URL : | http://www.johndcook.com/blog/ | |
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Filed Under: | Academics | |

Posts on Regator: | 1133 | |

Posts / Week: | 4.9 | |

Archived Since: | April 26, 2011 |

John Tukey preferred the term “data analysis” over “statistics.” In his paper Data Anaysis, Computation and Mathematics, he explains why. My title speaks of “data analysis” not “statistics”, and of “computation” not “computing science”; it does not speak of “mathematics”, but only last. Show More Summary

There are huge opportunities to take technology that is well-known and undervalued in one context and apply it in another where it is unknown but valuable. You could call this technical arbitrage, analogous to financial arbitrage, taking advantage of the price difference of something in two markets. As with financial arbitrage, the hard part is […]

In the novel Enchantment, the main character, Ivan, gives a bitter assessment of his choice of an academic career, saying it was for “men who hadn’t yet grown up.” The life he had chosen was a cocoon. Surrounded by a web of old manuscripts and scholarly papers, he would achieve tenure, publish frequently, teach a group of […]

A function f is periodic if there exists a constant period ? such that f(x) = f(x + ?) for all x. For example, sine and cosine are periodic with period 2?. There’s only one way a function on the real line can be periodic. But if you think of functions of a complex variable, […]

This is a post about letting go of something you think you need. It starts with an illustration from programming, but it’s not about programming. Bob Martin published a dialog yesterday about the origin of structured programming, the idea that programs should not be written with goto statements but should use less powerful, more specialized […]

One of my clients is writing software in Julia so I’m picking up the language. I looked at Julia briefly when it first came out but haven’t used it for work. My memory of the language was that it was almost a dialect of Python. Now that I’m looking at it a little closer, I […]

This is reprint of Nick Higham’s post of the same title from the Princeton University Press blog, used with permission. Color is a fascinating subject. Important early contributions to our understanding of it came from physicists and mathematicians such as Newton, Young, Grassmann, Maxwell, and Helmholtz. Today, the science of color measurement and description is […]

It would be hard to think of two programming languages more dissimilar than Haskell and R. Haskell was designed to enforce programming discipline; R was designed for interactive use. Haskell emphasizes correctness; R emphasizes convenience. Show More Summary

The most direct way to compute a Fourier transform numerically takes O(n2) operations. The Fast Fourier Transform (FFT)can compute the same result in O(n log n) operations. If n is large, this can be a huge improvement. James Cooley and John Tukey (re)discovered the FFT in 1965. It was thought to be an original discovery at […]

Each Fibonacci number is the sum of its two predecessors. My previous post looked at generalizing this to the so-called Tribonacci numbers, each being the sum of its three predecessors. One could keep going, defining the Tetrabonacci numbers and in general the n-Fibonacci numbers for any n at least 2. For the definition to be complete, […]

Take an n × n matrix A and a vector x of length n. Now multiply x by A, then multiply the result by A, over and over again. The sequence of vectors generated by this process will converge to an eigenvector of A. (An eigenvector is a vector whose direction is unchanged when multiplied […]

I got a call this afternoon from someone who records audio books for the blind. He wanted to know the name of a symbol he didn’t recognize. He then asked me if the equation was real. Here’s the equation in context, from the book Michael Vey 4: Hunt for Jade Dragon. The context is as follows. Suddenly math […]

Yesterday on Twitter I said I was thinking about writing the names of each of my clients and leads on balls so I could literally juggle them. I was only half joking. I didn’t write my clients and leads on balls, but I did write them on index cards. And it helped a great deal. It’s […]

A while back I wrote about a method to test whether a number is divisible by seven. I recently ran across another method for testing divisibility by 7 in Martin Gardner’s book The Unexpected Hanging and Other Mathematical Diversions. The method doesn’t save too much effort compared to simply dividing by 7, but it’s interesting. It looks […]

The previous post stated a formula for f(n), the nth square triangular number (i.e. the nth triangular number that is also a square number): ((17 + 12?2)n + (17 – 12?2)n – 2)/32 Now 17 – 12?2 is 0.029… and so the term (17 – 12?2)n approaches zero very quickly as n increases. So the f(n) […]

Of course a triangle cannot be a square, but a triangular number can be a square number. A triangular number is the sum of the first so many positive integers. For example, 10 is a triangular number because it equals 1+2+3+4. These numbers are called triangle numbers because you can form a triangle by having a row of […]

In the preface to his book Strength of Materials, J. P. Den Hartog says After the alphabet and the tables of multiplication, nothing has proved quite so useful in my professional life as these six little expressions. The six expressions he refers to are nicknamed the vergeet-me-nietjes in Dutch, which translates to forget-me-nots in English. They are also known […]

You’ve probably heard someone ask someone else what books they would take to a deserted island. It’s usually implied that you’re bringing books for pleasure, not books that would help you survive on the island or leave it. People often answer the question with a list of their favorite books, perhaps skewed in favor of long […]

This afternoon I helped someone debug a financial spreadsheet. One of the reasons spreadsheets can be so frustrating to work with is that assumptions are hard to see. You have to click on cells one at a time to find formulas, then decode cell coordinates into their meanings. The root problem turned out to be […]

Earlier this week I had a chance to talk with Anthony Scopatz and Katy Huff about their new book, Effective Computation in Physics. JC: Thanks for giving me a copy of the book when we were at SciPy 2015. It’s a nice book. It’s about a lot more than computational physics. KH: Right. If you think of […]

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