A Vertical Forest

Milan skyscrapers Bosco Verticale were named Best Tall Building Worldwide in 2015 by the Council on Tall Buildings and Urban Habitat, beating out 120 other contenders.

The two towers, 111 and 76 meters tall, are covered top to bottom with more than 900 trees, which attenuate noise, produce oxygen, and regulate temperature: During the summer, the leaves shade the apartments, and during the winter the leaves drop, allowing sunlight in. The building’s irrigation system directs water onto the porches to sustain the plants.

Each tree had to be pruned to fit within its balcony, a process that took two years. If all of them were transplated to the ground they’d make a forest of nearly two acres.

And “The Vertical Forest increases biodiversity,” architect Boeri Studio told Arch Daily. “It promotes the formation of an urban ecosystem where various plant types create a separate vertical environment, but which works within the existing network, able to be inhabited by birds and insects (with an initial estimate of 1,600 specimens of birds and butterflies). In this way, it constitutes a spontaneous factor for repopulating the city’s flora and fauna.”



“Once I saw a chimpanzee gaze at a particularly beautiful sunset for a full 15 minutes, watching the changing colors until it became so dark that he had to retire to the forest without stopping to pick a pawpaw for supper.” — Adriaan Kortlandt



In Rex Stout’s mystery novels, detective Nero Wolfe maintains that he was born in Montenegro, but the stories give conflicting evidence, and after careful study historian Bernard DeVoto concluded that he was really born in the United States sometime between 1892 and 1896, having been conceived in Montenegro between March 1891 and March 1895.

Now, Sherlock Holmes had his climactic battle with Professor Moriarty at the Reichenbach Fall at the beginning of May 1891, after which he disappeared into shadowy wanderings until 1894. Writer John D. Clark notes that Holmes could easily have visited Cetinje and remained there for several months, long enough to meet Irene Adler, whose fragile marriage would by then have broken up, sending her back to an itinerant life as an opera singer. The two would naturally have fallen in together, especially as English speakers were relatively rare in Montenegro, and an eventual affair was inevitable.

When Adler became pregnant she would have returned to her parents in New Jersey and given birth there. Nero Wolfe was born in New Jersey in late 1892 or early 1893, six months after Adler would had left Montenegro. She would then have returned to Central Europe, where her son grew up, just as he states. Clark concludes, “Whether Wolfe ever condescends to admit it, or whether he remains forever silent, his parentage can no longer be a matter of conjecture, nor can there be any doubt as to the source from which he inherited his remarkable talents.”

In 1955 Clark put this case to Stout, who responded with this note:

I am obliged to you for sending me the ms. for perusal, and I admire the finesse of your suggestion that ‘censorship’ by me might be desirable and acceptable. As the literary agent of [Wolfe’s assistant] Archie Goodwin I am of course privy to many details of Nero Wolfe’s past which to the general public, and even to scholars of Clark’s standing, must remain moot for some time. If and when it becomes permissible for me to disclose any of those details, your distinguished journal would be a most appropriate medium for the disclosure. The constraint of my loyalty to my client makes it impossible for me to say more now.

He never fully denied the theory. He died in 1975.

(John D. Clark, “Some Notes Relating to a Preliminary Investigation Into the Paternity of Nero Wolfe,” Baker Street Journal, January 1956.)

Four Play

It’s a popular recreation to try to arrange four 4s into various expressions to generate the whole numbers, like so:

1 = 4 ÷ 4 + 4 – 4
2 = 4 – (4 + 4) ÷ 4
3 = (4 × 4 – 4) ÷ 4
4 = 4 + 4 × (4 – 4)
5 = (4 × 4 + 4) ÷ 4

In 1881 a writer to the London journal Knowledge noted that each of the first 20 integers except 19 can be generated using the operations +, -, ×, and ÷. In 1964 Martin Gardner found that if you use square roots, decimals, factorials, concatenations (444), and overline (.444 …) then every positive integer less than 113 becomes possible. (113 is surprisingly hard; it becomes possible if you use percents or the gamma function.)

In 2001 a team of mathematicians from Harvey Mudd College found that you can even get four 4s to approximate some notable constants if you use a whip and a chair:

\displaystyle e \approx \left ( 4!! \right ) \sqrt[4!!]{\frac{\sqrt{4!!}}{4!!!}}

\displaystyle \pi \approx \sqrt{\sqrt{4!\cdot 4 + \sqrt{\sqrt{4\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{.4}}}}}}}}}} \approx 3.1415932

That expression for e is accurate to 21 decimal places; it can be made arbitrarily accurate by repeatedly replacing 4 with 4!. The authors note that similar expressions can be derived using three 3s or five 5s.

Amazingly, they also approximated g, the acceleration due to gravity, with four 4s, as well as Avogadro’s number NA.

(A. Bliss, S. Haas, J. Rouse and G. Thatte, “Math Bite: Four Constants in Four 4s,” Mathematics Magazine 74:4 [October 2001], 272.)

Some Enchanted Evening

In Southeast Asia, fireflies synchronize their flashing. Observing them in Siam in the 1920s, naturalist Hugh Smith wrote, “Imagine a tenth of a mile of river front with an unbroken line of [mangrove] trees with fireflies on every leaf flashing in synchronism. … Then, if one’s imagination is sufficiently vivid, he may form some conception of this amazing spectacle.”

The phenomenon was so unexpected that some initially dismissed the reports as an illusion; Phillip Laurent “could hardly believe [his] own eyes, for such a thing to occur among insects is certainly contrary to all natural laws.”

Each male fly’s flashes are initially sporadic, but they adjust their timing according to those around them until they’re synchronized. This helps identify them to females of their own species. Biologist John Buck observed, “Centers of synchrony built up slowly, two individuals often flashing independently for up to half a minute (about fifty cycles) before the flashes coincided. At this point their rhythms locked together and continued in synchrony thereafter.”

In 2015 Robin Meier and Andre Gwerder used LEDs to artificially direct the speed and rhythm of thousands of flashing fireflies (above), using this technique to “explore the idea of free will and transform a machine into a living actor inside a colony of insects.”

(Ying Zhou, Walter Gall, and Karen Nabb, “Synchronizing Fireflies,” College Mathematics Journal 37:3 [May 2006], 187-193.)

More Word Sums

Back in 2012 I mentioned that if A=1, B=2, C=3, etc., then ARM + BEND = ELBOW and KING + CHAIR = THRONE.

Peter Dawyndt of Ghent University challenged his students to come up with more, and they found these:

WHITE (65) + HOUSE (68) = GOVERNMENT (133)
PETER (64) + PAN (31) = NEVERLAND (95)
COMIC (43) + BOOK (43) = FANTASY (86)
ABSENT (61) + MINDED (49) = FORGETFUL (110)
BLOOD (48) + BATH (31) = MASSACRE (79)
DRUG (50) + ADDICT (41) = STONER (91)
MICRO (58) + SOFT (60) = COMPUTING (118)
RED (27) + BULL (47) = COCKTAIL (74)
EGG (19) + PLANT (63) = AUBERGINE (82)
CUSTARD (86) + CREAM (40) = BISCUITRY (126)
VISUAL (84) + BASIC (34) = MICROSOFT (118)
MONA (43) + LISA (41) = LEONARDO (84)
DOWN (56) + LOAD (32) = ITUNES (88)
BLACK (29) + JACK (25) = VEGAS (54)
SUN (54) + RISE (51) = HORIZON (105)
POLICE (60) + CAR (22) = PATROL (82)
CHURCH (61) + MAN (28) = RELIGION (89)
FAMILY (66) + TREE (48) = ANCESTORS (114)
HAND (27) + GUN (42) = MAGNUM (69)
RAIN (42) + BOW (40) = COLORS (82)
ANT (35) + LION (50) = DOODLEBUG (85)
BOTTOM (85) + LINE (40) = CONCLUSION (125)
BACK (17) + SLASH (59) = HYPHEN (76)
BILL (35) + FOLD (37) = MONEY (72)
URBAN (56) + LEGEND (47) = BULLSHIT (103)
CALL (28) + GIRL (46) = HARLOT (74)
STAR (58) + TREK (54) = VOYAGERS (112)

Names of famous people:

JOHN (47) + CLEESE (49) = HUMOUR (96)
TOM (48) + HANKS (53) = FORREST (101)
BOB (19) + MARLEY (74) = RASTAFARI (93)
KURT (70) + COBAIN (44) = NOVOSELIC (114)
EMMA (32) + WATSON (92) = VOLDEMORT (124)
JAMES (48) + BOND (35) = DANIEL (45) + CRAIG (38)
GEORGE (57) + LUCAS (56) = JAR (29) + JAR (29) + BINKS (55)
STEPHEN (87) + HAWKING (73) = TEXT (69) + TO (35) + SPEECH (56)
CLOCKWORK (111) + ORANGE (60) = STANLEY (96) + KUBRICK (75)

(Thanks, Peter.)

Swearing In

Houston attorney Robert Malinak sent this courtroom transcript to the Texas Bar Journal in 1999. He said it had been sent to him by “a credible New York lawyer”:

CLERK: Please repeat after me: “I swear by Almighty God.”

WITNESS: “I swear by Almighty God.”

CLERK: “That the evidence I give …”

WITNESS: That’s right.

CLERK: Repeat it.

WITNESS: “Repeat it.”

CLERK: No! Repeat what I said.

WITNESS: What you said when?

CLERK: “That the evidence that I give …”

WITNESS: “That the evidence that I give.”

CLERK: “Shall be the truth and …”

WITNESS: It will, and nothing but the truth!

CLERK: Please, just repeat after me: “Shall be the truth and …”

WITNESS: “Shall be the truth and.”

CLERK: Say: “Nothing …”

WITNESS: Okay. (remains silent)

CLERK: No! Don’t say nothing. Say: “Nothing but the truth …”


CLERK: Well? Do so.

WITNESS: You’re confusing me.

CLERK: Just say: “Nothing but the truth …”

WITNESS: Okay. I understand.

CLERK: Then say it.


CLERK: “Nothing but the truth …”

WITNESS: But I do! That’s just it.

CLERK: You must say: “Nothing but the truth …”

WITNESS: I WILL say nothing but the truth!

CLERK: Please, just repeat these four words: “Nothing” — “But” — “The” — “Truth.”

WITNESS: What? You mean, like, now?

CLERK: Yes! Now. Please. Just say those four words.

WITNESS: Nothing. But. The. Truth.

CLERK: Thank you.

WITNESS: I’m just not a scholar.