URL : | http://www.johndcook.com/blog/ | |
---|---|---|

Filed Under: | Academics | |

Posts on Regator: | 1107 | |

Posts / Week: | 5 | |

Archived Since: | April 26, 2011 |

Ten life lessons from differential equations: Some problems simply have no solution. Some problems have no simple solution. Some problems have many solutions. Determining that a solution exists may be half the work of finding it. Solutions that work well locally may blow up when extended too far. Boundary conditions are the hard part. Something […]

Harmonic numbers The nth harmonic number, Hn, is the sum of the reciprocals of the integers up to and including n. For example, H4 = 1 + 1/2 + 1/3 + 1/4 = 25/12. Here’s a curious fact about harmonic numbers, known as Wolstenholme’s theorem: For a prime p > 3, the numerator of Hp-1 […]

Numerically integrating functions of many variables almost always requires Monte Carlo integration or some variation. Numerical analysis textbooks often emphasize one-dimensional integration and, almost as a footnote, say that you can use a product scheme to bootstrap one-dimensional methods to higher dimensions. Show More Summary

Zawinski’s law of software development: Every program attempts to expand until it can read mail. Those programs which cannot so expand are replaced by ones which can. The folks behind Mathematica and Wolfram Alpha announced yesterday now they too can read email.

Scientific computing in Python is expanding and maturing rapidly. Last week at the SciPy 2015 conference there were about twice as many people as when I’d last gone to the conference in 2013. You can get some idea of the rapid develop of the scientific Python stack and its future direction by watching the final […]

My contact information arranged into a diagram: Yesterday at SciPy 2015 Allen Downey did something similar for his contact info and gave me the idea for the image above.

A certain question has the following possible answers. All of the below None of the below All of the above One of the above None of the above None of the above Which answer is correct? Source

If you raise any integer to the fifth power, it’s last digit doesn’t change. For example, 25 = 32. It’s easy to prove this assertion by brute force. Since the last digit of bn only depends on the last digit of b, it’s enough to verify that the statement above holds for 0, 1, 2, […]

Periodically someone on Twitter will suggest that one of my Twitter accounts is a bot. Others will reply in the second person plural, suggesting that there’s a group of people behind one of the accounts. These accounts aren’t run by a bot or a committee, just me. I do use software to schedule my tweets […]

From The Book of Strange New Things: … I said that if science could come up with something like the Jump it could surely solve a problem like that. Severin seized hold of that word, “science.” Science, he said, is not some mysterious larger-than-life force, it’s just the name we give to bright ideas that […]

Last week I wrote a short commentary on James Hague’s blog post Organization skills beat algorithmic wizardry. This week that post got more traffic than my server could handle. I believe it struck a chord with experienced software developers who know that the challenges they face now are not like the challenges they prepared for in school. Although […]

If you’re new to this blog, welcome! Let me show you around. Here are some of the most popular posts on this site and some other things I’ve written. If you’d like to subscribe to this site you can do so by RSS or email. I also have a monthly newsletter. You can find out more about me and my background here. […]

Here’s an insightful paragraph from James Hague’s blog post Organization skills beat algorithmic wizardry: When it comes to writing code, the number one most important skill is how to keep a tangle of features from collapsing under the weight of its own complexity. I’ve worked on large telecommunications systems, console games, blogging software, a bunch […]

Artificial intelligence, or at least the perception of artificial intelligence, has gone from disappointing to frightening in the blink of an eye. As Marc Andreessen said on Twitter this morning: AI: From “It’s so horrible how little progress has been made” to “It’s so horrible how much progress has been made” in one step. When […]

Ursula K. Le Guin is asking people to not buy books from Amazon because they market bestsellers, the literary equivalent of junk food. She said last week I believe that reading only packaged microwavable fiction ruins the taste, destabilizes the moral blood pressure, and makes the mind obese. I agree with that. That’s why I shop […]

There is no logical difference between writing A = B and writing B = A, but there is a psychological difference. Equations are typically applied left to right. When you write A = B you imply that it may be useful to replace A with B. This is helpful to keep in mind when learning something […]

Haskell advocates are fond of saying that a Haskell function cannot launch missiles without you knowing it. Pure functions have no side effects, so they can only do what they purport to do. In a language that does not enforce functional purity, calling a function could have arbitrary side effects, including launching missiles. But this […]

This afternoon I got a review copy of the book Creating Symmetry: The Artful Mathematics of Wallpaper Patterns. Here’s a striking curves from near the beginning of the book, one that the author calls the “mystery curve.” The curve is the plot of exp(it) – exp(6it)/2 + i exp(-14it)/3 with t running from 0 to 2?. Here’s Python […]

You can subscribe to this blog using this RSS feed. If you would like to only subscribe to posts in certain categories, you can do so using the category-specific feeds below. Business Clinical trials Computing Creativity Graphics Machine learning Math Music Python Science Software development Statistics Typography Misc You can also subscribe to my Twitter […]

This post gives some notes on ways to create a Unix-like command line experience on Windows, without using a virtual machine like VMWare or a quasi-virtual machine like Cygwin. Finding Windows ports of Unix utilities is easy. The harder part is finding a shell that behaves as expected. (Of course “as expected” depends on your expectations!) There […]

Copyright © 2015 Regator, LLC