One of a Kind,_Socotra_Island_(13510645265).jpg
Image: Wikimedia Commons

The Yemeni island Socotra, off the tip of the Horn of Africa in the Arabian Sea, is so isolated that nearly 700 of its species are found nowhere else on Earth. The island’s bitter aloe has valuable pharmaceutical and medicinal properties, and the red sap of Dracaena cinnabari, above, was once thought to be the blood of dragons.

And this is only what remains after two millennia of human settlement; the island once featured wetlands and pastures that were home to crocodiles and water buffaloes. Tanzanian zoologist Jonathan Kingdon says, “The animals and plants that remain represent a degraded fraction of what once existed.”

A Circle Theorem
Image: Wikimedia Commons

If two chords of a circle intersect in a particular angle at S, then the sum of the opposite arc lengths (say, AB + CD) remains the same regardless of the position of S within the circle.

(Nick Lord and David Wells, “A Circular Tour of Some Circle Theorems,” Mathematical Gazette 73:465 [1989], 188-191.)

What Needs More Words?

Ecologists often have to estimate the number of unseen species in an ecosystem: If I count x species of butterfly during my time on an island, how many species probably live there that I did not see? In 1975, Stanford statisticians Bradley Efron and Ronald Thisted applied the same question to the works of William Shakespeare: If we take the Bard’s existing works as a sample, what can we infer about the size of his total vocabulary?

Shakespeare’s known works comprise 884,647 words, which fall into 31,534 “types,” or distinguishable arrangements of letters. Efron and Thisted applied two approaches and found that they produced the same estimate: If a new cache of the playwright’s works were discovered today, equal in size to the old, it would likely contain about 11,460 new word types, with an expected error of less than 150.

So how many word types altogether did Shakespeare know? No upper bound is possible, but they established a lower bound of 35,000 beyond the 31,534 already used — in other words, to write the works that we know of, he likely used less than half his total vocabulary.

(Bradley Efron and Ronald Thisted, “Estimating the Number of Unseen Species: How Many Words Did Shakespeare Know?”, Biometrika 63:3 [1976], 435-447.) (Thanks, Brent.)

Mercury Pendulums

This is just a detail that I found interesting — early regulator clocks tended to slow down as their pendulums lengthened in warm conditions. One solution, offered by George Graham in 1721, was to attach two vials of mercury to the pendulum — as the pendulum warmed and expanded, so did the mercury, creeping upward in its vials and, at least in theory, preserving the pendulum’s center of mass.

One difficulty is that the mercury tends to warm more slowly than the pendulum itself, but the system worked well enough to persist into the 20th century.

All Together Now
Image: Wikimedia Commons

A neat astronomy fact: At the equinox, the sun rises due east and sets due west at every latitude on Earth (except at the poles, where east and west are undefined).

The celestial equator is the great circle writ on the sky above our own equator. For any point on Earth (except the poles), due east and due west mark the intersection of that circle with the horizon. At the equinox the sun is on the celestial equator, so it rises due east and sets due west, not just on our equator but everywhere.

(Thanks, Sanford.)

Sums and Sums

lee sallows self-descriptive magic square

Something new from Lee Sallows: a self-descriptive magic square. Each row, column, and long diagonal adds up to 20, and every letter used is correctly counted.

“You may notice that the square includes a fox. But don’t be foxed by the fox. Just enjoy him. For this is not merely any old fox. No, it is our old friend the quick brown fox that jumped over that lazy dog!”

(Thanks, Lee!)

Image: Wikimedia Commons

The Asian moth Macrocilix maia carries a stunning image on its wings.

“It’s the only mimic insect I know that paints an entire scene,” writes entomologist Alex Wild. “It looks like a watercolor. Two red-eyed muscomorph flies feed from fresh bird droppings, complete with light glinting off their wings. I’ve never seen anything like it!”

Very little seems to be known about it. It’s found in India, Japan, Taiwan, Korea, China, Malaysia, Sumatra, and Borneo.

“The Trembling Giant”

The heaviest known organism is a clonal stand of quaking aspen in the Fishlake National Forest of south-central Utah. Connected by an enormous underground root system, it occupies 43 hectares and is estimated to weigh 6,000 metric tons.

The root system is also among the oldest living organisms, with an estimated age of 80,000 years.

A New Worry

In 1984 University of Pennsylvania psychiatrist Jordan Smoller called attention to an alarming syndrome that hadn’t received much clinical attention: childhood. Features:

  1. Congenital onset
  2. Dwarfism
  3. Emotional lability and immaturity
  4. Knowledge deficits
  5. Legume anorexia

Billy J., age 8, was brought to treatment by his parents. Billy’s affliction was painfully obvious. He stood only 4’3″ high and weighed a scant 70 pounds, despite the fact that he ate voraciously. Billy presented a variety of troubling symptoms. His voice was noticeably high for a man. He displayed legume anorexia and, according to his parents, often refused to bathe. His intellectual functioning was also below normal — he had little general knowledge and could barely write a structured sentence. Social skills were also deficient. He often spoke inappropriately and exhibited ‘whining behavior.’ His sexual experience was non-existent. Indeed, Billy considered women ‘icky.’

Most children are unemployed and poorly educated, and the condition appears to run in families. Public schools don’t seem to reduce the number of victims, but a longitudinal study suggests that it tends to abate with time. “Clearly, much more research is needed before we can give any real hope to the millions of victims wracked by this insidious disorder.”

(Jordan W. Smoller, “The Etiology and Treatment of Childhood,” Journal of Polymorphous Perversity, 1984, 3-7.)