Castaway Depots

Following a series of shipwrecks in the 19th century, the government of New Zealand began to establish huts on remote subantarctic islands for the use of castaways, who otherwise might die of starvation or exposure.

The depots were stocked with firewood, rations, clothing, hunting and fishing equipment, medicine, and matches. Some included boat sheds, and steamers visited each island twice a year. To discourage opportunistic thieves, the government posted warnings on the provisions; one read, “The curse of the widow and fatherless light upon the man that breaks open this box, whilst he has a ship at his back.”

The project was discontinued after about 1927 as radio technology improved and the old clipper route fell out of use, but the depots were proving their value as late as 1908, when 22 crewmembers from the French barque President Félix Faure were shipwrecked in the Antipodes Islands. A depot there helped to sustain them until they could signal a passing warship.


“It has always puzzled me that so many religious people have taken it for granted that God favors those who believe in him. Isn’t it possible that the actual God is a scientific God who has little patience with beliefs founded on faith rather than evidence?” — Raymond Smullyan

Image: Flickr

The Cook pine, Araucaria columnaris, leans toward the equator. In 2017 botanist Matt Ritter of California Polytechnic State University noticed that pines growing in California and Hawaii leaned south; he called a colleague in Australia, who reported that the trees there leaned north.

“We got holy-smoked that there’s possibly a tree that’s leaning toward the equator wherever it grows,” Ritter told Nature.

In both hemispheres, the trees lean more sharply the farther they are from the equator. The average incline is 8 degrees, but one tree in South Australia leans 40 degrees.

The reason isn’t clear; it “may be related to an adaptive tropic response to the incidence angles of annual sunlight, gravity, magnetism, or any combination of these,” the authors write. But “It’s a shockingly distinct pattern,” Ritter said.

See Beef Tack.

(Jason W. Johns et al., “Worldwide Hemisphere-Dependent Lean in Cook Pines,” Ecology 98:9 [2017], 2482-2484.)

Take 5

An interesting problem from Crux Mathematicorum, March 2004: The increasing sequence 1, 5, 6, 25, 26, 30, 31, 125, 126, … consists of positive integers that can be formed by adding distinct powers of 5. That is, 1 = 50, 5 = 51, 6 = 50 + 51, and so on. What’s the 75th integer in this sequence?

Click for Answer

Active and Passive

[The British pub] is the only kind of public building used by large numbers of ordinary people where their thoughts and actions are not being in some way arranged for them; in the other kinds of public building they are the audiences, watchers of political, religious, dramatic, cinematic, instructional or athletic spectacles. But within the four walls of the pub, once a man has bought or been bought his glass of beer, he has entered an environment in which he is a participator rather than a spectator.

— Tom Harrisson, The Pub and the People, 1943

Podcast Episode 286: If Day

In 1942, Manitoba chose a startling way to promote the sale of war bonds — it staged a Nazi invasion of Winnipeg. For one gripping day, soldiers captured the city, arrested its leaders, and oppressed its citizens. In this week’s episode of the Futility Closet podcast we’ll describe If Day, which one observer called “the biggest and most important publicity stunt” in Winnipeg’s history.

We’ll also consider some forged wine and puzzle over some unnoticed car options.

See full show notes …

So There

Exploring the caves above the 53-meter statue of Gautama Buddha in the Bamyan valley of Afghanistan in the 1930s, a French archaeological delegation found this message scrawled on a wall:

If any fool this high samootch explore
Know Charles Masson has been here before.

Estimating Payments

In 1996 Peyman Milanfar, a reader of Mathematics Magazine, presented a quick way to estimate monthly payments on a loan, passed down from his grandfather, who had been a merchant in 19-century Iran:

\displaystyle \textup{Monthly payment} = \frac{1}{\textup{Number of months}} (\textup{Principal} + \textup{Interest})

The interest is calculated as

\displaystyle \textup{Interest} = \frac{1}{2} \textup{Principal} \times \textup{Number of years} \times \textup{Annual interest rate}.

The exact formula given in finance textbooks is

\displaystyle C = \frac{r(1 + r)^{N}P}{(1 + r)^{N} - 1},

where C is the monthly payment, r is the monthly interest rate (1/12 the annual interest rate), N is the total number of months, and P is the principal. Rendered in that notation, the folk formula becomes

\displaystyle C_{f} = \frac{1}{N} \left ( P + \frac{1}{2}PNr \right ).

“In many cases, Cf is a surprisingly good approximation to C,” particularly when the principal is fixed, the monthly interest rate is sufficiently low, and the total number of months is sufficiently high, Milanfar writes. For example, for a four-year loan of $10,000 at an annual rate of 7% compounded monthly, the precise formula gives a monthly payment of $239.46, while the folk formula gives $237.50.

“While its origins remain a mystery, the method is still in use among merchants all around Iran, and perhaps elsewhere.”

(Peyman Milanfar, “A Persian Folk Method of Figuring Interest,” Mathematics Magazine 69:5 [1996], 376.)

The Tonal System

In 1859, far ahead of its application in computing, engineer John W. Nystrom proposed that we adopt base 16 for arithmetic, timekeeping, weights and measures, coinage, and even music.

“It is evident that 12 is a better number than 10 or 100 as a base, but it admits of only one more binary division than 10, and would, therefore, not come up to the general requirement,” he wrote. “The number 16 admits binary division to an infinite extent, and would, therefore, be the most suitable number as a base for arithmetic, weight, measure, and coins.”

He named the 16 digits an, de, ti, go, su, by, ra, me, ni, ko, hu, vy, la, po, fy, and ton, and invented new numerals for the upper values. Numbers above this range would be named using these roots, so 17 in decimal would be tonan (“16 plus 1”) in Nystrom’s system. And he devised some wonderfully euphonious names for the higher powers:

Base 16 Number Tonal Name Base 10 Equivalent
10 ton 16
100 san 256
1000 mill 4,096
1,0000 bong 65,536
10,0000 tonbong 1,048,576
100,0000 sanbong 16,777,216
1000,0000 millbong 268,435,456
1,0000,0000 tam 4,294,967,296
1,0000,0000,0000 song 1612
1,0000,0000,0000,0000 tran 1616
1,0000,0000,0000,0000,0000 bongtran 1620

So the hexadecimal number 1510,0000 would be mill-susanton-bong.

The system was never widely adopted, but Nystrom was confident in its rationality. “I know I have nature on my side,” he wrote. “If I do not succeed to impress upon you its utility and great importance to mankind, it will reflect that much less credit upon our generation, upon scientific men and philosophers.”

His book is here.