Archive for the ‘Random Math Things’ Category:
iPhone 2.0, Numeracy 0.0
Even though I don’t have an iPhone and I can’t upgrade my iPod Touch’s firmware yet, I’ve been poking around the new iPhone app store to see what apps are in store for iPhone app store users. One of the first things I found, thanks to the alphabetical ordering of apps, is ACTGratuity from Houdah Software. It’s a $0.99 app that basically calculates the tip for you.
Before we lament how people can’t do a simple “what’s 20% of x” calculation in their heads, let me remind you that the iPhone comes with a nice, built-in calculator software. In fact, one of the nice things about iPhone 2.0 is the fact that its calculator has improved! So, basically, this is a one-dollar piece of software that, according to the company, “minimized the number of taps” because it “calculates as you type”. Sure, there is some value there. If you were going to use the iPhone to calculate a tip, five taps is probably better than ten. The scary fact, though, is that there are probably people who need it. What are we doing wrong? What can we do to fix this? Can we blame Bush and No Child Left Behind? Blah blah blah. Insert standard “our kids don’t know math” cried here.
Their other iPhone product, ACTCurrency, which does currency conversion, is a much better reason for automation. However, there are plenty of free alternatives to that on the iPhone store but thanks to the app store’s sorting algorithm they appear much later on the page.
One final iPhone-numeracy-related thing: before ACTGratuity comes the app Abacus. There’s just something very, very wrong with the fact that you can turn your iPhone into an abacus for merely 99 cents. What’s next? iPhone sand that you can do geometry on?
Subscribe to the comments for this postEpsilon Red Riding Hood
From 101 Analysis Bedtime Stories, a wonderful paper on, well, 101 analysis bedtime stories, comes the tale of Epsilon Red Riding Hood. So little, it’s hard to quantify her!
Check out the other 100 stories too. Some of them are real (ha, real, get it?) kickers.
Nature Where There was None
This fractal food web site has been floating around for a while. Other food and plant-related fractal pictures aren’t hard to find either. But more recently, there are some “fractal food” web sites that reverse-engineer fractal structures into food. There’s the “fractal pizza”, which seems to be a recursive layering of pizza upon pizza. And then there’s Sierpinski cookies, which is a bunch of cookies that form estimations of the Sierpinski carpet.
Is it just me or does it feel very unnatural to put fractal structures and patterns into foods that didn’t contain them to begin with? Bonus question: would this be a good excuse to bake cookies instead of having class one of these days?
Hot Girl Graph Theory
Via Reddit, here is a video segment of some Japanese people testing an algorithm for finding the most attractive female in Italy. They first find a random woman on the street and ask her to introduce them to her most attractive female friend. Then they ask said friend to introduce them to her most attractive female friend. And so on. I’m not clear when this algorithm terminates because I don’t know Japanese.
Even if women can be put into an objective total order this is a horrible algorithm. It’s very easy to see that it doesn’t always reach the maximal element in an arbitrary set of women. (Quick counterexample: start with the third most attractive woman, who know the second and fourth most attractive women; the second most attractive woman does not, however, know the most attractive one. Quicker counterexample: a disconnected set where the most attractive woman has no friends.) And you’re not guareenteed to “go up the ladder” at every step, since the most attractive woman than a woman knows may be herself! In fact, because of this, this algorithm never terminates and goes into an infinite loop even if it finds the most attractive woman in a set.
And besides, even if you find her, hot girl probability theory dictates that she’s already taken.
Concerning SquarO
Through a link on Reddit I found a game called SquarO. The game gives you a square grid with numbers in each square. The number tells you how many black vertices the square has. The goal of the game is to color in the vertices/lattice-points of the grid so that each square has the correct number of black vertices. It’s like a reverse Minesweeper. The “official rules” are here.
The rules page says that each of the grids in the game has a unique solution. This is obviously not true for any randomly generated grid with arbituary numbers placed in the squares. For a grid with multiple solutions, just place a 1 in all the squares. For a grid with no solutions, put a 1 in every square except for one, and put a 0 in that square. Since the game has hundreds of different puzzles I’d assume that they have a way of checking whether a grid has a unique solution. It could just be a brute force algorithm; the game doesn’t seem to generate these grids on-the-fly as they are numbered, so whoever designed the grids don’t have to check for a unique solution very quickly.
Calculus Based Web Host
I came back home from the Western Mass Sacred Harp Convention (possibly more on that later) to discover that this blog was completely down. Turns out my web host got its power shut off intentionally and unexpectedly; as you can probably see they just brought everything back up running.
Before they died, though, I actually wanted to post about their new pricing scheme. Before, they charged $1 for every GB of bandwidth used. Now, the more bandwidth is used the less they charge per GB. More precisely, the price per GB is based on a logarithmic scale. Even more precisely,
Numbers and Multiplication (Chinese Edition)
Via God Plays Dice, an article from The New Yorker talks about how people remember and use numbers. The bit that I find most interesting is on the last page.
Because Chinese number words are so brief—they take less than a quarter of a second to say, on average, compared with a third of a second for English—the average Chinese speaker has a memory span of nine digits, versus seven digits for English speakers. (Speakers of the marvellously efficient Cantonese dialect, common in Hong Kong, can juggle ten digits in active memory.)
What the author neglect to mention is that in Chinese, not only are number words shorter, but they have the same number of syllables. That is the most important thing to me when memorizing digits. It is awkward saying “seven” next to “four” and “nine”. In Mandarin Chinese, and even moreso in Cantonese, all the number words are exactly one-syllable. This creates a nice one-to-one correspondence between syllables and digits.
Three Games Involving Numbers
So here are a few games involving numbers. Not exactly “edutainment”—though one of the games claims it is—but plenty of entertainment in the form of fast clicking, brain teasing and lots of number crunching in very fun ways. Best of all, they’re all free!
Frankly, the mathematical content in these games amount to arithmetic and counting. However, TwoThree, the third game, actually poses two interesting (though elementary) number theory questions: can all positive integers other than 1 be expressed as the sum of 2s and 3s, and how do you do so with the fewest number of 2s and 3s?
An Expected Exponential Model
Short post: here’s a nice little article from Nick Confalone on Popeye’s chicken dipping sauces. It seems that the amount of dipping sauce that you can request for free is an exponential function of the amount of chicken strips you buy. You can bankrupt Popeye’s by getting enough chicken strips so that they have to give you, say, 2 to the 100 packets of sauce!
Tomorrow is Dance Flurry, so I will go pack now.
Amazon Text Statistics
So I knew for a long time that Amazon.com tells you various aweome statistics about books like the sales rank and page count. Pretty awesome. But I just found our today that Amazon also offers an incomplete concordance and some detailed text statistics for some books. It lists the 100 most frequently used words in the book along with some indices on how hard the book is. My favorite is the average syllable per word. They also have fun facts like words you buy per dollar and words per ounce of the book’s weight.
As to the book, I just finished “reading” (I read most of it but skimmed several bits) it. More thoughts later.