Sandbox
Forsooth
COLONEL ALDRIN: Infinity and beyond. (Laughter.)
THE PRESIDENT: This is infinity here. It could be infinity. We don’t really don’t know. But it could be. It has to be something -- but it could be infinity, right?
Okay. (Applause.)
Office of the White House Press Secretary, 30 June 2017.
Suggested by Mike Olinick
Quotations
In progress
Tests for gerrymandering
Let math save our democracy
by Sam Wang, New York Times, 5 December 2015
How gerrymandered is your Congressional district?
by Christopher Ingraham, Washington Post,15 May 2014
appeal to isoperimetric inequality: in the plane, a circle maximizes the area of a closed curve with a fixed perimeter.
How to rig an election
Economist, 25 April 2002
Subtitled: "In a normal democracy, voters choose their representatives. In America, it is rapidly becoming the other way around."
"Worst of all is the state's extraordinary 17th District, which is a crab (see chart). Though most of it lies in the western part of the state, two claws stretch out towards the eastern part to grab Democratic cities in order to make the surrounding 18th and 19th districts more reliably Republican."
"as used to be said of the old Texas 6th (which was a road from Houston to Dallas), that you could kill most of the constituents by driving down the road with the car doors open."
Diet science
Are fats unhealthy? The battle over dietary guidelines
by Aaron E. Carroll, “Upshot” blog, New York Times, 12 October 2015.
Related “Upshot”: Behind new dietary guidelines, better science, February 23, 2015
"Random" seat assignment
Ryanair's 'random' seat allocation not random - scientists
by John von Radowitz, Irish Independent, 30 June 2017
Ryanair is an Irish low-cost airline. This Wikipedia entry notes that they have often faced criticism for misleading advertising.
The Irish Independent article concerns a recent controversy. When customers book Ryanair flights, they can pay to select for particular seats, or else opt for "random" seat assignment, which is free. Advertising on the airline's website says, "Can't stand the middle seat? Don't leave it to chance, take your pick from a choice of seats. Get up to 50pc off reserved seats with prices starting at £2."
But is it up to chance? In light of customer complaints, the BBC consumer affairs show Watchdog sought expert opinion from Oxford University. To test the claim, researchers had four groups of four passengers book travel on four separate flights, all under the random seating option. On every flight, all of the passengers got middle seats. The the odds of this happening were estimated at about 1:540,000,000. Compare this to the 1:45,000,000 odds of winning the UK National Lottery jackpot. Dr. Jennifer Rogers, director of Oxford University's Statistical Consultancy, is quoted as saying, "This is a highly controversial topic and my analysis cast doubt on whether Ryanair's seat allocation can be purely random."
The article also includes a statement from Ryanair offering the following explanation which qualifies as an extended Forsooth!
We haven't changed the random seat allocation policy.
The reason for more middle seats being allocated is that more and more passengers are taking our reserved seats (from just £2) and these passengers overwhelmingly prefer aisle and window seats which is why people who choose random (free of charge) seats are more likely to be allocated middle seats.
Some random seat passengers are confused by the appearance of empty seats beside them when they check-in up to four days prior to departure.
The reason they can't have these window or aisle seats is that these are more likely to be selected by reserved seat passengers, many of whom only check in 24 hours prior to departure.
Since our current load factor is 95pc, we have to keep these window and aisle seats free to facilitate those customers who are willing to pay (from £2) for them.
Submitted by Patrick O'Beirne
Chance of gun death
Some math doodles
<math>P \left({A_1 \cup A_2}\right) = P\left({A_1}\right) + P\left({A_2}\right) -P \left({A_1 \cap A_2}\right)</math>
<math>P(E) = {n \choose k} p^k (1-p)^{ n-k}</math>
<math>\hat{p}(H|H)</math>
<math>\hat{p}(H|HH)</math>
Accidental insights
My collective understanding of Power Laws would fit beneath the shallow end of the long tail. Curiosity, however, easily fills the fat end. I long have been intrigued by the concept and the surprisingly common appearance of power laws in varied natural, social and organizational dynamics. But, am I just seeing a statistical novelty or is there meaning and utility in Power Law relationships? Here’s a case in point.
While carrying a pair of 10 lb. hand weights one, by chance, slipped from my grasp and fell onto a piece of ceramic tile I had left on the carpeted floor. The fractured tile was inconsequential, meant for the trash.
As I stared, slightly annoyed, at the mess, a favorite maxim of the Greek philosopher, Epictetus, came to mind: “On the occasion of every accident that befalls you, turn to yourself and ask what power you have to put it to use.” Could this array of large and small polygons form a Power Law? With curiosity piqued, I collected all the fragments and measured the area of each piece.
| Piece | Sq. Inches | % of Total |
|---|---|---|
| 1 | 43.25 | 31.9% |
| 2 | 35.25 | 26.0% |
| 3 | 23.25 | 17.2% |
| 4 | 14.10 | 10.4% |
| 5 | 7.10 | 5.2% |
| 6 | 4.70 | 3.5% |
| 7 | 3.60 | 2.7% |
| 8 | 3.03 | 2.2% |
| 9 | 0.66 | 0.5% |
| 10 | 0.61 | 0.5% |
The data and plot look like a Power Law distribution. The first plot is an exponential fit of percent total area. The second plot is same data on a log normal format. Clue: Ok, data fits a straight line. I found myself again in the shallow end of the knowledge curve. Does the data reflect a Power Law or something else, and if it does what does it reflect? What insights can I gain from this accident? Favorite maxims of Epictetus and Pasteur echoed in my head: “On the occasion of every accident that befalls you, remember to turn to yourself and inquire what power you have to turn it to use” and “Chance favors only the prepared mind.”
My “prepared” mind searched for answers, leading me down varied learning paths. Tapping the power of networks, I dropped a note to Chance News editor Bill Peterson. His quick web search surfaced a story from Nature News on research by Hans Herrmann, et. al. Shattered eggs reveal secrets of explosions. As described there, researchers have found power-law relationships for the fragments produced by shattering a pane of glass or breaking a solid object, such as a stone. Seems there is a science underpinning how things break and explode; potentially useful in Forensic reconstructions. Bill also provided a link to a vignette from CRAN describing a maximum likelihood procedure for fitting a Power Law relationship. I am now learning my way through that.
Submitted by William Montante