Nearly everyone in Whittier, Alaska, lives under the same roof. The 14-story Begich Towers was built after World War II, and the building was converted to a condominium when the military withdrew. About 200 people live in 150 two- and three-bedroom apartments, and they can go weeks without leaving the building, which contains a post office, a grocery, a medical clinic, the mayor’s office, a general store, the police department, a Methodist church, a laundry, a small hotel, a conference room, and a play area with an indoor pool. A tunnel system leads to the community school and a general store.
By most accounts, life in the tower is pretty agreeable. But “because we have four elevators, sometimes people pull pranks on you and hit every button,” resident June Miller told CBC News. “And it’s like, ‘Really? This again?'”
Australia’s Westfield ultramarathon had a surprise entrant in 1983: A 61-year-old potato farmer named Cliff Young joined a field of elite professional runners for the 500-mile race from Sydney to Melbourne. In this week’s episode of the Futility Closet podcast we’ll describe Young’s fortunes in the race and the heart, tenacity, and humor that endeared him to a nation.
We’ll also learn the difference between no and nay and puzzle over a Japanese baby shortage.
Please consider becoming a patron of Futility Closet — on our Patreon page you can pledge any amount per episode, and we’ve set up some rewards to help thank you for your support. You can also make a one-time donation on the Support Us page of the Futility Closet website.
Many thanks to Doug Ross for the music in this episode.
“People will tell you that science, philosophy, and religion have nowadays all come together. So they have in a sense … they have come together as three people may come together at a funeral. The funeral is that of Dead Certainty.” — Stephen Leacock
A Mrs. Harris published this verse in Golden Days on Oct. 10, 1885:
He squanders recklessly his cash
In cultivating a mustache;
A shameless fop is Mr. Dude,
Vain, shallow, fond of being viewed.
‘Tis true that he is quite a swell —
A smile he has for every belle;
What time he has to spare from dress
Is taken up with foolishness —
A witless youth, whose feeble brain
Incites him oft to chew his cane.
Leave dudes alone, nor ape their ways,
Male readers of these Golden Days.
It reads so naturally that it’s surprising to find that it contains a double acrostic: Taking the fourth letter of each line spells out QUANTITATIVE, and taking the last letter spells out HEEDLESSNESS.
David Hagen offered this puzzle in MIT Technology Review in 2007. The MIT logo can be thought of as a slider puzzle. In the figure above, can you slide the tiles about so that the gray I can escape through the opening at top left?
Review reader Brad Edelman offered this solution. First number the tiles 0 to 6, left to right, with pieces in the same column numbered in sequence from top to bottom. Now:
2 – down, down
4 – down
6 – right
3 – down, right, down, down
1 – right, right
2 – up, up, left
4 – left, down
3 – left
1 – down, right, down
2 – right, right
4 – up, up
3 – left
2 – down
5 – left
6 – up
1 – right
2 – right
3 – right
4 – right
0 – right, right, down, down
5 – left, left, left, down, down
4 – up, left, left, left, up
The original puzzle was posed in the November/December 2007 issue; the solution was presented two issues later.
At the time, readers made some interactive tools, in Word and Flash, to aid in the solving, but those don’t seem to be available any longer. If anyone knows of any, please let me know and I’ll add a link here.
The Ironman Heavymetalweight wrestling championship operates under 24/7 rules, meaning that the titleholder must defend it at all times against all comers. This has bred some chaos, with the belt changing hands more than 1,170 times. English wrestler Laura James won the belt in June and lost it the same day to her cat, Bunny (above). Other notable winners:
a miniature Dachshund
a Hello Kitty doll
a baseball bat
three different ladders
a chicken doll
a ringside mat
a pint of beer
a steel chair
two inflatable love dolls
Vince McMahon’s star on the Hollywood Walk of Fame
an “invisible wrestler”
three elementary school girls
the entire audience of Beyond Wrestling’s Americanrana ’16
Heroically, the belt itself became the 1,000th champion. Sanshiro Takagi, the 999th titleholder, was attempting to retire when Poison Sawada knocked him out with the belt, which fell on his chest, “pinning” him. The referee counted him out.
Here’s a triangle, ABC, and an arbitrary point, D, in its interior. How can we prove that AD + DB < AC + CB?
The fact seems obvious, but when the problem is presented on its own, outside of a textbook or some course of study, we have no hint as to what technique to use to prove it. Construct an equation? Apply the Pythagorean theorem?
“The issue is more serious than it first appears,” write Zbigniew Michalewicz and David B. Fogel in How to Solve It (2000). “We have given this very problem to many people, including undergraduate and graduate students, and even full professors in mathematics, engineering, or computer science. Fewer than five percent of them solved this problem within an hour, many of them required several hours, and we witnessed some failures as well.”
Here’s a dismaying hint: Michalewicz and Fogel found the problem in a math text for fifth graders in the United States. What’s the answer?
Is it unjust to adopt a constitution that binds both ourselves and future members of our society? We need a set of fundamental laws to regulate ourselves, but is it fair to extend that to future citizens? Shouldn’t they have the right to choose their own rules?
Thomas Jefferson thought so. In a 1789 letter to James Madison, he held that “the earth belongs in usufruct to the living”: He thought a constitution (or any law) should expire automatically when succeeding generations make up a majority of the population. “The constitution and the laws of their predecessors extinguished … in their natural course with those who gave them being,” he wrote. “This could preserve that being till it ceased to be itself, and no longer. … If it be enforced longer, it is an act of force, and not of right.”
There’s a tension here: In order for a constitution to be successful, it has to define the organization of its society and the freedoms of its citizens, and these rules need to remain in effect for at least several generations in order to produce a healthy liberal democracy. “But those born under a perpetual constitution are expected to acquiesce to the foundational norms approved by their predecessors with neither their consent nor their participation,” writes McGill University political philosopher Víctor M. Muñiz-Fraticelli. “If a constitution is discussed, negotiated, and approved by citizens who are, necessarily, contemporaries, what normatively binding force does it retain for future generations who took no part in its discussion, negotiation, or approval?”
(Víctor M. Muñiz-Fraticelli, “The Problem of a Perpetual Constitution,” in Axel Gosseries and Lukas H. Meyer, eds., Intergenerational Justice, 2009.)
This square of 8 × 8 = 64 square units can apparently be reassembled into a rectangle of 5 × 13 = 65 square units:
This paradox is described in W.W. Rouse Ball’s 1892 Mathematical Recreations and Essays; it seems to have been published first in 1868 in Zeitschrift für Mathematik und Physik.
In 1938 the Rockefeller Foundation’s Warren Weaver discovered an old trove of papers from the 1890s in which Lewis Carroll puzzled out the dimensions of all possible squares in which this illusion is possible (the other sizes include squares of 21 and 55 units on a side).
Regardless of publication, it’s not clear who first came up with the idea. Sam Loyd claimed to have presented it to the American Chess Congress in 1858. That would be interesting, as it was his son who later discovered that the four pieces can be assembled into a figure of 63 squares:
(Warren Weaver, “Lewis Carroll and a Geometrical Paradox,” American Mathematical Monthly 45:4 [April 1938], 234-236.)