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

192 点作者 stpapa超过 8 年前

5 条评论

j2kun超过 8 年前
Shameless promotion: I&#x27;m writing a book in which I introduce mathematics for programmers specifically. If you found yourself here you may be interested. <a href="https:&#x2F;&#x2F;jeremykun.com&#x2F;2016&#x2F;04&#x2F;25&#x2F;book-mailing-list" rel="nofollow">https:&#x2F;&#x2F;jeremykun.com&#x2F;2016&#x2F;04&#x2F;25&#x2F;book-mailing-list</a>
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calhoun137超过 8 年前
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: <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Nonlinear-Dynamics-Chaos-Applications-Nonlinearity&#x2F;dp&#x2F;0738204536" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Nonlinear-Dynamics-Chaos-Applications...</a>
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stpapa超过 8 年前
The reason I posted this article was that this is the second mathematician I&#x27;ve come across in two days to talk about the elegance and beauty of mathematics.<p>I wish I had seen some of this beauty from a younger age.<p>It goes to show how much the right teacher, especially early on, can have a profound impact on your life.
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ColinWright超过 8 年前
So here&#x27;s the dilemma. People who see the beauty and elegance of mathematics are <i>always</i> going to go into something that exercises that, and will <i>never</i> go into teaching.<p>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.<p>Why would anyone good at math <i>ever</i> go into teaching? No money, no status, no respect, no flexibility, no control, crushing hours, crushing workload ... why would <i>anyone</i> do that?!?<p>No wonder students are never exposed to the real beauty and elegance of mathematics.
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goldenkek超过 8 年前
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&#x27;s very uninspiring to not realize this and do math.<p>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&#x27;d just draw two orthogonal lines..and say the area inside the rectangle is the product.<p>So if counting is fundamentally related to the relationship between two dimensions, then so is addition since addition is repeated&#x2F;recursive counting. And multiplication is repeated&#x2F;recursive addition.<p>Once you realize this, physics seems less fundamental than mathematics, when it comes to understanding the universe.<p>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.<p>See: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Ring_(mathematics)" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Ring_(mathematics)</a><p>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&#x27;s dimensions.<p>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&#x2F;neurochemistry.<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Phaneron" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Phaneron</a><p>Want to study it at the thinking level? Zen buddhism.<p>Choose your pick. The causal chain of human to universe doesn&#x27;t discriminate. The whole chain could be the &quot;real&quot; reality. Pick your choice. It&#x27;s all beautiful. It&#x27;s all mystifying and enigmatic. Just do it.
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