The nuts-and-bolt illusion, devised by American magician Jerry Andrus.
“I can fool you because you’re a human,” he once said. “You have a wonderful human mind that works no different from my human mind. Usually when we’re fooled, the mind hasn’t made a mistake. It’s come to the wrong conclusion for the right reason.”
At the end of a narrow pedestrian alleyway off Paternoster Square near St. Paul’s Cathedral in London are a pair of stainless-steel “angel’s wings” 11 meters high. Designed by Thomas Heatherwick, the sculpture actually serves a practical purpose: It provides ventilation for an electrical substation below ground. Cool air is sucked in through grids on the ground, and hot air is conducted through the sculpture and released high overhead.
“The commissioner had been exploring options that involved creating a single structure that housed both inlet vents and outlet vents,” Heatherwick wrote. “It made a large bulky object that dominated the public square around it, reducing it to little more than a corridor. As this was a sensitive location near St. Paul’s, we decided to make it our priority to shrink the visible mass of the vent structure to a minimum.”
(From Mary Acton, Learning to Look at Sculpture, 2014.)
Imagine a society which does not have an established medium of painting but does produce a kind of work called guernicas. Guernicas are like versions of Picasso’s ‘Guernica’ done in various bas-relief dimensions. All of them are surfaces with the colors and shapes of Picasso’s ‘Guernica,’ but the surfaces are molded to protrude from the wall like relief maps of different kinds of terrain. Some guernicas have rolling surfaces, others are sharp and jagged, still others contain several relatively flat planes at various angles to each other, and so forth. Picasso’s ‘Guernica’ would be counted as a guernica in this society — a perfectly flat one — rather than as a painting. Its flatness is variable and the figures on its surface are standard relative to the category of guernicas. Thus the flatness, which is standard for us, would be variable for members of the other society … and the figures on the surface, which are variable for us, would be standard for them. This would make for a profound difference between our aesthetic reaction to ‘Guernica’ and theirs. It seems violent, dynamic, vital, disturbing to us. But I imagine it would strike them as cold, stark, lifeless, or serene and restful, or perhaps bland, dull, boring — but in any case not violent, dynamic, and vital. We do not pay attention to or take note of ‘Guernicas”s flatness; this is a feature we take for granted in paintings, as it were. But for the other society this is ‘Guernica”s most striking and noteworthy characteristic — what is expressive about it. Conversely, ‘Guernica”s color patches, which we find noteworthy and expressive, are insignificant to them.
— Kendall L. Walton, “Categories of Art,” Philosophical Review (1970), 334-367
Éric Angelini devised this progressively self-inventorying array:
10 71 32 23 14 15 16 27 18 19 20 81 72 53 44 35 26 47 38 29 40 101 82 73 64 65 56 77 58 39 60 131 92 93 74 75 86 107 88 69 80 201 122 113 84 85 96 117 138 89
The first line describes its own contents: It contains one 0, seven 1s, three 2s, and so on.
In the same style, the second line describes the joint contents of lines 1 and 2.
And so on: The fifth line describes the contents of the whole table: It contains eight 0s, twenty 1s, twelve 2s, etc.
He suspects that a six-line table is possible, but he hasn’t found one yet.
(Thanks, Éric.)
12 + 22 + 32 + … + 242 = 702
This is the only case in which the sum of the first k perfect squares is itself a square.
03/23/2020 UPDATE: Reader Pieter Post made a pyramid of 4900 golf balls in the Netherlands last summer:
It took him an hour and a half. (Thanks, Pieter.)
When I feel a pain in my leg, what do I mean by in? It might seem that I’m referring to spatial location: The pain resides within the tissues of my leg. But philosopher Ned Block points out that then this argument should be valid:
The pain is in my fingertip.
The fingertip is in my mouth.
Therefore, the pain is in my mouth.
“The conclusion obviously does not follow, so we must conclude that ‘in’ is not used in the spatial enclosure sense in all three statements. It certainly seems plausible that ‘in’ as applied in locating pains differs in meaning systematically from the standard spatial enclosure sense.”
(Ned Block, “Mental Pictures and Cognitive Science,” Philosophical Review 92:4 [1983], 499-541.)
belamour
n. a glance or look of love
oeillade
n. an amorous look
leman
n. one beloved
kilig
adj. exhilarated by a romantic experience
“I wonder … that a soothsayer doesn’t laugh when he sees another soothsayer.” — Cicero
In a 1988 experiment with 2-year-olds, psychologist Alan Leslie asked each child to “fill” two toy cups with imaginary “juice” or “tea” from a bottle. Leslie then said, “Watch this!”, upended one of the cups, shook it, and replaced it next to the other cup. Then he asked the child to point to the “full cup” and the “empty cup.” Though both cups had been empty throughout, all 10 of the 10 subjects indicated that the “empty” cup was the one that had been inverted.
“This leads to pretending something that is true, namely, that the empty cup is empty,” Leslie wrote. “At first glance, this may seem ridiculous. But there is, of course, an important difference between the empty cup is empty and pretending (of) the empty cup ‘it is empty.'” Children distinguish between pretense and reality even when the content of those beliefs is the same.
“These examples help us realize that, far from being unusual and esoteric, cases of ‘non-counterfactual pretence’, that is, pretending something is true when it is true, are ubiquitous in young children’s pretence and indeed has an indispensable role in the child’s ability to elaborate pretend scenarios.”
(Alan M. Leslie, “Pretending and Believing: Issues in the Theory of ToMM,” Cognition on Cognition [1995], 193-220.)
