Swedish botanist Elias Tillander (1640–1693) was so “harassed by Neptune” during a trip across the Gulf of Bothnia from Stockholm to Turku that he made the return journey overland and changed his name to Til-Landz (“to land”).
Linnaeus named the evergreen plant Tillandsia after him — it cannot tolerate a damp climate.
(From Wilfrid Blunt, Linnaeus: The Compleat Naturalist, 2001.)
From Lee Sallows:
(Thanks, Lee!)
In the 1967 Star Trek episode “The Trouble With Tribbles,” a small furry alien species is introduced on board the Enterprise and after three days grows to 1,771,561 individuals. In 2019 University of Leicester physics undergraduate Rosie Hodnett and her colleagues wondered how long it would take for the creatures to fill the whole starship. Using Mr. Spock’s estimate that each tribble produces 10 offspring every 12 hours and assuming that each tribble occupies 3.23 × 10-3 m3 and that the volume of the Enterprise is 5.94 × 106 m3, they found that the ship would reach its limit of 18.4 × 109 tribbles in 4.5 days.
A separate inquiry found that after 5.16 days the accumulated tribbles would be generating enough thermal energy to power the warp drive for 1 second.
(Rosie Hodnett et al., “Tribbling Times,” Journal of Physics Special Topics, Nov. 18, 2019.)
From reader Chris Smith:
Pick a three-digit number in which all the digits are different. Example: 314.
Now list every possible combination of two digits from the chosen number. In our example, these are 13, 14, 31, 34, 41, and 43.
Divide the sum of these two-digit numbers by the sum of the three digits in the original number, and you’ll always get 22. In our example, (13 + 14 + 31 + 34 + 41 + 43) / (3 + 1 + 4) = 176/8 = 22.
This works because 10a + b, 10a + c, 10b + a, 10b + c, 10c + a, and 10c + b sum to 22a + 22b + 22c = 22(a + b + c), so dividing by a + b + c will always give 22.
(Thanks, Chris.)
06/08/2024 Reader Tom Race points out that essentially the same trick can be performed using the entire number: If you add all six permutations of the original 3 digits, then divide that total by the sum of the 3 digits, the answer is always 222.
For example, using 561:
561 + 516 + 156 + 165 + 651 + 615 = 2664
5 + 6 + 1 = 12
2664 / 12 = 222
“This works because in the first sum each of the three digits (a, b and c) occurs twice in each of the three columns, so the sum is 222a + 222b + 222c = 222(a + b + c).” (Thanks, Tom.)
The upside-down catfish, Synodontis nigriventris, is right side up. Or, rather, it’s adapted to spend most of its time upside down — its belly is darker than its back, and it swims fastest in this inverted position. The behavior may have evolved to help it reach food on the undersides of submerged branches or to breathe dissolved oxygen near the surface.
Here’s a surprise: The Book of Knowledge of Ingenious Mechanical Devices, a 1206 manuscript by the Turkish author Ismail al-Jazari, depicts a chain pump in the form of a Möbius strip. A rope bearing a chain of cups dips them successively into a water source at the bottom and then pours them into a course at the top. The single, continuous rope makes two passes through this route, describing the edges of a strip with a half twist so that the cups suspended between the loops are turned 180 degrees with each pass. This would permit the cups to last longer, since they’re worn more evenly, and even a broken cup might still convey some water with every second pass.
(Julyan H.E. Cartwright and Diego L. González, “Mobius Strips Before Mobius: Topological Hints in Ancient Representations,” Mathematical Intelligencer 38:2 [June 2016], 69-76.)
Albert Einstein used to say that he went to his office at the Institute for Advanced Study “just to have the privilege of walking home with Kurt Gödel.” The two would meet at Einstein’s home each day between 10 and 11 and undertake the half-hour walk to the institute. At 1 or 2 in the afternoon they’d walk back, discussing politics, philosophy, and physics. Biographer Palle Yourgrau estimates that these walks consumed 30 percent of Einstein’s workday.
Einstein’s secretary, Helen Dukas, wrote in 1946, “I know of one occasion when a car hit a tree after its driver suddenly recognized the face of the beautiful old man walking along the street.”
Gödel caused no such problems. “I have so far not found my ‘fame’ burdensome in any way,” he wrote to his mother. “That begins only when one becomes so famous that one is known to every child in the street, as is the case of Einstein.”
(From A World Without Time: The Forgotten Legacy of Godel and Einstein, 2009.)
On each of these two black lines is a trio of red points marked by the same distances.
The midpoints of segments drawn between corresponding points are collinear.
(Discovered by Danish mathematician Johannes Hjelmslev.)
(Thanks, Colin and Joseph.)
A letter from Lewis Carroll to Nature, March 31, 1887:
Having hit upon the following method of mentally computing the day of the week for any given date, I send it you in the hope that it may interest some of your readers. I am not a rapid computer myself, and as I find my average time for doing any such question is about 20 seconds, I have little doubt that a rapid computer would not need 15.
Take the given date in 4 portions, viz. the number of centuries, the number of years over, the month, the day of the month.
Compute the following 4 items, adding each, when found, to the total of the previous items. When an item or total exceeds 7, divide by 7, and keep the remainder only.
The Century-Item. — For Old Style (which ended September 2, 1752) subtract from 18. For New Style (which began September 14) divide by 4, take overplus from 3, multiply remainder by 2. [The Century-Item is the first two digits of the year, so for 1811 take 18.]
The Year-Item. — Add together the number of dozens, the overplus, and the number of 4’s in the overplus.
The Month-Item. — If it begins or ends with a vowel, subtract the number, denoting its place in the year, from 10. This, plus its number of days, gives the item for the following month. The item for January is ‘0’; for February or March (the 3rd month), ‘3’; for December (the 12th month), ’12.’ [So, for clarity, the required final numbers after division by 7 are January, 0; February, 3; March, 3; April, 6; May, 1; June, 4; July, 6; August 2; September, 5; October, 0; November, 3; and December, 5.]
The Day-Item is the day of the month.
The total, thus reached, must be corrected, by deducting ‘1’ (first adding 7, if the total be ‘0’), if the date be January or February in a Leap Year: remembering that every year, divisible by 4, is a Leap Year, excepting only the century-years, in New Style, when the number of centuries is not so divisible (e.g. 1800).
The final result gives the day of the week, ‘0’ meaning Sunday, ‘1’ Monday, and so on.
Examples
1783, September 18
17, divided by 4, leaves ‘1’ over; 1 from 3 gives ‘2’; twice 2 is ‘4.’
83 is 6 dozen and 11, giving 17; plus 2 gives 19, i.e. (dividing by 7) ‘5.’ Total 9, i.e. ‘2.’
The item for August is ‘8 from 10,’ i.e. ‘2’; so, for September, it is ‘2 plus 3,’ i.e. ‘5.’ Total 7, i.e. ‘0,’ which goes out.
18 gives ‘4.’ Answer, ‘Thursday.’
1676, February 23
16 from 18 gives ‘2.’
76 is 6 dozen and 4, giving 10; plus 1 gives 11, i.e. ‘4.’ Total ‘6.’
The item for February is ‘3.’ Total 9, i.e. ‘2.’
23 gives ‘2.’ Total ‘4.’
Correction for Leap Year gives ‘3.’ Answer, ‘Wednesday.’
(Via Edward Wakeling, Rediscovered Lewis Carroll Puzzles, 1995.)
