You’re in a dark room. The only light comes from an old LED digital alarm clock with four seven-segment displays. The time is displayed in 24-hour format, HH:MM (no seconds), and the leading digit is blank if not used. How much time passes between the room’s darkest state and its lightest?
“Typesetting Tarradiddle”
Friend John, whose (:) was removed,
When asked why he had lately proved
So free of caution and of fear,
Said, “I’ve no (*), my dear.”
— Willard R. Espy
Mr. Lucky
In 1962, Croatian music teacher Frane Selak was riding from Sarajevo to Dubrovnik when his train jumped the rails and plunged into a river. Seventeen people died, but he escaped with hypothermia.
A year later a plane door malfunctioned and he was blown into midair. The plane crashed and he landed in a haystack.
Three years after that he was riding a bus that skidded into a river; he swam to safety. (“By this time my friends had stopped visiting me,” he said.)
In 1970 his car caught fire as he was driving it. He escaped before the fuel tank exploded.
Three years after that, another car caught fire; his hair was singed but he was otherwise unharmed.
In 1995 he was knocked down by a Zagreb bus but sustained only minor injuries.
The following year he nearly collided with a United Nations truck; he crashed through a mountain guardrail but managed to leap clear of the car.
In 2003, two days after his 73rd birthday, he won a lottery jackpot worth a million dollars. He married and bought two houses and a boat, and in 2010 gave away most of the rest to friends and family.
Math Notes
“Dare to Be Yourself”
Quotations from André Gide:
Nothing prevents happiness like the memory of happiness.
Understanding is the beginning of approving.
The color of truth is gray.
At times it seems that I am living my life backward, and that at the approach of old age my real youth will begin.
Only fools don’t contradict themselves.
Do not do what someone else could do as well as you. Do not say, do not write what someone else could say, could write as well as you.
It is easier to lead men to combat, stirring up their passion, than to restrain them and direct them toward the patient labor of peace.
Believe those who are seeking the truth. Doubt those who find it.
To read a writer is for me not merely to get an idea of what he says, but to go off with him and travel in his company.
Most quarrels amplify a misunderstanding.
Fish die belly-upward and rise to the surface; it is their way of falling.
Our judgments about things vary according to the time left us to live — that we think is left us to live.
Art is a collaboration between God and the artist, and the less the artist does the better.
The most decisive actions of our life — I mean those that are most likely to decide the whole course of our future — are, more often than not, unconsidered.
Brahmagupta’s Theorem
If a quadrilateral’s vertices lie on a common circle and if its diagonals are perpendicular, then a perpendicular to one side that passes through the intersection of the diagonals will bisect the opposite side.
Podcast Episode 350: Symmes’ Hole
In 1818, Army veteran John Cleves Symmes Jr. declared that the earth was hollow and proposed to lead an expedition to its interior. He promoted the theory in lectures and even won support on Capitol Hill. In this week’s episode of the Futility Closet podcast we’ll describe Symmes’ strange project and its surprising consequences.
We’ll also revisit age fraud in sports and puzzle over a curious customer.
Lorina Bulwer
When 55-year-old Lorina Bulwer was placed in the Great Yarmouth Workhouse in 1893, she embroidered protests into long pieces of patchwork fabric, ranting in unpunctuated capitals:
THE CHATTER IS I MISS LORINA BULWER CAMBS WOMAN DROVE TO THRIGBY HALL NORFOLK E. BULWER MARRIED AN HEMAPHRODITE EUNICH I MISS LORINA BULWER WAS EXAMINED BY DR PINCHING OF WALTHAMSTOW ESSEX AND FOUND TO BE A PROPERLY SHAPED WOMAN …
Much of the invective is directed against E Bulwer and Queen Victoria, apparently trying to connect Bulwer’s family to prominent families of the time and possibly referring to sexual abuse in a scandal of 1859. But her reasons for making the samplers aren’t entirely understood.
Ruth Burwood, adult learning officer for Norwich Museums, told the Eastern Daily Press, “In very basic terms there isn’t anything like them in the world, they’re just absolutely extraordinary; the fact she was a woman in a lunatic ward in Great Yarmouth workhouse and was somehow able to produce these embroideries. Workhouse inmates did do sewing but this is almost like she’s been allowed to do this as therapy.”
Choice Blindness
In a 2005 experiment, psychologist Petter Johansson and his colleagues presented each subject with two photographs of women’s faces and asked which they found more attractive. In each case the experimenter then presented the “chosen” photograph and asked the subject to explain their choice. But in fact, using sleight of hand, the experimenter had exchanged the photos and was presenting the one that the subject hadn’t picked.
Only 13 percent of the subjects noticed the change; the rest went on to confabulate an explanation justifying a choice they hadn’t made. And yet, in post-test interviews, 84 percent of the subjects said that they would have detected such a switch if one had been made.
A subsequent experiment involving supermarket taste tests of jam showed the same effect: Subjects indicated an initial preference and then (after the samples had been surreptitiously swapped) failed to recognize that they were now tasting the rejected variety and went on to justify that choice.
Johansson and his colleagues called this choice blindness. “We do not doubt that humans can form very specific and detailed prior intentions,” they wrote, “but as the phenomenon of choice blindness demonstrates, this is not something that should be taken for granted in everyday decision tasks.”
(Petter Johansson et al., “Failure to Detect Mismatches Between Intention and Outcome in a Simple Decision Task,” Science 310:5745 [Oct. 7, 2005], 116-119.) (Thanks, Colin.)
Fredkin’s Paradox
The more similar two options are, the more difficult it is to decide between them, and the less consequential the decision becomes. A rational decider might find herself spending the most time on the least important decisions.
Philosopher Edward Fredkin writes, “The more equally attractive two alternatives seem, the harder it can be to choose between them — no matter that, to the same degree, the choice can only matter less.”
To avoid this, the decider might resolve to apportion her decision-making time by the importance of the decision. But this requires assessing the importance of every decision, which requires evaluating the means she’s using to make those assessments, and so on.
Psychologist Gary Klein writes, “[[I]f I want to optimize, I must also determine the effort it will take me to optimize; however, the subtask of determining this effort will itself take effort, and so forth into the tangle that self-referential activities create.”