[A]ccording to the standard traditions, being in hell is the worst thing that could ever happen to anyone. As with less horrendous evils, the first question is how such an evil is, or could be, justified. The theological portrayals of hell make this question the most difficult for the theist to address. Ordinary pain and evil, it may be thought, can be accounted for if events in the future ‘make up for’ what leads to them, but the evil of hell leads nowhere; at no point in the future will something of value make up for the evil of hell or will some reward be granted to those who endure the suffering of hell. Hell is apparently paradigmatic as an example of truly pointless, gratuitous evil. Thus arises the problem of hell.

— Jonathan L. Kvanvig, The Problem of Hell, 1993

The Hawking Index

In a 2014 blog post for the Wall Street Journal, mathematician Jordan Ellenberg examined the distribution of highlighted passages within Amazon Kindle books as an unscientific measure of how far the average reader progresses through each title before giving up. If the “popular highlights” are clustered densely near the start of a book, that’s (arguably) a sign that many readers abandon the book before reading much farther. Ellenberg gave these examples (each considering the location of the five most highlighted passages in the text):

Hard Choices, by Hillary Clinton, 1.9%
Capital in the Twenty-First Century, by Thomas Piketty, 2.4%
Infinite Jest, by David Foster Wallace, 6.4%
A Brief History of Time, by Stephen Hawking, 6.6%
Thinking, Fast and Slow, by Daniel Kahneman, 6.8%
Lean In, by Sheryl Sandberg, 12.3%
Flash Boys, by Michael Lewis, 21.7%
Fifty Shades of Grey, by E.L. James, 25.9%
The Great Gatsby, by F. Scott Fitzgerald, 28.3%
Catching Fire, by Suzanne Collins, 43.4%
The Goldfinch, by Donna Tartt, 98.5%

Ellenberg called the measure the Hawking Index, after physicist Stephen Hawking’s A Brief History of Time, which is often called “the most unread book of all time” … though it reaches only fourth place even on this short list.

“So take it easy on yourself, readers, if you don’t finish whatever edifying tome you picked out for vacation,” he wrote. “You’re far from alone.”

A Packing Problem

You need to pack for a midnight flight and the power is out. Your closet contains six pairs of shoes, six black socks, six gray socks, six pairs of brown gloves, and six pairs of tan gloves, but it’s too dark to distinguish colors or to match shoes. How many of each item must you take to be sure of having a matched pair of shoes, two socks of the same color, and a pair of matching gloves?

Click for Answer

Podcast Episode 339: The Baron of Arizona


In 1883, Missouri real estate broker James Reavis announced that he held title to a huge tract of land in the Arizona Territory. If certified, the claim would threaten the livelihoods of thousands of residents. In this week’s episode of the Futility Closet podcast we’ll tell the story of the Baron of Arizona, one of the most audacious frauds in American history.

We’ll also scrutinize British statues and puzzle over some curious floor numbers.

See full show notes …

Brave New World


In 1921 Charles Steinmetz, “the electrical wizard of Schenectady,” described the conveniences of 2021:

When heating is all done electrically, and I want 70 degrees in my home, I shall set the thermostat at 70 and the temperature will not rise above that point. This temperature will be maintained uniformly regardless of the weather outside.

This will also hold true on the warm day when the temperature outside may be 90 or 100 degrees. The same electrical apparatus will cool the air, and what’s more it will also keep the humidity normal at all times.

“Look back 100 years and it is like jumping into the Dark Ages,” he wrote. “The electrical development is still in its infancy.”

(Via Reddit’s ArchivePorn.)


Image: Wikimedia Commons

This cottage, at 112 Mercer Street in Princeton, New Jersey, has been home to three Nobel winners: Albert Einstein lived there from 1935 to 1955; physicist Frank Wilczek between 1989 and 2001; and economist Eric Maskin until 2012.

It resides on the National Register of Historic Places and has been designated a U.S. National Historic Landmark, but it bears no outward marker of its significance.

The Basket Tree

Image: Flickr

In the 1940s, arborsculptor Axel Erlandson planted six sycamore trees in a circle and grafted them as they grew to form a “woven” unit with diamond interstices.

It’s now the centerpiece of California’s Gilroy Gardens.

Egg Hunt

A puzzle by Tim C., an applied research mathematician at the National Security Agency, from the agency’s January 2017 Puzzle Periodical:

Alice has a dozen cartons, arranged in a 3×4 grid, which for convenience we have labeled A through L:


She has randomly chosen two of the cartons and hidden an Easter egg inside each of them, leaving the remaining ten cartons empty. She gives the dozen cartons to Bob, who opens them in the order A, B, C, D, E, F, G, H, I, J, K, L until he finds one of the Easter eggs, whereupon he stops. The number of cartons that he opens is his score. Alice then reseals the cartons, keeping the eggs where they are, and presents the cartons to Chris, who opens the cartons in the order A, E, I, B, F, J, C, G, K, D, H, L, again stopping as soon as one of the Easter eggs is found, and scoring the number of opened cartons. Whoever scores lower wins the game; if they score the same then it’s a tie.

For example, suppose Alice hides the Easter eggs in cartons H and K. Then Bob will stop after reaching the egg in carton H and will score 8, while Chris will stop after reaching the egg in carton K and will score 9. So Bob wins in this case.

Who is more likely to win this game, Bob or Chris? Or are they equally likely to win?

Click for Answer

A Look Ahead

In The Art of Computer Programming, Donald Knuth notes an interesting pattern in the common units of liquid measure in 13th-century England:

2 gills = 1 chopin
2 chopins = 1 pint
2 pints = 1 quart
2 quarts = 1 pottle
2 pottles = 1 gallon
2 gallons = 1 peck
2 pecks = 1 demibushel
2 demibushels = 1 bushel or firkin
2 firkins = 1 kilderkin
2 kilderkins = 1 barrel
2 barrels = 1 hogshead
2 hogsheads = 1 pipe
2 pipes = 1 tun

“Quantities of liquid expressed in gallons, pottles, quarts, pints, etc. were essentially written in binary notation,” Knuth writes. “Perhaps the true inventors of binary arithmetic were British wine merchants!”

(Thanks, Colin.)