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Copyright 2003, all rights reserved

Tree ghosts, twin chicks, “dull” number

Q: My family and I were camping in Shawnee National Forest in Illinois. My brother, hunting firewood, knocked down a dead tree teeming with ants. That night, the wood glowed in the dark. In the day, the moist wood appeared white but, at night, it glowed neon green — clearly visible 40 feet away in the pitch black dark. Did chemicals from the ants cause the glow? — Dave, Indianapolis, Indiana

Honey mushroom fungi glow in the dark [Tom Volk, University of Wisconsin - La Crosse]

A: Chemicals, yes, but not from the ants. You saw a fungus, called foxfire, glow a cold chemical fire, like a firefly’s light. The fungus’ body grows inside the wood and eats it.

Foxfire rots wood by digesting it and extracting nutrients. That's why we often see mushrooms in or near dead trees. The mushroom is the fruit. The feeding body grows in the wood and the surrounding soil. Foxfire glows and thereby makes the inside of a rotting tree glow.

We don’t know why fungi glow. Perhaps to release excess energy or waste products.

"Foxfire may be any of several fungi, but, almost always, it’s the honey mushroom (Armillaria mellea) and related species," says Tom Volk, biology professor at the University of Wisconsin - La Crosse. This honey-colored mushroom is common all over the United States and found on every continent but Antarctica.

The best time to see foxfire (and it is a treat) is in late summer or fall.

Further Surfing:

University of Wisconsin - La Crosse: Tom Volk’s fungi

WonderQuest: How fireflies glow

Q: Have two chickens ever hatched from one egg? You know, like twins. — Jennifer, Houston Texas

Twin chicks usually hatch from double-yolk eggs but can occur from a single yolk. [Corel]

A: Yes but rarely. The two chicks are always tiny and usually hatch from a double yolk egg. Often only one embryo survives and sometimes neither does. The egg isn’t big enough to house two normal-size chicks so often one dies.

Ordinarily they aren’t identical twins but fraternal. "A double yolker forms when one egg follows another down the shoot a little too closely and they both get wrapped in the same shell," says Liz Armstrong of the Classroom @ the Coop.

Further Surfing

Texas A & M University: Poultry Q&A

Q: What is the smallest "dull" number? J. R., New Jersey

An Indian stamp issued in 1962 to commemorate the 75th anniversary of Ramanujan's birth. [India Postage]

A: It's early in the afternoon of a pleasant fall day.  The phone rings.  It's J. Richard Gott, Princeton astrophysicist.

"I’ve got a question for you," he says. "What is the smallest "dull" number?"

"A smallest dull number?" My voice rises, wondering what in the world...

Gott relates an incident. In 1917, a mathematical genius, Ramanujan, lay ill in a London hospital. His friend, G.H. Hardy, came to visit. Hardy remarked that his taxi number (1729) was dull.

"No," Ramanujan replied, "it’s an interesting number; it is the smallest number expressible as the sum of two cubes in two different ways."

1729 =   1³ +12³   =   9³ +10³

Zounds! I thought.  To be able to recognize such a fact upon hearing the number.

Gott’s reaction, however, was to wonder what is a dull number.

And he had an answer to his own question:  A number is dull if no one uses it. Earlier he had checked Google, repeatedly. What’s the smallest number with no hits on the Internet?

Eventually, he got close. The number 13,965,320 returned only a single hit. The next number returned no hits. He gave me the number; it is:

13,965,320 + 1.
I'm expressing it this way so Google won't find it, because of me.

That’s his answer. Can anyone find a smaller one?  Or, comments?

Further Surfing:

University of St Andrews, Scotland: Srinivasa Aiyangar Ramanujan

(Answered Oct. 17, 2003)