Sandbox

Forsooth

COLONEL [Buzz] 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.)

in: Remarks by the President signing an Executive Order on the National Space Council
Office of the White House Press Secretary, 30 June 2017.

Suggested by Mike Olinick

Quotations

“We know that people tend to overestimate the frequency of well-publicized, spectacular events compared with more commonplace ones; this is a well-understood phenomenon in the literature of risk assessment and leads to the truism that when statistics plays folklore, folklore always wins in a rout.”

-- Donald Kennedy (former president of Stanford University), Academic Duty, Harvard University Press, 1997, p.17

In progress

Statistical errors are often not due to mathematical errors
by Brian Zaharatos, letter to the editor, Chronicle of Higher Education, 11 July 2017

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Jeff Sessions used our research to claim that sanctuary cities have more crime. He’s wrong.
by Loren Collingwood and Benjamin Gonzalez-O'Brien, Washington Post, "Monkey Cage" blog, 14 July 2017

Sally Hernandez says cities labeled as sanctuaries have less crime, according to FBI statistics
by W. Gardner Selby, Politifact, 10 May 2017

Half-True Hernandez "FBI crime statistics have found that labeled ‘sanctuary’ cities experience lower rates of all crime types, including homicides."

— Sally Hernandez on Tuesday, April 18th, 2017 in an oped commentary co-authored by four other Texas sheriffs Sally Hernandez says cities labeled as sanctuaries have less crime, according to FBI statistics

Tests for gerrymandering

Partisan gerrymandering has benefited the GOP, analysis shows
NBCnews.com, 25 June 2017

After the 2010 election, the Republican-controlled Congress had control over redistricting. NBC reports on a statistical analysis by the Associated Press showing the effect in subsequent elections and the state and national levels. For example, in the 2016 election, they estimate that Republicans won 22 more seats in the US House of Representatives than they would have been obtained under their proportional share of the vote. The AP website reports that Texas had the largest gain, nearly 4 extra seats.

Gerrymandering is of course nothing new. The Texas reference brought to mind a famous description, retold in a 2002 story from the Economist (How to rig an election, 25 April 2002), "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."

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."

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

Chance of gun death

http://www.nytimes.com/2015/12/05/upshot/in-other-countries-youre-as-likely-to-be-killed-by-a-falling-object-as-a-gun.html?rref=upshot&module=Ribbon&version=context&region=Header&action=click&contentCollection=The%20Upshot&pgtype=Multimedia

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

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