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The Mathematical Hacker (2012)

evanmiller.org

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Re: The Mathematical Hacker (2012)

#41

Post by bmitc »

edgyquant wrote: post #37
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 disagree because Math is programming. All those symbols you see map to a set of steps (a program.). It’s just knowing what subroutine every esoteric symbol stands for that’s hard. I will agree it’s been more difficult learning math than programming for myself as well: but that’s because math is geared and targeted for people who like doing symbolic logic by hand. Math people think we’re a level below them (we are i…

> Math is programming.

That doesn't make any sense. What do you mean by that?

> I agree it’s been more difficult learning math than programming for myself as well: but that’s because math is geared and targeted for people who like doing symbolic logic by hand.

Mathematics is not about symbolic logic. Mathematics is the study of idealized structures, their properties, and their relationships. Symbols are just a convenient shorthand. They are not the mathematics in and of themselves.

> The fact we don’t have a nice and intuitive way of writing math via a keyboard is proof that these two fields are not on the same page.

What does that have to do with anything? Although LaTeX and the like are pretty decent at it, there's a lot of things we can't do easily via a keyboard. Why is that a constraint on anything or relevant?

Not trying to be provocative, but I honestly have little idea what you're talking about.

Re: The Mathematical Hacker (2012)

#42

Post by bmitc »

tombert wrote: post #22
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".

Mathematics is not just functions and calculus.

And it seems to me that you learned the concept of functions through programming first but that there's not evidence that you couldn't have learned it from mathematics at first. Functions are a pretty easy concept, so I think it's pretty easy to introduce it from a variety of points of view. So I'm not sure the anecdote backs up any argument about learning programming makes mathematics easy.

I am of the opinion that programming can be used to explore and learn mathematical ideas and am a big proponent of that, but that is something different than "I know how to program so mathematics will be easy now".

Re: The Mathematical Hacker (2012)

#43

Post by texaslonghorn5 »

adalacelove wrote: post #16
jdkee wrote: post #13

"Again, no recursion is required as long as one knows that a factorial is actually a special case of the gamma function. (The implementation of log-gamma is usually a polynomial approximation which requires constant time to evaluate.)" A prime idea behind using recursive techniques is that for many complex problems you do not have to know the "special case" as you can break complex problems into simpler pieces that c…

I would be surprised if there is not some kind of loop in the code that is used to evaluate the gamma function. You can also define factorial like for example the number of different permutations of any set of a given size.

outside of edge cases, c++ lgamma (log of gamma) uses Lanczos iteration with 8 iterations and gamma is just exp(lgamma)

Re: The Mathematical Hacker (2012)

#44

Post by zozbot234 »

subradios wrote: post #39
zozbot234 wrote: post #36

Earlier quoted context omitted.

Never mind calculus; a non-trivial fraction of the U.S. population has trouble learning elementary algebra . The fact that the U.S. K-12 educational system is notoriously a failure compared to otherwise similar countries should not be used to draw inferences about the inherent worth of any particular subject. Not least because that same system also often fails to teach functional literacy, or any amount of basic fact…

Then why do all New England states outcompete most European countries? Why is most STEM research produced in Eastern Europe, the US, or China? This really depends on what metrics you are using and has infinite room for gaming. US undergrads (both native and foreign born) absolutely crush all of these nondescript places you are suggesting are better, and graduate programs make the gap even wider. A non trivial fractio…

U.S. undergrads have to complete "general educational requirements" that are taken care of in high school in practically every other developed country. Why does that happen? Because U.S. colleges don't trust K-12 to provide a satisfactory education.

Re: The Mathematical Hacker (2012)

#46

Post by bmitc »

strangattractor wrote: post #18
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…

Implementing numerical solutions for math concepts can give you insight into the math ex. Newton-Raphson Method or FFT. I would not sell yourself short on being able to understand. You may not be skilled at doing all the symbol manipulation required for what people consider typical "math" but that does not mean you cannot understand it.

I do agree that programming is very useful as a medium of exploration, a la what you said. I really like how the book Turtle Geometry approaches this. But that is really something different than what the quoted text is attempting to get at.

> I would not sell yourself short on being able to understand.

I have a master's in mathematics and have continued to take courses while working full-time. It's just that I'm more than aware of the amount of mathematics I do not know compared to an active graduate student in mathematics and above. Or maybe you meant the royal you.

Re: The Mathematical Hacker (2012)

#47

Post by starwind »

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…

Math hard. Can confirm. Starwind have math degree. Starwind much better at programming than Starwind ever was at math.

Re: The Mathematical Hacker (2012)

#48

Post by dekhn »

tombert wrote: post #22
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".

functions in traditional programming and functions in math are two different things entirely. They should have been called procedures (I think there's historical debate about this but I can't find the reference). Obviously, functional programming is an attempt to address this.

Re: The Mathematical Hacker (2012)

#49

Post by constantcrying »

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…

Mathematics is not about computation. Certain means of arranging computation are entirely irrelevant to mathematics, computation is a mathematical tool, not an end.

Re: The Mathematical Hacker (2012)

#50

Post by texaslonghorn5 »

zozbot234 wrote: post #44
subradios wrote: post #39

Earlier quoted context omitted.

Then why do all New England states outcompete most European countries? Why is most STEM research produced in Eastern Europe, the US, or China? This really depends on what metrics you are using and has infinite room for gaming. US undergrads (both native and foreign born) absolutely crush all of these nondescript places you are suggesting are better, and graduate programs make the gap even wider. A non trivial fractio…

U.S. undergrads have to complete "general educational requirements" that are taken care of in high school in practically every other developed country. Why does that happen? Because U.S. colleges don't trust K-12 to provide a satisfactory education.

or that there's value in a college level comprehensive education as well
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