In writing novels as well as plays the cardinal rule is to treat the various characters as if they were chessmen, and not try to win the game by altering the rules; for instance, not move the knight as if it were a pawn, and so on. Again the characters ought to be strictly defined, and not put out of action in order to help the author to accomplish his purpose; for, on the contrary, it is through their activity alone he should try to win. Not to do this is to appeal to the miraculous, which is always unnatural.
Two numbers are mirror numbers if each presents the digits of the other in reverse order, such as 123 and 321. Find two mirror numbers whose product is 92,565.
This solution is by V. Dubrovsky. The size of the product shows that the factors must have three digits each. So let one of them be abc (or 100a + 10b + c) and the other be cba. The product ends in 5, so either a or c must be 5. Say that’s a. The other factor starts with 5, and 92,565 / 500 < 200, so c must be 1. As to b, we can see that the 6 in 92,565 is the last digit of 5b + b, or 6b, so b must be either 1 or 6, and we can test these candidates to learn that it’s 6. The numbers we seek are 165 and 561.
05/17/2024 UPDATE: Reader Robert Filman points out that we can solve this without actually having to multiply the numbers together. The sum of the digits of any number is the remainder of that number divided by 9, and the sum of the digits of 92,565 mod 9 = 0. So once we’ve established that the end digits of the factors we’re seeking are 1 and 5 and that the middle digit is 1 or 6, as above, we can notice that none of the resulting candidates (115, 165, 511, 561) has a digit sum divisible by 9 and hence each factor must be divisible by 3 — which means that the digit sum of each factor must be a multiple of 3. The only possibilities are 165 and 561. (Thanks, Robert.)
In 2005 Yale psychologists Deena Skolnick and Paul Bloom asked children and adults about the beliefs of fictional characters regarding other characters — both those that exist in the same world, such as Batman and Robin, and those that inhabit different worlds, such as Batman and SpongeBob SquarePants.
They found that while both adults and young children distinguish these two types of relationships, young children “often claim that Batman thinks that Robin is make-believe.”
“This is a surprising result; it seems unlikely that children really believe that Batman thinks Robin is not real,” they wrote. “If they did, they should find stories with these characters incomprehensible.”
One possible explanation is that young children can find it hard to take a character’s perspective, and so might have been answering from their own point of view rather than Batman’s. In a second study, kids acknowledged that characters from the same world can act on each other.
But this is a complex topic even for grownups. “James Bond inhabits a world quite similar to our own, and so his beliefs should resemble those of a real person. Like us, he should think Cinderella is make-believe. On the other hand, Cinderella inhabits a world that is sufficiently dissimilar to our own that its inhabitants should not share many of our beliefs. Our intuition, then, is that Cinderella should not believe that James Bond is make-believe; she should have no views about him at all.”
Does the green dot above flash before, as, or after the red dot reaches it? Most people say after, but in fact the flash occurs before the red dot arrives (below). This anomaly is known as the flash-lag effect, and its cause is unclear. Possibly it’s a sign that the visual system extrapolates the position of a moving object more readily than that of an unpredictably flashing one.
Henry James’ 1903 novella The Beast in the Jungle is written in his famously tortured syntax:
It led, briefly, in the course of the October afternoon, to his closer meeting with May Bartram, whose face, a reminder, yet not quite a remembrance, as they sat much separated at a very long table, had begun merely by troubling him rather pleasantly.
He had brought himself so fully in the end, poor Grantham, to accept his old friend’s invitation to accompany her to an ‘afternoon’ at ‘Cornerbright’ that now, on the very porch of the so evident house, he could have, for his companion, in all surrender, a high, fine — there was no other word for it — twinkle.
Thurber originally called this “The Return of the Screw.” See Homage and A Prose Maze.
James McNeill Whistler hated the work of J.M.W. Turner.
A lady once asked him, “Oh, Mr. Whistler, my husband has discovered in a secondhand shop what he thinks are two real Turners. Will you come and tell us whether they are real Turners or imitation Turners?”
“Well, ma’am,” Whistler said, “now that’s really a fine distinction.”
When a thread is pulled horizontally from the underside of a wound spool, the spool rolls in the direction of the pulling force, counter to intuition. When the thread is pulled upward vertically, the spool rolls in the opposite direction.
Why the difference? The spool must rotate about its point of contact with the table, but the direction of torque, clockwise or counterclockwise, varies with the angle of the thread. Interestingly there’s a critical angle at which the spool does not roll but slides.
