axioms:
[https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory](https://en.wikipedia.org/wiki/Zermelo–Fraenkel_set_theory)

~~~
posterboy
Do you know what the uni~ i universe means? It means only (one-ly). How could
there be multiple? That's just non-sense.

The parent implied counting, not the natural numbers, need two dimensions. But
even in Set Theory you need at least one level deep _nested_ sets to build the
natural numbers. Qunatification is the (a?) difference between zero and higher
order logic, I suppose.

~~~
TeMPOraL
> _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.

~~~
posterboy
> 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.

~~~
TeMPOraL
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.

