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The Mathematical Hacker (2012)

evanmiller.org

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Re: The Mathematical Hacker (2012)

#21

Post by petemir »

cs702 wrote: post #15

"Writing software" = "writing down math". Consider: * "Writing software" means arranging symbols (bits in a machine language, UTF or ASCII characters in a high-level language) in certain permitted ways, to transform an input sequence of symbols (e.g., a stream of byte values representing user actions from a video game controller) into an output sequence of symbols (e.g., byte values representing pixel RGB colors for…

I fear that's a very narrow view of mathematics. Nevertheless, most of the time you can see the output of what you created while programming, check if it's the correct result, etc. I don't think it's like that in math, where you deal in a much more abstract realm.

Re: The Mathematical Hacker (2012)

#22

Post by tombert »

bmitc wrote: post #9

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…

I think Yegge is actually completely correct. I started to learn to program when I was 14, and once I understood the concept of functions, I found it much easier to do my calculus and physics work. Fundamentally I understood how to break things down into computable steps.

Granted, I think get the impression we might be overloading the term "mathematics".

Re: The Mathematical Hacker (2012)

#23

Post by cs702 »

petemir wrote: post #21
cs702 wrote: post #15

"Writing software" = "writing down math". Consider: * "Writing software" means arranging symbols (bits in a machine language, UTF or ASCII characters in a high-level language) in certain permitted ways, to transform an input sequence of symbols (e.g., a stream of byte values representing user actions from a video game controller) into an output sequence of symbols (e.g., byte values representing pixel RGB colors for…

I fear that's a very narrow view of mathematics. Nevertheless, most of the time you can see the output of what you created while programming, check if it's the correct result, etc. I don't think it's like that in math, where you deal in a much more abstract realm.

"Mathematics" is not the same as "writing down math."

Re: The Mathematical Hacker (2012)

#24

Post by userxyz »

wwweston wrote: post #11

> Rather, mathematics is a tool for understanding phenomena in the world: the motion of the planets, the patterns in data, the perception of color, or any of a myriad things in the world that might be understood better by manipulating equations. OK, so on one hand I love this point, and I'd love for it to be more broadly understood and appreciated, especially since my educational background is Mathematics and my CS h…

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 sequences. This stuff together with theory that surrounds the Gamma function can easily take up a whole book. But there are a ton of books that treat either one really nicely: most textbooks on discrete math and real analysis.

[0] https://ibb.co/TR1f5Gz

Re: The Mathematical Hacker (2012)

#26

Post by zozbot234 »

tromp wrote: post #12

The suggested "efficient" solutions for fibonacci and factorial only work on small inputs as they return the result as a long int. For these small instances the use of floating point functions like pow, sqrt, and exp is likely less efficient than a simple iterative solution. For larger instances using bignums as output, floating point computations do not even offer an alternative. It's true though that mathematics of…

The matrix based method for Fib can be understood as applying the closed-form solution over Q(sqrt5). OP seems to miss this point.

Re: The Mathematical Hacker (2012)

#27

Post by bee_rider »

bmitc wrote: post #9

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…

What do you mean by “learning Mathematics?” It should be notes that significantly less than 50% of the US population even has to learn calculus so getting into the stuff that most people would consider pretty advanced is not so hard, right?

I’d be curious what people’s coolest math tricks are that they’ve used at work. I did like one Taylor Series expansion and felt cool for a week.

Re: The Mathematical Hacker (2012)

#28

Post by cod1r »

CS/programming for me was a good balance between practical application and theory. Spending more time programming and getting better at programming will probably land you a higher salary than if you were to spend your time learning complex math which you might/might not use.

Re: The Mathematical Hacker (2012)

#29

Post by petemir »

cs702 wrote: post #23
petemir wrote: post #21

Earlier quoted context omitted.

I fear that's a very narrow view of mathematics. Nevertheless, most of the time you can see the output of what you created while programming, check if it's the correct result, etc. I don't think it's like that in math, where you deal in a much more abstract realm.

"Mathematics" is not the same as "writing down math."

I stand by what I said, applicable even to proofs, but I take your point.

Re: The Mathematical Hacker (2012)

#30

Post by zozbot234 »

userxyz wrote: post #24
wwweston wrote: post #11

> Rather, mathematics is a tool for understanding phenomena in the world: the motion of the planets, the patterns in data, the perception of color, or any of a myriad things in the world that might be understood better by manipulating equations. OK, so on one hand I love this point, and I'd love for it to be more broadly understood and appreciated, especially since my educational background is Mathematics and my CS h…

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…

Non image-based link: https://en.wikipedia.org/wiki/Linear_recurrence_with_constan... (Also, https://en.wikipedia.org/wiki/Constant-recursive_sequence#Cl... )
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