171–180 of 186 posts
Earlier quoted context omitted.
> " Yet we regularly teach smart high school students and first-year undergraduates calculus... " High school students are taught plug-and-chug calculus where one uses rules and formulae without any real understanding of the underlying subtleties that make calculus work.
Bulletproof counter argument, you sure showed me.
Higher level math is at its most fun for me when you're solving difficult problems with peers. I wish there was a startup that could recreate that experience outside of a university setting.
Earlier quoted context omitted.
I think the author is making two points among others: 1. LISP based text/books always present the same two cliche examples 2. They never go beyond (1) given how much they talk about recursion. He mentions sqrt of 5 in the explicit formula of Fibonacci sequence and how that could be explored in more detail to find out where that comes from. For that you need to know [0]. That's part of a larger suit of theorems on seq…
I see someone disagreed with me. Not sure about what, but just in case I will show how to derive a formula for Fibonacci using the above. You be the judge if it belongs in a LISP programming textbook, even though this particular result is very elementary. Recurrence relation for Fibonacci is F_k = F_(k-1) + F_(k-2) for k=> 2 with F_0 = F_1 = 1. Also, t^2 - t - 1 = 0 implies t = (1 + sqrt(5))/2, (1 - sqrt(5))/2. Both…
That Fibonacci has a closed form it's completely irrelevant to teaching recursion as a programming technique. It could be mentioned in a small footnote giving some external reference. More relevant is the fact that the naive Fibonacci is terribly inefficient and can be vastly sped up by memoization. Even that is a problem that's not specific to the language and how to use recursion in that language. It has to do with using recursion well in any language, that belongs in an advanced chapter in a book which is not mainly about Lisp but about learning programming using Lisp.
Lisp already has a reputation for being scary, which is unfounded, but there it is. A Lisp book which goes into numerous mathematical rabbit holes will probably just contribute to that meme and have a discouraging effect.
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I think you're hitting the nail on the head here. Something about the learning process makes programming much easier to pick up. What if we had something similar for mathematics? Rapid feedback, error messages, maybe even linters and highlighting for the "mathematical syntax". I've though about this before and I think tools like this could unlock math for a lot of people, and also increase the effectiveness of profes…
Is it the learning process, or the subject itself? Programming works with manmade abstractions, carefully designed to have very few interactions, keep mutable state contained, and to have all the parts structured in a hierarchy without recursion. In math you have systems of equations that all reference each other. And they all happen at the same time because there's no steps and time or lines of code just 5 equations…
Not every programming language has a concept of time. Sometimes that's a good thing, it depends on what you're used to. Math arguably has less mutable state than most typical programing languages.
I'm sure I've used Fib in examples, without always mentioning that it needs to be memorized to avoid a monstrous inefficiency, and that there's a direct way to calculate it.
The blogger is implying that whatever you don't mention must be something you don't know. That when you write on any topic, you must go down all the related rabbit holes you can think of in order to show that you know the topic inside out so as not to appear ignorant to someone who thinks like he does.
The problem is if you want to write a book which actually teach you somebody a certain topic like a programming language, that goal is almost completely at odds with the goal of writing in order to publish something which shows how smart you are.
In Steve Yegge’s linked post: > Math is a lot easier to pick up after you know how to program. In fact, if you're a halfway decent programmer, you'll find it's almost a snap. This couldn’t be more wrong. Mathematics is the hardest thing I have ever done. I’m sorry, but mathematics is orders of magnitude more intensive and difficult than most programming. A simple fact that shows this is the amount of programmers who…
Closer to the right kind of math: https://sites.math.rutgers.edu/~zeilberg/GT.html
In Steve Yegge’s linked post: > Math is a lot easier to pick up after you know how to program. In fact, if you're a halfway decent programmer, you'll find it's almost a snap. This couldn’t be more wrong. Mathematics is the hardest thing I have ever done. I’m sorry, but mathematics is orders of magnitude more intensive and difficult than most programming. A simple fact that shows this is the amount of programmers who…
In Steve Yegge’s linked post: > Math is a lot easier to pick up after you know how to program. In fact, if you're a halfway decent programmer, you'll find it's almost a snap. This couldn’t be more wrong. Mathematics is the hardest thing I have ever done. I’m sorry, but mathematics is orders of magnitude more intensive and difficult than most programming. A simple fact that shows this is the amount of programmers who…
> mathematics is orders of magnitude more intensive and difficult than most programming But what level of programming and mathematics are you comparing here though? because college-level algebra and calculus is really not that hard imho (once it "clicks" for you, but it's the same for programming), and if we are comparing math as in what you see in a BSc/Msc of Mathematics (or research-level) then I agree it's hard b…