Steven Strogatz on chaos theory, game theory, and why math isn’t boring • Hacker News Board

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

#61

Post by j2kun » Mon, Nov 28, 2016, 4:12 PM UTC

sn9 wrote: post #55

j2kun wrote: post #11

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

There are two books I know of that address an audience of programmers interested in mathematics: Klein's Coding the Matrix and Stepanov's From Mathematics to Generic Programming . Have you looked at these two? It might help your writing process to find what readers of those books found confusing or frustrating in the presentation.

Thanks! I'll be looking into these. From a first glance, Coding the Matrix looks to be excellent and exhaustively complete, but also very verbose. From Mathematics to Generic Programming appears to be the kind of book I want to avoid. It seems to be more about a study of a few particular algorithms useful for generic programming than actually understanding the principles of mathematics.

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

#62

Post by posterboy » Mon, Nov 28, 2016, 10:16 PM UTC

mannykannot wrote: post #41

posterboy wrote: post #24

Earlier quoted context omitted.

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 ph…

>Does this get us into the question of whether anything mathematical exists before anyone (or anysomething) first thought of it

No, because you can't ask for it's existence, before you thought of it.

>exists even when no-one is currently thinking of it

Again, who cares, it's by definition undefined, null, niente, the inbetween state of a ternary logic.

>I can imagine things

You can't will a pot of gold into existence by mere imagination, but you can't imagine an idea without it's inherint structure being real.

I'll admit, that's a simplistic outlook, but I wasn't encouraging a complicated discusion.

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

#63

Post by goldenkek » Mon, Nov 28, 2016, 10:35 PM UTC

zeroer wrote: post #8

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…

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 But it's nonsense that the natural numbers require two dimensions. Time ap…

If you actually read my post more closely you would see I said any two orthogonal dimensions, that could be two spatial dimensions..not necessarily including time.

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

#64

Post by goldenkek » Mon, Nov 28, 2016, 10:36 PM UTC

Ar-Curunir wrote: post #42

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.

Haters gonna hate ;-)

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

#65

Post by agumonkey » Tue, Nov 29, 2016, 8:02 AM UTC

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.

To each his own. Education aside (which is often way too bad) your mind may only catch a subset of how math can be beautiful. Had to wander around 10 years on my own before finally see the value in complex planes, non linear abstractions, or even very simple geometric concepts you encounter at a young age (tan/cotan).

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

#66

Post by agumonkey » Tue, Nov 29, 2016, 8:22 AM UTC

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…

> (a+b)^2 = a^2 + 2ab + b^2

who else think it could be better to explain such identities with geometric combinatorial diagrams ? at least at first step toward formal memorization.