# Tag Archives: mathematics

# Basic Combinatorics

Because sometimes you need to count particular kinds of things.

- TopCoder post
- a small book: Basic Combinatorics
- Khan Academy

# Why Learn Math

From at least one, if not many more, perspective, I’m an old man, a somewhat established scholar. What could be more bizarre than wanting to quit everything else and spend six months learning all the math you wish you already knew? Apparently, I am not alone. Warren Henning, a software engineer, is doing much the same, and he explains his motives as follows in an essay on [Medium][]:

> To me, math is raw, untapped power. Statistics is helpful in computer programming, period. My dream is to learn the statistics, probability, and linear algebra needed to really understand machine learning and computer vision, which has had a major spurt of activity in the past 5–7 years. To realize this goal, I need a solid foundation so that I can truly understand what’s going on: why something works, when it won’t work, and what to do differently if it doesn’t.

[Medium]: https://medium.com/@warrenhenning/a-software-engineers-adventures-in-learning-mathematics-62140c59e5c

# Compound Interest

I gather that Al Bartlett is something of an internet legend when it comes to getting people to think about the power of *rates of change*, be it doubling, exponential, or compound interest. I wish the video was a little shorter. I’d like to share it with Lily.

# Winning at Monopoly with Math

I am a complete fool for articles like _Business Insider_’s [“How To Use Math To Crush Your Friends At Monopoly Like You’ve Never Done Before”][bi]. I like that the math involved can range from the simple — how the distribution of dice rolls affects where most people will land, given a particular starting point — to the complex. If the slide decks length puts you off — there’s sixty plus slides in there!, you can always scroll to the end and read the half dozen concluding slides that tell you what you should do. But, really, the fun is in the careful working through of the numbers.

[bi]: http://www.businessinsider.com/math-monopoly-statistics-2013-6

# Bezier Curves

As Father’s Day approaches, I found myself remembering all the time I spent in my own father’s office, playing with the various bits of office material as he tried to get work done. My father was an architect, and one place to park me was in front of the typewriter which was in the reception area and not in the immediate space where he worked, bent over a drafting table. I don’t know how many pages of his stationary I burned through writing various bits of nonsense, but maybe that love of typing, the sense of committing words to a page in a way that seemed more important than writing them by hand, was one of the things that later drove me to write. (In the same way that some painters say they paint because they love the smell of the paint itself.)

Sometimes, though, I would wander into his work space and play with the various tree stamps on pieces of tracing paper, or, perhaps best of all, I would get to handle the various hand tools which seemed to hold almost mystical power. Things like slide rules or scales. Or there was the entire collection of outlines of furniture in various scales that were in sheets of cut out plastic. Among those objects was a plastic curve maker:

Forgive the Amazon link: it was the best example of the exact thing I used to play with. In fact, I can remember my father letting me have it, and I took it home and drew my own version of a sports car, in profile, carefully considering the appropriate placement of the curves to be included. Later, when I started experimenting with drawing programs, I re-discovered the joy of curves, which I learned had a more interesting name, [Bezier curves][], named after the French engineer who used them to model, believe, curves on cars at Renault.

And now I find myself re-immersed in the world of math, not only because I find it fascinating and a possible research path for myself but also because I have a daughter who has a talent for math and I want to encourage it. I can only do that if I know enough to be useful to her. And so I start collecting links like this [Reddit thread][] on cure simulations. Check out these [animated Bezier curves][], for example, or this [Bezier curve simulation][].

Why should you care about Bezier curves?

[Bezier curves]: http://en.wikipedia.org/wiki/Bézier_curve

[Reddit thread]: http://www.reddit.com/r/InternetIsBeautiful/comments/27bsdl/curve_simulation/

[animated bezier curves]: http://www.jasondavies.com/animated-bezier/

[Bezier curve simulation]: http://tholman.com/bezier-curve-simulation/

# Sperner’s Lemma

# -1/12

I stopped listening to RadioLab after a while … it had, to my mind, jumped the shark, or, in public radio terms, gone the way of Ira Glass and become a show infatuated with the sound of its own voice. E.g., the show where Jad spends the entire time telling us breathlessly about the music album that has him just astounded, astounded, every time he listens to it. Good for you, Jad. Some of us listen to you for the science. (The corollary of this is the Malcolm Gladwell effect where the reporter begins to believe that they are scientists and start making shit up and thinking it’s science. It’s not science, no matter how popular you are. Science doesn’t work that way.)

Anyway, RadioLab appears to have righted itself … and I’ve come to think that maybe the real core of the show, and the reporter whom I trust in all of this is Robert Krulwich. [Krulwich maintains his own blog on the NPR website][kw], and it’s worth checking it now and then — and, if you don’t, but you read Reddit, don’t worry because his posts regularly turn up there.

In a [recent post][] he points to a video that reveals the math behind the fact that *the sum of all natural numbers is -1/12*. There’s more in the video, which is embedded in the post, and you really should check out Krulwich for yourself.

[kw]: http://www.npr.org/blogs/krulwich/

[recent post]: http://www.npr.org/blogs/krulwich/2014/01/21/263455905/treat-yourself-to-a-huh

# Monday Morning Links

I am reviving a blogging tradition because some days you just have lots of tabs open in your browser and it’s all interesting. Sometimes those links get shot out as individual dishes — and there are plenty of blogs that really make that their business (no names here, but you’ve encountered it) — and sometimes you get served a buffet:

* [TYWKIWDBI][] (pronunciation is provided) notes that “A graph of 40 years of data from the U.S. Census Bureau, shows that fewer American households are comprised of married couples with children. Now there are more men and women living alone, and other “nontraditional” arrangements. … As more Americans are opting to live alone than ever before, that now seems like an entirely unremarkable choice. But for years we’ve been building houses for that big nuclear family that’s now less common. And housing data released earlier this summer by the Census Bureau, illustrated at right, suggests that the U.S. is now a country where many people live alone in a land of 3-bedroom houses.” The two graphs accompanying the post are worth viewing.

* [Space.com][] reports that the evidence for **water on mars** is pretty overwhelming. There’s a slideshow available for those, like me, who enjoy space porn. *Water! Mars! Let’s go!*

* [The Octomatics Project][] argues that a number system based on 8 or 12 makes more sense — and those interested in the dozenal system (useful when you are trying to discuss time with a fourth grader!) should know that there is a [Dozenal Society of American][] (really, not making that up, but I would if I were writing a novel about maths at war … say, maybe I will!). I especially like the graphic that advances a numerical notation that “looks more technical”:

[TYWKIWDBI]: http://tywkiwdbi.blogspot.com/2013/09/changing-household-demographics.html

[Space.com]: http://www.space.com/22854-mars-water-curiosity-rover-discoveries.html

[The Octomatics Project]: http://www.octomatics.org

[Dozenal Society of American]: http://www.dozenal.org/drupal/

# Mathematical Drawings

# Boolean Operations

For anyone who uses the internet, Boolean operations are part of our everyday existence: they are, by default, at work in all of your searches. And because they are latent and not manifest and you don’t know you are using them, the search engines are using them in a way that gives you the most results for your search, leaving the sorting and evaluating of results to you. In most cases, that means you scan through pages of search results in search of results worth your time, OR, you only look at the first one or two pages of not-very-useful results and reinforce the business plans of hundreds of businesses built around expiating search engine results. (The made search engine optimization an acronym [SEO] for a reason: it’s done so often.)

But what if Boolean operators were more easily understood? Andy Finnell wrote about Boolean operators in terms of graphics, but his graphical illustrators actually make Boolean operations more understandable to a larger audience.

*Note: I have reproduced Finnell’s table here, and re-used his graphics, so as not to add undue traffic to his website. The graphics below are his originals. I hope in time to expand this post a bit and to re-do the graphics to make them more in keeping with gray-ness of this site.*

(None.) | |

Union (logical “or”) | |

Intersection (logical “and”) | |

Difference | |

Join (Exclusive “or”: written “EOR”) |

# What Tau Sounds Like

There is a movement, somewhere out there, to replace pi, the number that results from dividing the circumference of a circle by its diameter, with tau, the number that results from dividing the circumference of a circle by its radius. The argument goes that radii actually describe circles better than diameters. There is more at stake, and certainly more at stake than the simple doubling of pi, but with today being tau day, I am delighted to link to the work of Michael Blake, a musician who has turned tau’s infinitely long string of numbers into some amazing music:

# Kill Math

Bret Victor has a terrific essay, and series of simulations, that make the case for how we should change math education to take advantage of the strengths of the computer to address our own strengths as human beings. Read the essay to see how he transforms a decent mathematical question into an absolutely compelling mathematical exploration. Read it.