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Blog Profile / The Endeavour

Filed Under:Academics
Posts on Regator:1000
Posts / Week:5.4
Archived Since:April 26, 2011

Blog Post Archive


Roughly speaking, an ergodic system is one that mixes well. You get the same result whether you average its values over time or over space. This morning I ran across the etymology of the word: In the late 1800s, the physicist Ludwig Boltzmann needed a word to express the idea that if you took an […]

Miscellaneous math notes

This web site started as static HTML files. Later I added a WordPress blog, but still wrote some things as static HTML pages for various reasons. Now I’ve moved most of those static pages to WordPress pages so that they’ll have the same style as the blog. There’s not a good way to find these […]

Googol and googolplex

Numericon gives the history of the words googol and googolplex: … the famous googol, 10100 (a 1 followed by 100 zeros), defined in 1929 by American mathematician Edward Kasner and named by his nine-year-old nephew, Milton Sirotta. Milton went even further and came up with the googolplex, now defined as 10googol but initially defined by […]

Four brief reviews

Princeton University Press and No Starch Press both sent me a couple books this week. Here are a few brief words about each. The first from Princeton was The Best Writing on Mathematics 2014. My favorite chapters were The Beauty of Bounded Gaps by Jordan Ellenberg and The Lesson of Grace in Teaching by Francis Su. […]

New business cards

Here’s my new business card. Front: Back: Designed by my friend Scott Bronstad. Scott also designed the new look of the web site. (If something doesn’t look quite right, that’s probably my doing.)

Uniformitarian or Paretoist

A uniformitarian view is that everything is equally important. For example, there are 118 elements in the periodic table, so all 118 are equally important to know about. The Pareto principle would say that importance is usually very unevenly distributed. The universe is essentially hydrogen and helium, with a few other elements sprinkled in. From […]

Cyclic fractions

Somewhere along the way you may have noticed that the digits in the decimal expansion of multiples of 1/7 are all rotations of the same digits: 1/7 = 0.142857142857… 2/7 = 0.285714285714… 3/7 = 0.428571428571… 4/7 = 0.571428571428… 5/7 = 0.714285714285… 6/7 = 0.857142857142… We can make the pattern more clear by vertically aligning the […]

“Hello world” is the hard part

Kernighan and Ritchie’s classic book The C Programming Language began with a sample C program that printed “hello world.” Since then “hello world” has come describe the first program you write with any technology, even if it doesn’t literally print “hello world.” Hello-world programs are often intimidating. People think “I must be a dufus because […]

Help wanted

I’m looking for people to help with some miscellaneous tasks. I don’t expect one person to do everything, but if you’re excellent at any of the following and interested in small projects please let me know. CSS / responsive design WordPress customization Emacs customization Advanced LaTeX Data cleaning and visualization Python (miscellaneous automation scripts) I […]

People want Swiss Army Knives

I ran across this graphic this morning on Twitter: Obviously the intended message is that scalpels are better than Swiss Army Knives. Certainly the scalpel looks simpler. But most people would rather have a Swiss Army Knife than a scalpel. Many people, myself included, own a Swiss Army Knife but not a scalpel. (I also […]

Blog changes coming

I’m in the process of redesigning my blog and web site. Some things will move around, but nothing is going away. In particular, the URL may take you to the new home page rather than the latest blog post, at least temporarily. If you subscribe via email or RSS posts will come to you […]

Blue Bonnet Bayes

Blue Bonnet™ used to run commercials with the jingle “Everything’s better with Blue Bonnet on it.” Maybe they still do. Perhaps in reaction to knee-jerk antipathy toward Bayesian methods, some statisticians have adopted knee-jerk enthusiasm for Bayesian methods. Everything’s better with Bayesian analysis on it. Bayes makes it better, like a little dab of margarine […]

How well does sample range estimate range?

I’ve been doing some work with Focused Objective lately, and today the following question came up in our discussion. If you’re sampling from a uniform distribution, how many samples do you need before your sample range has an even chance of covering 90% of the population range? This is a variation on a problem I’ve […]

Integration trick

Here’s a clever example from Paul Nahin’s new book Inside Interesting Integrals. Suppose you want to evaluate Since the range of integration is symmetric around zero, you might think to see whether the integrand is an odd function, in which case the integral would be zero. (More on such symmetry tricks here.) Unfortunately, the integrand […]

Experts vs Professionals

Working with professionals can be a joy. Not only can they solve your problem, they may help you see what problem you should solve. I’ve had several instances lately when I hired a pro to do something I’d attempted myself. In each case I was very pleased and wondered why I hadn’t done this sooner. […]

What do you mean by can’t?

You can’t subtract 4 from 3 (and stay inside the natural numbers, but you can inside the integers) You can’t divide 3 by 4 (inside the ring of integers, but you can inside its field of fractions, the rational numbers). You can’t take the square root of a negative number (in the real numbers, but […]

Optimism can be discouraging

Here’s an internal dialog I’ve had several times. “What will happen when you’re done with this project?” “I don’t know. Maybe not much. Maybe great things.” “How great? What’s the best outcome you could reasonably expect?” “Hmm …  Not that great. Maybe I should be doing something else.” It’s a little paradoxical to think that […]

Titles better than their books

What got you here won’t get you there. I’ve been thinking about that title lately. Some things that used to be the best use of my time no longer are. I bought Marshall Goldsmith’s book by that title shortly after it came out in 2007. As much as I liked the title, I was disappointed […]

Public reaction to Ebola

Ebola elicits two kinds of reactions in the US. Some think we are in imminent danger of an Ebola epidemic. Others think Ebola poses absolutely zero danger and that those who think otherwise are kooks. Nothing can be discussed rationally. Even narrow scientific questions lead to emotionally-charged political arguments. Those who have a different opinion […]

John Napier

2 months agoAcademics : The Endeavour

Julian Havil has written a new book John Napier: Life, Logarithms, and Legacy. I haven’t read more than the introduction yet — a review copy arrived just yesterday — but I imagine it’s good judging by who wrote it. Havil’s book Gamma is my favorite popular math book. (Maybe I should say “semi-popular.” Havil’s books […]

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