In January 2004 Greg Clark was making a supply run from his home on Kosciusko Island in southeastern Alaska when he radioed that his boat had lost power. With him was his constant companion, Brick, an 8-year-old Labrador retriever. After a three-day search, the Coast Guard found part of the boat’s stern on rocks on the west side of the island, which lies within the 17-million-acre Tongass National Forest.
More than a month afterward, two local fishermen were motoring past Heceta Island, several miles from the accident, when they saw a black animal on the beach. They recognized Brick, who swam to the boat and was hauled aboard. He was underweight, his leg was injured, and his fur was matted with tree sap, but he was “wiggling with joy,” according to CBS News. How the dog had stayed alive for four weeks in the harsh Alaskan winter is unknown.
Simonides, that extraordinary author of lyric poems, found an excellent remedy for his straitened circumstances by travelling around the most famous cities of the Asia, singing the praises of victorious athletes in exchange for a fee. When he had grown wealthy in this venture, he was ready to take a sea voyage and go back to his native land (he was born, so they say, on the island of Ceos). He boarded a ship, but a terrible storm (plus the sheer age of the ship) caused it to sink in the middle of the sea. Some of the passengers grabbed their money belts, while others held onto their valuables and any possible means of subsistence. A passenger who was more curious than the rest asked the poet, ‘Simonides, why aren’t you taking along any of your own stuff?’ He replied, ‘All that is mine is right here with me.’ It turned out that only a few were able to swim ashore, while the majority drowned, weighed down by what they were carrying. Then bandits arrived and took from the survivors whatever they had brought ashore, stripping them naked. As it happened, the ancient city of Clazomenae was not far off, which is where the shipwrecked people then turned. In this city there lived a man inclined to literary pursuits who had often read Simonides’s compositions and who was his great admirer from afar. He recognized Simonides simply from his manner of speaking and eagerly invited him to his house, regaling him with clothes and money and servants. Meanwhile, the rest of the survivors carried around placards, begging for food. When Simonides happened to run into them, he took one look and exclaimed, ‘Just as I said: all that is mine is right here with me, but everything that you took with you has now vanished.’
In 1863, on the first day of the Battle of Gettysburg, a 69-year-old shoemaker took down his ancient musket and set out to shoot some rebels. In this week’s episode of the Futility Closet podcast we’ll follow John Burns’ adventures in that historic battle, which made him famous across the nation and won the praise of Abraham Lincoln.
We’ll also survey some wallabies and puzzle over some underlined 7s.
John T. Trowbridge, “The Field of Gettysburg,” Atlantic Monthly 16:97 (November 1865), 616-624.
A writer to the Civil War Times asks whether the man seated farthest left at this Gettysburg field hospital might be Burns (click to enlarge). “Burns favored that style of top hat, and they have the same jug ears and long noses. They also seem to wear similar scowls, but nowadays so do I, at least when I can’t get enough Advil.” More here.
A quickie from Raymond Smullyan: On the Island of Knights and Knaves, knights always tell the truth and knaves always lie. Every inhabitant is either a knight or a knave. One day a visiting anthropologist comes across a native and recalls that his name is either Paul or Saul, but he can’t remember which. He asks him his name, and the native replies “Saul.”
From this we can’t know whether the native is a knight or a knave, but we can tell with high probability. How?
An urn contains k black balls and one red ball. Peter and Paula are going to take turns drawing balls from the urn (without replacement), and whoever draws the red ball wins. Peter offers Paula the option to draw first. Should she take it? There seem to be arguments either way. If she draws first she might get the red ball straightaway, and it seems a shame to give up that opportunity. On the other hand, if she doesn’t succeed immediately then she’s only increased Peter’s chances of drawing the red ball himself. What should she do?
Imagine that Peter and Paula simply take turns drawing balls, without bothering to inspect their color, until the urn is exhausted. Then afterward they look to see who has the red ball. The winner in this procedure will always be the same as in the original, so each player’s chance of winning will be the same as in the original game.
If k is odd, then the total number of balls is even, and when the urn is empty each player will have the same number of balls, so each of them has a 1/2 chance of winning. But when k is even, then the total number of balls is odd, and the player who draws first will have an extra ball when the drawing is done. So, generally, Paula should accept Peter’s offer to draw first — it may help her, and at worst it leaves her chances unchanged.
(From Wolfgang Schwarz, 40 Puzzles and Problems in Probability and Mathematical Statistics, 2008.)
This can be seen as describing itself: It might denote the length of the string of identical digits at this point in the sequence. Well, in that case, if the length of this run is only one digit, then the next digit in the sequence can’t be another 1. So write 2:
Seen in the same light, the 2 would indicate that this second run of digits has length 2. So add a second 2 to the list to fulfill that description:
1 2 2
We can continue in this way, adding 1s and 2s so that the sequence becomes a recipe for writing itself:
This is a fractal, a mathematical object that encodes its own representation. It was described by William Kolakoski in 1965, and before him by Rufus Oldenburger in 1939. University of Evansville mathematician Clark Kimberling is offering a reward of $200 for the solution to five problems associated with the sequence:
Is there a formula for the nth term?
If a string occurs in the sequence, must it occur again?
If a string occurs, must its reversal also occur?
If a string occurs, and all its 1s and 2s are swapped, must the new string occur?
Does the limiting frequency of 1s exist, and is it 1/2?
Three meters wide, Frederic Edwin Church’s 1859 painting The Heart of the Andes was the IMAX feature of its day: On its debut in New York, 12,000 people waited in line for hours to pay 25 cents for a look at the canvas, which was displayed between theatrical curtains. One witness wrote, “Women felt faint. Both men and women succumb[ed] to the dizzying combination of terror and vertigo that they recognize[d] as the sublime. Many of them will later describe a sensation of becoming immersed in, or absorbed by, this painting, whose dimensions, presentation, and subject matter speak of the divine power of nature.” Mark Twain raved to his brother:
I have just returned from a visit to the most wonderfully beautiful painting which this city has ever seen — Church’s ‘Heart of the Andes’ … I have seen it several times, but it is always a new picture — totally new — you seem to see nothing the second time which you saw the first. We took the opera glass, and examined its beauties minutely, for the naked eye cannot discern the little wayside flowers, and soft shadows and patches of sunshine, and half-hidden bunches of grass and jets of water which form some of its most enchanting features. There is no slurring of perspective effect about it — the most distant — the minutest object in it has a marked and distinct personality — so that you may count the very leaves on the trees. When you first see the tame, ordinary-looking picture, your first impulse is to turn your back upon it, and say ‘Humbug’ — but your third visit will find your brain gasping and straining with futile efforts to take all the wonder in — and appreciate it in its fulness and understand how such a miracle could have been conceived and executed by human brain and human hands. You will never get tired of looking at the picture, but your reflections — your efforts to grasp an intelligible Something — you hardly know what — will grow so painful that you will have to go away from the thing, in order to obtain relief. You may find relief, but you cannot banish the picture — it remains with you still. It is in my mind now — and the smallest feature could not be removed without my detecting it.
Church had spent two years in South America retracing the steps of Alexander von Humboldt to create a composite of the continent’s topography. He hoped to share it with the explorer himself, but Humboldt died before the painting could reach Europe.